ABSTRACT
Isogenic cells living in the same environment show a natural heterogeneity associated with fluctuations in gene expression. When these fluctuations propagate through cellular regulatory networks, they can give rise to noise regulons, whereby multiple genes fluctuate in a coordinated fashion in single cells. The propagation of these fluctuations has been extensively characterized at the transcriptional level. For example, variations in transcription factor concentration induce correlated fluctuations in the abundance of target gene products. Here, we find that such noise regulons can also stem from protein degradation. We expressed pairs of yellow and red fluorescent proteins, subjected them to differential translation or degradation, and analyzed their fluctuations in single cells. While differential translation had little impact on fluctuations, protein degradation was found to be a dominant contributor. A mathematical model to decompose fluctuations arising from multiple sources of regulation revealed that cells with higher protein production capacity also exhibited higher protein degradation capacity. This association uncouples fluctuations in protein abundance from fluctuations in production rate, and can generate orthogonal noise regulons even for proteins relying on the same transcriptional program.
Introduction
Molecular noise is ubiquitous in biological systems (1⇓⇓⇓⇓⇓–7) and originates from two distinct sources (8⇓⇓–11). A first, intrinsic source stems from the stochastic nature of chemical reactions within cells. Considering proteins, intrinsic noise measures the variation of a protein’s concentration, when all cellular parameters are kept constant. The second source of noise is the extrinsic component, which corresponds to the variability of a protein’s concentration across different cell states. Isogenic cells living in the same environment indeed naturally explore a multitude of states reflected in differences in size, shape, cell cycle phase, concentrations of polymerases, ribosomes, regulation factors, etc. (12, 13). Such extrinsic noise is sometimes referred to as pathway noise (14, 15). Recent advances in single-cell RNA- seq have also contributed to unveiling the natural heterogeneity of cell populations and cell states, even allowing the identification of novel cell types (16⇓⇓–19).
Understanding the molecular bases driving cellular heterogeneity can yield fundamental insights into mechanisms of cell function and regulation (20⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–33). This idea was explored by Perdaza et al. who expressed two fluorescent proteins in a cascade and observed that fluctuations of the regulator propagated to the regulatee (20). More generally, correlated fluctuations of protein abundance have been widely observed in S. cerevisiae (21). In that work, the authors observed that proteins undergoing correlated fluctuations with a stress response factor were involved in stress response themselves. These correlations proved predictive of regulatory mechanisms although they were measured in unstressed cells (21). Identification of sources of extrinsic noise affecting a specific protein can thus reveal how proteins are regulated (22⇓⇓⇓⇓⇓⇓⇓–30). Based on this idea, Farkash-Amar et al. used correlation in protein abundance and localization to identify 74 genes related to human cell motility (29). In another example, it was observed in yeast that cell-specific growth rate and stress resistance were anti-correlated, and the cellular abundance of Tsl1, a trehalose synthase component, correlated with slow-growing, stress- resistant cell states (31).
At the root of heterogeneity lies the question, how can extrinsic noise be produced? Sources of extrinsic noise have been extensively characterized at the transcriptional level (5, 15, 20, 23, 34⇓⇓⇓⇓⇓⇓–41), and recent advances of single cell transcriptomics by RNA-seq have contributed to consolidating that view (42, 43). Theoretically, however, any regulatory mechanism that can affect a protein’s level could also influence its noise (34), e.g., by changing translation, mRNA, or protein degradation rates across cells. Importantly, recent advances in transcriptomics and proteomics methods have shown that post-transcriptional regulation greatly contributes to homeostasis of protein abundance (44, 45), a view also supported by single-cell measurements of mRNA and protein levels (44, 46). The fundamental role of post- transcriptional regulation in regulating protein levels is particularly well illustrated in a recent work, where yeast proteins were all expressed from the same constitutive promoter, but showed highly variable abundances, spanning over two orders of magnitude (47). At the functional level, post- transcriptional regulation is indeed crucial for many key cellular processes such as the cell cycle (48). More generally, entire classes of proteins can be subject to strict post-transcriptional regulation (49⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–51). For example, Gsponer et al. observed across several species that proteins rich in disordered regions are tightly regulated throughout their lifetime, from transcript synthesis to protein clearance (50).
