Information transfer in mammalian glycanbased communication
Abstract
Glycanbinding proteins, socalled lectins, are exposed on mammalian cell surfaces and decipher the information encoded within glycans translating it into biochemical signal transduction pathways in the cell. These glycanlectin communication pathways are complex and difficult to analyze. However, quantitative data with singlecell resolution provide means to disentangle the associated signaling cascades. We chose Ctype lectin receptors (CTLs) expressed on immune cells as a model system to study their capacity to transmit information encoded in glycans of incoming particles. In particular, we used nuclear factor kappaBreporter cell lines expressing DCspecific ICAM3–grabbing nonintegrin (DCSIGN), macrophage Ctype lectin (MCL), dectin1, dectin2, and macrophageinducible Ctype lectin (MINCLE), as well as TNFαR and TLR1&2 in monocytic cell lines and compared their transmission of glycanencoded information. All receptors transmit information with similar signaling capacity, except dectin2. This lectin was identified to be less efficient in information transmission compared to the other CTLs, and even when the sensitivity of the dectin2 pathway was enhanced by overexpression of its coreceptor FcRγ, its transmitted information was not. Next, we expanded our investigation toward the integration of multiple signal transduction pathways including synergistic lectins, which is crucial during pathogen recognition. We show how the signaling capacity of lectin receptors using a similar signal transduction pathway (dectin1 and dectin2) is being integrated by compromising between the lectins. In contrast, coexpression of MCL synergistically enhanced the dectin2 signaling capacity, particularly at lowglycan stimulant concentration. By using dectin2 and other lectins as examples, we demonstrate how signaling capacity of dectin2 is modulated in the presence of other lectins, and therefore, the findings provide insight into how immune cells translate glycan information using multivalent interactions.
Editor's evaluation
This manuscript lays out the framework for addressing an important challenge in our understanding of cellular signal transduction: how complex extracellular inputs can be detected and processed using multiple receptors. This problem is addressed in the context of glycan receptors lectins, mediating very common but still not completely understood cellcell interactions. Using information capacity analysis, the study addresses the importance of glycan input measurement by multiple receptors on the immune cells, showing how the signal detection can benefit from receptor crosstalk.
https://doi.org/10.7554/eLife.69415.sa0Introduction
Glycans are present in all living cells and play a key role in many essential biological processes including development, differentiation, and immunity. Being surface exposed, glycans often encode for information in cellular communication such as self/nonselfdiscrimination, cellular identity, and homing as well as apoptosis markers (Bode et al., 2019; Maverakis et al., 2015; Williams, 2017). Other than linear biopolymers, such as proteins and nucleic acids, glycans are branched structures, where subtle changes in the glycosidic bonds between each monomer can carry essential pieces of information. Adding to this complexity, glycans are products of large cellular machinery and are therefore not directly encoded by the genome (Cummings, 2009). Besides their composition, the recognition of glycans by their receptors is complicated, particularly due to the lack of specificity. Glycans are recognized by lectins, yet no glycan is recognized by a single receptor, and no individual lectin is highly specific for only one glycan. Additionally, affinities are low, and interactions often depend on the multivalency of both the receptor and the ligand. Overall, since alterations of the glycocalyx do not function as a deterministic on/off switch but rather a progressive tuning of the cellular response, glycan lectin communication should be considered as a stochastically behaving system, rather than a deterministic one (Dennis, 2015).
Many lectin receptors serve as triggers for multiple immunological signaling pathways, often funneling down to NFκB (nuclear factor kappaB) as a transcription factor. In this work, we focus on Ctype lectin receptors (CTLs). MINCLE (macrophageinducible Ctype lectin), for example, is a CTL involved in the recognition of pathogens as well as selfdamage (Miyake et al., 2015; Williams, 2017). MINCLE and its close relative dectin2 (dendritic cellassociated Ctype lectin2) signal via the FcRγ gamma chain (Miyake et al., 2015; Ostrop et al., 2015; Sato et al., 2006), leading to CARD9BCL10Malt1 activation (Figure 1A). This in turn results in the activation of NFκB, eventually triggering cytokine release. Importantly, these two receptors share the same signal transduction pathway, while having different functions (Thompson et al., 2021). Therefore, both dectin2 and MINCLE can be compared of whether these related proteins differently transmit glycan information from the receptor level. In contrast, dectin1 and dectin2 have different signal transduction pathways but are both involved in the detection of βglucans and mannan, respectively (Figure 1A).
Upon fungal infection, combination of these and other cell surface receptors expressed by antigen presenting cells then leads to a defined immune reaction via signal integration processes (Snarr et al., 2017). Such signal integration can result in synergism between the receptors triggering an effect greater than their individual contributions (Ostrop and Lang, 2017). For example, MCL (macrophage Ctype lectin), another CTL present on cells of the innate immune system, is known to synergistically work with dectin2 (Ostrop et al., 2015; Zhu et al., 2013). Additionally, to this type of synergism, other members of the CTL family, e.g., DCspecific ICAM3–grabbing nonintegrin (DCSIGN) and Langerin, rather modulate a response instead of initiating it by themselves (Geijtenbeek and Gringhuis, 2016; Osorio and Reis e Sousa, 2011). Therefore, it is important to quantitatively account for the resulting signaling to describe the complexity of how these cell surface receptors can modulate each other to translate a glycanencoded information into a biological response.
