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Scaling of subcellular actin structures with cell length through decelerated growth

  1. Shane G McInally
  2. Jane Kondev  Is a corresponding author
  3. Bruce L Goode  Is a corresponding author
  1. Department of Biology, Brandeis University, United States
  2. Department of Physics, Brandeis University, United States
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Cite this article as: eLife 2021;10:e68424 doi: 10.7554/eLife.68424

Abstract

How cells tune the size of their subcellular parts to scale with cell size is a fundamental question in cell biology. Until now, most studies on the size control of organelles and other subcellular structures have focused on scaling relationships with cell volume, which can be explained by limiting pool mechanisms. Here, we uncover a distinct scaling relationship with cell length rather than volume, revealed by mathematical modeling and quantitative imaging of yeast actin cables. The extension rate of cables decelerates as they approach the rear of the cell, until cable length matches cell length. Further, the deceleration rate scales with cell length. These observations are quantitatively explained by a ‘balance-point’ model, which stands in contrast to limiting pool mechanisms, and describes a distinct mode of self-assembly that senses the linear dimensions of the cell.

Introduction

The size of a cell’s internal parts are scaled to its overall size. This size-scaling behavior has been demonstrated for organelles as well as large macromolecular assemblies, illustrating the broad importance of adapting the size of internal structures to the geometric dimensions of the cell (Rafelski et al., 2012; Levy and Heald, 2010; Hazel et al., 2013; Good et al., 2013; Weber and Brangwynne, 2015; Greenan et al., 2010; Jorgensen et al., 2007; Decker et al., 2011; Neumann and Nurse, 2007; Lacroix et al., 2018). A popular model of cellular scaling is the limiting pool mechanism, wherein maintaining a constant concentration of molecular components enables the subcellular structure to increase in size proportionally with cell volume (Goehring and Hyman, 2012de Godoy et al., 2008) This allows larger cells to assemble larger structures, since the total number of molecular building blocks increases proportionally with cell volume. Additionally, this mechanism is biochemically simple because it does not require active processes that dynamically tune concentrations or activity levels of proteins involved in the construction . Indeed, cells appear to use a limiting pool mechanism to scale the size of their nucleoli, centrosomes, and mitotic spindles (Hazel et al., 2013; Good et al., 2013; Weber and Brangwynne, 2015; Greenan et al., 2010; Decker et al., 2011; Lacroix et al., 2018). However, limiting pool models cannot explain how the size of a linear subcellular structure scales with the linear dimensions of a cell, rather than its volume. Namely, these mechanisms predict that a two fold increase in the radius of a spherical cell will increase the length of a linear structure eight fold, following the eight fold increase in cell volume. This suggests that other mechanisms must account for how some subcellular structures are scaled with the linear dimensions of a cell.

Polarized actin cables in S. cerevisiae are an example of a linear structure that appear to grow to match the linear dimensions of the cell in order to effectively deliver secretory vesicles (Moseley and Goode, 2006). These cables are linear bundles of crosslinked actin filaments assembled by formins, which extend along the cell cortex and serve as tracks for intracellular transport of cargo from the mother cell to the growing bud, or daughter cell. Complementary sets of cables are assembled by two formins, Bni1 at the bud tip and Bnr1 at the bud neck (Pruyne et al., 2004). Throughout the cell cycle, cables are continuously polymerized, turn over at high rates, and appear to grow until they reach the back of the mother cell (Yu et al., 2011; Yang and Pon, 2002; Eskin et al., 2016). This prompted us to more rigorously investigate the relationship between cable length and cell size.

We started by comparing cable lengths to the lengths of the mother cells in which they grew. Cables were imaged in fixed wild-type haploid cells using super-resolution microscopy. Cable lengths were measured from their site of assembly (the bud neck) to their distal tip in the mother cell (note that mother cell and cell are synonymous and used interchangeably from this point on) (Figure 1—figure supplement 1A). Average cable length and average cell length were remarkably similar (4.5 ± 0.3 µm and 4.5 ± 0.2 µm, respectively), suggesting a scaling relationship. However, we note that there was a wider range in cable lengths (2.0–8.7 µm) compared to cell lengths (3.7–5.5 µm), presumably because cables in fixed cells are at different stages of growth. Further, because cables grow along the cortex of an ellipsoid shaped cell, their length can exceed the length of the cell while not growing past the back of the cell. Therefore, a cable that grows from the bud neck to the back of the cell is expected to be slightly longer than the direct distance between these two points.

The observations above led us to ask whether the relationship between cable length and cell length is maintained as cell size increases. To address this, we compared cable lengths in haploid and diploid cells, and cdc28-13ts temperature-sensitive mutants that grow abnormally large. Diploid mother cells had an ~2-fold increase in volume compared to haploid mother cells (81.8 ± 6.3 µm3 and 44.9 ± 4.7 µm3, respectively) (Figure 1A,B and E), consistent with previous studies (Jorgensen et al., 2002). The cdc28-13ts strain exhibited a normal haploid mother cell size at the permissive temperature. However, this strain displayed a ~ 5-fold increase in volume (198.3 ± 5.5 µm3 versus 40.9 ± 2.3 µm3) after growth at the restrictive temperature (37°C) for 8 hr, followed by 1 hr of growth at the permissive temperature (25°C) to allow cell polarization and bud growth (Figure 1C,D and E; and Figure 1—figure supplement 1B and CAllard et al., 2018). Accordingly, cell length increased with cell volume (Figure 1F). Cable length was greater in diploids (6.3 ± 0.7 µm) compared to haploids (4.5 ± 0.3 µm), and greater in induced (8.2 ± 0.4 µm) compared to uninduced (4.3 ± 0.1 µm) cdc28-13ts cells (Figure 1G). However, the distribution of cable lengths for all strains collapsed when we divided the lengths of cables by the lengths of the cells in which they grew (Figure 1H and I). These results strongly suggest that cables grow to a length that matches cell length.

Figure 1 with 2 supplements see all
Actin cable length scales with cell length.

(A–D) Representative images of haploid (A), diploid (B), uninduced cdc28-13ts (C), and induced cdc28-13ts (D) cells fixed and stained with labeled-phalloidin. Lengths of single actin cables are indicated (dashed lines) in maximum intensity projections (left, color) and single Z planes (right, inverted). Scale bar, 2 µm. (E–F) Mother cell volume (E) and length (F) measured in three independent experiments (≥30 cells/strain). Each data point is from an individual cell. Larger symbols represent the mean from each experiment. (G–H) Cable length (G) and ratio of cable length/cell length (H) measured from the same cells as in E and F (≥200 cables/strain). Each data point represents an individual cable. Larger symbols represent the mean from each experiment. Error bars, 95% confidence intervals. Statistical significance determined by students t-test. Significant differences (p≤0.05) indicated for comparisons with haploid (‘a’), diploid (‘b’), uninduced cdc28-13ts (‘c’), and induced cdc28-13ts (‘d’). Complete statistical results in Figure 1—source data 1. (I) Probability density functions for ratios in H. (J–K) Cable lengths plotted against mother cell length (J) or volume (K) on double-logarithmic plots and fit using the power-law. Hypothetical isometric scaling (dashed line) is compared to experimentally measured scaling exponent (solid line).