The fact that post-transcriptional regulation mechanisms play a major role in cellular circuits prompts us to ask whether they represent a source of extrinsic noise on top of transcription. For example, if a protein requires a specific factor to be degraded, the fluctuations in the abundance of the protein will be coupled the fluctuations of the degradation factor.
To evaluate whether post-transcriptional processes can impact fluctuations of protein abundance in single cells, we compared fluctuation patterns of fluorescent proteins in presence or absence of sequence tags inducing either decreased translation rate or increased degradation. We used a two-color reporter strategy (8, 9) to quantify the extent of change in extrinsic noise caused by the sequence tags (Fig 1). We observed that decreased translation rate did not significantly impact extrinsic noise despite inducing a 3-fold reduction in protein abundance. Increased degradation, however, which was triggered by a misfolded polypeptide tag, caused a dramatic change in the pattern of cell-to-cell fluctuations.
Results
Measuring protein abundance noise using a two-color reporter strategy
The noise of protein abundance in single cells can be decomposed into intrinsic and extrinsic components using two fluorescent reporter proteins of different colors, as originally proposed (8, 9). In this strategy, cell-to-cell differences impact the expression of the two reporters in the same way, such that correlation in their abundance across cells measures extrinsic noise, whereas differences in reporter abundance within cells reflect intrinsic noise.
We adopted this strategy and expressed a yellow and a red fluorescent protein in S. cerevisiae. The genes coding for the two reporters were integrated at homologous loci and used identical promoters (Details of constructs, strains, and sequences are given in Fig S1, Text S1 and Tables S1-S2). We measured the fluorescence of diploid yeast cells expressing the reporters using an automated confocal spinning disk microscope (Fig 1D). As expected, YFP and RFP abundance were highly correlated across cells (R=0.83, Fig 2), reflecting that both reporters were indeed influenced by identical sources of extrinsic noise.
Decreasing translation rate minimally impacts protein abundance fluctuations
We then altered the post-transcriptional regulation of only one of the reporters and analyzed the resulting impact on extrinsic noise (Fig 1B). In a first experiment, we fused an amino acid sequence at the C-terminus of RFP, which contained seven repeats of “CTT,” a leucine codon with low tRNA adaptation index in S. cerevisiae (52) (Methods, Text S2). We call this sequence a “translation bottleneck” (tb) and use RFP-tb to refer to this variant of RFP. As expected by design, the average cellular abundance of RFP-tb was lower than that of untagged RFP, by ~3-fold (Fig 2). Interestingly, the correlation remained close to the original value (R=0.79), indicating that fluctuations were not affected by the translation bottleneck. The total noise for RFP-tb was comparable to RFP ( =0.039 and 0.032 respectively, Fig 2C). Overall, the similarity in correlation in presence and absence of the translation bottleneck indicates that all cells, irrespective of their state (here represented by YFP abundance), deal with the bottleneck sequence with comparable efficiency. Lastly, we repeated these experiments using a different promoter and our observations remained highly similar (Fig 2).
A misfolded protein tag decouples protein abundance fluctuations
In a second experiment, we fused a misfolded protein to RFP (53) and refer to this variant as RFP-misP. Protein misfolding is a pervasive process that can be triggered by a stress such as heat shock (54), but can also occur during the normal life cycle of proteins due to translational errors, for example (55). As a result, cells have evolved elaborate quality-control machineries (56). By expressing RFP-misP with YFP, we tested whether the cell machinery dealing with RFP-misP would subject it to a new source of extrinsic noise, and whether that new source could decouple the fluctuations between RFP-misP and untagged YFP. We observed a 20- fold decrease in RFP-misP expression. This decrease likely originates from a change of protein stability rather than a change of mRNA stability or translation efficiency, because fusion of RFP-misP to an additional solubilizing tag rescues protein abundance (Fig S2). Strikingly, the correlation between RFP- misP and YFP underwent a large decrease, down to R=0.32. We also observed a two-fold increase in total noise ( = 0.065) relative to RFP alone ( = 0.032, Fig 2C and Methods).
We performed the same measurements using a different promoter and observed similar results: the correlation between YFP and RFP-misP decreased (R=0.18), and the total noise increased due to the misP tag ( = 0.055) compared to RFP alone ( = 0.034). In another control, we swapped fluorescent reporters, using YFP-misP together with RFP, and we observed similar results. The correlation vanished (R < 0.1), and the total noise increased due to the misP tag (Fig. S3).
