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Nanoscale organization of rotavirus replication machineries

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Cite this article as: eLife 2019;8:e42906 doi: 10.7554/eLife.42906

Abstract

Rotavirus genome replication and assembly take place in cytoplasmic electron dense inclusions termed viroplasms (VPs). Previous conventional optical microscopy studies observing the intracellular distribution of rotavirus proteins and their organization in VPs have lacked molecular-scale spatial resolution, due to inherent spatial resolution constraints. In this work we employed super-resolution microscopy to reveal the nanometric-scale organization of VPs formed during rotavirus infection, and quantitatively describe the structural organization of seven viral proteins within and around the VPs. The observed viral components are spatially organized as five concentric layers, in which NSP5 localizes at the center of the VPs, surrounded by a layer of NSP2 and NSP4 proteins, followed by an intermediate zone comprised of the VP1, VP2, VP6. In the outermost zone, we observed a ring of VP4 and finally a layer of VP7. These findings show that rotavirus VPs are highly organized organelles.

https://doi.org/10.7554/eLife.42906.001

eLife digest

Rotaviruses are small viruses that can infect cells in the intestine. They are responsible for most cases of severe infectious diarrhea, the most common cause of death among young children in developing countries. Controlling the spread of rotavirus infections is difficult, even with high levels of hygiene, so effective treatments are essential to curtail the virus’ infections. Understanding how new rotaviral particles are made in infected cells is one of the first steps toward developing new therapies.

Once rotaviruses enter the cells, proteins from the virus and the cell aggregate into compact spheres called viroplasms to make new viral particles. Studying these viroplasms used to be difficult because they are too small to see with the resolution of standard microscopes. In recent years, advances in microscopy and mathematical methods have focused on breaking the existing resolution limits, leading to the development of super-resolution microscopy. This new technique has made it possible to study objects with sizes in the order of a billionth of a meter, known as nanoscopic structures, including viroplasms.

Garcés et al. use super-resolution microscopy to determine how viral proteins are arranged in the viroplasm and gain a better understanding of how the viruses are assembled. The images revealed that, in infected monkey kidney cells, rotavirus proteins inside the viroplasm form highly organized concentric layers. This arrangement is reliably repeated in viroplasms of different sizes, indicating that the organization of the proteins is likely set up when the viroplasm starts to form.

These findings make use of new microscopy, image analysis and statistical tools to study rotaviruses, providing a new framework to understand many aspects of rotaviral biology. Additionally, the result showing that proteins organize consistently in viroplasms is a first step towards understanding how the machinery that makes new rotaviruses works, which could lead to future treatments for severe infectious diarrhea.

https://doi.org/10.7554/eLife.42906.002

Introduction

Rotavirus is a non-enveloped virus composed of three concentric layers of proteins that enclose a genome constituted by eleven segments of double stranded RNA (dsRNA) that encode six structural proteins (VP1 to VP4, VP6 and VP7) and six non-structural proteins (NSP1 to NSP6). The inner layer is formed by dimers of VP2 that enclose the viral genome and small numbers of molecules of the viral RNA-dependent RNA polymerase (RdRp), VP1, and the capping enzyme, VP3. This nucleoprotein complex constitutes the core of the virus, which is surrounded by an intermediate protein layer of trimers of VP6, to form double-layered particles (DLPs). The surface of the virion is occupied by two polypeptides, VP7, a glycoprotein, and VP4, which forms spikes that protrude from the VP7 shell (Estes and Greenberg, 2013). Replication of the rotavirus genome and assembly of DLPs take place in cytoplasmic electron dense inclusions termed viroplasms (VPs) (Estes and Greenberg, 2013). Once the double-shelled particles are assembled, they bud from the cytoplasmic VPs into the adjacent endoplasmic reticulum (ER). During this process, which is mediated by the interaction of DLPs with the ER transmembrane viral protein NSP4, the particles acquire a temporary lipid bilayer, modified by VP7 and NSP4, which after being removed in the lumen of the ER by an unknown mechanism, yields the mature triple-layered virions (Estes and Greenberg, 2013). It has been reported that VP4 is located between the VP and the ER membrane and it is incorporated into triple-layered particles (TLPs) during the budding process and maturation of the virus particle inside the ER (Estes and Greenberg, 2013; Navarro et al., 2016).

The viral non-structural proteins NSP2 and NSP5 serve a nucleation role that is essential for the biogenesis of VPs (Fabbretti et al., 1999; Silvestri et al., 2004; Vascotto et al., 2004; Campagna et al., 2005). In addition to viral proteins and genomic dsRNA, cellular proteins such as ER chaperones (Maruri-Avidal et al., 2008), proteins associated with lipid droplets (Cheung et al., 2010), and ribonuclear proteins (Dhillon et al., 2018), have been shown to colocalize with VPs. Several studies have characterized the intracellular distribution of the rotavirus proteins (González et al., 2000; Petrie et al., 1982; Petrie et al., 1984; Richardson et al., 1986). Immunofluorescence studies, based upon epifluorescence or confocal microscopy, have described the viral proteins that conform the VPs, however the images are inherently diffraction-limited to a spatial resolution in the range of hundreds of nanometer, precluding the identification of the nanoscopic molecular scale organization of VPs (González et al., 1998; González et al., 2000; Eichwald et al., 2004; López et al., 2005b; Criglar et al., 2014; Martin et al., 2011; Contin et al., 2010). On the other hand, transmission electron microscopy (TEM) studies often provide images with nanometric resolution, nevertheless, immunoelectron microscopy is challenging when looking for the localization of more than a single protein (Altenburg et al., 1980; Petrie et al., 1982; Petrie et al., 1984). Over the past 15 years, a variety of super-resolution microscopy (SRM) techniques have been developed to observe subcellular structures beneath the diffraction limit of optical microscopes, with resolutions in the tens of nanometers (Schnitzbauer et al., 2017; Deschout et al., 2014; Cox et al., 2011). In this work, we determined the organization of rotaviral proteins within and around VPs through the ‘Bayesian Blinking and Bleaching’ (3B) SRM technique. We developed a segmentation algorithm to automatically analyze and quantify the relative distribution of seven viral proteins, and propose a model that describes their relative spatial distribution. Also, we present a dependency model that explains the relationship between the viral proteins. This work establishes a structural framework for VP organization that future mechanistic and functional studies must take into account, and establishes key methodologies for future investigations on this subject.

Results

Qualitative analysis of VP morphology and structure through SRM

Rotavirus VPs are complex signaling hubs composed of viral and cellular proteins, packed together with viral RNAs. By TEM, they roughly resemble circular electrodense structures whose internal components lack an obvious degree of spatial organization (Altenburg et al., 1980; Eichwald et al., 2012). In this work, we determined the relative spatial distribution of VPs components by immunofluorescence and SRM in MA104 cells infected with the rhesus rotavirus strain RRV at 6 hr post-infection (hpi), using protein-specific antibodies. Due to their important role as nucleating factors during VP biogenesis, we selected either NSP2 or NSP5 as spatial relative reference for the distribution of the VP1, VP2 and VP6 proteins. VPs were optically sectioned through total internal reflection fluorescence microscopy (TIRF), with an excitation depth of field restricted to 200 nm from the coverslip. This approach avoids excitation of fluorophores marking structural components located away from this plane, that is towards the inner cellular milieu. Additionally, NSP2 was also co-immunostained with the viral outer layer protein VP4 as well as with the ER resident proteins NSP4 and VP7, all of which have been reported to form separate ring-like structures that closely associate with VPs (González et al., 2000). In order to gain more insight into the morphogenesis of rotavirus, we analyzed the distribution of both VP7 monomers (VP7-Mon) and trimers (VP7-Tri) since this protein is assembled into virus particles in the latter form (Kabcenell et al., 1988). The nanoscale distribution of VPs was then analyzed through 3B-SRM, with improvements in the technique, developed in the present work, to solve nanoscopic structures (‘Stochastic model fitted for 3B super resolution microscopy’Appendix 1). By different methods of analysis VPs exhibit roughly a circular shape (Figure 1A–E). However, unlike the diffraction-limited image (Figure 1B), in super-resolution microscopy structural details of VP are appreciated, like the different layer distributions of viral components with respect to NSP2 (Figure 1C–E). In addition to VPs, by diffraction-limited TIRF microscopy we detected in the cytoplasm several small and dispersed puncta of fluorescence (Figure 1B), and in these images it is also sometimes possible to differentiate the distribution of NSP2 from that of VP4, a closely viroplasm-associated viral protein (see also González et al., 2000); in this case, VP4 is detected as a ring-like structure that surrounds the VP. Nevertheless, the small size of the VPs effectively precludes measurement of component distribution for the majority of its structural elements, as their separation is below the spatial resolution of typical optical microscopes. In contrast, images obtained by 3B-SRM do allow the study of the relative distribution of the VP components (Figure 1C–E). In the case of SRM images of VP4 (Figure 1C), we observed that this protein forms a ring-like structure that does not colocalize with NSP2, and also ribbon-like projections that extend towards the cytoplasm, details that were not apparent in images captured with conventional fluorescence microscopy (Figure 1B). Additionally, we observed that the small puncta of proteins detected in the cytoplasm were in fact ribbon-like structures composed of various viral proteins that may represent different organization forms of the viroplasmic proteins (Figure 1C). In this regard, it is interesting to note that both NSP2 and VP4 have been reported to have at least two different intracellular distributions (González et al., 2000; Nejmeddine et al., 2000; Criglar et al., 2014). An examination of 3B-SRM images of VPs (Figure 1C–E) revealed that the viral components form ring like structures within the VPs and are arrayed as rather discrete concentric layers. As seen in Figure 1C–E, we find that although the structural proteins VP1, VP2 and VP6 partially overlap in position with NSP2, the bulk of the proteins form separate and distinct layers. Also, the monomeric as well as the trimeric forms of VP7 are clearly distinguished from NSP2, forming an outer ring. Of interest, the spatial distribution of NSP4 colocalized with that of NSP2, an unexpected result since, as mentioned, NSP4 is an ER integral membrane protein (see the Discussion section), and as such it was expected to colocalize with VP7 rather than with an internal viroplasmic protein (Petrie et al., 1984). With regard to NSP5, it was observed distributed inside the ring formed by NSP2 (Figure 1E).

Relative distribution of viral components in rotavirus-VPs.

RRV-infected MA104 cells (6hpi) were fixed and processed for transmission electron microscopy or immunofluorescence microscopy. (A) Transmission electron microscopy of a VP (identified by the dotted white ellipse). (B) Diffraction-limited image of VPs (white arrows). (C) 3B-SRM image reconstructed from B. (D–E) 3B-SRM images of individual VPs labeled with different antibodies (see Methods).

https://doi.org/10.7554/eLife.42906.003

Quantitative characterization of VPs structure by a novel segmentation algorithm

A qualitative analysis of the distribution of the VP components through 3B-SRM suggested that these are arranged as concentric spherical shells; thus, we set out to quantitatively validate the circularity of the VP shape. For this, we developed a segmentation algorithm based on a least squares approach, which we called ‘Viroplasm Direct Least Squares Fitting Circumference’ (VP-DLSFC) (see ‘Segmentation Algorithm’ in Appendix 1), to measure the spatial distribution of the components within individual VPs by adjusting concentric circumferences. This method is automatic, deterministic, easy to implement, and has a linear computational complexity. The performance of VP-DLSFC was tested on approximately 40,000 ‘ground truth’ (GT) synthetic images, showing a high robustness to noise and partial occlusion scenarios. Additionally, we compared our method with two other alternative methods (Gander et al., 1994), and our approach displayed an improved performance (see ‘Algorithm Validation’ in Appendix 1). Based on this new algorithm, we find that the mean radius of the NSP5 distribution was smaller than that of NSP2, suggesting that NSP5 is located in the innermost section, as a component of the core of VPs (Figure 2A). On the other hand, the distribution of the structural proteins VP1, VP2 and VP6 exhibit slightly larger mean radii than that of NSP2, and are thus primarily localized in a zone surrounding NSP2. Continuing further towards the outer regions of the VP, we observed a region occupied by the spike protein VP4. Finally, the two different forms of VP7 (VP7-Mon and VP7-Tri) were located together, close to the most external region of the VPs (Figure 2A). The distribution of the glycoprotein NSP4 showed a similar mean radius to that of NSP2 (around 0.4μm) suggesting, as described above, that these two proteins are located in the same structural layer of the VP (Figure 2A).

Exploratory analysis of the results obtained by the algorithm VPs-DLSFC.

(A) Boxplot for the radius of the fitting circumferences. In each experimental condition we plot two boxes, the red box is for the radius of NSP2 (reference protein), and the blue box represents the radius of the accompanying VP components (names in x-axis). (B) Boxplot and results of the Mann-Whitney hypothesis test for the distance between each viral element and NSP2. Each combination of the Mann-Whitney test is linked by a line, and the result of the test it is above the line. Note that this test reports significant differences between the distribution of the distance to NSP2 of two different VP components. (C) Distance of VP1 and VP2 to NSP2 and result of the Mann-Whitney test. Because the distributions of NSP2 in combination with VP1 and VP2 are statistically different to the other NSP2 distributions (see Appendix 1—figure 7B), we show these two cases independently in this exploratory analysis. (D) Hierarchically clustered heatmap for the standard deviation of the distance to NSP2, the mean distance to NSP2, the mean radius of NSP2, and the mean radius of the accompanying protein layers, NSP5, NSP4, VP6, VP4, and VP7.

https://doi.org/10.7554/eLife.42906.004

In order to confirm our preliminary observations and clarify the nanoscopic organization of the VPs, we evaluated the relative separation between NSP2 and each accompanying protein. Again, the results show a remarkable degree of organization in the structure of the VP (Figure 2B). As predicted from Figure 2A, we found that NSP5 is located in the internal part of the VP, in close proximity (0.05μm) to the area occupied by proteins NSP2 and NSP4, which themselves show the closest association. After the NSP2-NSP4 region, VP6 occupies a middle region at 0.05μm from NSP2, followed by the VP4 protein, which were located at a distance of 0.18μm. Finally, the VP7-Mon and VP7-Tri were situated at 0.38μm from NSP2 (Figure 2B). A Mann-Whitney test showed that the distances of the various viral components in relation to NSP2 were significantly different (Figure 2B), suggesting that they are situated in specific areas of the VPs. The two forms of VP7 were located at the same distance to NSP2, suggesting that the formation of trimers of VP7 takes place at the ER membrane, where the VP7 monomers should also be located. Note that in Figure 2B the relative distance of VP1 and VP2 to NSP2 was not included, since the radii obtained for NSP2 in these two combinations were significantly smaller than those found when it was determined in combination with the other VP components (see ‘Supplementary Exploratory Analysis’). In addition to this, we found no significant differences between the distance of both VP1 and VP2 to NSP2 (Figure 2C). Nonetheless, based on the inferential analysis, we could place these two proteins in the same layer as VP6 (see below).

Next, through a hierarchical cluster analysis, we studied the relationship between the components of the VP, taking into account multiple variables at the same time, like the mean distance to NSP2 [‘Mean(Dist)”], the standard deviation of the distance to NSP2 [‘Std(Dist)”], the mean radius of NSP2 [‘Mean(NSP2)”], and the radii of the other proteins [‘Mean(Other)”] (Figure 2D). Note that the proteins within a cluster should be as similar as possible and proteins in one cluster should be as dissimilar as possible from proteins in another. Because our variables are related with the distance to NSP2 and the radii of the proteins, this is a no-parametric analysis that should provide evidence about the spatial distribution/order of the viral proteins into the VP. As we are considering the distance to NSP2, VP1 and VP2 were not included in this analysis. The first level of the hierarchical agglomerative cluster (Figure 2D, left) partitioned the VPs and the surrounding proteins in five clusters, composed by NSP4, NSP5, VP6, VP4 and {VP7-Mon, VP7-Tri}, which suggest that these five proteins compose different layers of the VP. The second agglomerative level merged into the same group the proteins NSP4 and NSP5, meanwhile VP6 and VP4 continue as independent clusters, which indicate that NSP5 and NSP4 are closer to each other than to VP6 and VP4 in the VP. In the third level, VP6 and VP4 are clustered in the same group, and as consequence are more related between them than with the others viral proteins. The subsequent groups in the clustering analysis indicate that VP7 remains as an independent layer with respect to the other proteins. Based on this analysis, the viral proteins seem to be highly organized, with VP7 conforming the most external layer, while NSP5, NSP4, VP6 and VP4 are distributed very close but as independent layers. The clusters between NSP5-NSP4 and VP6-VP4 suggest that these two pairs of proteins (in each cluster) conform continuous layers in the VP.

The relative spatial organization of VPs is maintained regardless their size

The scatterplot between the radius of the spatial distribution of NSP2 (independent variable, x-axis) and the radius of the distribution of other viral components (response variable, y-axis) showed a strong linear relationship (Figure 3A). The distribution of NSP5 grows 0.87μm for each 1μm increase in the radius of NSP2 (slope interpretation), whereas the radius of the distribution of NSP4 increases 0.99μm (Figure 3B). These findings indicate that NSP5 is distributed in a proportionally smaller region than NSP2 regardless of the absolute size of the VP, supporting our observation that NSP5 is a constituent of the core of the VP. Moreover, the fact that the increase in the radius of the fitted distribution of NSP4 is directly proportional to the same parameter measured for NSP2 supports the idea that these proteins are both constituents of a putative second layer. VP1, VP2 and VP6 exhibit similar slopes which diverge between 0.03 and 0.05 μm (Figure 3B and Appendix 1—table 6); thus, these results confirm that VP1, VP2 and VP6 are components of the same layer in the VPs which, from the data in Figure 3, is located just after the layer of NSP2 and NSP4. Finally, as noted in our quantitative analysis, VP4 and VP7 form consecutive external layers with a slope of 1.39 and 1.94 μm, respectively (Figure 3B and Appendix 1—table 6). These findings indicate that the spatial distribution of the viral components in the VPs and in the surrounding areas is conserved regardless of their absolute size, and also form the basis of a predictive model, where, for a given radius of distribution of NSP2, it is possible to predict the radii of the remaining VP components (NSP5, NSP4, VP1, VP2, VP6) and of VP4 and VP7 proteins. This predictive model is available as a web app at https://yasel.shinyapps.io/Nanoscale_organization_of_rotavirus_replication_machineries/. The mathematical details and the residual analysis that validate these linear models are available in the Appendix 1, section ‘Linear dependency between the viral components’, Appendix 1—table 6 and Appendix 1—figure 9.

The organization of VPs scales with its size.

(A) Simple linear regression analyses for each component combination (eight subpanels). In all subpanels, the x-axis represents the radius of the distributions of NSP2, and the y-axis the radius of the distribution of the accompanying VP component. The 95% confidence interval, marked in grey, is imperceptible due to goodness of fit of the linear regression (solid line). (B) Slope and confidence interval for each linear regression model (dependent variables in x-axis). The slopes values were shown under each confidence interval.

https://doi.org/10.7554/eLife.42906.005

The structural organization of VPs is independent of the reference protein chosen for pairwise comparison

In order to confirm the observed structural organization of VPs, we analyzed two more experimental conditions in which we chose a different reference protein for pairwise comparisons. The first was based on the distribution of NSP5 and its comparison with the relative localizations of VP6 and VP4, and the second considered NSP4 as the reference protein to compare with the distribution of VP6. We found that both analyses produced an identical structural organization for the VPs, with a comparative localization error of approximately 0.05μm between models (close to the effective resolution limit of the 3B algorithm; see ‘NSP5 and NSP4 as reference proteins’ in Appendix 1). An extensive quantitative validation regarding the congruence between the NSP2, NSP5 and NSP4 models is available in the Appendix 1.