Accounting for the stochastic behavior of cellular signaling, information theory provides robust and quantitative tools to analyze complex communication channels. A fundamental metric of information theory is entropy, which determines the amount of disorder or uncertainty of variables. In this respect, cellular signaling pathways having high variability of the initiating input signals (e.g. stimulants) and the corresponding highly variable output response (i.e. cellular signaling) can be characterized as a high entropy. Importantly, input and output can have mutual dependence, and therefore, knowing the input distribution can partly provide the information of output distribution. If noise is present in the communication channel, input and output have reduced mutual dependence. This mutual dependence between input and output is called mutual information. Mutual information is, therefore, a function of input distribution, and the upper bound of mutual information is called channel capacity (Appendix 2; Cover and Thomas, 2012).
In this report, a communication channel describes signal transduction pathway of CTL, which ultimately lead to NFκB translocation and finally GFP expression in the reporter model (Figure 1A). To quantify the signaling information of the communication channels, we used channel capacity. Importantly, the channel capacity is not merely describing the resulting maximum intensity of the reporter cells. The channel capacity takes cellular variation and activation across a whole range of incoming stimulus of singlecell resolved data into account and quantifies all of that data into a single number.
Herein, we studied dectin2, dectin1, MINCLE, DCSIGN, MCL, TNFαR (TNF alpha receptor), and TLR1&2 in NFκB reporter cells using singlecell resolved flow cytometry (Figure 1A, see also Appendix 2). To accurately quantify the information transmission in the receptors’ signaling pathways in response to exogenous glycans, we use the channel capacity as a metric (Figure 1B). By employing channel capacity measurements, we found dectin2 channel has relatively low signaling capacity, which in turn is synergistically increased in the presence of coexpressed MCL receptor. Furthermore, the channel capacity of dectin1 and dectin2 channel for the same glycan ligand was compromised when both receptors are expressed by the cell while increasing the binding sensitivity (EC_{50}) to the ligand. Overall, our findings and approach provide a quantitative description of glycan lectin communication and signal integration of CTLs and other receptors, which may lead to a better understanding of key phenomena such as pathogen recognition and autoimmunity.
Results
Quantifying signal transduction in glycanbased communication
We employed a singlecell resolved reporter system to monitor CTL activity by GFP expression under control of the transcription factor NFκB in human monocytic U937 cells (Figure 1A). Dectin2 was expressed in these reporter cells, and stimulation was conducted using various ligands (Figure 1C–E). FurFurMan, an extract of Malassezia furfur, as well as the polysaccharide mannan and invertase, both from Saccharomyces cerevisiae, initiated dectin2 signaling. In contrast, owing to the lack of multivalency, mannose itself could not initiate signaling but was able to inhibit dectin2 function (Figure 1C and D, and also Appendix 1—figure 1 A; Ishikawa et al., 2013). In parallel, the invertase treated with αmannosidase does not activate the NFκB signaling, indicating the glycosylationdependent dectin2 activity (Appendix 1—figure 1 B). The activation of human dectin2 receptor is in line with previous reports on its murine homolog, which is triggered by Manα1–2 Man moieties presented on scaffolds like proteins, glycans, or polystyrene beads (Ishikawa et al., 2013; Yonekawa et al., 2014; Zhou et al., 2018). Analogously, introduction of dectin1 into the reporter cells enabled detection of NFκBbased GFP expression after stimulation. However, while FurFurMan could also stimulate dectin1 cells, this was not inhibited by the addition of mannose, which is expected for this βglucan receptor (Figure 1D).
Next, we studied the doseresponse behavior of dectin2 reporter cells stimulated with FurFurMan over a wide range of input concentrations (Figure 1E). The cellular population revealed an overlap between the unstimulated and the maximally stimulated population, demonstrating the absence of a clear twostate behavior on a population level (Figure 1E, Appendix 1—figure 1 C). To ensure that change in the reporter level is not affected by protein expression rate, we confirmed that GFP expression required at least 16 hr of stimulation to reach its maximum in steadystate protein expression, while short stimulation with for 2–6 hr does not lead the maximum level of GFP production (Appendix 1—figure 1 D). We also ruled out any influence of the selection process for the cellular clones, by sorting dectin2 expressing cells according to their GFP expression level. When restimulated, both populations again showed the same broad GFP expression, confirming the wide range of the response to be independent of genetic differences between individual cells (Appendix 1—figure 1 E). Taken together, observing noisy dectin2 signaling on a singlecell level in relevant model cell lines reveals a broad population distribution when stimulated.
Dectin2 transmits less information than other receptors
To investigate whether other receptors with similar signaling pathways follow the same principle, we analyzed the dose response of dectin1, MINCLE, and the nonCTLs TNFαR and TLR1 and 2 (Bode et al., 2019; Holbrook et al., 2019; Ishikawa et al., 2009; Ozinsky et al., 2000). To quantify the underlying signal transmission in a cellular population, the channel capacity was used as a metric. Note that we choose the stimulation time, the period of incubation time of the cell with the input ligands, as the time point when GFP response and channel capacity reach the maximum and steadystate value (Appendix 1—figure 2 A and B). And therefore, the stimulation was 13 and 16 hr for TNFα and the rest of the ligands, respectively. Previous work on TNFα signaling found the TNFα channel to have a channel capacity of about 1 bit in particular 1.64 bits when a reporter cell system was used (Cheong et al., 2011). In addition, this channel capacity can be further increased if one can measure the temporal evolution of output dynamics instead of static output dataset (Selimkhanov et al., 2014). Such channel capacity suggests that a cellular population can use a receptor to distinguish between two states: on/off or presence/absence of a stimulant. For U937 cells, we found the TNFαR transmits 1.34 bits of channel capacity for TNFα stimulant (Figure 2A and B), which was not influenced by the introduction of additional lectins (i.e. MINCLE, dectin2, and DCSIGN, see Appendix 1—figure 2 C). In the case of dectin1 expressing U937 cells, the channel capacities were 1.20 and 1.09 bits for depleted zymosan (DZ) and FurFurMan input, respectively, while both MINCLE and TLR1&2 had a channel capacity of 0.98 and 0.99 bits, respectively. Since these receptors signal via NFκB, these differences can be explained by receptor expression levels and downstream pathways. In contrast, dectin2 stimulation resulted in a channel capacity of 0.70 bits using FurFurMan as a ligand. Stimulation using heat inactivated invertase or mannan had 0.80 and 0.49 bits, respectively (Figure 2B). Also, in THP1 cells, a similar trend of lower GFP expression upon stimulation is observed, further supporting the notion that dectin2 has a lower signal transmission capacity compared to the other receptors such as TNFαR (Appendix 1—figure 2 DF).