Post-transcriptional co-regulation re-couples fluctuations of protein abundance in single cells
Two hypotheses could explain the decoupling of YFP and RFP-misP expression. One possibility is that tagging RFP with misP increases its intrinsic noise. In that case, tagging RFP and YFP simultaneously with misP should not re-couple fluctuations. Alternatively, RFP-misP may be subject to a new source of extrinsic noise. In this case, tagging both RFP and YFP with misP should restore the coupling in protein expression. We observed the latter scenario, where tagging both proteins with misP restored their correlation (R=0.76, Fig 3). The same experiments based on a different promoter gave similar observations (R=0.71, Fig 3C).
Thus, subjecting proteins to a new layer of post-transcriptional regulation can change their pattern of fluctuation at the single cell level. Moreover, the restoration of the correlation that we observed indicates that this change is caused by a source of extrinsic noise, supposedly reflecting the “degradation capacity” of misfolded proteins in each cell. We assessed whether this cell-specific degradation capacity could be linked to the cell cycle, and measured the correlation between the abundance of YFP-misP and RFP-misP in sub-populations of cells grouped by size or cell cycle stage. The correlation depended on neither property (Fig S4, S5), indicating that cell size and cell-cycle stage do not influence the extrinsic factor represented by the “degradation capacity.”
Post-transcriptional regulation creates anti-fluctuations that partially cancel the transcriptional fluctuations in our system
To explain the decoupling and recoupling of protein fluctuations by post- transcriptional regulation, we introduce a mathematical model of the fluctuations of reporters subjected to multiple noise sources. Two reporters G and R sharing the same promoter and lacking the misP tag share the same source of extrinsic noise Z. Following a framework introduced by Elowitz et al. (8), we model the fluorescence of the reporters as where G and R represent the single cell fluorescence of the green (GFP or YFP) and red (RFP) reporters. The b constants account for differences in average protein abundances and differences in abundance-to- fluorescence scaling. 𝜖 is the intrinsic noise due to stochasticity inherent to gene expression. We use a multiplicative model because, with mass action kinetics, fluctuations in protein production and degradation have multiplicative effects on protein abundance (Methods).
Adding a misfolded tag to one reporter subjects it to a new source of extrinsic noise 𝑊. In the case of RFP-misP for example, 𝑊 accounts for the effect of the misP tag on fluorescence in single cells now denoted 𝑅∗, with
By log-transforming fluorescence (log 𝐺 → 𝐺, log 𝑅∗ → 𝑅∗) to linearize these equations, we can compute how the noise sources Z and W impact the correlation between log protein abundance of the two reporters 𝐺 and 𝑅∗ across a cell population by
This equation (see Methods for details of the derivation) formalizes the intuition of Fig 1: subjecting R* to a new source of noise W can decrease the correlation between the reporters in two distinct mechanisms. First, W can inject extra noise into 𝑅∗ to increase Var(R*). As the first term of Equation 4 shows, increasing Var(R*) decreases the correlation between G and R*. Second, if the coupling between Z and W is negative, fluctuations in Z are (partially) canceled by anti-fluctuations in W which decouple R* from G. This is reflected in the second term of Equation 4, where Cov(Z,W) << 0 decreases the correlation between G and R*.
In our experiments, and , which implies Cov(Z,W) < 0. The data thus suggest that the loss of correlation between G and R* is due both to increased noise in R* and to negative coupling between Z and W, with the latter effect being slightly stronger than the former.
If YFP abundance captures the production capacity Z of individual cells, and if fluctuations induced by the misP tag 𝑊 depend on the capacity to degrade proteins, our results imply that cells with a higher production capacity have a higher degradation capacity. The correlation coefficient between Z and W can, in fact, be computed from measurements of G, R and R* (Equation 18, Methods). We find R(Z,W) ≅-0.54, confirming that Z and W are anti-correlated.
