Measurement and modeling of signaling at the single-cell level

Single-Cell Measurements and Modeling and Computation of Decision-Making Errors in a Molecular Signaling System with Two Output Molecules

A cell constantly receives signals and takes different fates accordingly. Given the uncertainty rendered by signal transduction noise, a cell may incorrectly perceive these signals. It may mistakenly behave as if there is a signal, although there is none, or may miss the presence of a signal that actually exists. In this paper, we consider a signaling system with two outputs, and introduce and develop methods to model and compute key cell decision-making parameters based on the two outputs and in response to the input signal. In the considered system, the tumor necrosis factor (TNF) regulates the two transcription factors, the nuclear factor κB (NFκB) and the activating transcription factor-2 (ATF-2). These two system outputs are involved in important physiological functions such as cell death and survival, viral replication, and pathological conditions, such as autoimmune diseases and different types of cancer. Using the introduced methods, we compute and show what the decision thresholds are, based on the single-cell measured concentration levels of NFκB and ATF-2. We also define and compute the decision error probabilities, i.e., false alarm and miss probabilities, based on the concentration levels of the two outputs. By considering the joint response of the two outputs of the signaling system, one can learn more about complex cellular decision-making processes, the corresponding decision error rates, and their possible involvement in the development of some pathological conditions.

Corrected score methods for estimating Bayesian networks with error-prone nodes

Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error-prone data. Two methods for inferring causal relationships between nodes in a network are proposed based on penalized estimation methods that account for measurement error and encourage sparsity. We discuss consistency of the proposed network estimators and develop an approach for selecting the tuning parameter in the penalized estimation methods. Empirical studies are carried out to compare the proposed methods with a naive method that ignores measurement error. Finally, we apply these methods to infer signaling networks using single cell flow cytometry data.

Mechanistic Model of Signaling Dynamics Across an Epithelial Mesenchymal Transition

Intracellular signaling pathways are at the core of cellular information processing. The states of these pathways and their inputs determine signaling dynamics and drive cell function. Within a cancerous tumor, many combinations of cell states and microenvironments can lead to dramatic variations in responses to treatment. Network rewiring has been thought to underlie these context-dependent differences in signaling; however, from a biochemical standpoint, rewiring of signaling networks should not be a prerequisite for heterogeneity in responses to stimuli. Here we address this conundrum by analyzing an in vitro model of the epithelial mesenchymal transition (EMT), a biological program implicated in increased tumor invasiveness, heterogeneity, and drug resistance. We used mass cytometry to measure EGF signaling dynamics in the ERK and AKT signaling pathways before and after induction of EMT in Py2T murine breast cancer cells. Analysis of the data with standard network inference methods suggested EMT-dependent network rewiring. In contrast, use of a modeling approach that adequately accounts for single-cell variation demonstrated that a single reaction-based pathway model with constant structure and near-constant parameters is sufficient to represent differences in EGF signaling across EMT. This result indicates that rewiring of the signaling network is not necessary for heterogeneous responses to a signal and that unifying reaction-based models should be employed for characterization of signaling in heterogeneous environments, such as cancer.

A systematic approach to decipher crosstalk in the p53 signaling pathway using single cell dynamics

The transcription factors NF-κB and p53 are key regulators in the genotoxic stress response and are critical for tumor development. Although there is ample evidence for interactions between both networks, a comprehensive understanding of the crosstalk is lacking. Here, we developed a systematic approach to identify potential interactions between the pathways. We perturbed NF-κB signaling by inhibiting IKK2, a critical regulator of NF-κB activity, and monitored the altered response of p53 to genotoxic stress using single cell time lapse microscopy. Fitting subpopulation-specific computational p53 models to this time-resolved single cell data allowed to reproduce in a quantitative manner signaling dynamics and cellular heterogeneity for the unperturbed and perturbed conditions. The approach enabled us to untangle the integrated effects of IKK/ NF-κB perturbation on p53 dynamics and thereby derive potential interactions between both networks. Intriguingly, we find that a simultaneous perturbation of multiple processes is necessary to explain the observed changes in the p53 response. Specifically, we show interference with the activation and degradation of p53 as well as the degradation of Mdm2. Our results highlight the importance of the crosstalk and its potential implications in p53-dependent cellular functions.