Based on our extensive quantitative, descriptive and inferential statistical analyses, we propose that the VP and the surrounding viral proteins form an ordered biological structure composed of at least five concentric layers organized as depicted in Figure 4. In this structure, NSP5 constitutes the innermost layer, followed by a {NSP2-NSP4} layer. Then, there is a layer composed by {VP1-VP2-VP6} and two consecutive external layers formed by VP4 and VP7. The different layers of proteins are most likely highly porous to allow the entry of positive-sense single-stranded viral RNA (+RNA) during genome replication and also of the antibodies used for VP staining.

Relative structural distribution of VP components.

The radii of the circumferences maintain the relative values determined for the different VP layers.

https://doi.org/10.7554/eLife.42906.006

Discussion

VPs have been previously studied using electron and fluorescence microscopy, however, due to the limited resolution of classic fluorescence microscopy techniques, and the difficulty of analysis of immunoelectron microscopy, the existence of any complex structural organization of the viral elements inside the VPs has not been reported. In recent years, the development of SRM has facilitated research into the nanoscale organization of a diverse range of cellular structures (Grant et al., 2018; Reznikov et al., 2018), however, until now SRM had not been applied to study the replication cycle of rotavirus. In this work, thanks to the use of the 3B SRM algorithm, we visualized and determined quantitatively the location of several viroplasmic proteins, leading us to propose a detailed model of the VP that should be of great value for understanding virus morphogenesis.

Other SRM algorithms had been used to study the organization of viral and cellular structures showing concentric arrangements, as those proposed by Laine et al. (2015) and Manetsberger et al. (2015). The main similarities between those studies and our approach is the use of conics, such as circles or ellipses, to fitting structures showing concentric organization. The method provided by Manetsberger et al. (2015) could actually be implemented to analyze our data set, which as outcome will produce similar results. This method could also provide information about the degree of asymmetry within the VP, which may be valuable to establish functional relationships between the protein distribution belts that shape these intriguing structures. The selection of the 3B SRM algorithm over other super-resolution approaches was based on the fact that this method allows to deal with samples with high density of labeling, obtaining data with a reasonable resolution, although at the cost of higher computational effort.

The quantification of the viral protein distribution within the VPs was possible thanks to a novel segmentation algorithm (VPs-DLSFC) that was proven to be robust and efficient in noisy and partial occlusion scenarios. The manual pre-segmentation step of this algorithm was necessary in our case because we did not want to introduce any bias in the isolation of the VPs through an automatic approach. Setting aside the manual pre-segmentation step, the VPs-DLSFC algorithm is automatic, deterministic, non-iterative and has a linear computational complexity.

Previous reports have suggested that VPs have a spherical-like structure (Eichwald et al., 2004; Cabral-Romero and Padilla-Noriega, 2006; Campagna et al., 2013); in this study we confirmed this suggestion by comparing the VPs-DLSFC approach with a similar approach based on an ellipse adjustment (Garcés et al., 2016). The results showed no significant statistical differences between these two models, and as consequence we can confidently model the structure of the VPs as a circumference. We also ratified that the center displacement of the circumferences that adjust two paired proteins are not statistically different.

Our study indicates that the viral components in the VPs, as well as VP4 and VP7, are arranged as largely discrete concentric layers (note that we are describing the structure of viroplasms, not of virus particles). This organization, however, does not preclude the interaction among the VP components proposed in this model as being located in separate layers since, for instance, NSP5 has been shown by different biochemical methods to interact with NSP2 (Eichwald et al., 2004; Poncet et al., 1997; Afrikanova et al., 1998; Jiang et al., 2006), VP1 (Afrikanova et al., 1998) and VP2 (Berois et al., 2003). In this regard, based on the super resolution microscopy images, it seems clear that there is some overlapping between different protein layers, as is the case for NSP2 and NSP5 in Figure 1E, but also between NSP2 and VP1, VP2, VP6 and NSP4 in Figure 1. These general overlapping zones between different proteins most likely are relevant for coordinating the genome replication and virion assembly, as suggested. Of interest, we observed the presence of protein projections (‘spike-like’) from different viral shells that could also contribute to the interaction of proteins mapped to different layers (Appendix 1—figure 8). Although our present analysis is limited to a general characterization of the spatial distribution of the viral proteins within VPs, and not to understand specific details about the interactions between proteins in different layers, it could be used as departure point to analyze these interactions. Taking as initial solution the result of the algorithm VPs-DLSFC and the SRM image, it is possible to employ other segmentation approaches, like deformable/active contours (snakes) (Kass et al., 1988), level-set (Osher and Fedkiw, 2003), or region growing methods (Mehnert and Jackway, 1997; Synthuja et al., 2012), to evolve the circular contour and fit precisely the spatial distribution of the viral proteins. Then, establishing a polar coordinate system in the VP, and considering the results of both segmentation algorithms, it would be possible to quantify the radial angle in which a spike from the central distribution of a viral protein that interacts with a different protein exists. It would be also possible to determine how strong these interactions are (intersection between two segmentation curves), and to study whether the spikes are randomly distributed between layers or a specific pattern in the connection between different protein layers exists. In the latter case, this could allow us to explore whether these patterns influence the assembly of the virus-like particles or only provide a skeleton that maintain the structure of the VP. The results obtained could also be used to study topological changes that the VP might experience at different times post infection, and associate these changes with maturation of the subviral particles. In this regard, in preliminary experiments carried out at three hpi, the viral proteins in he VP have been found to have a similar ‘layered’ organization as shown for the mature VP at six hpi (data not shown). This observation indicates that this organization is already present when the formation of viral particles has not yet taken place, suggesting that it might be important for the assembly of DLPs within VPs. In an additional application, SRM could also be used to observe the assembly of the virus particles and the interactions that may occur of these particles in different layers of the VP. Nevertheless, to develop this idea it would be important to establish an experimental protocol to observe the viral particles during the early stages of the assembly process, to distinguish simultaneously the layers of the viroplasm and the viral particles, and to collect the SRM images with a very short acquisition rate and a very high resolution (25–30 nm), which makes this experimental plan a challenge.

Previous studies based on conventional microscopy techniques have reported that NSP5 and NSP2 colocalize (González et al., 2000; Eichwald et al., 2004; Fabbretti et al., 1999); in contrast, we found that although NSP5 and NSP2 are located in close proximity, their positions in the VP were separable. This difference is attributable to the increased spatial resolution in the final image created by the super-resolution techniques employed in our study. Here, NSP5 was found to represent the innermost layer of the VPs, suggesting that this protein might serve as the core scaffold upon which the subsequent viroplasmic proteins are assembled to form the VPs. This finding contrasts with a report by Eichwald et al. (2004), who described that NSP5 locates to a region external to NSP2. In addition to the superior spatial resolution obtainable through 3B-SRM, compared to the traditional confocal microscopy employed in the previous report, the difference might be due to the fact that in our study we characterized the endogenous structures produced during virus replication, while Eichwald et al. characterized VP-like structures formed by transiently expressed proteins fused to GFP.

Immediately outside the NSP5 core, we observed a layer composed of NSP2 and NSP4 proteins. The finding that NSP4 is located in the inner part of VPs was unexpected, since it is known that NSP4 is an integral membrane protein of the ER and since it has been reported that functions as a receptor for the new DLPs located at the periphery of the VPs, during their budding towards the lumen of the ER (Chasey, 1980; Petrie et al., 1982; Petrie et al., 1984; Au et al., 1989). Furthermore, it has been shown that NSP4 associates with VP4 and VP7 to form a hetero-oligomeric complex that could be involved in the last steps of rotavirus morphogenesis (Maass and Atkinson, 1990). Based on these findings, NSP4 was expected to locate close to VP4 and VP7, in the surroundings of the VP. On the other hand, and in line with our observations, previous confocal microscopy studies have shown that a portion of NSP4 also shows a limited colocalization with NSP2 (González et al., 2000).

The dual location of NSP4 as an integral glycoprotein of the ER membrane and as internal to VPs, as our results indicate, is not easy to reconcile; however, in a previous work it was suggested that there are three pools of intracellular NSP4 molecules. The first pool is represented by NSP4 localized in the ER, a second minor pool localized in the ERGIC compartment, and the third pool distributed in cytoplasmic vesicular structures associated with the autosomal marker LC3 (Berkova et al., 2006). Furthermore, in that work the authors suggested that NSP4 and autophagic marker LC3-positive vesicles may serve as a lipid membrane scaffold for the formation of large VPs by recruiting early VPs or VP-like structures formed by NSP2 and NSP5 (Berkova et al., 2006). This observation is in line with our model that NSP4 lies in an internal protein shell within VPs.

An additional, and very interesting possibility to explain the internal location of NSP4 in VPs is the hypothesis that VP morphogenesis occurs on the surface of lipid droplets (LDs) (Cheung et al., 2010). In that work, it was proposed that LDs serve as a platform to which NSP2 and NSP5 proteins attach to form VP-like structures; NSP2 octamers, in turn, associate with the viral polymerase VP1 and rotavirus +RNAs. The assorted RNA complex containing NSP2, VP1, the capping enzyme VP3 and viral +ssRNA is predicted to nucleate VP2 core assembly. In this model, core assembly results in the displacement of +RNA-bound NSP2 octamers, while VP1 within new formed cores direct dsRNA synthesis, using +RNAs as templates (Cheung et al., 2010; Borodavka et al., 2017; Borodavka et al., 2018). These events are followed by incorporation of the middle virus capsid protein VP6 to form DLPs. At some stage, these assemblies become VPs containing cores and DLPs and may lose some or all of their lipids (Cheung et al., 2010). In this regard, it is important to have in mind that the currently accepted model for the LD biogenesis is that neutral lipids are synthesized between the leaflets of the ER membrane, and the mature LD is then thought to bud from the ER membrane to form an independent organelle that is contained within a limiting monolayer of phospholipids and associated LD proteins (Walther and Farese, 2012). Thus, during budding of the LDs from the ER membrane they could take along rotavirus NSP4 (topologically oriented towards the cell's cytoplasm) which could help as a scaffold on the surface of LDs for the assembly of other rotavirus viroplasmic proteins, localizing then to the interior of VPs.

Further support for our model of localization of at least one pool of NSP4 molecules inside of the VPs is the observation that knocking-down the expression of NSP4 by RNA interference significantly reduces the number and size of VPs present in the cell, as well as the production of DLPs (López et al., 2005a). That study also showed that during RNAi inhibition of NSP4 expression the NSP2 and NSP5 proteins maintained an intracellular distribution restricted to VPs, while the VP2, VP4, VP6 and VP7 proteins failed to locate to VPs. Based on these observations, it is tempting to suggest that, in addition to the role NSP4 has on the budding of DLPs into the ER lumen, it may also play an important role as a regulator of VP assembly.

After the NSP2/NSP4 layer, we observed a middle zone composed of the structural proteins VP1, VP2 and VP6. Their location in the same zone is expected given their close association in the assembled DLPs (Estes and Greenberg, 2013). Also, the fact that VP1, VP2 and VP6 form a complex with NSP2 that has replicase activity (Aponte et al., 1996), suggests that the production of new DLPs could take place in this zone of the VP.

Finally, we found that VP4 and VP7 conform independent layers just external to the viroplasmic proteins. The position of these two proteins agrees with the proposed model of rotavirus morphogenesis in which VP4 is assembled first on DLPs, and subsequently VP7 binds the particles and locks VP4 in place (Trask and Dormitzer, 2006). Furthermore, the fact that VP7-Mon and VP7-Tri occupied the same layer in our model indicates that in the ER sites into which the DLPs bud, VP7 is already organized as trimers, which are subsequently assembled into the virus particles. Of interest, VP4 has been reported to exist in two different forms in infected cells. One of them is associated with microtubules (Nejmeddine et al., 2000), while the other one has been reported to be found between the VP and the ER membrane (González et al., 2000). In this regard, based on our findings, we suggest that the latter form of VP4 can be actually considered as an integral component of the VP. Since several studies have found the presence of different cellular proteins and lipids in association to VPs (Maruri-Avidal et al., 2008; Cheung et al., 2010; Dhillon et al., 2018), it will be interesting to study the relative localization of this components using the methodologies described here.

Materials and methods

Key resources table
Reagent type
(species) or
resource
DesignationSource or
reference
IdentifiersAdditional
information
Virus strain (Rhesus rotavirus)RRVHarry B. Greenberg, Stanford University.
Cell line (Cercopithecus aethiops)MA014 cellsAmerican Type Culture CollectionATCC:CRL-2378.1; RRID:CVCL_3846
AntibodyMouse monoclonal antibody 3A8Harry B. Greenberg, Stanford University.IF (1:1000)
AntibodyMouse monoclonal antibody 2G4Harry B. Greenberg, Stanford University. PMID: 2431540IF (1:1000)
AntibodyMouse monoclonal antibody 255/60Harry B. Greenberg, Stanford University. PMID: 6185436IF (1:1000)
AntibodyMouse monoclonal antibody M60Harry B. Greenberg, Stanford University. PMID: 2431540IF (1:2000)
AntibodyMouse monoclonal antibody 159Harry B. Greenberg, Stanford University. PMID: 2431540IF (1:2000)
AntibodyMouse polyclonal antibody VP1Our Laboratory.RRID:AB_2802095IF (1:500)
AntibodyMouse polyclonal antibody NSP2Our Laboratory. PMID: 9645203RRID:AB_2802096IF (1:100)
AntibodyRabbit polyclonal antibody NSP2Our Laboratory. PMID: 9645203RRID:AB_2802097IF (1:2000)
AntibodyRabbit polyclonal antibody NSP4Our Laboratory. PMID: 18385250RRID:AB_2802094IF (1:1000)
AntibodyRabbit polyclonal antibody NSP5Our Laboratory. PMID: 9645203RRID:AB_2802098IF (1:2000)
Software, algorithmRR Development Core Team, 2017. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.r-project.org/RRID:SCR_001905Version 3.4.4 (2018-03-15)
Software, algorithmMatlabMATLAB and Statistics Toolbox Release 2018b, The MathWorks, Inc, Natick, Massachusetts, United States.RRID:SCR_001622
Software, algorithmFijiPMID:22743772RRID:SCR_002285
Software, algorithmVP-DLSFCThis paperSee ‘Segmentation Algorithm’ in Appendix 1.

Cell and virus

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The rhesus monkey kidney epithelial cell line MA104 (ATCC) was grown in Dulbecco’s Modified Eagle Medium-Reduced Serum (DMEM-RS) (Thermo-Scientific HyClone, Logan, UT) supplemented with 5% heat-inactivated fetal bovine serum (FBS) (Biowest, Kansas City, MO) at 37°C in a 5% CO2 atmosphere. The cells were confirmed to be free of mycoplasm by testing with the INTRON Mycoplasma PCR Detection Kit (#25234). Rhesus rotavirus (RRV) was obtained from H. B. Greenberg (Stanford University, Stanford, Calif.) and propagated in MA104 cells as described previously (Pando et al., 2002). Prior to infection, RRV was activated with trypsin (10 μg/ml; Gibco, Life Technologies, Carlsbad, CA) for 30 min at 37°C.

Antibodies

Monoclonal antibodies (MAbs) to VP2(3A8), VP4 (2G4), VP6 (255/60), VP7 (60) and VP7 (159) were kindly provided by H. B. Greenberg (Stanford University, Stanford, CA) (Shaw et al., 1986; Greenberg et al., 1983). The rabbit polyclonal sera to NSP2, NSP4 and NSP5, and the mouse polyclonal serum to NSP2 were produced in our laboratory (González et al., 1998). The hyperimmune serum to NSP4 (C-239) was generated in our laboratory by immunizing New Zealand white rabbits with a recombinant protein expressed in E. coli with a histidine-tail, representing the carboxy-terminal end (amino acids 120 to 175) of the rhesus rotavirus RRV NSP4 protein; see also Maruri-Avidal et al. (2008), in which this serum was used. The hyperimmune serum to VP1 was also generated in our laboratory by immunizing BALB/c mice with a recombinant protein expressed in E. coli with a histidine-tail, representing amino acids 227 to 539 of the rhesus rotavirus RRV VP1 protein. Goat anti-mouse Alexa-488- and Goat anti-rabbit Alexa-568-conjugated secondary antibodies were purchased from Molecular Probes (Eugene, Oreg.).

Immunofluorescence

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MA104 cells grown on glass coverslips were infected with rotavirus RRV at a multiplicity of infection (MOI) of 1. Six hours post infection, the cells were fixed with and processed for immunofluorescence as described (Silva-Ayala et al., 2013). Finally, the coverslips were mounted onto the center of glass slides with storm solution (1.5% glucose oxidase +100 mM β-mercaptoethanol) to induce the blinking of the fluorophores (Dempsey et al., 2011; Heilemann et al., 2009).

Transmission electron microscopy

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Cells grown in 75-cm2 flasks were infected with rotavirus RRV at an MOI of 3 as described above. Six hours postinfection the cells were fixed in 2.5% glutaraldehyde-0.1 M cacodylate (pH 7.2), postfixed with 1% osmium tetroxide, and embedded in Epon 812 resin. The ultrathin sections obtained were stained with 2% uranyl acetate-1% lead citrate (Reynolds mix). The grids were examined with a Zeiss EM-900 electron microscope at 80 kV.

Set up of the optical microscope

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All super-resolution imaging measurements were performed on an Olympus IX-81 inverted microscope configured for total internal reflection fluorescence (TIRF) excitation (Olympus, cellTIRFTM Illuminator). The critical angle was set up such that the evanescence field had a penetration depth of ~200 nm (Xcellence software v1.2, Olympus soft imaging solution GMBH). The samples were continuously illuminated using excitation sources depending on the fluorophore in use. Alexa Fluor 488 and Alexa Fluor 568 dyes were excited with a 488 nm or 568 nm diode-pumped solid-state laser, respectively. Beam selection and modulation of laser intensities were controlled via Xcellence software v.1.2. A full multiband laser cube set was used to discriminate the selected light sources (LF 405/488/561/635 A-OMF, Bright Line; Semrock). Fluorescence was collected using an Olympus UApo N 100x/1.49 numerical aperture, oil-immersion objective lens, with an extra 1.6x intermediate magnification lens. All movies were recorded onto a 128 × 128-pixel region of an electron-multiplying charge coupled device (EMCCD) camera (iXon 897, Model No: DU-897E-CS0-#BV; Andor) at 100 nm per pixel, and within a 50 ms interval (300 images per fluorescent excitation).

Bayesian analysis of the blinking and bleaching

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Sub-diffraction images were derived from the Bayesian analysis of the stochastic Blinking and Bleaching of Alexa Fluor 488 dye (Cox et al., 2011). For each super-resolution reconstruction, 300 images were acquired at 20 frames per second with an exposure time of 50 ms at full laser power, spreading the bleaching of the sample over the length of the entire acquisition time. The maximum laser power coming out of the optical fiber measured at the back focal plane of the objective lens, for the 488 nm laser line, was 23.1 mW. The image sequences were analyzed with the 3B algorithm considering a pixel size of 100 nm and a full width half maximum of the point spread function of 270 nm (for Alexa Fluor 488), measured experimentally with 0.17 μm fluorescent beads (PS-SpeckTM Microscope Point Source Kit, Molecular Probes, Inc). All other parameters were set up using default values. The 3B analysis was run over 200 iterations, as recommended by the authors in Cox et al. (2011), and the final super-resolution reconstruction was created at a pixel size of 10 nm with the ImageJ plugin for 3B analysis (Rosten et al., 2013), using parallel computing as described in Hernández et al. (2016). The resolution increase observed in our imaging set up by 3B analysis was up to five times below the Abbe’s limit (~50 nm). The resolution provided by 3B was improved by computing the photo-physical properties of Alexa Fluor 488, and Alexa Fluor 568 dyes, which were provided to 3B algorithm, as an input parameter which encompass the probability transition matrix between fluorophore’s states. The method was validated with 40 nm gattapaint nanorules (PAINT 40RG, gattaquant, Inc) labeled with ATTO 655/ATTO 542 dyes (see ‘3B Algorithm’ in Appendix 1).