Figure 1—source data 1

Complete results from statistical tests performed in this study.

The p-value is indicated for student’s t-test used to compare the data presented in Figure 1 and Figure 1—figure supplement 1.

https://cdn.elifesciences.org/articles/68424/elife-68424-fig1-data1-v2.xlsx

Next, we used a power law analysis to rigorously test the scaling relationships of cable length with cell length and volume (Figure 1J and K). Generally, scaling relations can be described by the power law y=Axa, where a is the scaling exponent that reflects the relationship between the two measured quantities, x and y (Reber and Goehring, 2015). This analysis revealed isometric scaling (aL=0.91±0.03,R2=0.50) between cable length and cell length (Figure 1J), whereas scaling between cable length and cell volume was hypoallometric (aV=0.36±0.01,R2=0.46) (Figure 1K).

To uncouple cell length from cell volume, we compared the length of cables in cells of different morphology. We computed the aspect ratio (the ratio of cell length to cell width) for the same cells analyzed above. This revealed that while some cells had nearly spherical morphologies, others had highly elongated morphologies (Figure 1—figure supplement 2A and B). Despite these differences in cell shape, the ratio of cable length to cell length, and the scaling exponents were similar for all cells (Figure 1—figure supplement 2C–G). Therefore, in cells of vastly different size and shape, the cable length directly scales with cell length, rather than with other dimensions such as cell surface area or volume.

We considered two distinct models to explain the control of cable length. In both models, the length of a cable is determined by competing rates of actin assembly (k+) at the barbed ends of cables and disassembly (k-) at the pointed ends of cables (Figure 2A and B). Therefore, at any given time, the extension rate of a cable is determined by the difference in its assembly and disassembly rates (Figure 2B). In the boundary-sensing model, the assembly rate is greater than the disassembly rate until the extending cable physically encounters the rear of the cell, causing one or both rates to abruptly change (Figure 2C, and Figure 2—figure supplement 1AReber and Goehring, 2015). This model predicts that the cable extension rate will be constant until the cable tip encounters the back of the cell. In contrast, the balance-point model requires that either the assembly rate, the disassembly rate, or both rates are length-dependent, and defines steady state cable length as the point at which these two rates are balanced (Figure 2D, and Figure 2—figure supplement 1BMohapatra et al., 2016). In clear contrast to the boundary-sensing model, this model predicts that the cable extension rate will steadily decrease as the cable lengthens.

Figure 2 with 2 supplements see all
Models for control of actin cable length.

(A) Actin staining in haploid cell (left) and cable traces (right). (B) Relevant parameters and equation for cable extension, where assembly (k+) and disassembly (k-) rates change as a function of cable length. Cables are polymerized by formins (orange) from actin monomers (gray), bundled by crosslinkers (blue), and disassembled by factors not shown. Cable extension rate is the difference in assembly and disassembly rates. (C–D) Two models for cable length control. Additional information in Figure 2—figure supplement 1. (E) Maximum intensity projection of haploid cells expressing cable marker (Abp140-GFPEnvy) shown in color (top panels) and inverted gray scale (bottom panels). Yellow circle highlights tip of elongating cable over time. Scale bar, 5 µm. (F–G) Extension rate (F) and length (G) measured in five independent experiments (n = 82 cables). Symbols at each time point represents mean for individual experiment. Solid lines and shading, mean and 95% confidence interval for all five experiments. Dashed yellow lines, predictions of boundary-sensing model in C.

To directly test the predictions of the two models, we used live imaging to track the tips of cables as they grew from the bud neck into the mother cell (Figure 2E, Video 1, and Figure 2—figure supplement 2A–C). Initially cables extended at 0.36 ± 0.02 µm s−1, and as they grew longer their extension rates steadily decreased (Figure 2F, Figure 2—figure supplement 2D). Accordingly, we observed greater changes in cable length during earlier phases of cable growth (Figure 2G, Figure 2—figure supplement 2E). Thus, as cables lengthen their growth rate decelerates.

Video 1
Maximum intensity projection of haploid cells expressing a cable marker (Abp140-GFPEnvy) shown in color.

Yellow circle highlights tip of an elongating cable over time. Video is played at 7 frames per second and time (seconds) is indicated in the top left corner. Scale bar, 5 µm.

Note that we detected cables that were very short (<2 µm) by live imaging, which were not seen in our analysis of fixed cells. We expect that this is because shorter cables extend at a faster rate compared to longer cables and are therefore less prevalent in fixed cell populations.

Our experimental observations above support a balance-point model in which steady state cable length is reached when the assembly and disassembly rates are balanced. In this model, the rate of cable extension at any given time is given by the difference between the assembly and disassembly rates, which we call the feedback function, f=k+-k-. To account for the observed scaling of cable length with cell length (Figure 1H and I), we assume that f depends on the cable length (Lcable) scaled by the cell length (Lcell), that is fLcable,Lcell=f(Lcable/Lcell). The steady state cable length (Lcable*) is reached when the feedback function equals zero, f(Lcable*/Lcell)=0. Therefore, the scale-invariant feedback function leads to the scaling of Lcable* with Lcell seen in Figure 1J. (Further mathematical details in Materials and methods.)

Smy1 is a factor implicated in cable length control, and therefore we considered whether it might be required for cable deceleration. It has been reported that cables are longer in smy1∆ compared to wildtype cells, and that Smy1 directly inhibits Bnr1-mediated actin assembly (Eskin et al., 2016; Chesarone-Cataldo et al., 2011). Further, Smy1 is transported by myosin along cables to the bud neck where Bnr1 is anchored. Based on these observations, an ‘antenna mechanism’ has been proposed in which longer cables deliver more Smy1 to slow cable extension and limit cable length (Mohapatra et al., 2015). We confirmed the increase in cable length in smy1∆ cells (Figure 3A, and Figure 3—figure supplement 1A and BEskin et al., 2016), but found that cables continued to decelerate in the absence of Smy1 (Figure 3B and C). Furthermore, we observed an increase in the initial cable extension rate in smy1Δ (0.42 ± 0.04 µm s−1) compared to wild-type cells (0.35 ± 0.02 µm s−1) (Figure 3D and E). Interestingly, the initial extension rate in smy1Δ cells increased by the same magnitude (1.2-fold ± 0.2) as the measured increase in cable length (1.2-fold ± 0.1). Thus, Smy1 affects cable length by limiting the initial cable growth rate (Figure 3F) but does not provide the feedback that results in cable deceleration. Importantly, this does not rule out the possibility of other cellular factors acting through an antenna mechanism to control cable growth in a length-dependent manner.

Figure 3 with 1 supplement see all
Smy1 controls initial cable extension rate.

All data are from three independent experiments. (A) Cable lengths (≥130 cables/strain). Each data point represents an individual cable. Larger symbols, mean from each experiment. Error bars, 95% confidence intervals. Statistical significance determined by students t-test. (B–C) Cable extension rates for wildtype (B) and smy1∆ (C) yeast (≥47 cables/strain). Symbols, mean from each experiment. Solid lines and shading, mean and 95% confidence interval for all experiments. Deceleration rates were derived from the slopes (±95% CI) of the dashed lines, which were determined by linear regression using the first ~10 s of extension. (D) Average extension rate as a function of cable length. Solid lines and shading, mean and 95% confidence interval for all experiments. Dashed box highlights region of no overlap in confidence intervals. (E) Initial cable extension rate for each strain. Small symbols, individual cables. Larger symbols, mean from each experiment. Error bars, 95% confidence intervals. Statistical significance determined by students t-test. (F) Cartoon comparing cable extension in wildtype and smy1∆ cells.