Cells can respond to external and internal inputs by transducing information to the nucleus where transcription factors initiate corresponding cellular responses. Cellular signaling is mediated by several pathways; molecular networks that can interact with each other, which alters signal processing and modulates cellular responses. As deregulated signaling can lead to the development of tumors it is important to understand not only how signaling pathways function but also the contribution of their interaction on the signaling dynamics. Here, we analyzed the interplay of the IKK/ NF-κB and p53 pathway, which are both critical for the cellular response to DNA damage and have been implicated in tumor development. To systematically identify interaction points between both pathways, we perturbed IKK/ NF-κB signaling and tracked the changes in the response of p53 to DNA damage. Using computational methods, we show that several reactions in the p53 pathway are simultaneously affected by NF-κB signaling and that this combined action is necessary to explain altered behaviour of the p53 pathway. Hence, our results provide new insights into the interplay between the NF-κB and p53 pathway and help to gain a more comprehensive understanding of the crosstalk.

Modeling and measurement of signaling outcomes affecting decision making in noisy intracellular networks using machine learning methods

Characterization of decision-making in cells in response to received signals is of importance for understanding how cell fate is determined. The problem becomes multi-faceted and complex when we consider cellular heterogeneity and dynamics of biochemical processes. In this paper, we present a unified set of decision-theoretic, machine learning and statistical signal processing methods and metrics to model the precision of signaling decisions, in the presence of uncertainty, using single cell data. First, we introduce erroneous decisions that may result from signaling processes and identify false alarms and miss events associated with such decisions. Then, we present an optimal decision strategy which minimizes the total decision error probability. Additionally, we demonstrate how graphing receiver operating characteristic curves conveniently reveals the trade-off between false alarm and miss probabilities associated with different cell responses. Furthermore, we extend the introduced framework to incorporate the dynamics of biochemical processes and reactions in a cell, using multi-time point measurements and multi-dimensional outcome analysis and decision-making algorithms. The introduced multivariate signaling outcome modeling framework can be used to analyze several molecular species measured at the same or different time instants. We also show how the developed binary outcome analysis and decision-making approach can be extended to more than two possible outcomes. As an example and to show how the introduced methods can be used in practice, we apply them to single cell data of PTEN, an important intracellular regulatory molecule in a p53 system, in wild-type and abnormal cells. The unified signaling outcome modeling framework presented here can be applied to various organisms ranging from viruses, bacteria, yeast and lower metazoans to more complex organisms such as mammalian cells. Ultimately, this signaling outcome modeling approach can be utilized to better understand the transition from physiological to pathological conditions such as inflammation, various cancers and autoimmune diseases.

Multisite EGFR phosphorylation is regulated by adaptor protein abundances and dimer lifetimes

Differential epidermal growth factor receptor (EGFR) phosphorylation is thought to couple receptor activation to distinct signaling pathways. However, the molecular mechanisms responsible for biased signaling are unresolved due to a lack of insight into the phosphorylation patterns of full-length EGFR. We extended a single-molecule pull-down technique previously used to study protein-protein interactions to allow for robust measurement of receptor phosphorylation. We found that EGFR is predominantly phosphorylated at multiple sites, yet phosphorylation at specific tyrosines is variable and only a subset of receptors share phosphorylation at the same site, even with saturating ligand concentrations. We found distinct populations of receptors as soon as 1 min after ligand stimulation, indicating early diversification of function. To understand this heterogeneity, we developed a mathematical model. The model predicted that variations in phosphorylation are dependent on the abundances of signaling partners, while phosphorylation levels are dependent on dimer lifetimes. The predictions were confirmed in studies of cell lines with different expression levels of signaling partners, and in experiments comparing low- and high-affinity ligands and oncogenic EGFR mutants. These results reveal how ligand-regulated receptor dimerization dynamics and adaptor protein concentrations play critical roles in EGFR signaling.

Sample Preparation and Analysis of Single Cells Using High Performance MALDI FTICR Mass Spectrometry

Imaging mass spectrometry is a powerful technology that combines the molecular measurements of mass spectrometry with the spatial information inherent to microscopy. This unique combination of capabilities is ideally suited for the analysis of metabolites and lipids from single cells. This chapter describes a methodology for the sample preparation and analysis of single cells using high performance MALDI FTICR MS. Using this approach, we are able to generate profiles of lipid and metabolite expression from single cells that characterize cellular heterogeneity. This approach also enables the detection of variations in the expression profiles of lipids and metabolites induced by chemical stimulation of the cells. These results demonstrate that MALDI IMS provides an insightful view of lipid and metabolite expression useful in the characterization of a number of biological systems at the single cell level.