Code and statistical analysis

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The segmentation algorithm (VPs-DLSFC) was developed in Matlab R2018a (9.4.0.813654) software. A detailed explanation of each the developed methods is available in Appendix 1. Statistical analysis were performed using R version 3.4.4 (2018-03-15) software. All the codes are available at https://github.com/Yasel88/Nanoscale_organization_of_rotavirus_replication_machineries (Garcés Suárez, 2019; copy archived at https://github.com/elifesciences-publications/Nanoscale_organization_of_rotavirus_replication_machineries).

Appendix 1

This appendix is divided in seven sections. In –Segmentation algorithm–, we discuss the mathematical details of the algorithm 'Viroplasm Direct Least Square Fitting Circumference' (VPs-DLSFC). In Section –Algorithm validation–, we compare the algorithm VPs-DLSFC with other two classic methods for the adjustment of circumferences; this analysis was done thanks to the use of approximately 40000 synthetic 'ground truth' images. In Section – Model Considerations–, we prove that the distribution of the studied viral elements follow a concentric circumference spatial distribution. Sections –Exploratory Analysis– and – Linear Regression Model– contains a supplementary exploratory analysis about the spatial distribution of the viral elements, and details about the results and the residual error analysis of the linear regression models, respectively. In Section –NSP5 and NSP4 as reference proteins– we developed a similar study that was made with NSP2, but considering NSP5 and NSP4 as reference proteins. Also, we shown that there is no statistically significative differences between the distributions of the viral elements when we changed the reference protein. Finally, in Section –3B Algorithm– we explain the fitting model for the 3B algorithm where the transition matrix is modeled by ordinary differential equations (ODE).

Segmentation algorithm

The use of primitive models for the segmentation of the SRM images has many benefits, like computational efficiency, simple programmation, and understandable information about the objects that were segmented. In this regard, we developed a simple method for fitting a circumference to scattered data, which we called ‘Direct Least Squares Fitting Circumference’ (DLSFC). This approach considers basic mathematical analysis tools for the computation of the extreme value of a continuous function with N variables.

Direct least squares fitting circumference (DLSFC)

The spatial distribution of a viral proteins into the VP can be seen as a set of points P={(xi, yi)|i=1:N¯}R2 (scattered data in the plane). Taking into account the implicit equation of a circumference (x-xc)2+(y-yc)2=r2, where (xc,yc) is the center, and r is the radius. The problem of adjust a circumference to P, is a optimization problem given by:

(1) minxc,yc,ri=1N((xi-xc)2+(yi-yc)2-r2)2.

The center of mass of P is given by:

(2) (x¯,y¯)=(1Ni=1Nxi,1Ni=1Nyi).

Then, considerering Equation (2), the problem (Equation (1)) can be rewritten as:

(3) minuc,vc,αi=1N((ui-uc)2+(vi-vc)2-α)2

where ui=xi-x¯, vi=yi-y¯(for alli=1,2,,N), α=r2, and (uc,vc) is the center of the circumference after the change of variable.

For simplicity, we will define as fuc,vc,α(ui,vi):=(ui-uc)2+(vi-vc)2-α the distance function, and by F(uc,vc,α):=i=1Nfuc,vc,α(ui,vi)2 the objective function of our minimization problem.

Note 1 Note that, with the new convention of notation, the problem (Equation (3)) is equivalent to:

(4) minuc,vc,αF(uc,vc,α)

A simple alternative to resolve Equation (4) is to consider the extreme values of F(uc,vc,α), this is:

(5) F(uc,vc,α)=(Fuc,Fvc,Fα)=(0,0,0).

The partial derivates of the function F(uc,vc,α) are:

1. For α:

Fα=2i=1Nfuc,vc,α(ui,vi),

Taking into account the condition given in Equation (5) for Fα, we obtain that:

(6) i=1Nfuc,vc,α(ui,vi)=0.

2. For uc:

(7) Fuc=4i=1N[fuc,vc,α(ui,vi)(uiuc)]=4[i=1Nuifuc,vc,α(ui,vi)uci=1Nfuc,vc,α(ui,vi)]=4i=1Nuifuc,vc,α(ui,vi)

3. For vc: It is the same process than uc, the final result is,

(8) Fvc=4i=1Nvifuc,vc,α(ui,vi).

Expanding the Equation (7) we obtain:

Fuc=4i=1Nuifuc,vc,α(ui,vi)=4i=1Nui[(uiuc)2+(vivc)2α]=4i=1Nui[(ui2+uc22uiuc)+(vi2+vc22vivc)α]=4[i=1Nui3+uc2i=1Nui2uci=1Nui2+i=1Nuivi2+vc2i=1Nui2vci=1Nuiviαi=1Nui],

and taking into account that ui=xix¯i=1Nui=i=1NxiNx¯=i=1NxiNi=1NxiN=0, we obtain that:

(9) Fuc=4[i=1Nui32uci=1Nui2+i=1Nuivi22vci=1Nuivi].

Let C(uk,vt):=i=1Nuikvit, then the equation Equation (9) can be written as:

Fuc=4[C(u3, v0)2ucC(u2, v0)+C(u1, v2)2vcC(u1, v1)],

and considering the extreme condition Fuc=0 (see Equation (5)) we obtain:

(10) ucC(u2,v0)+vcC(u1,v1)=12(C(u3,v0)+C(u1,v2)).

Following the same process, but now considering the Equation (8), we obtain:

(11) ucC(u1,v1)+vcC(u0,v2)=12(C(u0,v3)+C(u2,v1)).

The extreme values uc^ and vc^ of the function F(uc,vc,α) are obtained as solution of the linear system formed by Equation (10) and Equation (11).

Note 2 The coordinate system translation to the mass center of the original data, allow the simplification of the equation (Equation (9)).

The radius of the circumference is obtained developing the Equation (6):

0=i=1N[ui2+uc22uiuc+vi2+vc22vivcα]=i=1Nui2+Nuc2+i=1Nvi2+Nvc2Nα,

and writing the equation in function of α, we obtain that:

(12) α^=uc2+vc2+C(u2,v0)+C(u0,v2)N.

The point (uc^,vc^,α^) is a critical point of the function F(uc,vc,α). Finally, we need to compute the Hessian matrix of F(uc,vc,α) to test if (uc^,vc^,α^) is a maximum, a minimum, or an inflection point:

(13) H=(2Fα22Fαuc2Fαvc2Fucα2Fuc22Fucvc2Fvcα2Fvcuc2Fvc2)=(2N4Nuc4Nvc08i=1Nui28i=1Nuivi08i=1Nuivi8i=1Nvi2)

The principal minors of H are:

H1=2N>0,H2=|2N4Nuc08i=1Nui2|=16Ni=1Nui2>0,H3=|2N4Nuc4Nvc08i=1Nui28i=1Nuivi08i=1Nuivi8i=1Nvi2|=128N(i=1Nui2i=1Nvi2(i=1Nuivi)2]Cauchy- Schwarz inequality>0.

Note 3 The Cauchy-Schwarz inequality is equal to zero if and only if exist a real value r such that uir+vi=0, for all i=1,2,,N, that is, all the points are in a straight line. In our problem, the proteins do not follow a straight line distribution in the space, then, we can guarantee the strict inequality. Note that H2=0 if and only if ui=0,for alli=1,2,,N, which is a particular case of a straight line.

The principal minors of the matrix H are greater than zero, then, the point (uc^,vc^,α^) is a local minimum, but this point is the only critical point of the function F(uc,vc,α), and as consequence it is a global minimum.

The center of the fitted circumference in the original coordinate system is (xc,yc)=(uc^,vc^)+(x¯,y¯), and the radius is R=α^.

Note 4 This method is based on a simple and very popular mathematical techniques (specifically Differential Calculus). Even when we do not found a published paper with this approach, we want to take cares and not adjudicate this technique to our work.

Note 5 Note that, by definition, the distance function fuc,vc,α(ui,vi) is not a geometric distance to the circle, which is probably more intuitive to use in this kind of problems. Let consider for a second the geometric distance of a set of points P to a circle, which is given by:

G(xc,yc,r):=i=1N(r-(xi-xc)2+(yi-yc)2)2,

where (xc,yc) is the center of the circumference and r is the radius. Considering the extreme condition for the function G(xc,yc,r), it is obtained that:

Gr=2i=1N(xixc)2+(yiyc)2+2NrGxc=2ri=1Nxixc(xixc)2+(yiyc)22Nx¯+2NxcGyc=2ri=1Nyiyc(xixc)2+(yiyc)22Ny¯+2Nyc,

where x¯ and y¯ are the mean values of the variables x and y respectively. Simultaneously equating these partials to zero does not produce closed form solutions for xc,yc, and r. With numerical methods it is possible to carry out the optimization of these parameters, but these alternatives are iterative, no-deterministic process, which also are highly sensitives to the initial values, while our proposal not have these kind of unwished characteristics. In any case, in Appendix 1 Section –Algorithm validation– we compared our approach with an algorithm based on geometric distance and explained in details the benefits of each one.

The final segmentation algorithm is composed by three steps (Appendix 1—figure 1). The first is a manual pre-segmentation that guarantees the existence of one and only one viroplasm per image (Appendix 1—figure 1A). In the second step, we adjust a circumference to the reference protein (remember that these are paired experiments, where NSP2 is present in all the combinations as reference protein) through the algorithm DLSFC (Appendix 1—figure 1B), and finally the radius of the accompanying protein is adjusted using the Equation (12). Note that, the center of the accompanying protein is the same that the center of the reference protein (concentric model). Out of the manual pre-segmentation step, this algorithm is automatic, deterministic, not iterative and with a linear computational complexity.

Appendix 1—figure 1
Scheme of the ‘Viroplasm Direct Least Square Fitting Circumference’ algorithm (VPs-DLSFC).

SRM) Complete SRM image; A) Manual pre-segmentation step, an expert selects and isolates each viroplasm as a single image; B) Fit a circumference to the reference protein through the algorithm DLSFC; C) The center of the reference protein is taken as the center of the accompanying protein, and then the radius of the adjust circumference for this second protein is computed.

https://doi.org/10.7554/eLife.42906.009

Note 6 The hypothesis that the viral proteins in the viroplasm are distributed like as concentric circumferences was proved in Appendix 1 Section – Model Considerations– (‘Model Considerations’).

Algorithm validation

The algorithm DLSFC was compared with other two approaches proposed by Gander et al. (1994). For a more comprehensive and clear comparison we named these others two methods as ‘Algebraic Least Square Fitting Circle’ (ALSFC) and ‘Geometric Least Square Fitting Circle’ (GLSFC).

The algorithm ALSFC considers the algebraic representation of a circle in the plane:

(14) F(p)=Aptp+Btp+C;

where p=(x,y) is a point in 2, B=(B1,B2)2, A0, and C is the independent term. Then, let pi=(xi,yi)2,i=1,2,,N the set of points that we want to adjust. The objective function for this minimization problem is i=1nF(pi), which can be represented as matrix form:

(15) Ψu=x12+y12x1y11x22+y22x2y21xn2+yn2xnxn1ψAB1B2Cu

The final optimization problem is given by:

(16) {minuΨusubjet to:u=1,

where u=1 is a contrain to avoid the trivial solution u=(0,0,0,0). The notation v=v12+v22++vm2 represent the Euclidean norm. Finally, the problem (Equation (16)) is solved considering the right singular eigenvector associated with the smallest singular eigenvalue of Ψ (Gander et al., 1994).

On the other hand, the algorithm GLSFC deals with the minimization of the geometric distance:

(17) minxc,yc,ri=1n((xc,yc)-pi-r)2.

Note that ((xc,yc)-pi-r)2 is the geometric distance of the point pi to the circle (x-xc)2+(y-yc)2=r2. This problem is nonlinear, and in Gander et al. (1994), the authors consider to resolve it trought a Gauss-Newton algorithm. The Gauss-Newton method is an iterative algorithm that depends of an initial approximation, and in this case, Gander and collaborators consider the solution of the problem (Equation (16)) as the initial value for the iterative process. More details about the algorithms ALSFC and GLSFC can be consulted in Gander et al. (1994). In summary, the method ALSFC is very simple and computational efficient, but the algebraic distance might not reflect with accuracy the real distance between the points and the circumference and, as consequence, the parameters of the model might be biased. On the contrary, the algorithm GLSFC is highly precise, but it is an iterative process (demand more computation time), and depends of good initial values to achieve the convergence. The Matlab codes for the algorithms GLSFC and ALSFC were obtained from Brown (2007).

For the validation, we simulated the spatial distribution of viral elements as circumferences, for which we know their parametric form (‘ground truth’ dataset) (Appendix 1—figure 2A). The use of ‘ground truth’ allows us to quantify the error in the adjustment of the algorithms DLSFC, ALSFC and GLSFC at different noise levels (Appendix 1—figure 2B) and partial occlusion conditions (Appendix 1—figure 2C). We generated over 40 000 images (size 512×512 pixels) taking into account different levels of additive white Gaussian noise (AWGN) in order to consider auto-fluorescence and the error in the localization of the fluorophores by the algorithm 3B-ODE (see Appendix 1 Section –3B Algorithm–), and partial occlusion angles. Several radii and position of the synthetic viroplasms were generated randomly through a uniform distribution function. The codes for this simulation are availables at https://github.com/Yasel88/Nanoscale_organization_of_rotavirus_replication_machineries (Garcés Suárez, 2019; copy archived at https://github.com/elifesciences-publications/Nanoscale_organization_of_rotavirus_replication_machineries).

Appendix 1—figure 2
Simulation of the viral proteins.

(A) ‘Ground truth’ (GT) circumference; (B) Addition of gaussian noise to the GT circumference (see Appendix 1 subsection –noise generation–); (C) Generation of partial occlusion (see Appendix 1 subsection –Partial Occlusion Generation).

https://doi.org/10.7554/eLife.42906.010

Noise generation

Let a synthetic image and pi2,i=1,2,,N points of the ‘ground truth’ circunference 𝒞, the AWGN over pi, i=1,N¯ was generated as:

(18) pic=pi+σXi,

where pic is the corrupted point after the contamination with AWGN, σ is a scalar that represents the level of noise, and Xi is a trial of a random variable XN(0,1) (standard gaussian distribution). In our experimental design we included 20 different levels of noise σ=0:0.5:10 (increase by 0.5 from 0 to 10). Note that the noise was added to the points of the circumferences and not to the images. This is because we are working with SRM images, and as consequence does not exist background noise.

Partial occlusion generation

The partial occlusion can be seen as the existence of incomplete information of the objects of interest, for example, an image where we have only information about the half of the VPs. In our perspective, it is important that a segmentation algorithm have a good performance even in these situations.

Definition 1 We called an angle θ as a partial oclussion angle for a set of points pi=(xi,yi)R2,i=1,2,,N, if not exist j{1,2,,N},rR and β[α,α+θ] such as:

pj=(x¯+rcosβ,y¯+rsinβ),

where α is an angle in [0,2π], and (x¯,y¯)=(1Ni=1Nxi,1Ni=1Nyi) is the center of mass of the points pi.

Note 7 Note that, in the Definition 1 we considered the interval [α,α+θ] as a partial oclusion angle θ, but it is possible to obtain the same oclussion angle with [α,α-θ]. For our validation we took α=0 for simplicity, but this has not consequences in our experiments, because we generate the points as a circumference.

The relationship between cartesian and polar coordinates is given by:

(19) {x=a+rcosβy=b+rsinβ,

where, (a, b) is the circumference center, r is the radius and β is the angular coordinate. Then, for example, to provoke a partial occlusion of θ, it is just needed to avoid the generation of points in the angle [0,θ] or [2π,2π-θ] through the Equation (19). Appendix 1—figure 3 shows this strategy, in this example, a half of the information is removed from the ‘ground truth’ circumference.

Appendix 1—figure 3
Generation of partial occlusion in the angle θ=π (red line).

The circle just conserves the information relative to the angle [0,π].

https://doi.org/10.7554/eLife.42906.011

In general, the average of the points that will be conserved after the generation of partial occlusion is given by:

P%=100(1-θ2π).

In the validation of the algorithm DLSFC, we considered four different partial occlusion conditions: 1- Not partial occlusion: Conserves all the points of the ‘ground truth’ circumference; 2– 25% of partial occlusion: Partial occlusion angle θ=π/2; 3– 50% of partial occlusion: Partial occlusion angle θ=π; 4– 75% of partial occlusion: Partial occlusion angle θ=3π/2.

In the experiments, we represent the noise through the mean and the standard deviation of the distance of the points pic,i=1,2,n to the ‘ground truth’ circumference 𝒞, this is:

(20) d𝒞¯=i=1ndi𝒞nMean Value,σd𝒞=i=1n(di𝒞d𝒞¯)2N1Standard Deviation

where di𝒞=|μ-pic-r| is the geometric distance between the point pic and the circumference 𝒞, || represent the absolute value, μ=(xc,yc) is the center of the circumference and r is the radius. The mean and standard deviation are an useful alternative to understand the amount of dispersion generated by a noise σ in a circumference 𝒞.

The Appendix 1—figure 4 shows the adjustment through the algorithms DLSFC, GLSFC and ALSFC of one ‘ground truth’ circumference (solid black line) that was corrupted by different levels of AWGN and partial occlusion angles. As was expected, the performance of the algorithms seems to get worse when increase the level of partial occlusion, but the three algorithms shows good results for high AWGN levels. This example suggests that the algorithm GLSFC (solid red line) has a better performance than DLSFC (solid blue line) and ALSFC (solid green line) when the partial occlusion is less than π (columns A-C), but when θ=3π/2, this method breaks down, and this observation is more relevant when increase the level of noise. The algorithm ALSFC shows relative good results for all the experimental conditions, but it is interesting to note that, in most cases, the adjustment is worse than in the DLSFC and GLSFC alternatives, probably as consequence of the algebraic distance (see Appendix 1 Section –Algorithm validation–). This example is just for a first visual analysis, but a complete study of the results obtained by the three algorithms over the 40 000 synthetic images will be presented below.

Appendix 1—figure 4
Data adjustment through the algorithms DLSFC (solid blue line), ALSFC (solid green line) and GLSFC (solid red line).

The data was generated corrupting the points of a ‘ground truth’ circumference (solid black line) with different noise levels (rows) and four differents occlusion angles conditions (columns). Column 1 (A.1-A.4) Not Occlusion angle, Column 2 (B.1-B.4) θ=π/2, Column 3 (C.1-C.4) θ=π, Column 4 (D.1-D.4) θ=3π/2. The noise increase by rows: Row 1: d𝒞¯[1.5μm, 1.54μm], σ(d𝒞)[1.29, 1.74], σAWGN=2.1053; Row 2: d𝒞¯[4.19μm, 5.28μm], σ(d𝒞)[3.64, 5.71], σAWGN=4.7368; Row 3: d𝒞¯[7.5μm, 9.23μm], σ(d𝒞)[7.49, 10.38], σAWGN=7.3684; Row 4: d𝒞¯[12.58μm, 17.78μm], σ(d𝒞)[11.12, 17.96], σAWGN=10.

https://doi.org/10.7554/eLife.42906.012

A circumference can be represented as a vector 𝒞=(r,xc,yc)3, where r is the radius, and (xc,yc) the center. Let 𝒞^=(r^,xc^,yc^) and 𝒞=(r,xc,yc) the ‘ground truth’ and the adjusted circumference, respectively. The fit error committed by the algorithms can be quantified as:

ε=𝒞^𝒞

Now, thanks to the use of ‘ground truth’ circumferences, it is possible to compare the obtained outcome with the ideal result. We consider that an adjustment is good enough if the estimation error of each circumference’s component 𝒞 is less than 0.1 μm. This value is approximately two-fold smaller than the theoretical Abbe’s limit (250nm), and taking into account that the synthetic images resolution vary between 4.6 and 25.8 μm in mean (see Appendix 1—figure 5), we are demanding that the algorithm has a nanoscopic precision (less than 100 nm) even when the images have a very bad resolution. Combining the threshold explained above with Equation (21), we obtain the final condition based on the euclidean norm between these two vectors:

(22) ε=𝒞^𝒞(0.1, 0.1, 0.1)=0.1732μm.
Appendix 1—figure 5
Error in the adjustment of the algorithms DLSFC, GLSFC and ALSFC.