The most striking difference was found between MINCLE and dectin2, as both lectins use the same signaling pathway via FcRγ (Ishikawa et al., 2013), suggesting that the substantial differences between the channel capacities rely on very early ligand recognition events. We hypothesized overexpression of the signaling protein FcRγ might increase the information transmitted via dectin2. The overexpression of FcRγ resulted in at least twofold increase of NFκB controlled GFP expression (Figure 2C). Overexpression of both dectin2 and FcRγ yielded a highbasal NFκB activation of the cells while the sensitivity for its ligand (EC_{50}) increased about 50fold. While the maximal GFP signal of dectin2 (MFI, mean fluorescence intensity) was increased in the presence of FcRγ overexpression, the channel capacity however decreased simultaneously (0.41 bits; Figure 2 C–E). Since competition with mannose reduced this effect, we speculate that decreased channel capacity might originate from selfrecognition of dectin2 of ligands being present either on the same cell or those in close proximity during the culture conditions (Figure 2E). From this, we concluded the channel capacity of a glycanbased communication channel is not necessarily coupled to its sensitivity. Also, the ability of a communication channel to transmit information is not well described by its maximal signal alone (i.e. MFI), but rather by the channel capacity. Next, we quantified the number of receptors and excluded that the difference in MINCLE and dectin2 channel capacities is due to differences in receptor expression levels (Appendix 1—figure 2 G). Taken together, dectin2 has relatively less channel capacity, and while its sensitivity (EC_{50}) can be modulated with FcRγ, the transmitted information does not increase. Additionally, the number of receptors has little influence on the channel capacity or amplitude.
Signal integration compromises between dectin1 and dectin2 receptors when both are engaged
To expand our insight from isolated cell surface receptors to the interplay between multiple lectins, we prepared reporter cells expressing dectin2 and dectin1 simultaneously. FurFurMan served as a stimulant since it interacts with both dectin1 and dectin2. First of all, we found that the level of receptor expression did not change upon expression of an additional lectin (Figure 3A). Dectin1 expressing cells gave a higher maximal signal (i.e. maximal MFI) and channel capacity than dectin2 expressing cells; however, the latter channel showed higher sensitivity (EC_{50}) to FurFurMan. We found that the double positive cells did compromise between the two receptors, displaying the values corresponding to the intermediate values of the EC_{50} and channel capacity of dectin1 and dectin2 (Figure 3B and C). Additionally, mannose could be used to interfere with dectin2 signaling, thus U937 dectin1 dectin2 expressing cells showed the same doseresponse curve as dectin1 expressing cells (Figure 3D). When DZ, a dectin1 specific stimulants, was used, dectin2 expression did not significantly influence the response of the double positive cells. Hence, dectin2 specific signaling was not influenced by dectin1 expression (Appendix 1—figure 3 AC). Moreover, inhibition of dectin2 signaling initiated by FurFurMan by the addition of 25 mM mannose resulted a response that was not a compromise. Taken together, we see that the simultaneous stimulation of dectin1 and dectin2 resulted in a compromise between their channels, which demonstrates how these two channels integrate glycan signal into response.
Macrophage Ctype lectin (MCL) increases the channel capacity of dectin2
To further expand our insights into signal transmission through multiple lectins, we wondered whether coexpression of other lectins would synergistically increase the channel capacity of dectin2 signaling. For this, we included DCSIGN and MCL (Figure 4A). Although DCSIGN does not elicit NFκB signaling by itself in U937 cells, it is known to recognize highmannose structures present on invertase (Gringhuis et al., 2009). As expected, U937 dectin2 DCSIGN cells experience significantly increased ligand binding (Appendix 1—figure 4 A and B). We then speculated that this would either (a) promote the ligand recognition by preconcentration of the stimulants on the cell surface or (b) sequester the input signal from dectin2, reducing the cellular response. In fact, DCSIGNmediated ligand binding did not alter the dectin2 channel capacity for FurFurMan or invertase stimulation or did DCSIGN expression itself modulate TLR4 signaling (Figure 4B, Appendix 1—figure 4 C). However, the sensitivity, as assessed by EC_{50}, increased for dectin2 DCSIGN expressing cells (Figure 4A). The increased sensitivity due to DCSIGN coexpression might increase the channel capacity if the allowed dose range spans lowconcentration region. Therefore, we calculated the channel capacity by increasing the maximum input concentration. However, this was not the case (Figure 4C). Contrary to DCSIGN, overexpression of MCL significantly increased the channel capacity of dectin2 expressing cells, particularly when limiting our dataset to lowmaximum invertase concentrations (Figure 4B and D, Appendix 1—figure 4 D and E). This indicates that MCL enhances the fidelity of invertase information transmission of dectin2 channel, providing quantitative measurement of synergistic effect of MCL (Ostrop et al., 2015; Zhu et al., 2013).
