Institute of Fundamental Technological Research

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.

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.

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.

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.

Background
As suggested by the origin of the word, sphingolipids are mysterious molecules with various roles in antagonistic cellular processes such as autophagy, apoptosis, proliferation and differentiation. Moreover, sphingolipids have recently been recognized as important messengers in cellular signaling pathways. Notably, sphingolipid metabolism disorders have been observed in various pathological conditions such as cancer and neurodegeneration.

Results
The existing formal models of sphingolipid metabolism focus mainly on de novo ceramide synthesis or are limited to biochemical transformations of particular subspecies. Here, we propose the first comprehensive computational model of sphingolipid metabolism in human tissue. Contrary to the previous approaches, we use a model that reflects cell compartmentalization thereby highlighting the differences among individual organelles.

Conclusions
The model that we present here was validated using recently proposed methods of model analysis, allowing to detect the most sensitive and experimentally non-identifiable parameters and determine the main sources of model variance. Moreover, we demonstrate the usefulness of our model in the study of molecular processes underlying Alzheimer’s disease, which are associated with sphingolipid metabolism.

Sphingolipid metabolism, Kinetic model, Sensitivity analysis

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.