Institute of Fundamental Technological Research

Cellular signaling systems are immensely complex. Dedicated experimental and theoretical approaches are therefore required to decipher how they function. In this issue of Cell Systems, two studies systematically interrogate the Bone Morphogenetic Protein (BMP) pathway, uncovering mechanisms and consequences of distinct responses to combinations of BMP ligands.

Cellular signaling responses show substantial cell-to-cell heterogeneity, which is often ascribed to the inherent randomness of biochemical reactions, termed molecular noise, wherein high noise implies low signaling fidelity. Alternatively, heterogeneity could arise from differences in molecular content between cells, termed molecular phenotypic variability, which does not necessarily imply imprecise signaling. The contribution of these two processes to signaling heterogeneity is unclear. Here, we fused fibroblasts to produce binuclear syncytia to distinguish noise from phenotypic variability in the analysis of cytokine signaling. We reasoned that the responses of the two nuclei within one syncytium could approximate the signaling outcomes of two cells with the same molecular content, thereby disclosing noise contribution, whereas comparison of different syncytia should reveal contribution of phenotypic variability. We found that ~90% of the variance in the primary response (which was the abundance of phosphorylated, nuclear STAT) to stimulation with the cytokines interferon-γ and oncostatin M resulted from differences in the molecular content of individual cells. Thus, our data reveal that cytokine signaling in the system used here operates in a reproducible, high-fidelity manner.

Although we can now measure single-cell signaling responses with multivariate, high-throughput techniques our ability to interpret such measurements is still limited. Even interpretation of dose–response based on single-cell data is not straightforward: signaling responses can differ significantly between cells, encompass multiple signaling effectors, and have dynamic character. Here, we use probabilistic modeling and information-theory to introduce fractional response analysis (FRA), which quantifies changes in fractions of cells with given response levels. FRA can be universally performed for heterogeneous, multivariate, and dynamic measurements and, as we demonstrate, quantifies otherwise hidden patterns in single-cell data. In particular, we show that fractional responses to type I interferon in human peripheral blood mononuclear cells are very similar across different cell types, despite significant differences in mean or median responses and degrees of cell-to-cell heterogeneity. Further, we demonstrate that fractional responses to cytokines scale linearly with the log of the cytokine dose, which uncovers that heterogeneous cellular populations are sensitive to fold-changes in the dose, as opposed to additive changes.

Background - Cell-to-cell heterogeneity is an inherent feature of multicellular organisms and is central in all physiological and pathophysiological processes including cellular signal transduction. The cytokine IL-6 is an essential mediator of pro- and anti-inflammatory processes. Dysregulated IL-6-induced intracellular JAK/STAT signalling is associated with severe inflammatory and proliferative diseases. Under physiological conditions JAK/STAT signalling is rigorously controlled and timely orchestrated by regulatory mechanisms such as expression of the feedback-inhibitor SOCS3 and activation of the protein-tyrosine phosphatase SHP2 (PTPN11). Interestingly, the function of negative regulators seems not to be restricted to controlling the strength and timely orchestration of IL-6-induced STAT3 activation. Exemplarily, SOCS3 increases robustness of late IL-6-induced STAT3 activation against heterogenous STAT3 expression and reduces the amount of information transferred through JAK/STAT signalling. Methods - Here we use multiplexed single-cell analyses and information theoretic approaches to clarify whether also SHP2 contributes to robustness of STAT3 activation and whether SHP2 affects the amount of information transferred through IL-6-induced JAK/STAT signalling. Results - SHP2 increases robustness of both basal, cytokine-independent STAT3 activation and early IL-6-induced STAT3 activation against differential STAT3 expression. However, SHP2 does not affect robustness of late IL-6-induced STAT3 activation. In contrast to SOCS3, SHP2 increases the amount of information transferred through IL-6-induced JAK/STAT signalling, probably by reducing cytokine-independent STAT3 activation and thereby increasing sensitivity of the cells. These effects are independent of SHP2-dependent MAPK activation. Conclusion - In summary, the results of this study extend our knowledge of the functions of SHP2 in IL-6-induced JAK/STAT signalling. SHP2 is not only a repressor of basal and cytokine-induced STAT3 activity, but also ensures robustness and transmission of information. Plain English summary - Cells within a multicellular organism communicate with each other to exchange information about the environment. Communication between cells is facilitated by soluble molecules that transmit information from one cell to the other. Cytokines such as interleukin-6 are important soluble mediators that are secreted when an organism is faced with infections or inflammation. Secreted cytokines bind to receptors within the membrane of their target cells. This binding induces activation of an intracellular cascade of reactions called signal transduction, which leads to cellular responses. An important example of intracellular signal transduction is JAK/STAT signalling. In healthy organisms signalling is controlled and timed by regulatory mechanisms, whose activation results in a controlled shutdown of signalling pathways. Interestingly, not all cells within an organism are identical. They differ in the amount of proteins involved in signal transduction, such as STAT3. These differences shape cellular communication and responses to intracellular signalling. Here, we show that an important negative regulatory protein called SHP2 (or PTPN11) is not only responsible for shutting down signalling, but also for steering signalling in heterogeneous cell populations. SHP2 increases robustness of STAT3 activation against variable STAT3 amounts in individual cells. Additionally, it increases the amount of information transferred through JAK/STAT signalling by increasing the dynamic range of pathway activation in heterogeneous cell populations. This is an amazing new function of negative regulatory proteins that contributes to communication in heterogeneous multicellular organisms in health and disease.