Our model makes an interesting quantitative prediction for cables that have abnormally fast initial extension rates, such as those measured in smy1Δ cells above. Specifically, our model predicts that this increase in initial extension rate will lead to a proportional increase in the initial deceleration (see Equation 7 in Materials and methods). Thus, the measured 1.2-fold increase in initial extension rate seen in smy1∆ cells is expected to lead to a 1.2-fold increase in initial deceleration of cables, shortly after they emerge from the bud neck. Indeed, linear fits to the cable extension rate, as a function of time over the first 10 s (i.e. the first few microns of cable extension), yield, dosmy1Δ=-0.018±0.010μm/s2 and dowt=-0.015±0.005μm/s2, for smy1∆ and wild-type cells, respectively (Figure 3B and C). The ratio of these two, d0smy1Δ/d0wt=1.2±0.7, matches the ratio of the initial extension rates, f0smy1Δ/f0wt=1.2±0.2. Therefore, these data lend additional quantitative support for our model.

A key prediction of our balance-point model is that cable extension rates should depend on cell length, that is a cable of a given length should grow faster (or slow down more gradually) in longer cells compared to shorter cells (Figure 4A, top). Further, it predicts that the cable extension rate profiles from cells of different lengths will collapse when cable length is normalized to cell length (Figure 4A, bottom; predictions of model derived in Materials and methods). To test these predictions, we compared cable extension dynamics in uninduced and induced cdc28-13ts cells (Figure 4B and C, Figure 4—figure supplement 1A and B, and Videos 2, 3, 4). When cables began to grow, they extended at similar rates in shorter and longer cells (Figure 4—figure supplement 1C). However, as the cables grew longer, they decelerated more gradually in the longer cells (Figure 4D–F). This led to longer cables in longer cells (Figure 4—figure supplement 1D). Linear regression analysis revealed that there is a nearly 2-fold greater initial deceleration in the shorter, uninduced cdc28-13ts cells (d0uninduced=-0.019±0.005μm/s2) compared to the longer, induced cdc28-13ts cells (d0induced=-0.010±0.003μm/s2). To determine how deceleration changes with respect to cell length, we compared the ratio of initial deceleration and cell length in induced (Linduced=8.2±0.4μm) and uninduced (Luninduced=4.3±0.1μm) cdc28-13ts cells. We found that the initial deceleration rate is inversely proportional to cell length (d0uninduced/d0induced=2±1(Luninduced/Linduced)-1=1.9±0.1), consistent with the predictions of our balance-point model (Figure 4D and E and Equation 7 in Materials and methods). Further, once cable length was normalized to cell length, cables extended with similar dynamics (Figure 4G), as predicted by our model.

Figure 4 with 1 supplement see all
Cell length-dependent deceleration of actin cable growth.

(A) Predictions of balance-point model comparing how cable deceleration (d0) changes as a function of cable length (top graph) in shorter (green curve) and longer (yellow curve) cells. This difference in the deceleration profiles is eliminated when cable length is normalized to cell length (bottom graph). (B–C) Maximum intensity projections of uninduced (B) and induced cdc28-13ts (C) cells expressing cable marker (Abp140-GFPEnvy). Yellow circle highlights tip of elongating cable over time. Scale bar, 5 µm. (D–E) Cable extension rates for uninduced (D) and induced cdc28-13ts (E) cells, from at least three independent experiments (≥57 cables/strain). Symbols and shading, mean and 95% confidence intervals for all experiments. Deceleration rates were derived from the slopes (±95% CI) of the dashed lines, which were determined by linear regression using the first ~10 s of extension. (F–G) Average extension rates in uninduced and induced cdc28-13ts cells (data from experiments in D and E) plotted as a function of cable length (F), or the ratio of cable length/cell length (G). Solid lines and shading, mean and 95% confidence interval for all experiments.

Video 2
Maximum intensity projections of uninduced cdc28-13ts cell expressing cable marker (Abp140-GFPEnvy) shown in color (top panels).

Yellow circle highlights tip of elongating cable over time. Video is played at 7 frames per second and time (s) is indicated in the top left corner. Scale bar, 5 µm.

Video 3
Maximum intensity projections of induced cdc28-13ts cell expressing cable marker (Abp140-GFPEnvy) shown in color (top panels).

Yellow circle highlights tip of elongating cable over time. Video is played at 7 frames per second and time (s) is indicated in the top left corner. Scale bar, 5 µm.

Video 4
Maximum intensity projections of uninduced cdc28-13ts cells expressing cable marker (Abp140-GFPEnvy) shown in color (top panels).

Yellow circle highlights tip of elongating cable over time. Video is played at 7 frames per second and time (s) is indicated in the top left corner. Scale bar, 5 µm.

Collectively, our observations demonstrate that cables grow until their length matches the length of the cell, and that this is achieved by length-dependent deceleration of cable extension. The precise mechanism providing the feedback to enable cable deceleration is not yet clear. One possibility is that it is controlled by a gradient of actin disassembly-promoting activity that is highest at the rear of the cell. Such a gradient could be established by the retrograde transport of disassembly factors on cables, leading to their release at the rear of the cell. This would produce a higher concentration of disassembly factors, and greater disassembly rate for cables, at the back of the cell. An alternative possibility is a reaction-diffusion mechanism, achieved by anchoring an activator of disassembly factors (such as a kinase) at the rear of the cell while having an inhibitor (such as a phosphatase) in the cytosol. This would be similar conceptually to how Ran GTPase gradients form around chromatin (Kalab et al., 2002), although it would require additional features to produce the scaling that we observe (Ben-Zvi et al., 2011). Either of these two mechanisms (retrograde transport or modified reaction-diffusion) has the potential to create a gradient that is shallower in longer cells compared to shorter cells, accounting for the cell-length-sensitive cable deceleration (Figure 2—figure supplement 1D). This mechanism also would allow cables to sense the rear of the cell without requiring physical interactions with that boundary. A third possibility, which is not mutually exclusive with either mechanism above, would be length-dependent inhibition of cable assembly, that is an antenna mechanism, albeit one that is dependent on cellular factors other than Smy1 (Mohapatra et al., 2015).

It has recently been shown for other subcellular structures (e.g. nucleus, spindle, centrosome, and nucleolus) that their sizes scale with cell volume, and this scaling is explained by limiting pool models (Hazel et al., 2013; Good et al., 2013; Weber and Brangwynne, 2015; Decker et al., 2011; Neumann and Nurse, 2007; Lacroix et al., 2018). However, we found that polarized actin cables scale with cell length rather than volume. This length control cannot be explained by a limiting pool mechanism, and instead is explained, both theoretically and experimentally, by a balance-point model. These results reveal a new strategy by which cells solve engineering challenges, enabling them to scale internal structures with the linear dimensions of the cell (Kirschner et al., 2000). Similar principles may underlie the length control of other polarized, linear actin structures, such as filopodia and stereocilia. Further, related strategies may be used to control the growth of radial microtubule arrays that reach the cell periphery (Lacroix et al., 2016; Wühr et al., 2010), and may explain the scaling relationships observed between flagellar length and cell length (Bauer et al., 2021) and between contractile ring diameter and cell diameter (Kukhtevich et al., 2020). Ultimately, the model of size control that we have presented here expands our understanding of the mechanisms used by cells to sense specific aspects of their geometry, including length, surface area, and volume, to assemble structures that scale with these different dimensions (Rieckhoff et al., 2020; Brownlee and Heald, 2019).