We then wondered whether the difference in channel capacity between dectin2 and TNFαR could simply be a result of affinity. Since TNFαR has a nanomolar affinity for its ligand (Grell et al., 1998), we applied an antidectin2 antibody to stimulate dectin2 cells. Even under these conditions, we did not monitor an increase in channel capacity (Appendix 1—figure 4 F). Therefore, we found that MCL but not DCSIGN significantly increase the dectin2 channel capacity, while both MCL and DCSIGN enhance cellular binding of the stimulants and the resulting cellular sensitivity to invertase.
Dectin2 channel has a low signaltonoise ratio
The relatively low channel capacity of dectin2 could be a result of its limited maximum GFP expression even at highstimulant concentrations compared to the other channels (Figure 2B). For this, we define the signal power as the variation of the mean GFP expression under individual stimulant dose (Figure 5A). In addition, the level of background noise (i.e. noise power) of the channel can be defined as the average of the variance of GFP expression at a given stimulant dose. These definitions allow to decompose signal and noise power (Appendix 3) and analyze them separately to infer how those two parameters shape the channel capacity.
TNFaR, MINCLE, and dectin1 have a similar level of noise power. Amongst the three receptors, TNFaR shows the highest signal power and consequently the highest signaltonoise ratio (Figure 5B and C). All three channels have a signaltonoise ratio higher than one. For dectin2, both signal and noise power are low compared to the other receptors; however, the noise power exceeds the signal power, resulting in a significantly lower signaltonoise ratio. Since the signal power is independent of the noise power, our data indicate that the lower variation of the mean GFP expression (i.e. signal power) of dectin2 dictates the reduced channel capacity compared to the other receptors. A similar conclusion cannot be drawn for the noise power since it is inherently coupled to the signal power (see Appendix 3).
We further employed the decomposition method to dectin2 signaling in the presence of either dectin1 coexpression or FcRγ overexpression (Appendix 1—figure 5). Analogous to the compromised channel capacity when dectin1 and dectin2 were coexpressed (Figure 3C), the analysis revealed that both the signal and the noise power were compromised as well (Appendix 1—figure 5 A and B). In case of FcRγ overexpression, dectin2 signaling after invertase stimulation is characterized by increased noise power, resulting in decreased signaltonoise ratio (Appendix 1—figure 5 CE). Therefore, despite the highGFP expression at highstimulant concentrations (Figure 2C), the overexpression of FcRγ, as additional signaling hubs, involved in the dectin2/NFκB cascade did not increase the signal power but instead elevated the noise power, leading to reduced channel capacity. Taken together, the relatively lowchannel capacity of dectin2 is directly related to its lowsignal power, and the overexpression of FcRγ further decreases the channel capacity through increasing the noise power.
Discussion
We set out to better understand how glycanencoded information is read in cellular communication. We established a glycanresponsive in vitro model and exploited the channel capacity as a quantitative metric. For the receptors other than dectin2, the channel capacities were around 1 bit or higher, similar values that have been reported for other systems previously (Suderman et al., 2017). In particular, TNFα receptor has a channel capacity of 1.64±0.36 bits, which was found in a comparable reporter cell system (Cheong et al., 2011). Interestingly, the number of receptors expressed on the cell surface did not determine the channel capacity of a signaling channel (Appendix 1—figure 2 G). Our results exemplify that lectin signaling pathways and especially the dectin2 pathway should not be viewed as a deterministic on/offswitch, but rather as difference in the probability of cells to be active at a certain dose. This is in line with previous reports strengthening a quantitative view of cellular signaling and taking the cellular microheterogeneity into account (Levchenko and Nemenman, 2014; Zhang et al., 2017). We found that the mannose binding CTL dectin2 to transmits less information compared to other receptors of the same family (Figure 2B).
To understand how these insights could be expanded on the interplay between multiple receptors like the CTLs occur on innate immune cells rather than isolated lectins, we employed combinations of CTLs on our model cells. Dectin2 and dectin1 recognize different epitopes on FurFurMan, and we found that the effects were not additive, but a compromise between the two receptors, showing intermediate sensitivity (EC_{50}) and channel capacity between dectin2 and dectin1 (Figure 3A and B). This effect implies at high concentrations of FurFurMan the dectin2 channel is actively inhibiting dectin1 signaling, resulting in a lower cellular NFκB activation. It is well known that lectins are able to modulate the signals of other receptors (Geijtenbeek and Gringhuis, 2009; Gringhuis et al., 2009; Miyake et al., 2015). Yet this compromise is an exciting discovery since to the best of our knowledge previous studies have not quantified lectin signal integration. Hence, it is likely that during a fungal infection, exposing multiple epitopes of pathogens are recognized by the precise arsenal of immune receptors, and their underlying signaling pathways are integrating the information contained within the epitopes. This in turn leads to a compromise of all activated receptors and results in a specifically tailored biochemical response of the given immune cell (Ostrop and Lang, 2017).
Dectin2 itself we found to have relatively less channel capacity when compared to the closely related MINCLE that uses the same pathway with more signal power (Figure 2A and B). It is therefore likely the receptor itself determines very early on the information flow into the cell. This could be a result of MINCLE being stimulated with crystalline insoluble ligands which could result in larger signaling clusters at the cellular surface. Alternatively, dectin2 signaling could be influenced by mannose structures that are present on the cellular surface by giving rise to background signaling and selection for reducing signaling power in an in vitro setting of highcellular density. Additionally, since dectin2 binds highmannose structures of eukaryotic origin (McGreal et al., 2006), a too sensitive reaction might lead to permanent selfrecognition of human Man9 structures for example and hence potential autoimmune reactions. This hypothesis is supported by the dectin2dependent highbasal activity of FcRγ overexpressing dectin2 cells, which in turn is responsible for a lower channel capacity in dectin2 FcRγ cells (Figure 2C–E). Hence, dectin2 could have evolved to use the CARD9BCL10Malt1 pathway to NFκB less effective. Along the same lines, recent reports show that CTLs are in general becoming more important in autoimmunity, dectin2 in particular is known to be responsible for the development of allergic reactions (Dambuza and Brown, 2015; Parsons et al., 2014).