signal transduction, SHP2, PTPN11, JAK/STAT, MAPK, information theory, channel capacity, mutual information

An individual eukaryotic cell senses identity and quantity of ligands through molecular receptors and signaling pathways, dynamically activating signaling effectors. A distinct ligand often activates multiple different effectors, and a distinct effector is activated by numerous different ligands, which results in cross-wired signaling. In apparently identical cells, the activity of signaling effectors can vary considerably, raising questions about the accuracy of cellular signaling and the interpretation of heterogeneous responses, as either functional or simply noise. Cell-to-cell variability of signaling outcomes, signaling dynamics, and cross-wiring all give rise to signaling complexity, complicating the analysis of signaling mechanisms. Here, we consider a simple input–output modeling approach of information theory that is suitable to analyze signaling complexity and highlight recent studies that have advanced our understanding of the role different components of signaling complexity play in achieving effective information transfer along cellular signaling pathways.

signaling pathways, hormones, growth factors or cytokines, signaling dynamics, cross-wired signaling, Shannon information, Fisher information

Signaling systems expand by duplications of various components, be it receptors or downstream effectors. However, whether and how duplicated components contribute to higher signaling capacity is unclear, especially because in most cases, their specificities overlap. Using information theory, we found that augmentation of capacity by an increase in the copy number is strongly limited by logarithmic diminishing returns. Moreover, counter to conventional biochemical wisdom, refinements of the response mechanism, e.g., by cooperativity or allostery, do not increase the overall signaling capacity. However, signaling capacity nearly doubles when a promiscuous, non-cognate ligand becomes explicitly recognized via duplication and partial divergence of signaling components. Our findings suggest that expansion of signaling components via duplication and enlistment of promiscuously acting cues is virtually the only accessible evolutionary strategy to achieve overall high-signaling capacity despite overlapping specificities and molecular noise. This mode of expansion also explains the highly cross-wired architecture of signaling pathways.

paralog expansion, gene duplication, allostery, cooperativity, biochemical signal processing, information capacity

Mathematical methods of information theory appear to provide a useful language to describe how stimuli are encoded in activities of signaling effectors. Exploring the information-theoretic perspective, however, remains conceptually, experimentally and computationally challenging. Specifically, existing computational tools enable efficient analysis of relatively simple systems, usually with one input and output only. Moreover, their robust and readily applicable implementations are missing. Here, we propose a novel algorithm, SLEMI—statistical learning based estimation of mutual information, to analyze signaling systems with high-dimensional outputs and a large number of input values. Our approach is efficient in terms of computational time as well as sample size needed for accurate estimation. Analysis of the NF-κB single—cell signaling responses to TNF-α reveals that NF-κB signaling dynamics improves discrimination of high concentrations of TNF-α with a relatively modest impact on discrimination of low concentrations. Provided R-package allows the approach to be used by computational biologists with only elementary knowledge of information theory.

Cellular communication via intracellular signalling pathways is crucial. Expression and activation of signalling proteins is heterogenous between isogenic cells of the same cell-type. However, mechanisms evolved to enable sufficient communication and to ensure cellular functions. We use information theory to clarify mechanisms facilitating IL-6-induced JAK/STAT signalling despite cell-to-cell variability. We show that different mechanisms enabling robustness against variability complement each other. Early STAT3 activation is robust as long as cytokine concentrations are low. Robustness at high cytokine concentrations is ensured by high STAT3 expression or serine phosphorylation. Later the feedback-inhibitor SOCS3 increases robustness. Channel Capacity of JAK/STAT signalling is limited by cell-to-cell variability in STAT3 expression and is affected by the same mechanisms governing robustness. Increasing STAT3 amount increases Channel Capacity and robustness, whereas increasing STAT3 tyrosine phosphorylation reduces robustness but increases Channel Capacity. In summary, we elucidate mechanisms preventing dysregulated signalling by enabling reliable JAK/STAT signalling despite cell-to-cell heterogeneity.