Materials and methods

Key resources table
Reagent type
(species) or
resource
DesignationSource or referenceIdentifiersAdditional information
Strain, strain background (S. cerevisiae)See: Supplementary file 1This paperNCBITaxon:4932Strains maintained in the Goode lab
Chemical compound, drugAlexa Fluor 488- phalloidinLife TechnologiesA12379
Chemical compound, drugAlexa Fluor 568-phalloidinLife TechnologiesA12380
Recombinant DNA reagentpFA6a-link-GFPEnvy-SpHis5PMID:25612242RRID:Addgene_60782
Recombinant DNA reagentpFA6a-TRP1PMID:9717241RRID:Addgene_41603

Plasmids and yeast strains

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All strains (see Supplementary file 1) were constructed using standard methods. To integrate a bright GFP variant (GFPEnvy) at the C-terminus of the endogenous ABP140 gene, primers were designed with complementarity to the 3’ end of the GFPEnvy cassette and the C-terminal coding region of ABP140. PCR was used to generate amplicons from the pFA6a-link-GFPEnvy-SpHis5 (Slubowski et al., 2015) template that allow for selection of transformants using media lacking histidine. The parent strains, BGY12 (haploid) and cdc28-13ts, were transformed with PCR products, and transformants were selected by growth on synthetic media lacking histidine. Similarly, smy1Δ strains were generated by replacement of SMY1 with the TRP1 auxotrophic marker by designing primers with complementarity to regions 40 base-pairs immediately up-stream and down-stream of the SMY1 coding region (Longtine et al., 1998). Deletion of SMY1 was confirmed by genomic PCR with primers specific to the TRP1 promoter and the 5’UTR region of SMY1. The cdc28-13ts strain was a generous gift from Brian Graziano (UCSF). pFA6a-link-GFPEnvy-SpHis5 was a gift from Linda Huang (UMass Boston) (Addgene plasmid # 60782; http://n2t.net/addgene:60782; RRID:Addgene_60782).

Induction of cell size changes

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To induce enlargement of mother cells, cdc28-13ts cells were grown at the permissive temperature (25°C) overnight in synthetic complete media (SCM), then 10μL of overnight culture was diluted into 5mL of fresh SCM. Cultures were then shifted to the restrictive temperature (37°C) for 8 hr (except for the experiments in Figure 1—figure supplement 1B and C, where cultures were also shifted for only 4 hr). After this induction, cells were returned to the permissive temperature (25°C) for 1 hr of growth to allow cell polarization and bud growth, and then fixed or mounted for live-cell imaging.

Quantitative analysis of actin cable length and architecture in fixed cells

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Strains were grown at 25°C to mid-log phase (OD600 ~0.3) in yeast extract/peptone/dextrose (YEPD), or were first induced for cell size changes as indicated above. Then cells were fixed in 4.4% formaldehyde for 45 min, washed three times in phosphate-buffered saline (PBS), and stained with Alexa Fluor 488- phalloidin or Alexa Fluor 568-phalloidin (Life Technologies, Grand Island, NY) for ≥24 hr at 4°C. Next, cells were washed three times in PBS and imaged in mounting media (20 mM Tris, pH 8.0, 90% glycerol). 3D stacks were collected at 0.22 μm intervals on a Zeiss LSM 880 using Airyscan super-resolution imaging equipped with 63 × 1.4 Plan-Apochromat Oil objective lens. 3D stacks were acquired for the entire height of the cell. Airyscan image processing was performed using Zen Black software (Carl Zeiss). ImageJ was used to generate inverted greyscale and maximum projection images for analysis. Next ImageJ was used to manually trace each individual cable, from the bud neck to their terminus in the mother cell. The 3D stack was used to differentiate between cables that overlapped and to precisely determine both the origins and distal tips of the cables. For length analysis, we included every discernable cable in the cell that extended from the bud neck to some endpoint in the mother cell; the only cables excluded were the minority that became closely intertwined with other cables making it impossible to resolve their individual lengths. Then the xy-coordinates for each cable trace were exported into custom written Python scripts to compute cable length. Cell length was determined by measuring the distance from the bud neck to the distal end of the mother cell. Cell width was determined by measuring the widest point perpendicular to the cell length axis. Cell height was determined from the number of slices in the 3D stack and the interval size between slices. These values were recorded and imported into custom Python scripts to compute the ratio of cable length to mother cell length, the cell volume (using the ellipsoid formula), the aspect ratio (cell length/cell width), and to fit the scaling exponent for cable length versus mother cell length, width, and volume. For cell shape analysis, cells were binned based on their aspect ratio rounded to the nearest quarter value.

Live-cell imaging and quantitative analysis of actin cable extension rate

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Strains were grown at 25°C to mid-log phase (OD600 ~0.3) in either YEPD, or were first induced for cell size changes as indicated above, then harvested by centrifugation (30 s, 9000 x g). Media was decanted and cells were resuspended in 50 μL fresh media. Cells (~5 μL) were mounted onto 1.2% agarose pads made with SCM, and images were acquired on a Nikon i-E upright confocal microscope equipped with a CSU-W1 spinning-disk head (Yokogawa, Tokyo, Japan) and an Andor Ixon 897 Ultra CCD camera controlled by Nikon NIS-Elements Advanced Research software using a 100x, 1.45 NA objective. 3D stacks were acquired at 0.3 μm intervals for approximately half of the cell height with no time delay for 2 min (approximately 0.30–0.43 frames per second). Images were processed in ImageJ by generating maximum intensity projections of each stack and applying a Gaussian blur (sigma = 1) to facilitate manual tracking of cable tips. Cables included for analysis were those whose tips could be resolved in every frame, from when they emerged from the bud neck and until they stopped extending. Cables that could not be reliably tracked (e.g. dim cables, overlapping cables that prevented tracking of their tips, or cables that grew into regions not captured in the 3D stack) were excluded from the analysis. Individual cable trajectories were imported into custom Python scripts to compute the distance the cable tip travelled between each frame, the rate of extension between each frame, and the total distance travelled. The boundary-sensing model prediction depicted in Figure 2F was determined by plotting the mean initial cable extension rate as a function of time. The boundary-sensing model prediction depicted in Figure 2G was determined by using linear regression to measure the slope from the first ~10 s of cable extension. Initial cable extension rates (Figure 3C and Figure 4—figure supplement 1C) were determined by computing the extension rate measured during the first time interval.

Mathematics of the balance point model

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The rate of change of the cable length with time is given by the difference between the assembly (k+) and disassembly (k-) rates,

(1) dLcabledt=k+(Lcable,Lcell)k(Lcable,Lcell).

where we have made explicit the possibility that one or both rates depend on the length of the extending cable (Lcable) and the cell length (Lcell). The steady state length Lcable* is the cable length at which the assembly and disassembly rates are the same.