The error was quantified through Equation (21). In all panels, the horizontal black line represents the value y=0.1732μm (see Equation (21)). (A) Boxplot of the error distribution for each algorithm taking into account the partial occlusion angles (four sub-panels). The x-axis specifies the name of the algorithm and the y-axis the error in microns. The blue shadow in the sub-panel 3π2 represents the occlusion angle in which the mean value of the errors are greater than 0.1732μm. (B) Mean error of the adjustment by the algorithms DLSFC, GLSFC and ALSFC. The bottom x-axis is the Mean distance of the corrupted points to the ‘ground truth’ circumference (see Equation (20)), and the up x-axis is the Standard Deviation. The figure is split out in four sub-panels in accordance with the occlusion angle. The black boxes show examples in which the algorithm GLSFC does not reach the convergence (extremely high error). The arrows mark out some examples where the algorithm ALSFC does not have have a good adjustment. (C) Zoom of the performance of the algorithms DLSFC and ALSFC. (D) Results of the algorithm DLSFC. The graphics in the panel (C)) and (D)) also shows the confidence interval around the mean (see green and blue shadows), it was computed as d𝒞¯±σ(d𝒞).

https://doi.org/10.7554/eLife.42906.013

The Appendix 1—figure 5(a) shows the descriptive analysis (through boxplots) of the errors generated by the algorithms DLSFC, GLSFC and ALSFC over the 40000 synthetic images. In some experiments we obtained extremely good adjusts (ε10-15μm), but in general the 75% of the errors are in the interval [10-3,1]μm. For all occlusion angles, the algorithm GLSFC had a bad behaviour in a wide range of experiments with an error of 1010μm. This kind of situation was expected for big partial occlusion angles (for example θ=3π/2), but in conditions where does not exist partial occlusion (θ=0), the bad adjustment of GSFC is evidence that this algorithm is not a good alternative in this kind of problems. Note that a similar situation happens with the algorithm ALSFC, but in this case the maximum error is 103μm, which is high too, but significantly less than that obtained by GLSFC. The algorithm DLSFC does not show the previous problems; observe that the maximun error is under 1μm for all experimental conditions, even when θ=3π/2. Now, if we forget the outliers and take into account only the 75% of the experiments (boxes), a direct relationship between the error of each algorithm and the partial occlusion angles (increase occlusion angle imply a major error) is observed. However, the raise of the mean error is small in relationship with the occlusion angle, which suggests that these three methods are robust to partial occlusion. The blue shadow band highlights the occlusion angle (θ=3π/2) for which the algorithms have a median error greater than 0.1732μm. Therefore, it is necessary at least the 50% of the data to obtain a good adjustment (with an error under 0.1732μm) in the 75% of the experiments.

The Appendix 1—figure 5(b) displays the mean error obtained by each algorithm in relationship with the resolution of the images (mean and the standard deviation of the points distance to the ‘ground truth’ circumference, Equation (20)). This graph shows again that the method GLSFC did not reach the convergence in some experiments (remember that GLSFC is based on an iterative optimization algorithm), even for small partial occlusion angles, but it is interesting to point out that in all these cases (at least for the occlusion angles θ={0,π2,π}), these high errors (1010μm) seem to be related with bad initial values. Note that in these experiments the algorithm ALSFC do not has a good performance (remember that the result of ALSFC is the initial value for GLSFC), which is an evidence of the sensibility of the GLSFC to the initial values. For the occlusion angle θ=3π2, a lot of bad fits were obtained through the algorithm GLSFC. In our opinion, even when the algorithm GLSFC can reach an extremely good fit, its sensitivity to initial values, the computational cost (iterative process), and the possibility of not convergence, are strongs reasons to consider that this alternative is not viable to use in this kind of problems.

In the Appendix 1—figure 5(c), the mean error of the algorithms DLSFC and ALSFC was splitted to see more clearly the performance of each one. For small partial occlusion angles (θ={0,π2}) the algorithm DLSFC has errors 0.1732μm, while ALSFC, in high noise scenes, get a poor adjustment (black arrows). When θ=π, the method ALSFC has errors 0.1732μm in many cases, that increase when the level of noise grows. Both algorithms generate an error 0.1732μm when θ=3π2, but in the case of DLSFC, in some experiments had errors <0.1732μm, even for high noise levels. The Appendix 1—figure 5(d) show only the performance of the algorithm DLSFC. As noted, the method DLSFC shows a behaviour extremely robust and stable to noise and partial acclusion; note that for θ={0,π2,π} does not exist an increment in the mean error when the noise level is incremented. In extreme experimental conditions, when only the 25% of the data remain in the image (θ=3π2), DLSFC has a mean error between [0.3,0.5]μm with a 95% confidence interval equal to [0.1,0.9]μm.

So far we have shown the behaviour of the three algorithms considering several noise levels and partial occlusion angles conditions. However, it is interesting to know through a hypothesis test (inferential statistics) the performance of DLSFC and ALSFC taking into account the experiments we developed (samples). Note that we are not going to study the algorithm GLSFC, because, as we mentioned above, its sensitivity to initial values and its computational cost (iterative process) are strong reasons to consider that this algorithm is not viable to use in this kind of problems. Taking into account the threshold in Equation (22), for each experiment we have two possible outcomes:

(23) {success,ifε0.1732μmfailure,ifε>0.1732μm.

From this point of view, each experiment follows a Bernoulli’s distribution, and then, all the experiments for the same experimental condition (partial occlusion angle) follows a Binomial distribution. The generated samples are independent (random generation), the decision rule (Equation (23)) is dichotomous, and our experimental design is a fair representation of the population (we considered many experimental conditions in more than 40000 images); then, it is possible to develop a ‘Binomial Test’ (Prybutok, 1989; Howell, 1982) to evaluate the population proportion of success, which we will denote by p. The null (H0) and alternative (H1) hypothesis for this test are:

(24) {H0:p=0.7H1:p>0.7.

The null hypothesis is that the population proportion with an error less that 0.1732 is 0.7, and the alternative hypothesis is that the proportion is more that 0.7. The significance level for these tests is fixed at α=0.05. For more information about this test and its implementation review (R Development Core Team, 2017; Prybutok, 1989; Howell, 1982) Online documentation is available in url https://stat.ethz.ch/R-manual/R-devel/library/stats/html/00Index.html.

The Appendix 1—table 1 shows the results of the ‘Binomial Test’ for the algorithms DLSFC and ALSFC. For small occlusion angles θ={0,π2}, the results of both methods are very similar and indicate a high performance. Note that in these cases the null hypothesis was rejected with a probability error of type I of 10-16α, and the 95% confidence intervals are equal to [0.99,1], which means that, at a population level, we hope that at least the 99% of the adjustments had an error 0.1732μm. For θ=π, the algorithm DLSFC has a probability of success greater than 0.7 with a p-value of 10-16α. On the contrary, for the same oclussion angle, the test revealed that the null hypothesis can’t be rejected in the case of the algorithm ALSFC. Finally, as was analyzed above, the performance of the algorithms decrease significally for θ=3π2, and we can’t reject the null hypothesis, in others words, we don’t have enough evidence to assume that in this case the probability of success is greater than 0.7.

Appendix 1—table 1
Results of the Binomial Test.

Column 1: Names of the algorithms. Column 2: ‘P. Success’ is the Probability of Success; ‘P. Value’ denote the probability of the error type 1, that is, reject the null hypothesis when it is true; ‘C. Interval’ is the 95% confidence interval. Column 3–6: Partial Occlusion Angles. The blue shadowed area in the table cell indicates the conditions in which it is not possible to reject the null hypothesis.

https://doi.org/10.7554/eLife.42906.014
AlgorithmStatisticsPartial occlusion angles
0π/2π3π/2
P. Success110.8040.384
DLSFCP. Value2.2 × 10−162.2 × 10−162.2 × 10−161
C. Interval[0.999, 1][0.999, 1][0.797, 1][0.376, 1]
P. Success0.9930.990.6430.273
ALSFCP-value2.2 × 10−162.2 × 10−1611
C. Interval[0.99, 1][0.99, 1][0.635, 1][0.265, 1]

The study carried up in this section shows that the algorithm GLSFC has a good performance and is capable to obtain a low error in the adjustment, but this alternative is sensitive to the initial values (Appendix 1—figure 5 (a,b)), and as any iterative process, consumes more computational resources. The method ALSFC proved to have a good behavior in many experimental conditions, although in diverse occasions a bad fit was obtained. Also, the behaviour of this algorithm was always inferior than that of DLSFC (Appendix 1—figure 5(C) and Appendix 1—table 1). Finally, the algorithm DLSFC had a great performance and stability in all the experimental conditions, even in extreme partial occlusion angles (Appendix 1—figure 5 and Appendix 1—table 1). This method proved to be robust in high noise conditions and it is a deterministic and not an iterative algorithm. For all these reasons we consider that the algorithm DLSFC is the best choice in comparison with GLSFC and ALSFC, to fitting the spatial distribution of the viral elements.

Model considerations

To proof the hypothesis that the viral elements of the VPs can be approximated through circumferences, we carried up a series of experiments based on the comparison between the circumference obtained by the algorithm DLSFC, and a least squared ellipse resulting of the ‘Direct Least Square Fitting Ellipse’ (DLSFE) algorithm (Fitzgibbon et al., 1999). The algorithm DLSFE has been used previously to adjust the viral replication centers of adenoviruses in fluorescence images (limited by diffraction) (Garcés et al., 2016), and has also been shown to be robust to noise, computationally efficient, and easy to implement (Fitzgibbon et al., 1999).

Let us denote by (xi,yi),i=1,2,,N the set of N points relative to the protein 𝒫, and by C𝒫 and E𝒫 the adjusted implicit form of the conics obtained by the algorithms DLSFC and DLSFE respectively. The variable C𝒫=(r,xc,yc) is a vector where r is the radius, and (xc,yc) is the center of the circumference. On the other hand, the implicit form of the ellipse can be represented as E𝒫=(a,b,xcE,ycE,θ), where {a,b} are the semi-major and semi-minor axis respectively, (xcE,ycE) is the center of the ellipse, and θ is the rotation angle. Under the assumption that the protein 𝒫 can be approximate by a circumference, we expect that does not exist significative statistical differences between the radius of the circumference (r) and each one of the ellipse semi-axis (a,b).

Note 8 Note that this approach is independent of which protein we choose to test the circularity hypothesis.

For each protein combination, we accomplish a Shapiro-Wilk hypothesis test to study if any of the three distributions functions (circumference radius (r), semi-major axis (a) and semi-minor axis (b)) came from a normally distributed population (Shapiro and Wilk, 1965). The results revealed that, our data does not seem to follow a Gaussian distribution, and as consequence, it is impossible to use a parametric test (for example t-student). Based on our data conditions, we considered the Mann-Whitney test (Mann and Whitney, 1947; Hollander et al., 2013) to evaluate the differences between the radii of the circumferences and each of the ellipses semi-axis. This is a nonparametric test that can be applied when the observations are independent (our variables are independent because the radius and the semi-axes were obtained by different algorithms), the variables are ordinal (also our variables meet this requirement because they are numeric), and finally, we want to test if the radius of the circumferences and each one of the ellipses semi-axis, are equal (null hypothesis) or are not (alternative hypothesis).

The statistical analysis reveal that does not exist a significative statistical differences between RC and a (see Appendix 1—table 2) with a significance level of α=0.05. The same results were obtained for RC and b (see Appendix 1—table 3), and as consequence not matter if we use circumferences or ellipses to fitt the spatial distribution of the viral proteins.

Appendix 1—table 2
Two-sample Mann-Whitney hypothesis test between a (major semi-axis of the ellipse ) and r (circumference radius).

H0(H1): The radii of the circumferences and the values of the major semi-axis of the ellipses came from the same distribution function (different). Column 1: W represent the distribution value of the statistical test; Difference is the estimation of the location parameter (median difference between a and r); P. Value is the p-value of the test; C. Interval is the 95% confidence interval. For each one of the nine viral elements combinations, we carry up the hyphotesis test taking into account NSP2 independenly in each combination, just for the semi-major axis this table shows the results of 18 Mann-Whitney hypothesis tests. More information about this test is available in Mann and Whitney (1947) and Hollander et al. (2013).

https://doi.org/10.7554/eLife.42906.015
Proteins Combinations
NSP2/NSP4NSP2/NSP5NSP2/VP1NSP2/VP2
StatisticsNSP2
NSP4
NSP2
NSP5
NSP2
VP1
NSP2
VP2
W90090214261415559539174184
Difference0.03520.033690.03580.03570.02130.0260.05290.0512
P. Value0.12330.1270.0910.080250.17760.1170.11370.1789
95% CI[−0.082, 0.011][−0.08,0.013][−0.086, 0.007][−0.08,0.006][−0.054,0.012][−0.057, 0.006][−0.1168,0.0204][-0.15, 0.028]
NSP2/VP4NSP2/VP6NSP2/VP7-TriNSP2/VP7-Mon
StatisticsNSP2VP4NSP2VP6NSP2VP7-TriNSP2VP7-Mon
W77176011913414251421551528
Difference0.02640.02210.03930.0310.03010.0320.04870.055
P. Value0.10120.08330.07470.18140.15670.15030.15130.092
95% CI[−0.0549, 0.0044][−0.051,0.003][−0.0909,0.0067][−0.103,0.034][−0.0675,0.0105][−0.073, 0.014][−0.1165,0.0221][−0.119,0.01]
Appendix 1—table 3
Two-sample Mann-Whitney hypothesis test between b (minor semi-axis of the ellipse ) and r (circumference radius).

H0(H1): The radii of the circumferences and the values of the minor semi-axis of the ellipses came from the same distribution function (different). This table is equivalent to Appendix 1—table 2. We considered to split the results for each semi-axis of the ellipse for better analysis and visualization.

https://doi.org/10.7554/eLife.42906.016
Proteins Combinations
NSP2/NSP4NSP2/NSP5NSP2/VP1NSP2/VP2
StatisticsNSP2
NSP4
NSP2
NSP5
NSP2
VP1
NSP2
VP2
W126312611966196080482411351134
Difference0.03250.0410.02820.030.03080.02780.01850.0216
P. Value0.14990.19360.23340.23940.22590.23850.19950.1335
95% CI[−0.027,0.092][−0.026,0.108][−0.019,0.077][−0.0213,0.08][−0.018,0.085][−0.021,0.082][−0.015,0.05][−0.012,0.057]
NSP2/VP4NSP2/VP6NSP2/VP7-TriNSP2/VP7-Mon
StatisticsNSP2VP4NSP2VP6NSP2VP7-TriNSP2VP7-Mon
W22721319311895798814291279
Difference0.0380.0290.02590.02880.04270.0460.04350.038
P. Value0.18140.35430.170.24070.22330.16410.25780.3953
95% CI[−0.023,0.097][−0.031,0.106][−0.013,0.066][-0.02, 0.074][−0.022,0.107][−0.019,0.113][−0.0317,0.107][−0.058,0.135]

On the other hand, we carried up a study to validate the viral elements concentricity hypothesis based on the distance between the centers of the adjusted circumferences of both proteins. For all the proteins, the median value is very close or smaller than 0.05μm (Appendix 1—figure 6 and Appendix 1—table 4 (Column 2)), which is in accordance with the resolution limit of the algorithm 3B-ODE (0.04-0.05μm) (Cox et al., 2011). Also, the 95% confidence interval (Appendix 1—table 4, Column 3) shows that the distance between the centers in each case is, 95% of the times in the order of 10-2μm, which we consider a small error taking into account the limitations of the algorithm 3B-ODE.

Appendix 1—figure 6
Boxplot of the differences in location between the center of the circumference that adjust NSP2 and the centers of the others nine viral elements.

The red line y=0.052μm represents approximately the maximun median value of distance between NSP2 and each of the others viral elements, while the second red line (y=(0.1,0.1)=0.141μm) is the maximun error that we considered in the algorithm validation section (see Appendix 1 Section –Algorithm validation–). Each box contains the 50% of the observations, the bottom and the top of the box are the first and third quartiles (25% and 75% of the observations respectively). The line inside the box is the median (second quartiles (50% of the observations)). The upper whisker extends from the hinge to the largest value no further than 1.5×IQR from the hinge (where IQR is the interquartile range, or distance between the first and third quartiles). The lower whisker extends from the hinge to the smallest value at most 1.5×IQR of the hinge. The notches around the median extend to ±(1.57×IQR/n). This gives a roughly 95% confidence interval for comparing medians (McGill et al., 1978).

https://doi.org/10.7554/eLife.42906.017
Appendix 1—table 4
Difference in location between the centers of NSP2 and {NSP5, NSP4, VP1, VP2, VP6, VP4, VP7-Tri, VP7-Mon}.

The 95% Confidence Interval (Column 3) was computed in accordance with Chambers et al. (1983) as: x^±(1.57×IQR/n), where, x^ is the median of x, IQR is the interquartile range, and n is the length of x.

https://doi.org/10.7554/eLife.42906.018
CombinationDifference in location95% CI
NSP2/NSP50.0367391[0.03302618, 0.04045203]
NSP2/NSP40.02126683[0.01708335, 0.02545032]
NSP2/VP20.03795674[0.03043561, 0.04547787]
NSP2/VP10.04006871[0.03508308, 0.04505433]
NSP2/VP60.03787043[0.03153263, 0.04420824]
NSP2/VP40.0432802[0.03410000, 0.05246041]
NSP2/VP7-Tri0.05184999[0.04138659, 0.06231340]
NSP2/VP7-Mon0.05184999[0.03922319, 0.06447680]

Note 9 The Mann-Whitney test was used to study the differences in population medians (difference in location) (Mann and Whitney, 1947).

Supplementary exploratory analysis

The algorithm VPs-DLSFC allows the quantification of the radius of two proteins in the same VP, and also the relative distance between them. At a first stage, we analyzed approximately 590 images (see histogram in Appendix 1—figure 7A) that were obtained by the pre-segmentation step of the algorithm VPs-DLSFC (Appendix 1—figure 1). In agreement with previous reports (Eichwald et al., 2012; Eichwald et al., 2004; Carreño-Torres et al., 2010), we found a wide heterogeneity in the size of VPs measured by NSP2, which exhibited radii ranging from 0.2 to 0.75 μm. In order to compare the distribution of each protein taking NSP2 as reference, we selected a subset of the individual VPs, in a way that there were no significant statistical difference between the radii of NSP2 from each condition.

Appendix 1—figure 7
Supplementary exploratory analysis of the results obtained by the algorithm VPs-DLSFC.