Numeric simulations confirm the coupling between protein production and degradation in single cells
To confirm that coupling between production and degradation leads to decoupling between passively- degraded (YFP) and actively degraded proteins (RFP-misP) we simulated the stochastic variability of proteins using the Gillespie algorithm with rate constants determined to yield average mRNA and protein copy numbers matching those of the literature (Fig 4A, Methods). Each simulated “yeast cell” consisted of a unique set of rate constants shared by all four proteins, except for protein degradation rates. Those were always identical for equivalent proteins but differed between passively (YFP and RFP) and actively degraded variants (YFP-misP, RFP-misP). The expression of all four proteins was simulated for 80 hours to reach equilibrium, at the end of which protein abundance was recorded for the four proteins. Finally, one thousand of these simulations were performed to obtain cell population statistics. We implemented two models of protein degradation. First, degradation rates were normally distributed across cells but were identical for YFP-misP and RFP-misP within cells. This simulates extrinsic noise in protein degradation. As expected, such cell-specific degradation rates reproduced the correlation between RFP-misP and YFP-misP observed experimentally (Fig 4B, model 1, R=0.8). However, the noise added by degradation did not decrease the correlation between YFP and RFP-misP to the extent observed experimentally (Rsim(G,R*)=0.65). In a second model, the rate of protein degradation (k5) was coupled to the rate of production (arbitrarily chosen as k2). Equation 18 (Methods) enabled us to calculate the correlation that should exist between those rates to recapitulate the experimental results. We thus sampled values of k5 such that, on average, the correlation between log(k2) and log(k5) would be 0.54. With this added constraint, the correlation between YFP-misP and RFP-misP remained high, with Rsim(G*,R*)=0.72, but the correlation between YFP and RFP-misP decreased to Rsim(G,R*) = 0.28, in good agreement with our experimental results where Rexp(G,R*) = 0.32.
Discussion and conclusions
Functional implications of the findings
The fact that fluctuations in protein abundance can be coupled at the level of single cells brings about the question of function (4). The variability inherent to gene expression can be a constraint that is costly to suppress (57), but can also represent a beneficial, tunable and selectable trait as a primitive form of gene regulation (58), and in a bet-hedging context (31, 59⇓⇓⇓–62). While bet-hedging is generally studied through variability of a single component, correlated fluctuations can be exploited to couple the fluctuations of many components together (63). The possibility to tune cell-to-cell fluctuations of multiple components could, for example, contribute to adjusting the stoichiometry of subunits in complexes at the level of single cells.
There may also be contexts where coupling is not desirable. For example, if preparing for all possible environmental stresses is too costly or hard to achieve functionally, cells may benefit from decoupling the expression of gene modules needed to overcome different types of stresses. Decoupling the expression of stress-response genes could allow individual cells to prepare to different kinds of stress, instead of all individuals preparing for all stresses. Doing so may increase the chance that at least a few cells survive sudden environmental stresses. In support of this conjecture, proteins involved in chemical homeostasis and defense response have high decay rates (64).
Interaction between protein degradation and protein production
Modeling the experimental data suggested a connection between the rates of protein production and degradation (Fig 5). At the mRNA level, such dependence has been observed and is implemented through several mechanisms. For example, two RNA polymerase subunits (Rpb4 and Rpb7) were found to bind the transcribed mRNA to later direct it for degradation (65, 66). In another mechanism, a promoter element binding Rap1p stimulates both transcription and mRNA degradation (67). Additionally, RNA decay factors such as Xrn1 have been observed to enhance both the transcription and degradation of certain RNAs (68).
Our data imply a similar linkage between production and degradation at the protein level. However, because untagged proteins are not subject to rapid degradation despite having the same promoter region as tagged proteins, the coupling between production and degradation is unlikely to involve a signal associated with the mRNA. The underlying mechanisms must thus be different from those described above. We hypothesize that the production-degradation linkage we observed reflects a more general mechanism. According to this hypothesis, a global extrinsic component – or, as coined by Stewart-Ornstein et al., a “noise regulon” would be composed of proteins needed for growth, and include ribosome and metabolic enzymes, but also degradation factors. All the proteins in such a regulon would fluctuate together, thus simultaneously increasing production and degradation in a cell- specific manner. Such association may reflect a natural optimization of cells where, like in a factory, ramping up production naturally produces excess waste that needs to be cleared.