To account for the scaling of the steady state length with the cell length (as observed in Figure 1H,I and J), we make an additional assumption, namely that the feedback function, fk+-k-, which determines the rate of cable extension, is a function of the ratio of the cable length to the cell length, that is fLcable,Lcell=f(Lcable/Lcell). Thus, our mathematical model of cable length control is described by the differential equation:

(2) dLcabledt=f(Lcable/Lcell),

which is graphically summarized in Figure 2—figure supplement 1C.

At the molecular scale, this feedback could be accomplished with a constant rate of cable assembly and a variable rate of disassembly controlled by a gradient of depolymerizing activity that is highest at the back of the cell; see Figure 2—figure supplement 1C. In this mechanism, as the cable lengthens its distal end is subject to increasingly stronger depolymerizing activity. Further, the profile or decay-length of the depolymerizing gradient needs to scale with cell length. Such scaling of a cellular gradient with the linear distance between the two poles of the cell has been observed for the protein Bicoid in different size embryos, from different species of flies (Gregor et al., 2005). Other experimental observations and theoretical models of such scale-invariant gradients are reviewed in Ben-Zvi et al., 2011.

Figure 4F and G are a direct test of our model. In Figure 4F, we observe that the cable extension rate is dependent on cell length, consistent with Equation 1. In Figure 4G, we see that the two feedback functions, from cells of different size, collapse to a single function when the cable lengths are scaled by the cell length.

The scaling property of the feedback function immediately leads to scaling of steady state cable length with cell length. Namely, in steady state, the right-hand side of Equation 1 is zero, which implies f(Lcable*/Lcell)=0. If the zero of the feedback function is x* (i.e.,fx*=0), then the steady state length Lcable*=x*Lcell, which is the scaling relation we observe in Figure 1H and J between the steady state length and the cell length.

The scaling property of the feedback function also makes a prediction for the initial rate of cable extension in cells of different size. Namely, for small cable lengths, when LcableLcell, we can expand Equation 2 into a Taylor series

(3) dLcabledt=f(LcableLcell)f(0)+f(0)LcableLcell,

which states that the initial cable extension decreases linearly with the cable length (since f'0 is negative) and is inversely proportional to cell length, Lcell.

Equation 3, with the initial condition Lcablet=0=0, can be solved for the cable length as a function of time,

(4) Lcable(t)=Lcellf(0)f(0)[ef(0)Lcellt1],

which in turn yields, by differentiation, an exponentially decreasing in time extension rate:

(5) dLcabledt=f(0)ef(0)Lcellt.

Since Equations 4 and 5 only hold at early times when the cable length is much smaller than the cell length (roughly, first 10 s of cable extension; see Figure 2G), we can further simplify Equation 5 by expanding it into a Taylor series:

(6) dLcabledt=f(0)+f(0)f(0)Lcellt.

Equation 6 makes very specific predictions about the initial deceleration of cable extension, in particular our model (Equation 2) predicts that the initial deceleration

(7) d0=d2Lcabledt2|t=0=f(0)f(0)Lcell

scales inversely with the cell length, and proportionally with initial cable extension rate. Indeed, these predictions are supported in two independent experimental tests of this model. Our analysis of smy1Δ cells indicates that increasing f0, while f'0 and Lcell are fixed, leads to a proportional increase in initial deceleration rate. Additionally, our analysis of induced and uninduced cdc28-13ts cells, where Lcell increases ~2-fold, while f0 and f'0 are fixed, leads to a two fold difference in initial deceleration.

Finally, our model also makes a qualitative prediction about the probability distribution of cable lengths at steady state. Namely, the feedback function near the steady state cable length, Lcable*=x*Lcell can be Taylor expanded to

(8) dLcabledtf(x)+f(x)LcableLcableLcell=f(x)LcableLcableLcell,

which shows that the strength of the feedback diminishes with cell length. This in turn implies that the steady state fluctuations of cable length will be larger in longer cells, which is consistent with data in Figure 1G. It is important to note that the above arguments pertain to cable length fluctuations over time, whereas the data in Figure 1G show cell-to-cell fluctuations in cable length, which could be influenced by cell-to-cell heterogeneity in some of the factors that affect cable assembly. Further experiments that carefully delineate between different sources of cable length fluctuations could provide more detailed tests of our model.

Data and materials availability

Request a detailed protocol

Data are available in the main text or in the supplementary material. All images (McInally et al., 2021b) and source code (McInally, 2021a) are archived at Zenodo.

Data availability

All data points are shown in the main figures and figure supplements, and all cell images and source code are archived at Zenodo.

References

Decision letter

  1. Mohan K Balasubramanian
    Reviewing Editor; University of Warwick, United Kingdom
  2. Jonathan A Cooper
    Senior Editor; Fred Hutchinson Cancer Research Center, United States
  3. Arjun Raj
    Reviewer; University of Pennsylvania, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This manuscript will be of interest to researchers in the fields of cell size control and the cytoskeleton. A combination of modelling and experimental data show that actin cables, which extend in budding yeast cells from the bud tip and bud neck, display an average length similar to the length of the cell, likely due to progressive decrease in their extension rate up to cell length. The distinct scaling relationship with cell length rather than volume may be a new paradigm that drives new investigations in related phenomena in other organisms.

Decision letter after peer review:

Thank you for submitting your article "Scaling of subcellular structures with cell length through decelerated growth" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Jonathan Cooper as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Arjun Raj (Reviewer #1).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission. The vast majority of points raised can be addressed by rewriting and reanalyzing data already generated. However, a single new experiment has been sought by one of the referees, which I agree will further sharpen the models you are trying to advance.

Essential Revisions:

1. I'm not as familiar with the details of the models, but it seems that a key assumption is that f(Lcable,Lcell) = f(Lcable/Lcell), which allows for the cells to scale length appropriately. Can the authors speculate on potential mechanisms underlying this length scaling? If there is a gradient, what could form it with such a property?

2. The effect of Smy1 KO on initial elongation rate is modest. I think it would be useful to quantify the effect size and put it in the main text. Also, does the degree of increase quantitatively match the increased cable length observed? If not, can the authors speculate on the source of the discrepancy?

3. To uncouple cell length and cell volume, the authors could use mutants with abnormal cell shape (for instance using more ellipsoid or more rounded cells). Many such mutants have been described over the years in S. cerevisiae, so this should be a technically straightforward approach to take. This would allow to probe whether actin cable length indeed correlates better with cell length than the cubic root of volume (or other shape measurements).

4. An indication of how cables were selected for tracking and their number amongst how many cells would help better explain the extension rate measurements and increase confidence in the data. Extending this comparison to other mutants with altered cell shape as suggested above would also strengthen the conclusions.

5. Measurement of cable length and steady state length. The study depends heavily on the ability to measure actin cable length. But how cable length was measured in 3D is not presented with sufficient detail. I think it is essential to show convincing 3D images of cable end identification for the majority of actin cables in a cell. I am suggesting this since cables that reach the cell back may "turn around" and/or form bundles or unbundle through interactions with other cables.