(A) Histogram with the numbers of VPs that were obtained as part of the pre-segmentation step of the algorithm described in Appendix 1—figure 1A. Note that because each image contains one and only one VP, this histogram represents also the numbers of pre-segmented images that we had in our study. (B) Graphical representation of the Mann-Whitney hypothesis test in two-by-two comparison between the radii distributions of NSP2 in each experiment (Mann and Whitney, 1947). To avoid confusions, for each box, under the NSP2 name in x-axis, we included the name of the accompanying protein that specifies in which experiment we obtain that distribution of NSP2. Each combination is linked by a line, and the result of the test is up of the line. The red dashed square highlights the only two combinations (VP1 and VP2) in which the distribution of NSP2 had a significant statistical difference with the other NSP2 distributions. (C) Two-sample Mann-Whitney hypothesis test, considering as variables the radius of NSP2 in contrast to the radius of the others seven proteins. In each combination, we show the difference in location between NSP2 and the other protein (x-axis) and the confidence interval at a level of 95%. The numbers over the intervals confidence are the p-value of the statistical test.

https://doi.org/10.7554/eLife.42906.019

In accordance with this criterion, we were able to adjust the size of NSP2, such that the mean in the distribution of the radius was similar when this protein was paired with NSP5, NSP4, VP6, VP4 and VP7 (Appendix 1—figure 7B). Unfortunately, in the case of NSP2~VP1 and NSP2~VP2, even though we could selected a group of VPs in which the mean radius of NSP2 (0.35 μm) was closer to the size of the NSP2 from the other conditions (0.4μm), the analysis of the distributions in the radius of NSP2 by the Mann-Whitney hypothesis test (Appendix 1—figure 7B), revealed that the VPs of VP1 and VP2 were significative smaller than the mean size of viroplasms of the others proteins. As consequence, was not possible to compare directly the position of VP1 and VP2 with the others viral elements through an exploratory analysis. However, this problem did not limit the inferential study that we developed.

The use of super-resolution microscopy and the algorithm VPs-DLSFC allows the detection of small differences (resolution of nanometers) in the relative position of the viral elements. To validate that the different viral elements were in fact located in a different region from NSP2, we developed a Mann-Whitney test to study the existence of significative differences between the radii of NSP2 and the radii of each of the other viral elements. According with our previous results (see main text), this test revealed that only NSP4 has a similar spatial distribution that of NSP2 (Appendix 1—figure 7C and Appendix 1—table 5), while the others viral elements have different radii. Moreover, the small negative differences in location of NSP5 turned out to be significative different with respect to NSP2 (the p-values of the test are available in the (Appendix 1—figure 7C and Appendix 1—table 5). These results support that NSP5 is located in the innermost part of the viroplasm and that NSP4 shares the same layer with NSP2. The structural proteins VP1, VP2 and VP6 seem to be in the same layer of the viroplasm, with similar values, but with a significative statistical difference in location with NSP2 at a level α=0.01. Also, this test suggests that VP4 and VP7 form independent layers in the most external zone of the VPs (Appendix 1—figure 7C and Appendix 1—table 5), which is in accordance with our proposed model.

Appendix 1—table 5
Two-sample Mann-Whitney hypothesis test, considering as variables the radii of NSP2 in contrast with the radii of the others seven viral proteins.

Under the null hypothesis, both samples come from the same distribution (H0: true location is equal to zero), while the alternative hypothesis (H1: true location is not equal to zero) establishes that exist a difference between the median of the distributions. Protein: Name of the viral element compared with NSP2; W: value of the Mann-Whitney statistical hypothesis test; Difference: Estimation of the location parameter (median difference between the radii of NSP2 and the radii of the other viral element); C. Interval: 95% confidence interval; P. Value: p-value of the test.

https://doi.org/10.7554/eLife.42906.020
ProteinWDifference in location95% CIp-value
NSP51327−0.048972049[−0.086040620,–0.01563190]2.968772×103
NSP44711−0.003348142[−0.032696239, 0.02632726]8.197094×101
VP116990.044239569[0.012214263, 0.07804365]7.728702×103
VP235570.040956503[0.010802771, 0.06990018]5.166044×103
VP643160.063282322[0.032020596, 0.09793399]1.407904×104
VP426370.150597251[0.115162890, 0.18499337]1.824306×1011
VP7-Mon42800.392334895[0.350192949, 0.43852366]1.130338×1021
VP7-Tri18140.400145108[0.324450625, 0.46457274]1.611397×1014
Appendix 1—figure 8
Examples of small zones of colocalization between differents viral proteins.

The interations between the viral elements could be explained throught the spikes that come from the central distribution of the viral elements which colocalize with other proteins. A more specific study it is necessary in order to explain these interactions.

https://doi.org/10.7554/eLife.42906.022

Linear dependency between the viral components

The spatial distribution of the viral elements in the VPs is conserved regardless of their size; that is, the radius of each protein shows a linear dependency with the radius of NSP2.

Let Pi=(xi,yi)2,i=1,2,,N a set of points, where xi and yi are the radii of NSP2 and the acompayning viral element Y, respectively. The adjustment of the linear model can be solved through the following optimization problem:

(25) minβi=1N(yi-βxi)2.

The model (Equation (25)) does not include an offset term because we don’t have any quantification about the radius of the accompanying viral element when NSP2 have been silenced.

The solution of this problem is given by Kiefer (1987):

(26) β^=cor(x,y)×σ(y)σ(x)=cov(x,y)σ(x)σ(y)×σ(y)σ(x)=1n(xix¯)(yiy¯)Var(x),

where cor(x,y) is the linear correlation between x and y, cov(x,y) is the covariance between x and y, Var(x) is the variance of x, and x¯ is the mean value of the variable X.

The ‘Residual Standard Error’ (RSE or (σ2)) is a measure of fit of the linear regression model.

(27) σ2=1N-2i=1Nϵi2,

where ϵi=yi-β^xi. The ‘Standard Error’ (σβ^2) in the estimation of the slope β^ is:

(28) σβ^2=σ2(xi-x¯)2.

Consider the statistic tβ=β^-βσβ^ and the null (H0) and alternative hypothesis (H1):

(29) {H0:β=0H1:β0

Under the null hypothesis, t0=β^σβ^ follow a t-Student distribution with N-1 degrees of freedom. The p-value of this tests is computed as:

(30) p.value=2×(1-P(Tt0)),

where P(Tt0) is the probability that a t-Student variable with N-1 degrees of freedom be less than t0. Note that through this hypothesis test it is possible to evaluate if the slope β is significative to explain the linear relationship between the variables.

The variance of the dependent variable y is:

(31) i=1N(yi-y¯)2Full Variance=i=1N(yi-y^i)2Residual Variance+i=1N(y^i-y¯)2Regression Variance,

where, y^i=β^xi. In accordance with the Equation (31), the variance rate that could be explained by the regression model is the regression variance divided by the full variance, this is:

(32) R2=(y^i-y¯)2(yi-y¯)2[0, 1].

Let Ψ be the lineal regression model that adjusts the data (xi,yi), and be R2 the associated r-square value, then, 100×R2 is the percent of the data variance that it was explained by the model. For strong linear dependencies, the expected R2 value should be close to 1. For more information about linear regression models consult (Kiefer, 1987).

The results of the regression models are available in Appendix 1—table 6. In all regression models, the standard errors are in the order of 10-2μm, with a p-value<10-33 which is a strong evidence of the linear relationship that exist between NSP2 with the other seven viral proteins. Also, the RSE have values in the order of 10-2μm, except for VP7 which have a RSE of 0.15μm, which could suggest that exist a greater dispersion of VP7 in comparison with the others viral proteins, something expected since, according to our model, VP7 is the most external protein.

Appendix 1—table 6
Results and validation of the linear regression models.

NSP2 was considered as the independent variable and the other viral elements as the dependent variable (see Equation (25)). The slope and standard error for each regression model (Column 2 and 3) were computed in accordance with the Equation (26) and (28) respectively. The t-value of the t-Student distribution function with N-1 degrees of freedom are in Column 4 (see Appendix 1 Section – Linear Regression Model– for details). The p-value for each linear regression model are shows in Column five and were measure as was described in (Equation (29)) and (Equation (30)). Finally, the RSE and the R2 summarize the adjustment of the data through the proposed lineal models. As was advised, the RSE (Column 6) is a fit measure of the linear model to the data (see Equation (27)). The ‘% Error’ is the average error in the prediction and it is computed as: 100×RSE/β, while the 100×R2 is the percent of the data variance that it is explained by the model (see Equation (32)).

https://doi.org/10.7554/eLife.42906.021
ModelSlope (β)Std.error (σβ^2)t-valuep-valueRSE% ErrorR2
NSP5=βNSP5×NSP20.86674940.01794773848.292962.550154 × 10−500.078%0.974
NSP4=βNSP4×NSP20.99115170.006973701142.127082.271571 × 10−1140.0353.5%0.995
VP2=βVP2×NSP21.12439310.01481798575.880306.242800 × 10−720.043.5%0.987
VP1=βVP1×NSP21.15061380.01906973060.337182.238867 × 10−480.0443.8%0.986
VP6=βVP6×NSP21.18063350.011218918105.235951.087989 × 10−860.0383.2%0.992
VP4=βVP4×NSP21.38870830.02431998357.101535.757257 × 10−500.075%0.983
VP7-Mon=βVP7-Mon×NSP21.94072040.04035422548.092121.560719 × 10−520.1427.3%0.972
VP7-Tri=βVP7-Tri×NSP21.94165420.05465632735.524785.778910 × 10−330.1537.8%0.967

The average errors are under 8% in all models (Appendix 1—table 6), which confirm the capacity of our linear models to predict with high accuracy the radius of the described viral elements. On the other hand, the percentage variance rate that could be explained by the regression models (100×R2, see Equation (32)), was greater than the 96% in all cases (Appendix 1—table 6), demonstrating again the high linear dependency between NSP2 and the others viral elements into the viroplasm.

Appendix 1—figure 9
Residuals errors for each linear regression model.

Gray line represent the regression model, the points over the line are the predicted values yi^ (see Equation (31)) by the models, and the dots filled with a color gradient are the real values yi. The errors between the predicted and real values, ϵ=|yi^-yi|, are represented as a gradient of colors as follows (from lowest/coldest to highest/warmest). For each model, the RSE and R2 (R-squared) were included, note that this statistics are the same that were presented in Appendix 1—table 6. (A) NSP50.8667×NSP2, (B) NSP40.9912×NSP2, (C) VP1=1.1506×NSP2, (D) VP21.1244×NSP2, (E) VP61.1806×NSP2, (F) VP41.3887×NSP2, (G) VP7-Tri1.9417×NSP2, (H) VP7-Mon1.9407×NSP2.

https://doi.org/10.7554/eLife.42906.023

NSP5 and NSP4 as reference proteins

As was mentioned in the main text, we carried out a similar study using NSP5 and NSP4 as reference proteins. Since these experiments were developed to validate our previous results with NSP2, they were not as deep and extensive as in the case of the NSP2 model.

The number of VPs studied was 38 and 23 for NSP5~VP6 and NSP5~VP4 respectively (Appendix 1—figure 10A.1). The distribution of NSP5 relative to VP6 and VP4 did not show significative statistical differences according to the Mann-Whitney test, and the radius of VP6 was smaller than VP4, which is in accordance with our model of the viroplasm (Appendix 1—figure 10A). Furthermore, the distance of VP6 and VP4 towards NSP5, reflects that VP6 is closer to NSP5 than VP4, with a significance level 0.001 (Appendix 1—figure 10B). On the other hand, we found that exists a linear relationship between the radii of NSP5 and {VP6, VP4} (Appendix 1—figure 10 C-E). The linear models of both, VP6 and VP4, explain approximately 97% of the data variability and exhibit a RSE in the order of 10-2μm (see Appendix 1—figure 10 (D,E) and Appendix 1—table 7). Additionally, we performed a Mann-Whitney test to study the differences of the radii of NSP5 and each of the accompanying proteins (VP6 and VP4). This test demonstrated that the differences in location between NSP5 and VP6 is 0.1μm, while in the case of VP4 is 0.23μm, with a p-value in the order of 10-7 and 10-8 respectively (see Appendix 1—table 8), indicating that although these protein are near to each other, they occupy different layers on the VPs.

Appendix 1—figure 10
VP6 and VP4 spatial distribution taking NSP5 as reference protein.

(A) Boxplot for the radii of the fitting circumferences for NSP5 and {VP6,VP4}. Mann-Whitney hypothesis test for the radius distribution of NSP5 shows that does not exist a significative statistically differences between the reference protein (NSP5) in the two experiments. A.1) Histogram of the numbers of viroplasm by combination. (B) Boxplot for the distance of the viral proteins VP6 and VP4 to NSP5, and result of the Mann-Whitney test between these two distributions. (C) Linear regression model taking the radius of NSP5 as independent variable and the radius of {VP6, VP4} as dependent variable. The gray shadow represent the 95% confidence interval for the regression adjustment. (D and E) Residual error for the VP6 and VP4 linear models, respectively. The details about this kind of representation can be consulted in Appendix 1—figure 9.

https://doi.org/10.7554/eLife.42906.024
Appendix 1—table 7
Linear regression results with NSP5 used as independent variable.

For more information about the variables involved (columns) consult Appendix 1—table 6 or Appendix 1 Section – Linear Regression Model.

https://doi.org/10.7554/eLife.42906.025
ModelSlope (β )Std.error (σβ^2)t-valuep-valueRSER-squared
VP6=βVP6×NSP51.2732460.0327846738.836631.364503 × 10−310.0710.976
VP4=βVP4×NSP51.6232260.0524875030.925961.262448 × 10−190.0930.977

In the case of the model based on NSP4, we studied 60 viroplasms through the algorithm VPs-DLSFC. The results show that the radius of VP6 were bigger than the radius of NSP4 in approximately 0.04 μm (Appendix 1—figure 11 A-B). This difference is statistically significative (p-value0.05) according with the Mann-Whitney test (Appendix 1—figure 11A). Like the models based on NSP2 and NSP5, we found a linear relationship between NSP4 and VP6 (Appendix 1—figure 11C). This linear model was validated through a residual analysis (Appendix 1—figure 11D and Appendix 1—table 9), obtaining a RSE=0.079μm, and a R2=0.97.

Appendix 1—figure 11
VP6 spatial distribution taking NSP4 as reference protein.

(A) Boxplot for the radii of the fitting circumference of NSP4 and VP6. The inside panel shows the results of the Mann-Whitney hypothesis test (see the Appendix 1—table 5 for details). (B) Boxplot for the distance between NSP4 and VP6. (C) Linear regression fitting taking the radius of NSP4 as independent variable and the radius of VP6 as dependent variable. The gray shadow represents the confidence interval at a level of 95%. (D) Residual error analysis of the model. This graph is analogous to Appendix 1—figure 9; the details about this kind of representation can be consulted in that figure.

https://doi.org/10.7554/eLife.42906.027

Consistency between models

As was described, our study involves three differents reference proteins (NSP2, NSP5 and NSP4). Since the three models should respond to an unique spatial organization of the viral elements into the VP, it is expected to obtain similar results independenly of the selected model.

The equivalence of the differents models (models based on NSP2 and NSP5) can be proven through a comparison of the distances between NSP5 and VP6. If the two models describe the same distribution of the VPs, we expect that the distance of NSP5 to VP6 computed by the NSP5 model be similar to the the distance between NSP5 and NSP2, plus the distance of NSP2 to VP6 that were computed by the model based on NSP2. Hence:

(33) dNSP2(NSP5,NSP2)+dNSP2(NSP2,VP6)dNSP5(NSP5,VP6)

The subindex (‘name’) in dname() specifies the model employed to compute the distance. Therefore, replacing the corresponding values (available in Appendix 1—table 5 and Appendix 1—table 8) in the above equation, we obtain that:

(34) dNSP2(NSP5,NSP2)+dNSP2(NSP2,VP6)=0.048972049+0.063282322=0.1122544ε=|dNSP5(NSP5,VP6)0.1122544|=|0.0965550.1122544|=0.0156994μm.
Appendix 1—table 8
Two-sample Mann-Whitney hypotheses test, considering the radius of NSP5 in contrast with the radius of VP6 and VP4.

For more information about the parameters (columns) see the Appendix 1—table 5.

https://doi.org/10.7554/eLife.42906.026
ProteinWDifference in location95%p-value
VP611740.096555[0.05986,0.13473]9.359731 × 10−07
VP45020.227230[0.17693,0.28280]3.574209 × 10−09

Since the level of precision in our radii estimation of the viral components are limited by the resolution of the algorithm 3B (0.04-0.05μm), we set this parameter as a threshold for the errors when we compared the results obtained for each model. For example, the error between the models based on NSP2 and NSP5 for VP6 is 0.016μm (see Equation (34)), which is under the resolution limit that can be reached by the algorithm 3B, and as consequence the error is asociated to the limitations of the optic and not to the reference protein that we selected for the estimation of the VP6’s radius.

This same approach was applied for VP4. In this case, and considering again the results in Appendix 1—table 5 and Appendix 1—table 8 we obtain:

(35) dNSP2(NSP5,NSP2)+dNSP2(NSP2,VP4)=0.048972049+0.150597251=0.1995693ε=|dNSP5(NSP5,VP4)0.1995693|=|0.2272300.1995693|=0.0276607μm,

which again is an error under the resolution limit of the alorithm 3B.

On the other hand, taking into account the models based on NSP2 and NSP4, and the results in Appendix 1—table 5 and Appendix 1—figure 11A, we obtain that:

(36) dNSP2(NSP4,NSP2)+dNSP2(NSP2,VP6)=0.003348142+0.063282322=0.06663046ε=|dNSP4(NSP4,VP6)0.06663046|=|0.040705260.06663046|=0.0259252μm.

As before, the error is under the limit of resolution of the algorithm 3B. Altogether, the comparison of the three models shows up that different experimental approaches describe the same spatial distributions of the viral elements inside the viroplasm.

The previous analysis only considers the consistency of the models based on the difference in the radius of the viral elements, but besides this, we developed a similar study using the lineal regression models.

Again, consider the model NSP5 and NSP2 as predictors of VP6:

(37) VP6=βNSP2VP6×NSP2
(38) VP6=βNSP5VP6×NSP5,

where βNSP2VP6 and βNSP5VP6 are the slope associated with VP6 in the model based on NSP2 and NSP5 respectively. Also, the radius of the NSP5 can be estimated with the model based on NSP2, this is:

(39) NSP5=βNSP2NSP5×NSP2.

Substituting Equation (39) into Equation (38) we obtain:

(40) VP6=(βNSP5VP6×βNSP2NSP5)×NSP2,

and taking into acount Equation (37), we can assert that:

(41) βNSP2VP6(βNSP5VP6×βNSP2NSP5)
(42) ϵ=|βNSP2VP6(βNSP5VP6×βNSP2NSP5)|(absolute error)
(43) δϵ=|βNSP2VP6(βNSP5VP6×βNSP2NSP5)|βNSP2VP6(relative error).

Note 10 The relative error was computed under the assumption that the slope of the model based on NSP2 is the ideal value. This consideration was based in the fact that we have more evidence of a linear relationship in the NSP2 model (see the R2 and RSE in Appendix 1—table 6) that in the models based on NSP5 and NSP4 (Appendix 1—table 7 and Appendix 1—table 9 respectively).

Appendix 1—table 9
Linear regression results with NSP4 as independent variable.

For more information about the variables involved (columns) consult Appendix 1—table 6 or Appendix 1 Section – Linear Regression Model.

https://doi.org/10.7554/eLife.42906.028
ModelSlope (β)Std.error(σβ^2)t-valuep-valueRSER-squared
VP6=βVP6×NSP41.1036830.021234551.975925.626321×10−510.0790.978

For the prediction of VP6 through the models NSP2 and NSP5, the relative error is (Equation (43)):

(44) δϵ=|1.1806335(1.273246×0.8667494)|1.1806335=0.06526013.

The relative error asociated with the prediction of the radius of VP4 through the models NSP2 and NSP5 is:

(45) δϵ=|βNSP2 VP4(βNSP5VP4×βNSP2NSP5)|βNSP2VP4=|1.3887083(1.623226×0.8667494)|1.3887083=0.01312145.

Finally, in the case of VP6 considering the models NSP2 and NSP4 the relative error is:

(46) δϵ=|βNSP2 VP6(βNSP4VP6×βNSP2NSP4)|βNSP2VP6=1.1806335(1.103683×0.9911517)1.1806335=0.07344889.