Many components of signaling pathways are functionally pleiotropic, and signaling responses are marked with substantial cell-to-cell heterogeneity. Therefore, biochemical descriptions of signaling require quantitative support to explain how complex stimuli (inputs) are encoded in distinct activities of pathways effectors (outputs). A unique perspective of information theory cannot be fully utilized due to lack of modeling tools that account for the complexity of biochemical signaling, specifically for multiple inputs and outputs. Here, we develop a modeling framework of information theory that allows for efficient analysis of models with multiple inputs and outputs; accounts for temporal dynamics of signaling; enables analysis of how signals flow through shared network components; and is not restricted by limited variability of responses. The framework allows us to explain how identity and quantity of type I and type III interferon variants could be recognized by cells despite activating the same signaling effectors.

NF-κB and STAT3 are essential transcription factors in immunity and act at the interface of the transition from chronic inflammation to cancer. Different functional crosstalks between NF-κB and STAT3 have been recently described arguing for a direct interaction of both proteins. During a systematic analysis of NF-κB/STAT3 crosstalk we observed that appearance of the subcellular distribution of NF-κB and STAT3 in immunofluorescence heavily depends on the fixation procedure. Therefore, we established an optimized fixation protocol for the reliable simultaneous analysis of the subcellular distributions of both transcription factors. Using this protocol we found that cytokine-induced nuclear accumulation of NF-κB or STAT3 did not alter the subcellular distribution of the other transcription factor. Both knockout and overexpression of STAT3 does not have any major effect on canonical TNFα-NF-κB signalling in MEF or HeLa cells. Similarly, knockout of p65 did not alter nuclear accumulation of STAT3 in response to IL-6. However, p65 expression correlates with elevated total cellular levels of STAT3 and STAT1 and supports activation of these transcription factors. Our findings in MEF cells argue against a direct physical interaction of free cellular NF-κB and STAT3 but point to more intricate functional interactions.

STAT3, NF-κB, Signal transduction, Nuclear translocation, Crosstalk

Background
Compared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. Progress in developing mathematics to manipulate such multi-parameter models and so enable their efficient interplay with experiments has been slow. Existing solutions are significantly limited by model size.

Results
In order to simplify analysis of multi-parameter models a method for clustering of model parameters is proposed. It is based on a derived statistically meaningful measure of similarity between groups of parameters. The measure quantifies to what extend changes in values of some parameters can be compensated by changes in values of other parameters. The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters. As a results, a relevant insight into identifiability analysis and experimental planning can be obtained. Analysis of NF- κB and MAPK pathway models shows that highly compensative parameters constitute clusters consistent with the network topology. The method applied to examine an exceptionally rich set of published experiments on the NF- κB dynamics reveals that the experiments jointly ensure identifiability of only 60 % of model parameters. The method indicates which further experiments should be performed in order to increase the number of identifiable parameters.

Conclusions
We currently lack methods that simplify broadly understood analysis of multi-parameter models. The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design. The method can also find applications in related methodological areas of model simplification and parameters estimation.

Motivation: Stochasticity is an indispensable aspect of biochemical processes at the cellular level. Studies on how the noise enters and propagates in biochemical systems provided us with non-trivial insights into the origins of stochasticity, in total, however, they constitute a patchwork of different theoretical analyses.

Results: Here we present a flexible and widely applicable noise decomposition tool that allows us to calculate contributions of individual reactions to the total variability of a system’s output. With the package it is, therefore, possible to quantify how the noise enters and propagates in biochemical systems. We also demonstrate and exemplify using the JAK-STAT signalling pathway that the noise contributions resulting from individual reactions can be inferred from data experimental data along with Bayesian parameter inference. The method is based on the linear noise approximation, which is assumed to provide a reasonable representation of analyzed systems.