We first thought a combination of multiple lectins might synergistically enhance signaling capacity of dectin2. But while DCSIGN greatly enhanced ligand binding to the cells, meaning the increased sensitivity (EC_{50}), it did not significantly increase the channel capacity (Figure 4A–C, Appendix 1—figure 4A and B). In contrast to DCSIGN, the closely related MCL to dectin2 has a significant synergetic effect on dectin2 channel capacity at particularly lowstimulant concentrations, potentially making double positive cells more discriminative, at earlier timepoints of infection compared to dectin2 expressing cells, substantiating the importance of signal integration to understand an cellular innate immune response (Ostrop and Lang, 2017).
Finally, it is important to take into consideration that our conclusions came from model cell lines, which were used as a surrogate for celltypespecific lectin expression patterns of primary immune cells. Human monocytes and dectin2 positive U937 cells have comparable receptor densities and respond similar to stimulation with zymosan particles (Appendix 1—figure 6A and B). Importantly, since our channel capacity calculations are applicable regardless of the nature of signal and medium, one could use it to quantify cellular responses in similar assays in the future. Work is ongoing to address central questions of cellular communication based on glycan lectin interactions.
Materials and methods
All reagents were bought from Sigma Aldrich, if not stated otherwise.
Reporter cell generation and reporter cell assay
Request a detailed protocolU937 cells were transduced with an NFκBGFP Cignal lentivirus (Qiagen) according to the manufacturer’s instructions to generate NFκB reporter cells. 0.5 mL of 2e5 cells were mixed with the lentivirus at an MOI (multiplicity of infection) of 15 and spin transduced for 1.5 hr at 33°C and 900 g. After 48 hr of rest, cells were selected with puromycin (gibco) for three passages. Eight cultures from a single cell each were subsequently made and evaluated according to their GFP expression, clone #5 only monoclonal cells were used for all experiments of this paper.
Reporter cell assay
Request a detailed protocolU937 reporter cells were used in its log phase, and 100 µL were plated in a 96well plate with 3e4 cells per well. Cells were challenged in complete media (RPMI with 10% FBS (fetal bovine serum), 1% Glutamax, 1% Pen/Strep, and all by gibco) with TNFα and various other ligands and at various concentrations for 13 hr and 16 hr, respectively. After incubation, cells were resuspended once in DPBS (Dulbecco's phosphatebuffered saline) and the expressed GFPs fluorescent intensity was measured by flow cytometry (Attune Nxt, Thermo Fisher).
Cell culturing and passage
Request a detailed protocolU937 cells were kept between 1e5 and 1.5e6 cells/mL in complete media with passage 2–4 times a week. 293 F cells were adherently cultured in DMEM (Dulbecco's modified Eagle’s medium) with 10% FBS, 1% Glutamax, 1% Pen/Strep (Gibco), and split 2–3 times per week. All cells were tested for mycoplasma contamination using Minerva biolabs VenorGeM Classic.
Antibody staining and quantitation
Request a detailed protocolFor the surface staining, cells were incubated in with the respective antibodies and isotype controls for 30 min at 4°C in DPBS, then washed once in DPBS +0.5% BSA and measured via flow cytometry. For perforated stains cells were first fixed in 4% PFA (Carl Roth) at 4°C for 20 min, then perforated in perforation solution (DPBS +0.5% BSA+0.1% Saponine) for 20 min at 4°C. The cells were then resuspended in perforation solution containing the respective antibodies, incubated for 20 min at 4°C and measured via flow cytometry after being washed once. To quantify the fluorescent intensities, we used the BD PE quantitation kit, which allowed us to calibrate FI to the number of PE molecules present in a sample. A list of all used antibodies can be found in the Supplementary file 1.
Generation of lectin overexpressing cells
Request a detailed protocolcDNA of MINCLE, dectin2, MCL, FcRγ, dectin1, and DCSIGN were cloned into vector BICPGKZeoT2amAmetrine:EF1a as previously reported (Wamhoff et al., 2019). This bicistronic vector expresses mAmetrine under the PGK promoter. To combine multiple GOI (gene of interest), we also used the lentiviral vector EF1aHygro/Neo a gift from Tobias Meyer (Addgene plasmid # 85134). Briefly, 293F cells were transfected with vectors coding for the lentivirus and GOI. Lentivirions were generated for 72 hr, and the supernatant was frozen to kill any remaining 293 F cells. This supernatant was used to transduce the GOI into U937 cells via spin infection at 900 g and 33°C in the presence of 0.8 µg/mL polybrene (van de Weijer et al., 2014). After 48 hr of rest, the U937 cells were selected with appropriate antibiotics (Zeocin 200 µg/mL, G418 500 µg/mL, or Hygromycin B 200 µg/mL; Thermo Fisher, Carl Roth, Thermo Fisher, respectively). A list of used primers can be found in the Supplementary file 2.
Labeling of proteins
Request a detailed protocolInvertase (5 mg in 1 mL) was heat inactivated for 40 min at 80°C and mixed with 3×molar excess of Atto647NNHS dye (AttoTech) according to the manufacturer’s protocol. The labeled protein was purified using Sephadex G25 column, and aliquots were frozen at –80°C. Since we found the labeled invertase to contain less impurities, we used Atto647 labeled invertase for all experiments shown in this study. Human TNFα (Peprotech) was labeled with the same procedure, yet without heat inactivation. The degree of labeling was determined to be around 1 as determined with a labeled protein concentration measurement of a NanoPhotometer NP80 (Implen).