Since the relative errors represent the average error of the slopes computed with the models NSP5 and NSP4 in relation with the NSP2 model. These results indicate that the model based on NSP5 has an error of 6.5% for the prediction of the radius of VP6, while for VP4 the error is around 1.3% compared to the prediction of the model based on NSP2. On the other hand, if we use the model based on NSP4, we get approximately a 7.3% of differences in the radius of VP6. As in the previous analysis, these errors are small too, and could be associated with experimental variations and with the resolution limit of the algorithm 3B.

Even when the relative error provide important information about the differences in the prediction between differents models, we are not taking into account the standard error associated with the slopes of each model. In the case of the prediction of VP6 through the models NSP2 and NSP5 (all others cases have the same deduction), if we consider βNSP5VP6 and βNSP2NSP5 as random variables with a standard error σ(βNSP5VP6) and σ(βNSP2NSP5) respectively, the variance of the variable (βNSP5VP6×βNSP2 NSP5) could be computed through the ‘Delta Method’ (Oehlert, 1992; Ver Hoef, 2012). The ‘Delta Method’ makes possible to obtain an approximation of the variance of a function f(X1,X2,,Xn) as:

(47) Var(f)=i(fXi)2Var(Xi)+iji(fXi)(fXj)Cov(Xi,Xj),

were Cov(Xi,Xj) denote the covariance between Xi and Xj (Lawrence, 1953).

Note 11 The standard error is defined as:

Standard Error=Standard Deviation/n,

but, in our case n=1 because we only have the final slope estimation and the associated standard error, hence the standard error is equal to the standard deviation (Altman and Bland, 2005).

Because βNSP5VP6 and βNSP2NSP5 are independent (obtained by the linear regression analysis of the segmentation results in differents experiments and images) the covariance Cov(βNSP5VP6,βNSP2NSP5)=0. This point can be proved easily because Cov(X,Y)=𝐄(XY)-𝐄(X)𝐄(Y), were 𝐄() is the expected value. If X and Y are independents 𝐄(XY)=𝐄(X)𝐄(Y)Cov(X,Y)=0. Therefore, Equation (47) can be simplified to:

(48) Var(f)=i(fXi)2Var(Xi).

Now, considering the function f(p1,p2)=p1p2, we can rewrite Equation (48) as:

Var(f)=p22Var(p1)+p12Var(p2),

and substituting the variance for the standard deviation (same that the standard error in this case, see Note 11), we have:

(49) Var(f)=p22σ2(p1)+p12σ2(p2).

The 99% confidence interval for p1p2 can be computed as:

(50) CI=p1p2±2.576Var(p1p2).

Set p1=βNSP5VP6 and p2=βNSP2NSP5. We can compute the confidence interval of βNSP5VP6×βNSP2NSP5 through Equation (49) and Equation (50).

(51) Var(βNSP5VP6×βNSP2NSP5)=(βNSP2NSP5)2σ2(βNSP5VP6)+(βNSP5VP6)2σ2(βNSP2NSP5 )=(0.8667494)2(0.03278467)2+(1.273246)2(0.017947738)2=0.001329683
(52) σ(βNSP 5VP6×βNSP2NSP5)=0.001329683=0.03646482.

Now, considering Equation (50) we obtain:

(53)  CIβNSP5VP6×βNSP2NSP5=(βNSP5VP6×βNSP2NSP5)±2.576(σ(βNSP5VP6×βNSP2NSP5))=(1.273246×0.8667494)±(2.576×0.03646482)=[1.009652,1.197519].

The slope of VP6 in the NSP2 model (βNSP2VP6, see Appendix 1—table 6) is 1.1806335[1.009652,1.197519], which proves that, in reference to VP6, the models based on NSP2 and NSP5 are consistent.

The rest of combinations runs as before. In the case of VP4 and the models based on NSP2 and NSP5, we obtained:

(54) Var(βNSP5VP4×βNSP2NSP5)=(βNSP2NSP5)2σ2(βNSP5VP4)+(βNSP5VP4)2σ2(βNSP2NSP5)=(0.8667494)2(0.05248750)2+(1.623226)2(0.017947738)2=0.002918405.
σ(βNSP 5VP4×βNSP2NSP5)=0.002918405=0.05402226.CIβNSP5VP4×βNSP2NSP5=(βNSP5VP4×βNSP2NSP5)±2.576(σ(βNSP5VP4×βNSP2NSP5))=(1.623226×0.8667494)±(2.576×0.05402226)=[1.267769,1.546092].

Again, the slope of VP4 in the NSP2 model is 1.3887083[1.267769,1.546092] (see Appendix 1—table 6), and as consequence the models are consistent between them.

Finally, the stability between the models NSP4 and NSP2 based on the protein VP6 was evaluated.

(55) Var(βNSP4VP6×βNSP2NSP4)=(βNSP2NSP4)2σ2(βNSP4VP6)+(βNSP4VP6)2σ2(βNSP2NSP4)=(0.9911517)2(0.0212345)2+(1.103683)2(0.006973701)2=0.0005021999
(56) σ(βNSP4VP6)=0.0005021999=0.02240982CIβNSP4VP6×βNSP2NSP4=(βNSP4VP6×βNSP2NSP4)±2.576(σ(βNSP4VP6×βNSP2NSP4))=(1.103683×0.9911517)±(2.576×0.02240982)=[1.036190,1.151645].

In this case the slope βNSP2VP6=1.1806335[1.036190,1.151645], which is surprising taking into account that the relative error of NSP4 as predictor of VP6 instead of the model based on NSP2 is around the 7.3% (see Equation (46)). Even when this percent doesn’t represent a great difference, it could be enough to generate small variations that cause that the slope βNSP2VP6 be out of the confidence interval given in Equation (56). Moreover, note that the difference between the upper endpoint of the confidence interval of the slope between NSP2 and VP6 is approximately 0.03 μm, which is under the resolution limit of the 3B algorithm. A deeper study with different antibodies for NSP4 and the contrast of NSP4 with others viral elements would help to clarify our results.

Stochastic model fitted for 3B super resolution microscopy.

The algorithm 3B (Cox et al., 2011) creates a super resolution image from experimental data (hundreds of images acquired by the microscope). The 3B algorithm generates a probability map of fluorophore location through Markov Chains and Bayesian inference. The implementation of the algorithm requires a priori information on the dynamics of the photophysical properties of the fluorophores under study; however, the software does not provide a method to calculate it. In this section we propose a method to obtain this information from the experimental data.

3B microscopy generates a probability map of fluorophore localization by deriving a weighted average over all possible models; the set of models includes varying numbers of emitters, emitter localizations and temporal dynamics of the states of the fluorophores. The information stored in the image sequence is iteratively compared with the models using Bayesian inference, producing a SRM image. This technique allows the reduction of the number of necessary images, so it reduces the photo damage in the sample. However, the necessary computation time is significant (Hu et al., 2013); therefore, we employed 3B parallelization techniques for a cluster and PC from Hernández et al. (2016) in order to decrease the time to enhance the SR images.

The dynamics of the photophysical properties of a fluorophore is modeled in 3B-algorithm as a Markov chain, where, for each time, the fluorophore can be in three posible states: the emitting state S0, the non-emitting state S1, and the bleached state S2 (Appendix 1—figure 12). Hence, in the complete sequence of images a fluorophore can be transiting between these states with a probability Pi.

Appendix 1—figure 12
Diagram of probabilities for the transitions between the states of a fluorophore for the 3B-algorithm.

From left to right are represented the emitting state, non-emitting state and bleached state for a fluorophore, with their respective transition probabilities among the states. As an example, a fluorophore can transit from the emission state to the non-emission state or remain in this state with a probability P2 and P1, respectively.

https://doi.org/10.7554/eLife.42906.029

In this way, the temporary stack of images acquired by the microscope contains information on the dynamics of an unknown number of fluorophores transiting between these three states, with a probability Pi. This information is represented as a transition matrix:

(57) P:=(P1P20P3P4P5001),

where the entry in the ith row and jth column is the probability that a fluorophore in the state Si moves to the state Sj.

The initial probability distribution

(58) ϕ¯0:=(ϕ0(0),ϕ0(1),ϕ0(2)),

describes the probability of a fluorophore to be in each energy state in the beginning of the process: ϕ0(i) corresponds to the state Si.

The 3B algorithm considers the Markov chain determined by the transition matrix (Equation (57)) and the initial probability distribution (Equation (58)). Then,

(59) ϕ¯1=ϕ¯0Pϕ¯2=ϕ¯1Pϕ¯n=ϕ¯n1P,

are the probabilities that a fluorophore is in the states S0,S1 and S2 in time 1,,n; that is, for all i=1,,n, ϕ¯i is the 3-vector whose entries are the probabilities that the fluorophore is in each energy state at time i.

The 3B algorithm has the transition matrix (Equation (57)) as an input, together with the initial probability distribution (Equation (58)). However, the software does not provide a method to calculate the transition matrix from the experimental data.

We deal with this issue by proposing a method to determine P from the data. Namely, we propose to adjust the experimental data (the stack of images) with an ordinary differential equation (ODE) model that allows us to calculate the probabilities of the system.

Following the Jablonski diagram for a given fluorophore, we propose a model with three states (S0,S1 and S2) and three transition probabilities (kisc,kT and kb) between them (Appendix 1—figure 13).

Appendix 1—figure 13
Left panel: The reduced Jablonski diagram for the fluorophore model (Appendix 1—figure 12).

Right panel: Diagram of probabilities for the transitions between the states of a fluorophore for our fluorophore’s model. In our model, the basal (E1) and the excited (E2) states, from the reduced Jablonski diagram, are collapsed in a new excited state S0 (green). The justification for this lies in the fact that the fluorescence phenomenon (kex,kem) occurs on the scale of nanoseconds or less; however, an image collected with an EM-CCD camera regularly has millisecond exposure times, therefore, it involves the integration of 105-106 cycles of photon emission; as a consequence, the E1 state is never detected. The entrance into the triplet excited state (kisc,kT) happens on the scale of seconds; if the emission process occurs, it releases photons of lower energy that are not detected and, therefore, the triplet state is considered as a dark state S1 (violet). Finally, the photobleaching state S2 (gray) is a irreversible process (kb) culminating with the destruction of the coordinating center of resonant electrons (orbitals π) which is responsible for absorbing photons.

https://doi.org/10.7554/eLife.42906.030

For i=0, 1, 2, we define the dynamics of the energy state Si as the time evolution of the concentration [Ei] of molecules (fluorophores) emitting photons:

d[S0]dt=kT[S1]kisc[S0],d[S1]dt=kisc[S0](kT+kb)[S1],d[S2]dt=kb[S1].

The sequence of images taken through the time keeps track of the state the fluorophore is in. If in the ith image the fluorophore has intensity (the value of the pixel approaches the maximum value), then the fluorophore is in its emitting state; in any other case, the fluorophore is off, and it can be in two states: the non-emitting state or the bleached state. We normalize the data and compute the mean intensity at time t of the fluorophores in the emitting state: by definition, the initial mean value is one; after that, it is going to decay depending on the acquiring protocol.

Following the classical regression methods, we fit the experimental data to the proposed differential equations system. The estimate of the rate constant kisc, kT and kb from the stack of images is obtained following the example taken from Rawlings and Ekerdt (2013).

Let us consider the matrix P from Equation (57) as the transition matrix of our model. Then, by the definition of our model, P2=kisc, P3=kT and P5=kb. Also, by the general properties of the probability function, the sum of the entries of each row of this matrix is one; so we obtain the transition matrix as follows:

(60) P=(P1P20P3P4P5001)=(?kisc0kT?kb001)=(1kisckisc0kT1(kT+kisc)kb001)

As we mentioned earlier, the estimate of the transition matrix depends on the acquisition protocol. There are image sequences for which the fitting does not converge; this happens when the average intensity decays exponentially. However, when the average intensity decreases linearly, the adjustment of the data to the converging model results in a transition matrix that fits the data.

After the fitting to the experimental data we simulate a Markov chain for the calculated transition matrix (Appendix 1—figure 14). We also observe that greater number of fluorophores leads to better concordance between the simulation and the experimental data.

Appendix 1—figure 14
Markov Chain simulations with the new transition matrix.

(A–C) shows the simulation of the dynamics for 1, 10 and 1000 fluorophores respectively. A.1, B.1 and C.1 indicates the state of each fluorophore in the time; A.2, B.2 and C.2 point out the amount of fluorophores that are in the state S0 in the time.

https://doi.org/10.7554/eLife.42906.031

To corroborate that the proposed fitting is adjusted properly we use the experimental data provided by the authors of the 3B SRM microscopy algorithm. The podosomes data is available at the ThreeB plugin for ImageJ (Rosten et al., 2013), is a time serie of 300 images. Taking this stack as initial experimental data, we simulate Markov chains for 1000 fluorophores with the original transition matrix and the transition matrix fitted by our model. Although we found that our model fits better to the experimental data (Appendix 1—figure 15); the comparision between the SR images of the podosomes are not conclusive about the resolution enhancement with our model (Appendix 1—figure 16).

Appendix 1—figure 15
Simulation estimation chart of 1000 fluorophores.

The y-axis is the normalization of fluorophores in the S0 state (emission) in the time i (x-axis). The normalized data extracted from the images are shown in black. The purple and the brown dots represent the simulation of 1000 fluorophores as a Markov chain with the transition matrix that we propose and with the original 3B matrix, respectively. The transition matrix that we propose is shown in the bottom of the figure.

https://doi.org/10.7554/eLife.42906.032
Appendix 1—figure 16
Super-resolution images generated with different transition matrices.

(A) SR image using the transition matrix constructed by our model. (B) SR image with the original transition matrix. (C) Composite image comparing the two SR images in green (A) and in red (B).

https://doi.org/10.7554/eLife.42906.033

Furthermore, in order to validate our method, we use Gatta-paint nanorulers, DNA molecules label with 488, 550 and 655 fluorophores at a distance of 40nm (GATTA-PAINT 40RG/40B, immobilized in buffer on glass-slide) to resolve the resolution enhacement of our method.

As in the previous analysis, we find that our model fits better to the experimental data obtained from the different ATTOS. Because our model involves a greater number of fluorophores, there is more information of the fluorophores localization. For example, in the Appendix 1—figure 17A.1, the information in the SR image with the original matrix, resolves only one fluorophore; however, with our method, three fluorophores in the same area can be resolved. In this way, we observed that in all cases the distance between the fluorophores (each peak) of the grahps shown in panels A.1-A.3 from Appendix 1—figure 17 is approximately 40 nm; this coincides with the information provided by the manufacturers of the samples. All together, these results demonstrate that the new proposed method improves the resolution capacity of 3B algorithm by reflecting better the photophysical behavior of the fluorophores.

Appendix 1—figure 17
Comparison between the original model of 3B against the obtained with the transition matrix that we propose.

Columns A-C represent the nanorulers GATTA-PAINT labelled with ATTO 488, 550 and 655 respectively. Panels A-C show the normalized experimental data (black dots) and the simulation for 1000 fluorophores with the matrix that we propose (purple dots) and with the original 3B matrix (burgundy dots); each point represents the mean value of the fluorescence. The time is indicated in frames, acquisition time between images is 100 ms. A complete experiment consists of 300 images collected in a CellTIRF microscope with a 160× magnification. Panels A.1- C.1 show two ROI’s from the complete SR images: 3B) canonical reconstruction and 3B-ODE) reconstruction with the ODE’s model. The graph shows a line profile from the two reconstructions, in green the results from original 3B and in black with the transition matrix that we propose, the x-label is the distance in nm and the y-label is the intensity pixel value. The peaks from the graph denote the localization of a fluorophore.

https://doi.org/10.7554/eLife.42906.034

Once the transition matrix for the nanorulers was calculated and taking into account that the data consists of hundreds of images, we parallelized the data on a cluster and on a personal computer (Hernández et al., 2016) (the cluster has 314 nodes with RedHat Enterprise Linux Version 6.2, 2 Intel Xeon Sandy Bridge E5-2670 processors at 2.6 GHz with 8 cores each 64 GB of RAM) to reduce the computation time.

https://doi.org/10.7554/eLife.42906.008

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Decision letter

  1. Arup K Chakraborty
    Senior and Reviewing Editor; Massachusetts Institute of Technology, United States
  2. Ulrich Desselberger
    Reviewer; University of Cambridge, United Kingdom
  3. Clemens F Kaminski
    Reviewer; University of Cambridge, United Kingdom

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

[Editors’ note: this article was originally rejected after discussions between the reviewers, but the authors were invited to resubmit after an appeal against the decision.]

Thank you for submitting your work entitled "Nanoscale organization of rotavirus replication machineries" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Ulrich Desselberger (Reviewer #1); Clemens F Kaminski (Reviewer #3).

Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife.

Your conclusions could be of considerable interest to the field, but reviewers believe that a significant number of experiments would have to be done to validate the conclusions that are reached. We feel that this additional work would require more than two months, and it is our policy to not ask for a revision in such a circumstance. However, if the points made by the reviewers in the attached reviews could be addressed, and the conclusions in the paper validated adequately, we would be open to considering such a manuscript.

Reviewer #1:

This manuscript describes the application of super-resolution microscopy to the analysis of the structure of viroplasms (vpls), the 'factory' for rotavirus (RV) early morphogenesis and RNA replication. It was found that within vpls 7 RV-encoded proteins and RV double-stranded (ds) RNA are organized in 6 concentric rings, with NSP5 localized at the centre, surrounded by a layer of NSP2 and NSP4, those in turn being surrounded by VP1, VP2, VP6 and viral dsRNA in an intermediate zone, and the outmost zone consisting of rings of VP4 and VP7 the latter in monomeric and trimeric form (Figure 4). From this it was concluded that the RV vpls are highly organized organelles.

The theoretical basis of the super-resolution microscopy used is explained and explored in Appendix 1, starting with mathematical details of the applied algorithm 'Viroplasm Direct least square fitting circumference', and followed by algorithm validation and model considerations. The distribution of the studied viral elements (proteins and dsRNA) as an arrangement of concentric rings was considered as proven, since the result was independent of which viral protein is used as a reference.

This manuscript is a bold proposal, which, however, in this reviewer's view contains several inconsistencies:

1) The RV NSP4 is considered to be located near the centre of the concentric ring structures. However, it was previously found to co-localize with the autophagosomal marker LC3 in cap-like structures on the outside of vpls (Berkova et al., 2006).

2) RV NSP2 octamers and NSP5 interact, and NSP5 and RV RNA compete for a binding site in the major groves of NSP2 octamers (Jiang X, et al., 2006). From the data presented it is not clear how this can happen.

3) For the localization of the viral RNA an antibody was used (SciCons J2) with apparent specificity for dsRNA. It is not clear whether it recognized the stems of stem-loop structures of viral ssRNA or the complete genomic dsRNA segments, nor that it is specific for RV dsRNA.

4) The analysis of vpl structure was carried out at 6 h post infection (pi). At this time point, vpls and infected cells can be shown to contain numerous single-layered (core) and double-layered particles which, however, are asymmetrically distributed. Since vpls appear at 2-3 h pi, those earlier structures should also be analysed.

5) For further testing of the model, authors should produce transmission electron micrographs (TEM) of sections of cells infected for 6 h. Those will show a highly asymmetric distribution of the content of vpls.

6) The authors' proposal reminded reviewer of concentric rings representing the density of RV dsRNA in the cores of particles reconstructed from cryo-EM photographs. These rings were, however, only seen when eicosahedral symmetry conditions were imposed on the image reconstruction, and not when reovirus cores were explored by cryo-EM tomography. This reviewer has the impression that the super-resolution microscopy data are based on an averaging procedure which does not recognize asymmetric structures.