Motivation: cis-regulatory DNA sequence elements, such as enhancers and silencers, function to control the spatial and temporal expression of their target genes. Although the overall levels of gene expression in large cell populations seem to be precisely controlled, transcription of individual genes in single cells is extremely variable in real time. It is, therefore, important to understand how these cis-regulatory elements function to dynamically control transcription at single-cell resolution. Recently, statistical methods have been proposed to back calculate the rates involved in mRNA transcription using parameter estimation of a mathematical model of transcription and translation. However, a major complication in these approaches is that some of the parameters, particularly those corresponding to the gene copy number and transcription rate, cannot be distinguished; therefore, these methods cannot be used when the copy number is unknown.

Results: Here, we develop a hierarchical Bayesian model to estimate biokinetic parameters from live cell enhancer–promoter reporter measurements performed on a population of single cells. This allows us to investigate transcriptional dynamics when the copy number is variable across the population. We validate our method using synthetic data and then apply it to quantify the function of two known developmental enhancers in real time and in single cells.

Our understanding of most biological systems is in its infancy. Learning their structure and intricacies is fraught with challenges, and often side-stepped in favour of studying the function of different gene products in isolation from their physiological context. Constructing and inferring global mathematical models from experimental data is, however, central to systems biology. Different experimental setups provide different insights into such systems. Here we show how we can combine concepts from Bayesian inference and information theory in order to identify experiments that maximize the information content of the resulting data. This approach allows us to incorporate preliminary information; it is global and not constrained to some local neighbourhood in parameter space and it readily yields information on parameter robustness and confidence. Here we develop the theoretical framework and apply it to a range of exemplary problems that highlight how we can improve experimental investigations into the structure and dynamics of biological systems and their behavior.

A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability from cell to cell. Here we focus on the case where single-cell fluorescent protein imaging time series data are available for a population of cells. Based on van Kampen’s linear noise approximation, we derive a dynamic state space model for molecular populations which is then extended to a hierarchical model. This model has potential to address the sources of variability relevant to single-cell data, namely, intrinsic noise due to the stochastic nature of the birth and death processes involved in reactions and extrinsic noise arising from the cell-to-cell variation of kinetic parameters. In order to infer such a model from experimental data, one must also quantify the measurement process where one has to allow for nonmeasurable molecular species as well as measurement noise of unknown level and variance. The availability of multiple single-cell time series data here provides a unique testbed to fit such a model and quantify these different sources of variation from experimental data.

Linear noise approximation, kinetic parameter estimation, intrinsic and extrinsic noise, state space model and Kalman filter, Bayesian hierarchical modeling

Nitrogen regulation in Escherichia coli is a model system for gene regulation in bacteria. Growth on glutamine as a sole nitrogen source is assumed to be nitrogen limiting, inferred from slow growth and strong NtrB/NtrC-dependent gene activation. However, we show that under these conditions, the intracellular glutamine concentration is not limiting but 5.6-fold higher than in ammonium-replete conditions; in addition, α-ketoglutarate concentrations are elevated. We address this glutamine paradox from a systems perspective. We show that the dominant role of NtrC is to regulate glnA transcription and its own expression, indicating that the glutamine paradox is not due to NtrC-independent gene regulation. The absolute intracellular NtrC and GS concentrations reveal molecular control parameters, where NtrC-specific activities were highest in nitrogen-starved cells, while under glutamine growth, NtrC showed intermediate specific activity. We propose an in vivo model in which α-ketoglutarate can derepress nitrogen regulation despite nitrogen sufficiency.

Stochasticity is an essential aspect of biochemical processes at the cellular level. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others. Here we propose a method that allows us to calculate contributions of individual reactions to the total variability of a system’s output. We demonstrate that reactions differ significantly in their relative impact on the total noise and we illustrate the importance of protein degradation on the overall variability for a range of molecular processes and signaling systems. With our flexible and generally applicable noise decomposition method, we are able to shed new, to our knowledge, light on the sources and propagation of noise in biochemical reaction networks; in particular, we are able to show how regulated protein degradation can be employed to reduce the noise in biochemical systems.

Motivation: The growing interest in the role of stochasticity in biochemical systems drives the demand for tools to analyse stochastic dynamical models of chemical reactions. One powerful tool to elucidate performance of dynamical systems is sensitivity analysis. Traditionally, however, the concept of sensitivity has mainly been applied to deterministic systems, and the difficulty to generalize these concepts for stochastic systems results from necessity of extensive Monte Carlo simulations.