6. The extension rate of actin cables that grow from the bud neck to the cell back is shown in movies and quantified in the figures. However, it's not clear if these cables eventually *stop* elongating. For example, in Figure 4D the extension rate does not decay to zero at the longest times. That seems to me to be an essential point since I would expect that if one is able to measure the length of most actin cables in the cell, then one should be able to see most of these cables stop extending.

7. I found the contrast between the two models, "boundary-sensing" and "balance-point" was not so sharp: the difference is on whether the extension rate decays more or less abruptly with distance along the cell. I also don't see if either of these models as presented is excluded by the data. The authors convincingly show that the cable extension rate decays with cable length, as would be expected from a balance-point model. However, as mentioned in comment 1, it is not clear where the extension rate decays to zero in graphs such as Figure 1F, 3B, 4D. If cable elongation ends abruptly at the longest time in these graphs, then this would indicate a boundary-sensing mechanism (so overall a combination/intermediate model).

8. I feel that the mechanism by which the actin cable system reaches a steady state needs to be clarified. We see a few cables that start from the bud neck and grow to the whole cell. Is this typical or are these rare cases? If rare, are they still representative? Do cables disappear to allow for new cable growth? Such processes change cable length so they are linked to the central theme of cable length regulation.

9. There is a lack of discussion and experimentation of known regulators of actin assembly and disassembly. Perhaps it's ok to leave the precise mechanism providing the feedback of cable deceleration for future work, however I feel that at least some discussion should be provided. For example, cofilin might sever filaments in age-dependent manner and cofilin-decorated filaments might be prone to breaking when buckled. Myosin motors are also known to regulate the extension rate of cables.

10. The authors don't measure cables shorter than 2 microns in Figure 1G, yet such cables should exist from the movies of cable growth versus time. I wonder if their measurement was biased towards the longest cables. In Figure 1D (cdc28-13 induced) there may be several short cables in addition to the long one. Perhaps a plot of total actin cable intensity vs distance would help.

Reviewer #1:

In this manuscript, the authors evaluate models for length determination of actin cables in yeast. The problem they pose is that actin cables must scale with the length of a cell, but given that length is a one dimensional measure, it cannot use "limiting pool" or "limiting factor" mechanisms in order to achieve such scaling. They first show that actin cables do indeed scale with cell length over a variety of cell cycle stages and perturbations. They then propose two models: a boundary sensing model and a balance-point model, the latter of which they show to be more consistent with the data. In line with their model, the rate of cable extension scaled with distance scaled by total cell length.

I found this manuscript to be a really nice example of quantitative cell biology. I think the problem of scaling of various cell components is fundamental and of great interest, and this work has framed an interesting example of the 1D scaling required for a linear component (actin cables). The paper is well written, the data is very solid with strong image analysis, and the claims are well supported.

Reviewer #2:

This is an interesting manuscript examining how the length of actin cables is set in budding yeast cells. The authors show that the average length of actin cables from bud neck to the distal pole of the mother cell is very similar to the length of the cell. The cable length appears to scale linearly with cell length in cells of diverse sizes (haploid, diploid, and cells artificially enlarged by a cell-cycle block), but cable length also scales with cell volume (with a power law – roughly with the cubic root of volume). The authors then propose a couple of possible models that would account for this scaling behaviour and show data that is in agreement with the idea that either assembly or disassembly rates are dependent on cable length, leading to a balance point at length equal that of the cell. The underlying molecular mechanism of this balance-point model is not examined, except for the finding that Smy1, which the authors previously proposed serves to limit cable length in an "antenna model" (Mohapatra et al., PLoS Comput Biol 2015), is not involved.

The correlation between cable length and cell length is very intriguing and suggestive that cell length is the relevant measure used by cells to set the length of their actin cytoskeleton. However, the presented data do not exclude that the relevant measure may be cell volume, with which actin cable length scales with cell volume using a more complex hypoallometric power law. To rigorously test whether cell length rather than cell volume is the relevant parameter, it would be necessary to decouple length from volume and test how actin cables length scales with these measurements.

The authors propose a balance-point model in which cable assembly and disassembly rates are balanced when the cable has the length of the cell due to either rate being cable length-dependent. They contrast this to a boundary model in which cable growth would abruptly stop when reaching the model cell distal pole. The experimental data to discriminate between these model focuses on measured cable extension rates in WT haploids, and normal-sized and enlarged cdc28-13 mutants. These measurements of actin cable extension by fluorescence microscopy are very challenging, and the authors should be commended for attempting it. However, they also raise uncertainty. Looking at the movies and the time-lapses, there are clearly many actin cables that do not behave as a simple birth at the neck followed by extension towards the opposite cell pole. Some of the tracking is also not certain – see for instance 17 to 18 s in movie 2: it looks like a big jump to a structure that was actually already present in the first of these two timepoints. This reduces somewhat the confidence in the conclusion that rate extension deceleration scales with cell length.

In summary, the finding of linear scaling between actin cable length and cell length is interesting, but whether cell length is the relevant parameter for this scaling is not fully established. There is a significant degree of uncertainty associated with the measurements of cable extension. While the current data is in agreement with a model in which cable extension diminishes with cable length, the mechanism of how this may be coupled to cell length is unknown.

Reviewer #3:

In this paper the authors find that the length of yeast actin cables scales with cell length. Cable length is studied using haploid, diploid, and cdc28-13 cells that grow abnormally large. Cable length extension rate is found to decrease with extension distance, at a different rate depending on cell size, supporting a "balance-point" mechanism of length regulation. The ratio between the shortest and longest cables in this work is a factor of order 2 (Figure 1F). This factor is significant to make this work interesting in the context of size regulation (though one can also be somewhat skeptical if a factor of 2 is large enough to unambiguously determine scaling mechanisms, given the multitude of actin regulators in cells that can provide such a change). Overall, this is a nicely written paper. However, I have several concerns as described below.

1) Measurement of cable length and steady state length. The study depends heavily on the ability to measure actin cable length. But how cable length was measured in 3D is not presented with sufficient detail. I think it is essential to show convincing 3D images of cable end identification for the majority of actin cables in a cell. I am suggesting this since cables that reach the cell back may "turn around" and/or form bundles or unbundle through interactions with other cables.

The extension rate of actin cables that grow from the bud neck to the cell back is shown in movies and quantified in the figures. However, it's not clear if these cables eventually *stop* elongating. For example, in Figure 4D the extension rate does not decay to zero at the longest times. That seems to me to be an essential point since I would expect that if one is able to measure the length of most actin cables in the cell, then one should be able to see most of these cables stop extending.

2) I found the contrast between the two models, "boundary-sensing" and "balance-point" was not so sharp: the difference is on whether the extension rate decays more or less abruptly with distance along the cell. I also don't see if either of these models as presented is excluded by the data. The authors convincingly show that the cable extension rate decays with cable length, as would be expected from a balance-point model. However, as mentioned in comment 1, it is not clear where the extension rate decays to zero in graphs such as Figure 1F, 3B, 4D. If cable elongation ends abruptly at the longest time in these graphs, then this would indicate a boundary-sensing mechanism (so overall a combination/intermediate model).

3) I feel that the mechanism by which the actin cable system reaches a steady state needs to be clarified. We see a few cables that start from the bud neck and grow to the whole cell. Is this typical or are these rare cases? If rare, are they still representative? Do cables disappear to allow for new cable growth? Such processes change cable length so they are linked to the central theme of cable length regulation.