Channel capacity calculation
Request a detailed protocolCalculations of channel capacity were based on Cheong et al., 2011 and Suderman et al., 2017. See Appendix 2 on channel capacity calculation for details.
Data representation, software, and statistical analysis
Request a detailed protocolData is shown as mean ± SD. Statistical analysis of data was performed by unpaired twotailed ttest, with significant different defined as (p<0.05). EC_{50} values were calculated in graph pad prism version 8.4.2 using four parametric dose vs. response function. When necessary statistical differences between EC_{50} values were compared using an extrasumofsquares F test. Detail of statistical tests and EC_{50} determinations can be found in the SI raw data file. FlowJo v.10 was used for analysis and export of flow cytometry data.
Data availability
Request a detailed protocolAll data is available at Dryad. The Jupyter notebook including the channel capacity calculation and noise analysis is available at: https://github.com/imaginationdykim/2022.CC, (copy archived at Fuchsberger, 2023).
Appendix 1
Appendix 2
Estimation of channel capacity between input doses and reporter GFP
1.1 Data structure
Cells can sense the environment and respond to it. In this work, we quantify the cellular capability to sense carbohydrate information through information theory. The carbohydrate information is given as carbohydrate ligand concentrations in the cell media, and the output is the GFP expression level triggered by NFκB translocation of individual cells (Appendix 2—figure 1). The inputs (i.e. concentration of ligand) are discrete values covering almost all variability of output distribution. We used 9 or 10 levels of carbohydrate ligand concentrations including the absence of ligand and measured around 100,000 cells for whole doses using flow cytometry. The measured GFP expression levels are integer values ranging from around 0 to 50,000.
1.2 Mutual information estimation
To estimate the mutual information between carbohydrate inputs and GFP expressions from NFκB translocation, the input and output array data described in Appendix 2—figure 1 is projected into twodimensional probability space divided by grids as shown in Appendix 2—figure 2A. The projection allows estimation of joint probability distribution of finite data points. On the other hand, finite sample size together with arbitrariness of binning interval produces over or underestimation of joint probability distribution, requiring additional statistical analysis to calculate unbiased channel capacity. The joint probability distribution of individual grid elements is the number of data points in the grid divided by the total number of data points. The joint probability distribution and marginalized input and output distributions is shown in Appendix 2—figure 2 B. The probability distribution for input and output is the marginalized joint probability distribution by output and input index, respectively, as follows:
and
where $i$ and $j$ are the input and output index, respectively, and $P}_{xy$ is the joint probability of input and output. The mutual information of the given input and output distribution is 0.53 bits, calculated from mutual information definition: $MI\left(input;output\right)=\text{}H\left(input\right)+H\left(output\right)\text{}H\left(input,\text{}output\right)$. Note that $H\left(input\right)$ , $H\left(output\right)$, and $H\left(input,\text{}output\right)$ are input entropy, input entropy, and joint entropy, respectively, defined as follows:
and
1.3 Channel capacity estimation
Suppose there is a joint probability distribution having four inputs and two outputs as described in Appendix 2—figure 2C above. Since the marginal probability distributions are equally distributed for input and output, the input entropy and output entropy yield 2 and 1 bits, respectively. The mutual information is therefore 0.5 bits by subtracting joint entropy from the sum of input and output entropy.
Consider that how much of information can be reliably transmitted from this channel? The input 0 and 3 certainly give output 0 and 1, respectively. On the other hand, the input 1 and 2 give uncertain outputs, distributed equally on all output range. Therefore, by completely suppressing the input channels 1 and 2, one can achieve the maximum information that this channel reliable transmits (i.e. channel capacity). The array multiplication (i.e. elementwise product) between weighting values $w\left(i\right)$, [2, 0 , 0, 2], and input distribution ${P}_{x}\left(i\right)$ , given in Appendix 2—figure 2C above, [1/4,1/4,1/4,1/4], produces the following weighted input probability distribution that maximize the mutual information:
And the changed input probability distribution, ${P}_{x}^{`}\left(i\right)$, must satisfy the law of total probability
under the constraint condition
The modified joint probability distribution yields 1 bit of channel capacity as shown in the below figure of Appendix 2—figure 2C.
Mathematically, the adjusted joint probability distribution by weighting values can be expressed as follows:
And therefore the adjusted input and output marginal probability distributions are
and
Altogether, the mutual information given the weighting values is defined as
Finding input weighting values, $w\left(i\right),$ that maximize the mutual information subject to $\sum _{i}^{input}w\left(i\right){P}_{x}\left(i\right)=1$ and $0\le w\left(i\right){P}_{x}\left(i\right)$ is a nonlinear optimization problem. Since the direction of the gradient of mutual information is the same as that of those two constraints at the minimum, using Lagrange multiplier method, one can restated the functions as Lagrangian $\mathcal{L}\left({w}_{i},\lambda ,\sigma \right)=MI\left(input;outputw\left(i\right)\right)\lambda \left[\sum _{i}^{input}w\left(i\right){P}_{x}\left(i\right)1\right]\sigma \left[w\left(i\right){P}_{x}\left(i\right)\right],$ and find out weightings using numeric approach (Kraft D. 1988. A Software Package for Sequential Quadratic Programming. Wiss. Berichtswesen d. DFVLR). We used sequential least squares programming provided by SciPy Python library (scipy.optimize.minimize, SciPy 1.7.3) to find out the optimizing input weighting values.