Exploiting cellular noise may help characterize post-transcriptional regulation mechanisms
The strategy described in this work, whereby two fluorescent proteins differing in a specific feature capture the extrinsic noise component acting on that feature, is readily generalizable to dissect more regulatory mechanisms and pathways. The use of modified or synthetic proteins as “queries” could indeed reveal regulators of specific features. Yeast proteins that anti-correlate with RFP-misP could be candidate degradation factors. In contrast, yeast proteins that correlate with RFP-misP could be hypothesized as stabilizing chaperones or proteins subjected to the same degradation mechanism. We thus anticipate that cellular noise and co-fluctuating proteins will reveal mechanisms of regulation in biological systems, of and beyond transcriptional regulatory networks. To this aim, the framework introduced in this work, to analyze the extrinsic noise of non-equivalent reporters, will be instrumental.
Materials and Methods
Strains and plasmids
We employed two fluorescent proteins, Venus (YFP) and mCherry (RFP), which were cloned into plasmids suitable for genome integration at the TRP1 locus (Supplementary Text 1). For genome integration, the plasmids were restricted by AccI (YFP) or BamHI (RFP), which released the cassette flanked by sequences bearing homology to the TRP1 locus. The restricted fragment was transformed to BY4741 (YFP), or BY4742 (RFP) following an established protocol (69). Transformants were selected by antibiotic resistance (G418 for YFP, Hygromycin for RFP) and correct locus integration was verified by tryptophan auxotrophy. Mating was done by growth on solid YPD agar overnight followed by selection on synthetic media lacking methionine, lysine and supplemented with antibiotics selecting for the presence of both cassettes. The yeast strains used in this work are described in Tables S1 and S2.
Microscope imaging
Cells were inoculated from their glycerol stock in 384-well glass-bottom optical plates (Matrical) with a pintool (FP1 pins, V&P Scientific) operated by a Tecan robot (Tecan Evo200 with MCA384 head). Cells were grown in YPD for a minimum of ten hours before they reached an optical density of at most 1, and were imaged. Imaging was performed with an automated Olympus microscope X83 coupled to a spinning disk confocal scanner (Yokogawa W1), using a 60X objective (Olympus, plan apo, 1.42 NA). Excitation was achieved with a green L.E.D for brightfield images, a 488 nm laser (Toptica, 100 mW) for YFP, and 561 nm laser (Obis, 75 mW) for RFP. Emission filter sets used to acquire the brightfield, YFP and RFP images were 520/28, 520/28 and 645/75 respectively. The same triple-band dichroic mirror was used for all channels (405/488/561, Yokogawa). Images were recorded on two Hamamatsu Flash4-V2 cameras, one for the brightfield and YFP channels and the second for the RFP channel. Each image set was composed of two brightfield (BF) images (one in focus and one defocused to facilitate cell segmentation, each with 50 ms exposure) as well as one image for each fluorescent channel (500 ms exposure for YFP and 700 ms exposure for RFP). The focus was maintained throughout the experiment by hardware autofocus (Olympus z-drift compensation system).
Image analysis
Images were processed with ImageJ by custom algorithms. Individual cells were segmented from the brightfield images and statistics for all four images (in-focus brightfield, out-of- focus brightfield, YFP, and RFP) were recorded. Fluorescence intensity was estimated from the 30th quantile of pixel intensity within each cell. All tabulated data were analyzed in R. Several filters were applied to the data extracted from the images (Text S3, Fig S6).
Modeling reporters subject to a common noise source
Untagged fluorescent reporters are considered equivalent and share the same extrinsic noise Z. We model their expression using the framework introduced by Elowitz et al. (8), with
Here, G and R are single-cell fluorescence measured in the green (GFP or YFP) and red (RFP) channels respectively. Z represents the extrinsic noise, while 𝜖 models the noise intrinsic to the process of gene expression. The b constants account for differences in average protein abundances and differences in abundance-to-fluorescence scaling between the two reporters. We use a multiplicative model between sources of noise because protein abundance is the result of chemical reactions with mass action kinetics. With such kinetics, protein abundance is given by the product of kinetic rates. For example, consider a cell with 3-fold more transcription activity and 3-fold more translation activity for a particular gene when compared to average. In such a cell, the fold change at the protein level will be 9-fold compared to average, and not 6-fold. This aspect of the model is important when comparing and modeling the correlation between fluorescent reporters whose abundance we alter experimentally, as we do here.