4) There is a lack of discussion and experimentation of known regulators of actin assembly and disassembly. Perhaps it's ok to leave the precise mechanism providing the feedback of cable deceleration for future work, however I feel that at least some discussion would need to be provided. For example, cofilin might sever filaments in age-dependent manner and cofilin-decorated filaments might be prone to breaking when buckled. Myosin motors are also known to regulate the extension rate of cables.

https://doi.org/10.7554/eLife.68424.sa1

Author response

Essential Revisions:

1. I'm not as familiar with the details of the models, but it seems that a key assumption is that f(Lcable,Lcell) = f(Lcable/Lcell), which allows for the cells to scale length appropriately. Can the authors speculate on potential mechanisms underlying this length scaling? If there is a gradient, what could form it with such a property?

The manuscript now has been edited to include two potential molecular mechanisms leading to a scale-invariant gradient of actin depolymerizing activity (see end of main text).

In addition, how scale-invariant gradients are potentially established is discussed in more depth in a new theory manuscript on BioRxiv (see: https://doi.org/10.1101/2021.05.18.444733). This theory paper proposes that regulatory proteins diffuse in the cytoplasm and are captured and transported to the cell pole by motors moving along the cell cortex (a form of the ‘antenna’ mechanism – see minor comment #4 below), producing a scale-invariant gradient of these regulatory proteins. The simple idea is that upon release at the pole, proteins diffuse a typical distance λ , until they are captured by the motor proteins at the cell surface; here D is the protein diffusion constant in the cytoplasm and τ is the time until a protein is captured at the surface by a motor protein. In a spherical cell of radius Lcell,τLcell2/D, which leads to λLcell. In other words, the combined action of cytoplasmic diffusion and motor transport at the cell surface, leads to a spatial protein gradient with a decay length to λLcell. Assuming this is a gradient of depolymerizing activity, and further assuming that the cable assembly rate is length-independent, leads to the scaling of the cable extension rate with the assumed scaling property. While no such gradient of cytoskeletal depolymerizing activity has been described in yeast thus far, its existence and role in regulating lengths of flagella in Giardia have been demonstrated (see: 10.7554/eLife.48694).

2. The effect of Smy1 KO on initial elongation rate is modest. I think it would be useful to quantify the effect size and put it in the main text. Also, does the degree of increase quantitatively match the increased cable length observed? If not, can the authors speculate on the source of the discrepancy?

The manuscript has been edited to include the direct comparison of the effect size for the increased cable length and cable extension rates measured in smy1Δ cells. As indicated in the edited text, the effect size of these phenotypes is similar, and thus we conclude that the observed increase in cable length is likely due to the initial increase in cable extension rate. Additionally, this comment inspired us to move the experimental test of our quantitative model (using smy1∆) from the supplement to the main text; these data previously appeared in the supplemental mathematics section, but we realized that they could be easily overlooked in that location. While the Smy1 data do not identify the molecular mechanism controlling cable deceleration, they confirm that increased initial cable extension rate will lead to a proportional increase in the initial deceleration of the cable, a specific prediction of our model in Equation 7. We believe that moving this section to the main text will strengthen our paper and be helpful to readers in light of the reviewer’s comment.

3. To uncouple cell length and cell volume, the authors could use mutants with abnormal cell shape (for instance using more ellipsoid or more rounded cells). Many such mutants have been described over the years in S. cerevisiae, so this should be a technically straightforward approach to take. This would allow to probe whether actin cable length indeed correlates better with cell length than the cubic root of volume (or other shape measurements).

To address this, we have performed an analysis of cable lengths in cells of different shape, as indicated by their different aspect ratios (ratio of cell length to width). This analysis allows us to compare cables in cells of the same length but with different volumes. These data (see new ‘Figure 1 —figure supplement 2’) show that cable length is not affected by differences in cell shape, supporting our conclusion that cable length scales with cell length, rather than other dimensions such as surface area or cell volume.

4. An indication of how cables were selected for tracking and their number amongst how many cells would help better explain the extension rate measurements and increase confidence in the data. Extending this comparison to other mutants with altered cell shape as suggested above would also strengthen the conclusions.

We have revised the methods to provide additional information regarding the inclusion criteria for cables used in live cell imaging analyses. Briefly, cables were only included in our analysis if we could observe their extending tips emerge from the bud neck, and track their tips until they stopped growing. The number of cables analyzed, and the number of independent experiments is indicated in each figure legend. The typical number of cables tracked in an individual cell (by live imaging) is ~1-2 due to technical constraints, such as the relatively short time (~2 minutes) that we can acquire images before the signal begins to bleach, and before there is substantial drift in the z-dimension that prevents accurate cable tip tracking. With future methodological improvements, it may become possible to track larger numbers of cables per cell, and for longer periods of time.

5. Measurement of cable length and steady state length. The study depends heavily on the ability to measure actin cable length. But how cable length was measured in 3D is not presented with sufficient detail. I think it is essential to show convincing 3D images of cable end identification for the majority of actin cables in a cell. I am suggesting this since cables that reach the cell back may "turn around" and/or form bundles or unbundle through interactions with other cables.

We revised the methods to provide additional information about how cable lengths were measured. We clarify that cables were not measured in 3D, but that the 3D stack was used to reliably determine where cables emerged from the bud neck and where their tips were in the mother cell. In addition, we have included annotated maximum intensity projects (see ‘Figure 1 —figure supplement 1A’) that display all of the cables traced in example cells. Additional annotated cell images are available in our imaging dataset uploaded to Zenodo (10.5281/zenodo.4791679).

To address the possibility that cables ‘turn around’, we have computed cable end-to-end distance and tortuosity. The end-to-end distance of a cable is the distance between the distal tip of the cable and its starting point back at the bud neck. Tortuosity is the ratio of cable length (obtained from the trace) to its end-to-end distance, where a perfectly straight cable has a value of one. This analysis shows that the majority of cables do not turn around or make sharp turns, and have a mean cable tortuosity of 1.2-1.3 (see ‘Figure 1 —figure supplement 1’). In our live imaging experiments, we have never observed individual cables interacting and dynamically bundling or unbundling with each other, although our data do not exclude the possibility that this could occur.

6. The extension rate of actin cables that grow from the bud neck to the cell back is shown in movies and quantified in the figures. However, it's not clear if these cables eventually *stop* elongating. For example, in Figure 4D the extension rate does not decay to zero at the longest times. That seems to me to be an essential point since I would expect that if one is able to measure the length of most actin cables in the cell, then one should be able to see most of these cables stop extending.

When we “measure the length of most actin cables in the cell” we are using super-resolution imaging of chemically fixed cells. In contrast, when we perform live imaging of cables we are only able track a subset of the cables in a cell for technical reasons stated earlier (see comment #4; also see comment #8 below). That said, we expect that the reason cable extension rates (by live imaging) do not decay to zero is a consequence of tracking the tips of cables, which can ‘wiggle’ or diffuse laterally while their length does not change. Additionally, all of the cable deceleration profiles we have measured stop at ~0.1um/sec, which is close to the size of a single pixel (0.133um/pixel) in our videos. Thus, we expect that this represents the limit of detection in our assays and should be interpreted as cables no longer extending.