7) This reviewer is not a mathematician and therefore cannot competently assess most of the content presented in the Appendix. It is strongly suggested to request the view of an alternative reviewer, who is experienced in and conversant with methods of super resolution light microscopy.

Reviewer #2:

In this manuscript by Garces et al., the authors investigated the nanometric-scale spatial organization rotavirus replication machinery using super-resolution microscopy. It is indeed the first quantitative visual analysis of rotavirus viroplasm components using this technique.

I have several comments that the authors need to address.

1) The authors state that the viral components form ring-like structures and are arrayed as concentric layers in Figures 1B and 1C. However, it is really hard to see the ring-like NSP2 in these figures, especially in the panels of NSP2 with VP1 and dsRNA.

2) The innermost layer of the viroplasm is composed of NSP5 that acts as the core scaffold for viroplasm formation. In the third paragraph of subsection “Quantitative characterization of VPs structure by a novel segmentation algorithm”, it is described that NSP5 is distributed inside the ring formed by NSP2 (Figure 1C). But it looks like there is NSP2 with the red NSP5 ring. And why there is nothing within the NSP5 circle? Is it hollow in the viroplasm sphere or is it that the anti-NSP5 antibody is not able to penetrate the protein layers enough to stain it?

3) It is interesting to observe the co-localization of NSP2 and NSP4, which may play a significant role in viroplasm formation and genome replication. Please give more details about how the rabbit polyclonal sera to NSP4 was generated. How was it characterized? Please give the references if it has been used in previous publications. Does it stain the NSP4 on ER?

4) Control imaging experiments should be included. For instance, an image with anti-rabbit secondary antibody in the absence of the rabbit polyclonal sera to NSP4. Does the anti-rabbit secondary antibody cross-react with the mouse polyclonal sera to NSP2?

5) The proposed model in Figure 4 show the viroplasm viral proteins as in different layers. How would this model explain the interplay between these proteins that coordinate the genome replication and virion assembly? Does the overlapping region (Figure 2) of different layers play a role in these processes?

Reviewer #3:

In the paper by Garces et al., the authors report on the use of an optical super resolution method to report on the nanoscale organisation of rotavirus replication machineries. The authors use the Bayesian Blinking and Bleachung (3B) super resolution method and developed a semiautomatic segmentation algorithm that analyses and quantifies the relative organisation of several key proteins in viroplasms (VP). Using optical methods featuring inherently high molecular specificity and signal to noise ratio, they are able to discriminate a number of key structural and non-structural proteins and infer their relative positions with high resolution and precision within VPs. The method exploits stochastic fluctuations in the emission characteristics of fluorophores to locate fluorophore positions at much higher precision than would be possible with standard fluorescence imaging. The nice feature of 3B is that it does not require the use of special buffers or photochemistry to enable photoswitching, which is in contrast to other super resolution methods, such as STORM. Its downside is the considerable computational effort required for analysis. Based on their analyses, the authors present a structural model for the radial structural distribution of VP components, consisting of concentric shells in which individual VP components are tightly organised. There are new findings, e.g. a suggestions of a spatially distinct location for NSP2 and NSP5 and, unexpectedly, that NSP4 is located on the inner part of VP rather than on the outside, given the fact that it is an integral membrane protein. These are nice findings, and the data appear solid. The style of writing and the presentation of data are clear. I am largely supportive of this effort and think that it could add useful information to the existing literature on rotavirus organisation. However, I do have concerns and suggestions that I think the authors must address.

1) There are no reported controls for the antibodies. Given that these are made in the laboratory and that there are no references for them in the paper, it is essential that data are included to verify their specificity. This is particularly true for the potentially controversial finding of NSP4 – the authors must exclude potential artifacts and show that binding is specific. In general, controls are lacking in the paper.

2) Most of the technical detail in the paper is in the SI and devoted to the description of the algorithms for fitting the fluorescence data and locating VP components within shell structures. Given the sensitivity of the method to the photophysical behaviour of the specific dyes used, how representative are the validation and controls presented in the SI for the AF488 antibodies?

3) More details on the chosen approach should be included. Why was the 3B method chosen? For example, could the authors have used high signal to noise (but low resolution) widefield imaging and fitted concentric shells with appropriate noise models (see e.g. https://www.cell.com/biophysj/fulltext/S0006-3495(15)00993-5)? Nanometer fitting precision has been achieved with such an approach. The method would be easily implemented for the available data, and may work very well, given the comparatively large size of the VP structures investigated. Also, the paper gives the impression that this is the first time optical super resolution methods have been used to infer virus architecture, and notable efforts with related techniques have not been cited or discussed. E.g. in Laine et al., 2015, dSTORM was used and model based fitting was used to infer the concentric arrangement of virus proteins in HSV1 with nanometer precision. There are many similarities between the efforts presented there and those presented here. What are relative advantages and disadvantages of the available methods? I encourage the authors to review the existing literature more thoroughly and to provide guidelines to the reader on what the relative merits and disadvantages are for each technique.

[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]

Thank you for choosing to send your work entitled "Nanoscale organization of rotavirus replication machineries" for consideration at eLife. Your letter of appeal has been considered by a Senior Editor, a Reviewing editor, and an additional reviewer. We are prepared to consider a revised submission with no guarantees of acceptance. Our discussions about your appeal lead us to believe that it would be important to consider the following points prior to resubmission:

1) The authors have accepted that the dsRNA recognizing antibody used is non-specific (within the RNAs of RVA and beyond) and have now omitted all their dsRNA related data. RVA ssRNA-ssRNA segment interactions are at the core of pre-genome assembly in viroplasms and require interaction with NSP2. This has been convincingly described by: Borodavka et al., 2017.

The authors should comment on the processing of RVA RNAs in viroplasms in some more detail than by a single sentence in Discussion (p7, paragraph 3). The question of what is inside the NSP5 layer remains to be answered.

2) The data by Berkova et al., 2006 have now been compared with the new findings in more detail in Discussion.

3) The potential for interaction of the different viral protein layers identified has now been recognized.

4) Regarding potential structural asymmetries in viroplasms, authors provide a TEM photograph (Figure 1A) which shows an electron-dense viroplasm, but also many core particles and DLPs in the surrounding cytoplasm, proving that a first round of RVA particle formation has already taken place. See also Figure 1 in Altenburg et al., 1980, taken at 8 h p.i and figures in refs (Petrie et al., 1982, 1984; Richardson et al., 1986 and Eichwald et al, 2012). While the limits of TEM for multiple viral protein localization are recognized, it is still considered worthwhile to use the novel procedure on viroplasms at 2-3 h p.i., when viral particle formation has not yet taken place; preliminary data of this nature are not 'beyond the scope of this work' as authors suggest, but would be an important application.

5) Authors' argument that they “describe the structure of viroplasms, not virus particles” should be emphasized in Discussion.

6) Authors state that they “proved statistically that the spatial distribution of the viral proteins can be considered as concentric layers”. Although they further state that the novel observations cannot be used to understand specific details, such as the interactions between different layers, Discussion could be more outspoken about the use of the novel procedure to analyse RVA replication steps within viroplasms.

https://doi.org/10.7554/eLife.42906.040

Author response

[Editors’ note: the author responses to the first round of peer review follow.]

Reviewer #1:

[…] 1) The RV NSP4 is considered to be located near the centre of the concentric ring structures. However, it was previously found to co-localize with the autophagosomal marker LC3 in cap-like structures on the outside of vpls (Berkova et al., 2006).

It is important to keep in mind that immunofluorescence images based upon epifluorescence or confocal microscopy are inherently diffraction-limited to a spatial resolution in the range of hundreds of nanometer, with a resolution that precludes a detailed, nanoscopic molecular scale organization of VPs. Thus, in the work by Berkova et al. (1), it would be difficult to determine the exact spatial location of NSP4 in relation to other viroplasmic proteins and to the autophagosomal marker LC3. Also, in that work they used antibodies to NSP5 to identify viroplasms, and in the present work we show that NSP5 lies in a layer internal to that conformed by NSP4 and NSP2. If they had used NSP2 as the reference protein for viroplasm staining they could have found no difference in the distribution of NSP4 and NSP2, even at the level of resolution provided by confocal microscopy.

Also, it is interesting that in the paper by Berkova et al. (1) they hypothesize that there are three pools of intracellular NSP4. The first pool they propose is represented by NSP4 localized in the ER, a second minor pool of NSP4 molecules localized in the ERGIC compartment, and the third pool of NSP4 molecules distributed in cytoplasmic vesicular structures associated with the autosomal marker LC3, which appear in infected cells at 6 hpi; they propose that this third pool of NSP4 is involved in regulation of virus replication. Furthermore, and most interestingly, is their suggestion that “NSP4 and autophagic marker LC3-positive vesicles may serve as a lipid membrane scaffold for the formation of large viroplasms by recruiting early viroplasms or viroplasm-like structures formed by NSP2 and NSP5.” This observation is in line with our proposal that NSP4 lies in an internal protein layer within viroplasms.

An additional, and very interesting possibility to explain the internal location of NSP4 in viroplasms is the hypothesis that viroplasm morphogenesis occurs on the surface of lipid droplets (LDs) (see (2)). In that work, it was proposed that LDs serve as a platform to which NSP2 and NSP5 attach to form viroplasm-like structures, which in turn associate with pre-core complexes (consisting of VP1, VP3, and segmental plus RNA), VP2 and VP6. In this regard, it is important to have in mind that the currently accepted model for the LD biogenesis is that neutral lipids are synthesized between the leaflets of the ER membrane, and the mature LD is then thought to bud from the ER membrane to form an independent organelle that is contained within a limiting monolayer of phospholipids and associated LD proteins (3). Thus, during budding of the LDs from the ER membrane they could take along the rotavirus NSP4 ER membrane protein (topologically oriented towards the cell’s cytoplasm) that could help as a scaffold on the surface of LDs for the assembly of other rotavirus viroplasmic proteins, thus remaining in the interior of viroplasms.

The two possible explanations for the location of NSP4 in an internal shell of viroplasms just discussed above have been included in the Discussion section of the manuscript.

2) RV NSP2 octamers and NSP5 interact, and NSP5 and RV RNA compete for a binding site in the major groves of NSP2 octamers (Jiang X, et al., 2006). From the data presented it is not clear how this can happen.

Please, see the answer to comment #5 of reviewer #2. In short, in that answer it is stated that, based on the super resolution microscopy images, it seems clear that there is some overlapping between different protein layers, as is the case for NSP2 and NSP5 in Figure 1E. These overlapping regions between different protein layers are most likely the responsible for the previously reported NSP2-NSP5 biochemical interactions. We have clarified this point in the Discussion section of the main text (5th paragraph).

3) For the localization of the viral RNA an antibody was used (SciCons J2) with apparent specificity for dsRNA. It is not clear whether it recognized the stems of stem-loop structures of viral ssRNA or the complete genomic dsRNA segments, nor that it is specific for RV dsRNA.

We agree with the reviewer. There is no way to distinguish between viral structured ssRNA and dsRNA and the MAb is not specific for rotavirus dsRNA. A more specific and detailed study is necessary to locate the viral dsRNA within viroplasms. For these reasons, all the information related to the dsRNA location was removed from the article.

4) The analysis of vpl structure was carried out at 6 h post infection (pi). At this time point, vpls and infected cells can be shown to contain numerous single-layered (core) and double-layered particles which, however, are asymmetrically distributed. Since vpls appear at 2-3 h pi, those earlier structures should also be analysed.

We do not understand this comment. There is no connection, or at least we are proposing none, between the inner structure of viroplasms and the symmetrically or asymmetrically distribution of single-layered (core) and double-layered particles in the cell or within viroplasms. Our study restricts and describes that viroplasms have a structured organization and does not claim to describe the dynamics of virus particle morphogenesis within the viroplasm or of viroplasms themselves. Our study does not reach that far, and we believe that analysis of viroplasms at earlier times of infection is beyond the scope of this work. In this regard, the present study includes the analysis of a wide range of viroplasm sizes (see Figure 3) which follow a pretty scaling rule which is well described for a linear model. These results point to the conservation of structural organization from smaller (0.5 µm) to bigger (up to 2 μm width) viroplasms.

5) For further testing of the model, authors should produce transmission electron micrographs (TEM) of sections of cells infected for 6 h. Those will show a highly asymmetric distribution of the content of vpls.

This observation by the reviewer is connected with the previous one. Again, we are not claiming that the viroplasm is homogeneous about its content of double-layered or core particles. The morphogenetic process of formation of these particles, where it occurs within the viroplasms, and its dynamics of formation is far away from the purposes of this paper. Thus, the TEM analysis proposed will not limit or add to our conclusions; this sort of analysis has already been reported by our group (see, for instance, Figure 9 in Trejo et al. (4)). However, we agree with the reviewer that it will be useful to include a TEM image for comparison with the images obtained by immunofluorescence and super-resolution microscopy. This image is now the new Figure 1A, where it can be seen that viroplasms are electrodense structures but no organization of the viral proteins can be observed at first sight.

6) The authors' proposal reminded reviewer of concentric rings representing the density of RV dsRNA in the cores of particles reconstructed from cryo-EM photographs. These rings were, however, only seen when eicosahedral symmetry conditions were imposed on the image reconstruction, and not when reovirus cores were explored by cryo-EM tomography. This reviewer has the impression that the super-resolution microscopy data are based on an averaging procedure which does not recognize asymmetric structures.

The reviewer is correct into that the 3B-SRM algorithm provides an averaged structure, which is the average of all the models computed by the method. It is also correct that our working hypothesis is based on the concentric arrangement of viral protein rings that shape the viroplasms, which does not recognize asymmetric structures. However, please remind that we are describing the structure of viroplasms, not of viral particles. There is no indication that viroplasms follows an eicosahedral symmetry or any other symmetry whatsoever. The eicoshedral symmetry the reviewer refers to, is for viral particles.

Reviewer #2:

[…] 1) The authors state that the viral components form ring-like structures and are arrayed as concentric layers in Figures 1B and 1C. However, it is really hard to see the ring-like NSP2 in these figures, especially in the panels of NSP2 with VP1 and dsRNA.

A more representative image has been included in Figure 1E for the pair NSP2-VP1. Regarding dsRNA, all the information was removed, because of the reasons explained in answer #3 to reviewer #1. Even when others authors suggested that the VPs have a spherical-like structure (5-7), we validated this hypothesis for all the viral proteins included in this study. In the section “Model Considerations” in the Appendix we proved, statistically that the spatial distribution of the viral proteins can be considered as concentric layers. Note that our intention is to provide a general characterization of the spatial distribution of the viral proteins, and not to understand specifics details of the distributions of each protein (like the interactions between different layers). Our segmentation algorithm provides a simple approach to quantify these distributions with a high robustness to noise (see the “Algorithm Validation” section in the Appendix), and also is the optimal solution that minimize the mean square error of the circumference fitting to the spatial distribution of the viral proteins (see the “Segmentation Algorithm” section in the Appendix).

2) The innermost layer of the viroplasm is composed of NSP5 that acts as the core scaffold for viroplasm formation. In the third paragraph of subsection “Quantitative characterization of VPs structure by a novel segmentation algorithm”, it is described that NSP5 is distributed inside the ring formed by NSP2 (Figure 1C). But it looks like there is NSP2 with the red NSP5 ring. And why there is nothing within the NSP5 circle? Is it hollow in the viroplasm sphere or is it that the anti-NSP5 antibody is not able to penetrate the protein layers enough to stain it?

For the first part of the question (interaction between the NSP2 and NSP5 protein rings), please see our answer to comment #5 below. Regarding the question about what is there inside the NSP5 circle, the answer is that it is not known. An interesting possibility is the hypothesis that viroplasm morphogenesis occurs on the surface of lipid droplets (2), since viroplasms co-localize with lipid droplets (2) (see also the answer to comment #1 of reviewer #1); thus, it is possible that the inner content of viroplasms could contain lipids. As suggested by the reviewer, it might also be that the anti-NSP5 antibody is not able to penetrate the protein layers enough to stain the center of the viroplasm. An additional alternative, although less likely, is that the space could contain cellular proteins, like those that have been shown to co-localize with viroplasms (see (8, 9)).

3) It is interesting to observe the co-localization of NSP2 and NSP4, which may play a significant role in viroplasm formation and genome replication. Please give more details about how the rabbit polyclonal sera to NSP4 was generated. How was it characterized? Please give the references if it has been used in previous publications. Does it stain the NSP4 on ER?

The hyperimmune serum to NSP4 (C-239) was generated by immunizing New Zealand white rabbits with a recombinant protein expressed in E. coli having a histidine-tail, and representing the carboxy-terminal end (amino acids 120 to 175) of the rhesus rotavirus RRV NSP4. This description, and the description of the hyperimmune serum to VP1 is now included in the Materials and methods section. Regarding the other part of the reviewer’s comment, the specificity of this anti-NSP4 serum was characterized by immunofluorescence and Western blot and RNAi (see Author response image 1 for the WB and RNAi data). This polyclonal antibody was previously used in Maruri-Avidal et al. (8), although the details of its generation were not described there either. In that paper, it was shown that NSP4 colocalizes with grp94, calreticulin, and PDI in the ER. This reference is now included also in the manuscript.

The paragraph of the antibody description now reads: “Monoclonal antibodies (MAbs) to VP2(3A8), VP4 (2G4), VP6 (255/60), VP7 (60) and VP7 (159) were kindly provided by H. B. Greenberg (Stanford University, Stanford, CA) (10, 11). The rabbit polyclonal sera to NSP2, NSP4 and NSP5, and the mouse polyclonal serum to NSP2 were produced in our laboratory (12). The hyperimmune serum to NSP4 (C-239) was generated in our laboratory by immunizing New Zealand white rabbits with a recombinant protein expressed in E. coli with a histidine-tail, representing the carboxy-terminal end (amino acids 120 to 175) of the rhesus rotavirus RRV NSP4 protein; see also reference (8) below, in which this serum was used. The hyperimmune serum to VP1 was also generated in our laboratory by immunizing BALB/c mice with a recombinant protein expressed in E. coli with a histidine-tail, representing amino acids 227 to 539 of the rhesus rotavirus RRV VP1 protein. Goat anti-mouse Alexa-488- and Goat anti-rabbit Alexa-568- conjugated secondary antibodies were purchased from Molecular Probes (Eugene, Oreg.).”

Author response image 1
Western blot analysis of rotavirus RRV-infected cells previously transfected with an siRNA directed to NSP4 or with a control, irrelevant (Irre) siRNA, using the rabbit polyclonal serum (C-239) to NSP4.
https://doi.org/10.7554/eLife.42906.036

4) Control imaging experiments should be included. For instance, an image with anti-rabbit secondary antibody in the absence of the rabbit polyclonal sera to NSP4. Does the anti-rabbit secondary antibody cross-react with the mouse polyclonal sera to NSP2?

Author response image 2 shows the requested control. As can be observed, there is a lack of reactivity of the anti-rabbit secondary antibody with the mouse polyclonal serum to NSP2 in the absence of the rabbit polyclonal sera to NSP4. It also shows that there is no cross-reactivity of the anti-mouse antibody with the rabbit polyclonal serum to NSP4 in the absence of the mouse polyclonal sera to NSP2. In general, the antibodies directed to different viral proteins that were used in this work have been extensively used in previous publications from our group and others (see at the end of this document -annex I- a list publications from our lab in which we have used the different antibodies), and their recognition patterns of viral proteins are well characterized. In Materials and methods the original publications that report the different antibodies are now included, or the method in our lab used for their generation is described. See also answer #3 to reviewer #2.

Author response image 2
Anti-rabbit and anti-mouse secondary antibodies are specific for their target species.