Results: Here we present a Matlab package, StochSens, that implements sensitivity analysis for stochastic chemical systems using the concept of the Fisher Information Matrix (FIM). It uses the linear noise approximation to represent the FIM in terms of solutions of ordinary differential equations. This is the first computational tool that allows for quick computation of the Information Matrix for stochastic systems without the need for Monte Carlo simulations.

The mitogen-activated protein kinase (MAPK) family of proteins is involved in regulating cellular fates such as proliferation, differentiation and apoptosis. In particular, the dynamics of the Erk/Mek system, which has become the canonical example for MAPK signaling systems, have attracted considerable attention. Erk is encoded by two genes, Erk1 and Erk2, that until recently had been considered equivalent as they differ only subtly at the sequence level. However, these proteins exhibit radically different trafficking between cytoplasm and nucleus and this fact may have functional implications. Here we use spatially resolved data on Erk1/2 to develop and analyze spatio-temporal models of these cascades, and we discuss how sensitivity analysis can be used to discriminate between mechanisms. Our models elucidate some of the factors governing the interplay between signaling processes and the Erk1/2 localization in different cellular compartments, including competition between Erk1 and Erk2. Our approach is applicable to a wide range of signaling systems, such as activation cascades, where translocation of molecules occurs. Our study provides a first model of Erk1 and Erk2 activation and their nuclear shuttling dynamics, revealing a role in the regulation of the efficiency of nuclear signaling.

We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models without the need for Monte Carlo simulations. This methodology is then used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request.

Fluorescent and luminescent proteins are often used as reporters of transcriptional activity. Given the prevalence of noise in biochemical systems, the time-series data arising from these is of significant interest in efforts to calibrate stochastic models of gene expression and obtain information about sources of nongenetic variability. We present a statistical inference framework that can be used to estimate kinetic parameters of gene expression, as well as the strength and half-life of extrinsic noise from single fluorescent-reporter-gene time-series data. The method takes into account stochastic variability in a fluorescent signal resulting from intrinsic noise of gene expression, kinetics of fluorescent protein maturation, and extrinsic noise, which is assumed to arise at transcriptional level. We use the linear noise approximation and derive an explicit formula for the likelihood of observed fluorescent data. The method is embedded in a Bayesian paradigm, so that certain parameters can be informed from other experiments allowing portability of results across different studies. Inference is performed using Markov chain Monte Carlo. Fluorescent reporters are primary tools to observe dynamics of gene expression and the correct interpretation of fluorescent data is crucial to investigating these fundamental processes of cellular life. As both magnitude and frequency of the noise may have a dramatic effect on the cell fitness, the quantification of stochastic fluctuation is essential to the understanding of how genes are regulated. Our method provides a framework that addresses this important question.

How living cells can reliably process biochemical cues in the presence of molecular noise is not fully understood. Here we investigate the fidelity of information transfer in the expression of a single gene. We use the established model of gene expression to examine how precisely the protein levels can be controlled by two distinct mechanisms: (i) the transcription rate of the gene, or (ii) the translation rate for the corresponding mRNA. The fidelity of gene expression is quantified with the information-theoretic notion of information capacity. Derived information capacity formulae reveal that transcriptional control generally provides a tangibly higher capacity as compared to the translational control. We next introduce negative feedback regulation in gene expression, where the protein directly inhibits its own transcription. While negative feedback reduces noise in the level of the protein for a given input signal, it also decreases the input-to-output sensitivity. Our results show that the combined effect of these two opposing forces is a reduced capacity in the presence of feedback. In summary, our analysis presents analytical quantification of information transfer in simple gene expression models, which provides insight into the fidelity of basic gene expression control mechanisms.

Interferons exhibit their key role of immune modulators through activation of the Jak-Stat signalling pathway. We know substantial amount of molecular details regarding functioning of the pathway. However, to what extend the action of the pathway is dose dependent at the single cell level remains largely unclear. Specifically it is not know if single cells respond in a digital fashion or their output is continuously dependent on the stimulant’s concentration. We have combined an information-theoretic framework with high-throughput confocal imaging of mouse embryonic fibroblasts to provide a thorough, single-cell analysis of the Jak-Stat signalling in response to interferon beta and interferon gamma. We showed that in a baseline state single cells have information hardly sufficient to distinguish between presence or absence of interferons. However they can be put in an alert state by an action of interferons, which allows them to respond more in an analogous fashion. Our results show that the accuracy with which signalling pathways transmit information is not fixed but can be modulated on the contextual basis.

Information Processing, Sensitivity Analysis, Signal Transduction

Interferon, Jak/Stat, Stimulation