7. I found the contrast between the two models, "boundary-sensing" and "balance-point" was not so sharp: the difference is on whether the extension rate decays more or less abruptly with distance along the cell. I also don't see if either of these models as presented is excluded by the data. The authors convincingly show that the cable extension rate decays with cable length, as would be expected from a balance-point model. However, as mentioned in comment 1, it is not clear where the extension rate decays to zero in graphs such as Figure 1F, 3B, 4D. If cable elongation ends abruptly at the longest time in these graphs, then this would indicate a boundary-sensing mechanism (so overall a combination/intermediate model).

As stated above, we do not think that the final cable extension rate falls to zero (see response to comment #6). Further, cable tips were not observed to abruptly stop. With these clarifications in mind, we believe that the difference between the ‘boundary-sensing’ and ‘balance-point’ models is fairly sharp. In one model, cables exhibit a constant rate of extension until they physically encounter the cell boundary and then they halt. In the other model, cable extension rate is constantly changing, starting out fast as the cable emerges from the bud neck and then slowing as a function of cell length – until the cable length matches the length of the cell (see ‘Figure 2C and 2D’).

8. I feel that the mechanism by which the actin cable system reaches a steady state needs to be clarified. We see a few cables that start from the bud neck and grow to the whole cell. Is this typical or are these rare cases? If rare, are they still representative?

As mentioned above, due to technical limitations we are only able to track a subset of the cables in a cell by live imaging (see response to comment #6). However, given our analysis of cables in fixed cells, where the majority of cables grow to reach the back of the cell, we are fairly confident that our live tracking of cables extending to reach the rear of the cell are representative of typical cable behavior.

Do cables disappear to allow for new cable growth? Such processes change cable length so they are linked to the central theme of cable length regulation.

How cables disappear to allow for new cable growth is an important question that we hope to address in the future. Little is known about how cables are disassembled in vivo once they reach the back of the cell. To date, these questions have been difficult to approach experimentally, in part due to the same technical limitations mentioned above (e.g., our imaging is limited to ~2 minutes before photobleaching and drift prevent accurate image acquisition). We anticipate that improvements in fluorescent tags (to mark cables) and better control of the microscope stage will allow for longer analyses in the future, and make it possible to begin answering these types of questions.

9. There is a lack of discussion and experimentation of known regulators of actin assembly and disassembly. Perhaps it's ok to leave the precise mechanism providing the feedback of cable deceleration for future work, however I feel that at least some discussion should be provided. For example, cofilin might sever filaments in age-dependent manner and cofilin-decorated filaments might be prone to breaking when buckled. Myosin motors are also known to regulate the extension rate of cables.

We have revised our Discussion to include several possible molecular mechanisms controlling cable deceleration (see response to comment #1). This includes the possibility of an activity gradient of cofilin and/or other actin disassembly factors, where their activity is higher at the rear of the cell. We also acknowledge that actin filament aging could play a role in the observed scaling relationship (cable length with cell length). However, this would require filament aging (in cables) to be cell length dependent, given that initial cable extension rates are similar in cells of different length. As such, cells would need to have a mechanism for slowing π release (from the F-actin in cables) in longer cells, or alternatively, accelerating π release from cables in shorter cells.

10. The authors don't measure cables shorter than 2 microns in Figure 1G, yet such cables should exist from the movies of cable growth versus time. I wonder if their measurement was biased towards the longest cables. In Figure 1D (cdc28-13 induced) there may be several short cables in addition to the long one. Perhaps a plot of total actin cable intensity vs distance would help.

We fully expect that there are cables smaller than 2 µm, but they are also growing much faster than longer cables, and are therefore less frequently observed. Additionally, as touched upon above (see response to comment #8) we don’t know what fraction of all the cables in a cell are undergoing de novo assembly at any given time.

https://doi.org/10.7554/eLife.68424.sa2

Article and author information

Author details

  1. Shane G McInally

    1. Department of Biology, Brandeis University, Waltham, United States
    2. Department of Physics, Brandeis University, Waltham, United States
    Contribution
    Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6145-4581
  2. Jane Kondev

    Department of Physics, Brandeis University, Waltham, United States
    Contribution
    Conceptualization, Supervision, Funding acquisition, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    kondev@brandeis.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7522-7144
  3. Bruce L Goode

    Department of Biology, Brandeis University, Waltham, United States
    Contribution
    Conceptualization, Supervision, Funding acquisition, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    goode@brandeis.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6443-5893

Funding

National Institutes of Health (R35 GM134895)

  • Bruce L Goode

National Science Foundation (2010766)

  • Shane G McInally

National Science Foundation (DMR-1610737)

  • Jane Kondev

National Science Foundation (2011486)

  • Jane Kondev
  • Bruce L Goode

Simons Foundation

  • Jane Kondev

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

Acknowledgements

We thank Ariel Amir, Lishibanya Mohapatra, James Moseley, Rob Phillips, Aldric Rosario, and Alison Wirshing for thoughtful discussions on cable length control and comments on the manuscript. We are also grateful to Brian Graziano for sharing the cdc28-13ts strain. Funding: This material is based upon work supported by the the NSF Postdoctoral Research Fellowships in Biology Program under Grant No. 2010766 to SGM, by grants from NSF (DMR-1610737) and the Simons Foundation (http://www.simonsfoundation.org/) to JK, a grant from the NIH to BLG (R35 GM134895), and the Brandeis NSF MRSEC, Bioinspired Soft Materials, DMR-2011486.

Senior Editor

  1. Jonathan A Cooper, Fred Hutchinson Cancer Research Center, United States

Reviewing Editor

  1. Mohan K Balasubramanian, University of Warwick, United Kingdom

Reviewer

  1. Arjun Raj, University of Pennsylvania, United States

Publication history

  1. Received: March 16, 2021
  2. Accepted: June 10, 2021
  3. Accepted Manuscript published: June 11, 2021 (version 1)
  4. Version of Record published: June 25, 2021 (version 2)

Copyright

© 2021, McInally 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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    Jesse R Holt et al.
    Research Article

    Keratinocytes, the predominant cell type of the epidermis, migrate to reinstate the epithelial barrier during wound healing. Mechanical cues are known to regulate keratinocyte re-epithelialization and wound healing however, the underlying molecular transducers and biophysical mechanisms remain elusive. Here, we show through molecular, cellular and organismal studies that the mechanically-activated ion channel PIEZO1 regulates keratinocyte migration and wound healing. Epidermal-specific Piezo1 knockout mice exhibited faster wound closure while gain-of-function mice displayed slower wound closure compared to littermate controls. By imaging the spatiotemporal localization dynamics of endogenous PIEZO1 channels we find that channel enrichment at some regions of the wound edge induces a localized cellular retraction that slows keratinocyte collective migration. In migrating single keratinocytes, PIEZO1 is enriched at the rear of the cell, where maximal retraction occurs, and we find that chemical activation of PIEZO1 enhances retraction during single as well as collective migration. Our findings uncover novel molecular mechanisms underlying single and collective keratinocyte migration that may suggest a potential pharmacological target for wound treatment. More broadly, we show that nanoscale spatiotemporal dynamics of Piezo1 channels can control tissue-scale events, a finding with implications beyond wound healing to processes as diverse as development, homeostasis, disease and repair.