The input weighting values that maximize the mutual information given in Appendix 2—figure 2B is shown in Appendix 2—figure 2D. $w\left(i\right)$ is $\left[\frac{5}{3},\frac{5}{3},\frac{5}{3},\mathrm{0,0},\mathrm{0,5},0\right]$; hence, ${P}_{x}^{\mathrm{`}}\left(i\right)$ becomes $\left[\frac{1}{6},\frac{1}{6},\frac{1}{6},\mathrm{0,0},0,\frac{1}{2},0\right]$. Note that other weighing values, for example, $\left[\mathrm{5,0},\mathrm{0,0},\mathrm{0,0},\mathrm{5,0}\right]$ and $\left[0,\frac{10}{3},\frac{5}{3},\mathrm{0,0},\mathrm{0,5},0\right]$, can be the solution due to the same output distribution for inputs 0, 1, and 2. The optimized input distribution yields around 0.71 bit of mutual information between input and output distribution.
1.4 Channel capacity calculation from modalized weighting values
Since we use optimization algorithms, we do not predefine the weighting values to find out the maximum mutual information. On the other hand, estimating mutual information under various Gaussianshaped input weighting values can give intuition of physiologically relevant input distribution and cellular response (Cheong et al., 2011).
Appendix 2—figure 3 shows the estimation of channel capacity between TNFα doses and NFκB reporter under various unimodal and bimodal Gaussian input distributions. Note that several superposition of two different Gaussian distribution that forms a unimodal distribution, having single maximum peak, is excluded (Appendix 2—figure 3 B). Appendix 2—figure 3 C and D, show the calculated mutual information values from the unimodal and bimodal input distributions, respectively. Since the input range from 0 to 5 yields the same output response, the variation of input distribution within those range does not affect the mutual information. Therefore, discrete increases of mutual information are pronounced if the mutual information values are sorted in ascending order, particularly, in the case of bimodal input distribution (Appendix 2—figure 3D). Appendix 2—figure 3 E and F show the probability space given from the mutual information maximizing unimodal and bimodal input distribution, respectively. Maximum mutual information from bimodal input distribution yields around 10% higher value than that of the unimodal distribution and less than 1% of lower value compared to the optimized input distribution described in the previous section.
1.5 Influence of the number of output binning on channel capacity
Projection of input and output distribution onto probability space is described in Appendix 2—figure 2 A and B. Since the input and output data points are finite, relatively large number of output binning will produce discontinuous joint probability distribution throughout different output indexes. On the other hand, insufficient number of output binning cannot capture the original probability distribution from the input and output but average out the local variation of joint probability distribution throughout the output indexes. Therefore, the number of output binning significantly influence the mutual information and channel capacity of input and output distribution. Note that the number of input binning is the same as the number of input doses.
Appendix 2—figure 4 describes the changing mutual information and channel capacity values in different output binning numbers. Since the input binning is given as the input doses, there is no variation in input entropy in the mutual information calculation. On the other hand, the increase of binning increases the output entropy and joint entropy. As increasing the output binning number, the increased output entropy than that of the joint entropy is bigger (Appendix 2—figure 4 D). Therefore, mutual information and channel capacity increase as increasing output binning.
1.6 Influence of the number of samples on channel capacity
As described in the previous section, it is important to consider the ratio between the number of output binning and the number of samples to estimate the channel capacity. If the number of samples is relatively smaller than the number of binning, the joint probability space become sparse and generate one to one input and output relationship which in turn increases the calculated channel capacity.
Appendix 2—figure 5 describes changing mutual information and channel capacity with respect to the total number of samples. Since the samples are random distribution, the ground truth mutual information and channel capacity are 0. On the other hand, the distribution yields the more mutual information and channel capacity as decreasing the total number of samples (Appendix 2—figure 5AC). The mutual information and channel capacity values deviating from 0 are a bias since the ground truth mutual information and channel capacity are 0.
1.7 Bootstrapping method to estimate channel capacity at infinite sample size
As shown in the previous section, the size of sample determines the degree of bias in the calculated channel capacity. Furthermore, the size of sample is always finite, therefore the calculated channel capacity is biased. On the other hand, using linear regression of subsampled datasets, the channel capacity value at infinite sample size can be estimated as followed (Appendix 2—figure 6). The sample distribution given in Appendix 2—figure 6 A is subsampled into various subsampling percentages shown in Appendix 2—figure 6 B. The subsampling uses random sampling with replacement in every drawing, therefore the original sample distribution shown in Appendix 2—figure 6 and 100% subsampled distribution from the original data show difference in distribution points (Appendix 2—figure 6 B). These subsampled distributions tend to yield higher channel capacity in smaller subsample size (Appendix 2—figure 6 C). By plotting channel capacity value with respect to the inverse of sample sizes, the channel capacity value at infinite sample size can be estimated (Appendix 2—figure 6 D). This bootstrapping method alleviates the degree of bias in the calculated channel capacity, but still the estimated channel capacity of random distribution at infinite sample size is around 0.15 bits, 0.15 bits higher than the ground truth channel capacity (i.e. 0 bit).
1.8 Channel capacity bias map depending on the output binning and total number of samples
As shown in the series of previous section, choosing an appropriate output binning and the total number of samples are essential to calculate the unbiased channel capacity. Since the two factors dependently influence the bias of channel capacity, it is required to estimate the channel capacity in various total sample numbers and binning numbers. Appendix 2—figure 7 above and B describe the bias map depending on the total number of samples and the number of binning calculated from random (A) and experimental dataset (B). Note that all channel capacities are estimated using bootstrapping method to interpolate the channel capacity value at infinite sample size.