MA104 cells monolayers grown in coverslips were infected with RRV at an MOI of 1. At 6 hpi the cells were fixed and processed for immunofluorescence with either the primary antibody against NSP2 (green), NSP4 (red), or a combination of both antibodies, as described under Materials and methods. Afterwards, the cells were stained with either anti-rabbit Alexa568, anti-mouse Alexa488, or a combination of both antibodies. The cells nuclei (blue) were stained with DAPI.

https://doi.org/10.7554/eLife.42906.037

5) The proposed model in Figure 4 show the viroplasm viral proteins as in different layers. How would this model explain the interplay between these proteins that coordinate the genome replication and virion assembly? Does the overlapping region (Figure 2) of different layers play a role in these processes?

The objective of this research was to provide a general model about the spatial distribution of the viral proteins in the viroplasm. Therefore, our model does not describe the interactions between the layers of different proteins. Nevertheless, and based on the super resolution microscopy images, it seems clear that, as suggested by the reviewer, there is some overlapping between different protein layers, as is the case for NSP2 and NSP5 in Figure 1E, but also between NSP2 and VP1, VP2, VP6 and NSP4. These general overlapping zones between different proteins most likely are the responsible for coordinating the genome replication and virion assembly, as suggested. To clarify this point we have extended the discussion on this subject in the Discussion section of the main text (5th paragraph). Also, we aggregated an extra figure (Figure S8) in the supplementary information showing the presence of protein projections (“spike-like”) from the central distribution of the viral protein layers, that could also contribute to the interaction of proteins mapped to different shells.

Reviewer #3:

[…] 1) There are no reported controls for the antibodies. Given that these are made in the laboratory and that there are no references for them in the paper, it is essential that data are included to verify their specificity. This is particularly true for the potentially controversial finding of NSP4 – the authors must exclude potential artifacts and show that binding is specific. In general, controls are lacking in the paper.

Please, see our answers to comments #3 and #4 of reviewer #2.

2) Most of the technical detail in the paper is in the SI and devoted to the description of the algorithms for fitting the fluorescence data and locating VP components within shell structures. Given the sensitivity of the method to the photophysical behaviour of the specific dyes used, how representative are the validation and controls presented in the SI for the AF488 antibodies?

This answer has two parts, one related to the improvements of the calculation performed by 3B, and the other related to the validation of the algorithm developed to segment and analyze vpls.

First, we agree with reviewer that the outcome of 3B might be influenced by the photophysical properties of the fluorophore in study, as 3B requires as an input a P matrix which contains the transition probabilities between fluorophore’s states. This is exactly the rationale for computing P directly from the experimental data. In the Appendix, we show to the reader how to compute P directly from the experimental data, and provide some examples with distinct ATTO dyes, sowing that using such method there is a slight improvement on the resolution provide by 3B. We agree with the reviewer that the photophysical properties of ATTO and Alexa dyes are distinct, which might limit the calculations of P with our method (3B-ODE). However, we are happy to state that we have tested 3B-ODE with distinct dyes, including Alexa, fluorescein derivates and other dyes, that is DAPI, Hoechst, Sir-Actin, FM-464. All of them give a better result than by the analysis obtained with the use of 3B without computing P directly form the experimental data. As an example, we provide Author response image 3, which shows the fluorescence dynamics, as average fluorescence signal at each time step, of one viroplasm stained with AF488 antibodies (black trace).

The result of modeling the fluorescence dynamics after computing P directly from the experimental data (purple trace), note the similarity of both traces. Compare with the brown trace, a model of the fluorescence dynamics using the values used by 3B after choosing the default option within the ImageJ implementation of the method (13).

Second, the algorithm validation was performed using synthetic ground truth images (more than 40000 in this study) generated considering different levels of noise and partial occlusion angles. These images contain circumferences of different sizes and positions, for which real parameters of their implicit equations are known. This facilitates the analysis of the algorithm’s response against several plausible events, hence permitting the comparison of the obtained results with “ground-truth” circumferences that simulated the VPs. For the analysis of the sensitivity of the algorithm with specific antibodies (like AF488), it is necessary to know the ground truth segmentation result of the VPs in real images, information that is not available in the viral images repository we have (note that we are talking about super resolution microscopy images). For this reason, in this work we used synthetic images and evaluated the algorithm performance with different levels of noise, which can be considered as coarse-grained simulation of the photon yields of different dyes. Our method proved to be robust in high noise conditions, and when the level of “signal contamination” is greater than the expected in an SRM image. We obtained nanometric errors through our segmentation algorithm (under 0.17 μm in all the cases, except for the occlusion angle 3pi/2, which is an extreme partial occlusion angle, where only remains ¼ of the information of the synthetic VPs).

3) More details on the chosen approach should be included. Why was the 3B method chosen? For example, could the authors have used high signal to noise (but low resolution) widefield imaging and fitted concentric shells with appropriate noise models (see e.g. https://www.cell.com/biophysj/fulltext/S0006-3495(15)00993-5)? Nanometer fitting precision has been achieved with such an approach. The method would be easily implemented for the available data, and may work very well, given the comparatively large size of the VP structures investigated. Also, the paper gives the impression that this is the first time optical super resolution methods have been used to infer virus architecture, and notable efforts with related techniques have not been cited or discussed. E.g. in Laine et al., 2015, dSTORM was used and model based fitting was used to infer the concentric arrangement of virus proteins in HSV1 with nanometer precision. There are many similarities between the efforts presented there and those presented here. What are relative advantages and disadvantages of the available methods? I encourage the authors to review the existing literature more thoroughly and to provide guidelines to the reader on what the relative merits and disadvantages are for each technique.

At the very preliminary steps of the present research we had no idea about any degree of organization within the rotavirus viroplasms. The primary purpose of this research was to scrutinize the internal architecture of the viroplasms, by studying their protein distribution through super-resolution optical microscopy. Previous florescence/confocal microscopy studies showed that the viroplasm is composed of various structural and non-structural viral proteins, however due to the limit of the resolution of those techniques (250 nm approx) the viroplasm was observed as a structure without apparent organization of the proteins that make it up (14-16). Although viroplasms have been observed by electron microscopy the characteristics of this technique limit the level of detail that can be observed, particularly they become challenging to assign a particular degree of organization to a particular collection of molecules, so only electron-dense structures are observed without any clear degree of organization (see answer to question 5 of reviewer #1). We started by performing optical sectioning of viroplasms through total internal reflection microscopy (TIRFM), which allows to discriminate information provided by optical sections thinner than the length of the point spread function. In other words, TIRFM allows optical sectioning at 100 – 500 nm, hence overcoming the diffraction limit in Z axis. By using TIRFM, we started to observe certain degree of organization within the viroplasms (see Figure 1B of this article). That is why we proposed using super-resolution microscopy to determine if such a conformational organization exists. We chose 3B, over other super-resolution approaches because this method allow to deal samples with high density of labeling, providing data with a reasonable resolution, at the cost of higher computational effort.

We agree with the reviewer that we can use other methods to study the organization of cellular structures showing concentric arrangements as those proposed by Laine et al. (17), and Manetsberger et al. (18), which might not necessarily need to be tailored on the use of super-resolution microscopy. The similarities seen between those studies and our approach is the use of conics such as circles or ellipses to study structures showing concentric organization. The present investigation started in 2014, prior to the publication of the manuscripts recommended by this reviewer and was inspired by an algorithm which we previously published for the automatic detection and measurement of viral replication compartments by ellipse adjustment on fluorescence images (18). We agree with the reviewer that the approach provided by Manetsberger et al. can be implemented to analyze our data set, which as outcome will provide similar results. However, the approach suggested by the reviewer can provide something we had not paid attention in the present research (i.e. for simplicity reasons) which is the study of the degree of asymmetry within the viroplasms, something which we believe might be valuable to establish functional relationships between the protein distribution belts that shape these intriguing structures. We have now included in the Discussion section (first paragraph) part of information provided to the reviewer to answer this comment.

In the same vein of thinking, we want to stress to reviewer that our study represent the first approach which address the nanoscopic organization of viroplasms. The focus of the present research is not the study of viral particles. Considering that, we do not understand the rationale to think that the organization of viral particles will be mirrored form the viroplasm architecture.

[Editors’ note: the author responses to the re-review follow.]

We are prepared to consider a revised submission with no guarantees of acceptance. Our discussions about your appeal lead us to believe that it would be important to consider the following points prior to resubmission:

1) The authors have accepted that the dsRNA recognizing antibody used is non-specific (within the RNAs of RVA and beyond) and have now omitted all their dsRNA related data. RVA ssRNA-ssRNA segment interactions are at the core of pre-genome assembly in viroplasms and require interaction with NSP2. This has been convincingly described by: Borodavka et al., 2017.

The authors should comment on the processing of RVA RNAs in viroplasms in some more detail than by a single sentence in Discussion (p7, paragraph 3). The question of what is inside the NSP5 layer remains to be answered.

As requested, we have discussed in more detail the assembly of the rotavirus assorted +RNA complex containing NSP2, VP1 and VP3 into cores. As stated by the reviewer, the question of what is inside the NSP5 layer remains indeed to be answered.

2) The data by Berkova et al., 2006 have now been compared with the new findings in more detail in Discussion.

As suggested, we integrated into the discussion the previously reported data by Berkova et al., 2006.

3) The potential for interaction of the different viral protein layers identified has now been recognized.

This is correct. See subsection “The structural organization of VPs is independent of the reference protein chosen for pairwise comparison”.

4) Regarding potential structural asymmetries in viroplasms, authors provide a TEM photograph (Figure 1A) which shows an electron-dense viroplasm, but also many core particles and DLPs in the surrounding cytoplasm, proving that a first round of RVA particle formation has already taken place. See also Figure 1 in Altenburg et al., 1980, taken at 8 h p.i and figures in refs (Petrie et al., 1982, 1984; Richardson et al., 1986 and Eichwald et al, 2012). While the limits of TEM for multiple viral protein localization are recognized, it is still considered worthwhile to use the novel procedure on viroplasms at 2-3 h p.i., when viral particle formation has not yet taken place; preliminary data of this nature are not 'beyond the scope of this work' as authors suggest, but would be an important application.

As requested, VPs were analyzed by SRM at 3hpi. This analysis was carried out using the Super-Resolution Radial Fluctuations (SRRF) algorithm (Nat. Commun. 7:12471, 2016; see below for its description). In Author response image 4, it is clearly seen that the viral proteins in the VP show a similar “layered” organization as shown for the mature VP at 6 hpi in the manuscript. This observation indicates that this organization is already present when viral particle formation has not yet taken place, suggesting that it might be important for the assembly of DLPs within VPs. Of interest, at 3 hpi the layer formed by the NSP4 protein does not coincide (at the resolution achieved with the SRRF analysis) with the NSP2 layer, as it was found by 3B-SRM in VPs at 6 hpi, but it lies slightly outside the NSP2 layer, strongly suggesting that the organization of the proteins within VPs is dynamic and can change during maturation of the VPs. Further analysis carrying out a detailed characterization of the organization of the viral proteins in VPs a different times post-infection and using the 3B-SRM conditions described in the manuscript should be carried out to confirm these preliminary observations.

Due to problems beyond our control, we could not use the clusters or supercomputers of our university to generate the 3B-SRM images; as a consequence, we decided to use SRRF even when the resolution of the resulting images is less than in the case of 3B-SRM. The images generated with SRRF (Author response image 4), however, allow us to show, as a proof of concept, that at 3hpi a layered organization in the distribution of the viral proteins already exists. The experimental design for this analysis was the same as that described for 6hpi.

In the SRRF algorithm, for each image in a sequential series of frames (image’s stack), it magnifies each pixel of the image into subpixels and uses the degree of local gradient convergence (radial symmetries) to compute the probability that a subpixel contains a fluorophore. The previous step generates a stack of radiality maps using the spatial information of each image, and therefore it is possible to process these radiality maps through a higher-order temporal analysis to generate a single SRM image (see Nat. Commun. 7:12471, 2016 for details). Like 3B-SRM, SRRF allows the creation of SR images without the necessity for special prepared samples or for a specific microscope system.

Author response image 4
The VPs of rotavirus present a ring-like structure at early times of infection.

MA104 cells grown in coverslips were infected with RRV (MOI of 3). At 3 hours post-infection, the cells were fixed and co-inmunostained with the indicate antibodies. The nanoscale distribution of viral proteins within the VP was then analyzed through SRRF-SRM. Scale bar is 0.5 um.

https://doi.org/10.7554/eLife.42906.039

5) Authors' argument that they “describe the structure of viroplasms, not virus particles” should be emphasized in Discussion.

The fact that we describe the structure of viroplasms, not virus particles, in our work, has been emphasized in the Discussion section.

6) Authors state that they “proved statistically that the spatial distribution of the viral proteins can be considered as concentric layers”. Although they further state that the novel observations cannot be used to understand specific details, such as the interactions between different layers, Discussion could be more outspoken about the use of the novel procedure to analyse RVA replication steps within viroplasms.

As requested, we have extended the discussion regarding the potential use of the SRM procedure described, to analyze replication steps within viroplasms beyond the determination of the organization of viral proteins within these structures.

References

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2) W. Cheung, M. Gill, A. Esposito, CF. Kaminski, N. Courousse, S. Chwetzoff, G. Trugnan, N. Keshavan, and U. Desselberger. Rotaviruses associate with cellular lipid droplet components to replicate in viroplasms, and compounds disrupting or blocking lipid droplets inhibit viroplasm formation and viral replication. Journal of Virology, 84(13):6782–6798, 2010.

3) TC. Walther and RV. Farese. Lipid droplets and cellular lipid metabolism. Annual Review of Biochemistry, 81(1):687–714, 2012.

4) Ó. Trejo-Cerro, C. Eichwald, EM. Schraner, D. Silva-Ayala, S. López, CF. Arias. Actin-Dependent Nonlytic Rotavirus Exit and Infectious Virus Morphogenetic Pathway in Nonpolarized Cells. Journal of Virology, 92, e02076-17.

5) C. Eichwald, JF. Rodriguez, and OR. Burrone. Characterization of rotavirus NSP2/NSP5 interactions and the dynamics of viroplasm formation. Journal of General Virology, 85(3):625–634, 2004.

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7) M. Campagna, L. Marcos-Villar, F. Arnoldi, CCH. Felipe, PP. Gallego, JC. González-Santamarı́a, DI. González, F. Lopitz-Otsoa, MS. Rodrı́guez, OR. Burrone, and C. Rivas. Rotavirus viroplasm proteins interact with the cellular SUMOylation system: implications for viroplasm-like structure formation. Journal of virology, 87(2):807–817, 2013.

8) L. Maruri-Avidal, S. López, and CF. Arias. Endoplasmic reticulum chaperones are involved in the morphogenesis of rotavirus infectious particles. Journal of Virology, 82(11):5368–5380, 2008.

9) P. Dhillon, VN. Tandra, SG. Chorghade, ND. Namsa, L. Sahoo, and CD. Rao. Cytoplasmic re-localization and colocalization with viroplasms of host cell proteins, and their role in rotavirus infection. Journal of Virology, 92(15), 2018.

10) RD. Shaw, PT. Vo, PA. Offit, BS. Coulsont, and HB. Greenberg. Antigenic mapping of the surface proteins of rhesus rotavirus. Virology, 155(2):434 – 451, 1986.

11) HB. Greenberg, V. McAuliffe, J. Valdesuso, R. Wyatt, J. Flores, A. Kalica, Y. Hoshino, and N. Singh. Serological analysis of the subgroup protein of rotavirus, using monoclonal antibodies. Infection and Immunity, 39(1):91–99, 1983.

12) RA. González, MA. Torres-Vega, S. López, and CF. Arias. in vivo interactions among rotavirus nonstructural proteins. Archives of Virology, 143(5):981–996, 1998.

13) E. Rosten, G. Jones, and S. Cox. Imagej plug-in for bayesian analysis of blinking and bleaching. Nature Methods, 10(2):97–98, 2013.

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https://doi.org/10.7554/eLife.42906.041

Article and author information

Author details

  1. Yasel Garcés Suárez

    Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Data curation, Software, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing
    Contributed equally with
    Jose L Martínez
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8401-8352
  2. Jose L Martínez

    Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Conceptualization, Supervision, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing
    Contributed equally with
    Yasel Garcés Suárez
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-0529-7558
  3. David Torres Hernández

    1. Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    2. Laboratorio Nacional de Microscopía Avanzada, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Investigation, Visualization, Methodology
    Competing interests
    No competing interests declared
  4. Haydee Olinca Hernández

    1. Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    2. Laboratorio Nacional de Microscopía Avanzada, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Software, Validation, Investigation, Visualization, Methodology
    Competing interests
    No competing interests declared
  5. Arianna Pérez-Delgado

    Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Investigation, Methodology
    Competing interests
    No competing interests declared
  6. Mayra Méndez

    Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca, Mexico
    Contribution
    Software, Validation, Investigation, Writing—review and editing
    Competing interests
    No competing interests declared
  7. Christopher D Wood

    1. Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    2. Laboratorio Nacional de Microscopía Avanzada, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Investigation, Methodology, Writing—review and editing
    Competing interests
    No competing interests declared
  8. Juan Manuel Rendon-Mancha

    Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca, Mexico
    Contribution
    Supervision, Investigation
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9629-7050
  9. Daniela Silva-Ayala

    Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Present address
    Harvard Medical School, Boston, United States
    Contribution
    Investigation, Methodology
    Competing interests
    No competing interests declared
  10. Susana López

    Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Conceptualization, Supervision, Funding acquisition, Investigation, Methodology, Project administration, Writing—review and editing
    Competing interests
    No competing interests declared
  11. Adán Guerrero

    1. Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    2. Laboratorio Nacional de Microscopía Avanzada, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Conceptualization, Software, Supervision, Validation, Investigation, Methodology, Writing—review and editing
    For correspondence
    adanog@ibt.unam.mx
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-4389-5516
  12. Carlos F Arias

    Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
    Contribution
    Conceptualization, Supervision, Funding acquisition, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing
    For correspondence
    arias@ibt.unam.mx
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3130-4501

Funding

Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (IG200317)

  • Susana López
  • Carlos F Arias

Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (IA202417)

  • Adán Guerrero

Universidad Nacional Autónoma de México (SC15-1-IR-89)

  • Adán Guerrero

Consejo Nacional de Ciencia y Tecnología (252213)

  • Adán Guerrero

Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (IN202312)

  • Haydee Olinca Hernández

Universidad Nacional Autónoma de México (SC16-1-IR-102)

  • Adán Guerrero

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

YG received a postdoctoral fellowship from DGAPA-UNAM at the Institute of Biotechnology (IBt-UNAM). AG thanks DGTIC-UNAM for generous computing time on the Miztli supercomputer (Grant numbers: SC15-1-IR-89; SC16-1-IR-102). JLM and DTH are recipients of scholarships from CONACyT. HOH received a grant from the Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPIIT-UNAM), IN202312. Microscopy equipment was provided and maintained through CONACYT grants 123007, 232708, 260541, 280487, 293624. AG thanks CONACyT (No. 252213) and DGAPA-PAPIIT (No. IA202417), SL and CFA thank DGAPA-PAPIIT grant IG200317 for funding. We are thankful to IBt-UNAM for providing access to the computer cluster and to Jerome Verleyen for his support while using it. We are also thankful to Arturo Pimentel, Andrés Saralegui and Xochitl Alvarado from LNMA-UNAM for their helpful discussions. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Senior and Reviewing Editor

  1. Arup K Chakraborty, Massachusetts Institute of Technology, United States

Reviewers

  1. Ulrich Desselberger, University of Cambridge, United Kingdom
  2. Clemens F Kaminski, University of Cambridge, United Kingdom

Publication history

  1. Received: October 17, 2018
  2. Accepted: July 22, 2019
  3. Accepted Manuscript published: July 25, 2019 (version 1)
  4. Version of Record published: August 13, 2019 (version 2)
  5. Version of Record updated: August 22, 2019 (version 3)
  6. Version of Record updated: September 17, 2019 (version 4)

Copyright

© 2019, Garcés Suárez et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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