Log-transforming the equations linearizes them. We apply x:=log(x) for all the variables in the model and redefine the 𝑏 constants such that 𝑍 and 𝜖 have mean 0 which yields
In this context, the total variance of single-cell fluorescence can be decomposed into contributions of extrinsic and intrinsic noise, with
To determine how coupling reporters to different sources of noise alter the correlation between fluorescence, we note that reporters lacking the misP tag are only influenced by Z. In this simple case, the correlation between G and R is derived from Equations 7 and 8 as
Here, the correlation r(G,R) quantifies the amount of extrinsic noise Var(Z) relative to the total noise of the fluorescent proteins. This formula, based on the correlation coefficient, is a normalized form of the original formula based on the covariance to estimate extrinsic noise (8).
Modeling of reporters subjected to different sources of noise
The model of Equation 10 assumes the two fluorescent reporters to be subject to the same source of extrinsic noise Z. However, the misP tag subjects the fluorescent reporter R* to an additional source of extrinsic noise W. We model the effect of W on the abundance R* as
Coupling R* to an additional noise source W tends to increase fluctuations, as shown by computing Var(R*) as a function of Var(R), which gives
Since Var(W) > 0, coupling R* to W tends to increase the variance of R*, unless Z and W are strongly anti-coupled, i.e., Cov(Z,W) << 0. Using Equations 7 and 11 which define G and R*, we can derive how Z and W impact the correlation between G and R*,
By dividing this equation by Equation 10, we obtain an expression for how Z and W impact the correlation between the two pairs of reporters,
This equation suggests two mechanisms through which the misP tag can alter the correlation between the two reporters. In one mechanism, W injects more noise into R*. This increase Var(R*) (first term), and thus decreases r(G,R*) relative to r(G,R). In another mechanism, W is anti-coupled to Z such that fluctuations in Z are partially canceled by anti-fluctuations in W. In this scenario, a negative covariance between Z and W decreases r(G,R*).
To quantify the strength of the coupling between Z and W, we compute r(Z,W). We first use Equations 7 and 8, which define G and R to find
From Equation 11 which defines R* and its equivalent form for G*, we find the variance of W as
By computing Cov(G,R) and Cov(G,R*) and solving for Cov(Z,W), we can show that
Lastly, combining Equations 15, 16 and 17, we obtain
Numerical simulations
The simulations were based on the Gillespie algorithm (70) adapted from Bahar- Halpern et al. (71). The algorithm was modified to account for protein translation and degradation, and was ported to the R language. The rates used in the simulations were for gene opening (k1=5/h) and closing (k-1=5/h) (72), mRNA transcription (k2~N(20/h,0.12/h2) and degradation (k3=0.5/h), protein translation (k4~N(30/h,0.05/h2)) and protein degradation (k5=0.005/h for untagged YFP or RFP). These rates gave copy numbers of mRNA (average of 20 per cell) and proteins (average of 120,000 per cell) comparable to expected values (73, 74) (BNID 104745,104185). We simulated the impact of the misP tag using two models of protein degradation. In model 1, values of k5 ~ N(0.05/h,0.006/h2) were identical for YFP-misP and RFP-misP in single cells. Model 2 was identical to model 1, with the added constraint that values of k5 were sampled so that log(k2) and log(k5) would show a correlation expected to be 0.54.
Statistical analysis
Two-tailed Welch exact t-test was used to compare mean values of measurements series. All correlations in this works were calculated with the Pearson coefficient. The Fisher exact test was used to evaluate the significance of the correlations.
Author contributions
OM and EDL designed the study. OM performed the experiments. AS and EDL processed the images. ES designed the yeast tagging plasmid. JH, OM, and EDL developed the theoretical analysis framework. OM, JH, and EDL analyzed the data. OM, JH, and EDL wrote the manuscript with comments from all authors. All authors read and approved the final manuscript.
Conflict of interest
The authors declare that they have no conflict of interest.
Acknowledgments
We thank Steve Altschuler, Naama Barkai, Michael Elowitz, and Eran Segal for valuable discussions and comments. We thank Naama Barkai, Hagen Hofmann, Amnon Horovitz, Shalev Itzkovitz and Schraga Schwartz for insightful comments on the manuscript. We thank Maya Schuldiner for kindly providing the BY4741/2 strains.
Footnotes
or.matalon{at}weizmann.ac.il, avital.steinberg{at}weizmann.ac.il, ehud.sass{at}weizmann.ac.il, jean.hausser{at}weizmann.ac.il, emmanuel.levy{at}weizmann.ac.il