In the case of random dataset, most of the regions spanning in range 0–160,000 total sample size and 0–1000 output binning number exhibit less than 0.01 bit of channel capacity. The white line in Appendix 2—figure 7 A indicate the contour line having 0.01 bit of estimated channel capacity. Therefore, the output binning number and total number of samples having the values above the white line exhibit less bias than 0.01 bits of channel capacity. On the other hand, the channel capacity values below the white line exhibit the value higher than 0.01 bits of channel capacity. In this work, the allowed bias is either 0.01 or 0.05 bits depending on the input and output layer (see section 123).
Appendix 2—figure 7 B is the bias map calculated from between TNFα doses and reporter GFP of U937 cells. In this example, the total number of samples is 170,472 and subsampled without replacement in different yaxis of the heatmap (Appendix 2—figure 7). Overall, as shown in the widely spreading orange and red color, the calculated channel capacity fluctuates near 1.4 bits. The exceptions are either the case where the number of output binning is less than 200 or the coordination of total number of samples and binning numbers are below the white line shown in Appendix 2—figure 7 A. In this work, the minimum sample number in whole dataset is 63,816 which is the above of the line in Appendix 2—figure 7 A. Therefore, expected maximum bias in channel capacity is less than 0.01 bits even in the case of 1000 output binning.
We determine the channel capacity value as the highest channel capacity values calculated from output binning numbers ranging from 10 to 1000. Appendix 2—figure 7C, D shows channel capacity values depending on the output binning number for 25,570 and 51,141 total sample sized random distribution and DosesGFP response data. In the case of 25,570 total sample size, around 600 output binning number, bias start to increase. On the other hand, in the case of 51,141 total sample size, there is no noticeable increase of bias in the given output binning range. The highest channel capacity values for 51,141 sample size is 1.41 bits at 985 output binning number. In the original sample size (i.e. 170,472), the maximum channel capacity is 1.41 bits at 510 output binning number. Therefore, in this example dataset, the estimated channel capacity is 1.41 bits.
In this work, if the input is discrete dose information, we estimate channel capacity using bootstrapping method described in Appendix 2—figure 6 with multiple output binning numbers ranging from 10 to 1000. The maximum value of channel capacity in the binning range is the final channel capacity value of the calculation. Appendix 2—figure 8 shows the results of channel capacity calculation from experimental datasets. The yintercepts of individual lines are the unbiased channel capacity. And the maximum value of those yintercepts in the individual dataset is selected as the final channel capacity value.
Appendix 3
Decomposition of signaling channel
2.1 Definition of signal and noise power
The signal power of a signaling channel is the variance of the average output distribution of individual input responses. Therefore, signal power can be written as $\mathrm{E}{[{\stackrel{}{R}}_{i}\mathrm{E}({\stackrel{}{R}}_{i}\left)\right]}^{2}$ hence $\mathrm{E}\left({\stackrel{}{R}}_{i}^{2}\right)\mathrm{E}{\left({\stackrel{}{R}}_{i}\right)}^{2}$, where $\mathrm{E}$ and ${\stackrel{}{R}}_{i}$ are the expectation operator and average output distribution at ith input dose, respectively. Since ${\stackrel{}{R}}_{i}=\sum _{j}{R}_{j}P\left({R}_{j}{S}_{i}\right)$, where ${R}_{j}$ and $P\left({R}_{j}{S}_{i}\right)$ are marginal output value at jth index and conditional probability of output at jth index given the ith input signal ${S}_{i}$, substituting ${\stackrel{}{R}}_{i}$ into $\mathrm{E}\left({\stackrel{}{R}}_{i}^{2}\right)\mathrm{E}{\left({\stackrel{}{R}}_{i}\right)}^{2}$ provides the signal power as ${\sigma}_{r}^{2}=\sum _{i}P\left({S}_{i}\right){\left[\sum _{j}{R}_{j}P\left({R}_{j}{S}_{i}\right)\right]}^{2}{\left[\sum _{i,j}{R}_{j}P\left({R}_{j}{S}_{i}\right)\right]}^{2},$ where $P\left({S}_{i}\right)$ is the input probability at ith index.
In the case of noise power, it is defined as the average of the variance of the output distribution of individual input responses. Therefore, noise power can be written as $E\left[{\overline{R}}_{i}^{\text{2}}{\overline{R}}_{i}^{2}\right]$ and can be further expanded as ${\sigma}_{n}^{2}=\sum _{i}P\left({S}_{i}\right)\left[\sum _{j}{R}_{j}^{2}P\left({R}_{j}{S}_{i}\right){\left[\sum _{j}{R}_{j}P\left({R}_{j}{S}_{i}\right)\right]}^{2}\right].$
Appendix 3—figure 1A, B describes how different input and output distributions contribute to signal and noise power. Increasing the variance of output response of individual input does not influence the signal power but only increase the noise power. Likewise, increasing the mean output while keeping the variance of individual output response for each input provides increased signal power without affecting the noise power (Appendix 3—figure 1 B).
Data availability
We have uploaded the raw data of the study to Dryad at https://doi.org/10.5061/dryad.18931zd2g. Our scripts for data evaluation are also linked to GitHub and stated in the manuscript.

Dryad Digital RepositoryData from: Information transfer in mammalian glycanbased communication.https://doi.org/10.5061/dryad.18931zd2g
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Article and author information
Author details
Funding
European Research Council (716024)
 Christoph Rademacher
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. Open access funding provided by Max Planck Society.
Acknowledgements
This project (GLYCONOISE) has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. 716024). We thank Max Planck Society for support and Prof. Dr. Peter H Seeberger for helpful discussions. We also thank the Deutsches Rheuma Forschungszentrum (DRFZ) for providing access to their cell sorting facility. The computational results presented were obtained using the CLIP cluster (https://clip.science).
Copyright
© 2023, Fuchsberger, Kim 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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