Counting growth factors in single cells with infrared quantum dots to measure discrete stimulation distributions

The distribution of single-cell properties across a population of cells can be measured using diverse tools, but no technology directly quantifies the biochemical stimulation events regulating these properties. Here we report digital counting of growth factors in single cells using fluorescent quantum dots and calibrated three-dimensional deconvolution microscopy (QDC-3DM) to reveal physiologically relevant cell stimulation distributions. We calibrate the fluorescence intensities of individual compact quantum dots labeled with epidermal growth factor (EGF) and demonstrate the necessity of near-infrared emission to overcome intrinsic cellular autofluoresence at the single-molecule level. When applied to human triple-negative breast cancer cells, we observe proportionality between stimulation and both receptor internalization and inhibitor response, reflecting stimulation heterogeneity contributions to intrinsic variability. We anticipate that QDC-3DM can be applied to analyze any peptidic ligand to reveal single-cell correlations between external stimulation and phenotypic variability, cell fate, and drug response.

Measuring growth factors in single cells at physiologically relevant stimulation doses is challenging. Here the authors use fluorescent quantum dots and calibrated three-dimensional deconvolution microscopy to digitally count growth factors in single cells and reveal stimulation distributions in cancer cells.

Perfection of eccentricity: Mitochondrial genomes of diplonemids

Mitochondria are the sandbox of evolution as exemplified most particularly by the diplonemids, a group of marine microeukaryotes. These protists are uniquely characterized by their highly multipartite mitochondrial genome and systematically fragmented genes whose pieces are spread out over several dozens of chromosomes. The type species Diplonema papillatum was the first member of this group in which the expression of fragmented mitochondrial genes was investigated experimentally. We now know that gene expression involves separate transcription of gene pieces (modules), RNA editing of module transcripts, and module joining to mature mRNAs and rRNAs. The mechanism of cognate module recognition and ligation is distinct from known intron splicing and remains to be uncovered. Here, we review the current status of research on mitochondrial genome architecture, as well as gene complement, structure, and expression modes in diplonemids. Further, we discuss the potential molecular mechanisms of posttranscriptional processing, and finally reflect on the evolutionary trajectories and trends of mtDNA evolution as seen in this protist group. © 2018 IUBMB Life, 70(12):1197-1206, 2018.

Morphological single cell profiling of the epithelial-mesenchymal transition

Single cells respond heterogeneously to biochemical treatments, which can complicate the analysis of in vitro and in vivo experiments. In particular, stressful perturbations may induce the epithelial-mesenchymal transition (EMT), a transformation through which compact, sensitive cells adopt an elongated, resistant phenotype. However, classical biochemical measurements based on population averages over large numbers cannot resolve single cell heterogeneity and plasticity. Here, we use high content imaging of single cell morphology to classify distinct phenotypic subpopulations after EMT. We first characterize a well-defined EMT induction through the master regulator Snail in mammary epithelial cells over 72 h. We find that EMT is associated with increased vimentin area as well as elongation of the nucleus and cytoplasm. These morphological features were integrated into a Gaussian mixture model that classified epithelial and mesenchymal phenotypes with >92% accuracy. We then applied this analysis to heterogeneous populations generated from less controlled EMT-inducing stimuli, including growth factors (TGF-β1), cell density, and chemotherapeutics (Taxol). Our quantitative, single cell approach has the potential to screen large heterogeneous cell populations for many types of phenotypic variability, and may thus provide a predictive assay for the preclinical assessment of targeted therapeutics.

Computation and measurement of cell decision making errors using single cell data

In this study a new computational method is developed to quantify decision making errors in cells, caused by noise and signaling failures. Analysis of tumor necrosis factor (TNF) signaling pathway which regulates the transcription factor Nuclear Factor κB (NF-κB) using this method identifies two types of incorrect cell decisions called false alarm and miss. These two events represent, respectively, declaring a signal which is not present and missing a signal that does exist. Using single cell experimental data and the developed method, we compute false alarm and miss error probabilities in wild-type cells and provide a formulation which shows how these metrics depend on the signal transduction noise level. We also show that in the presence of abnormalities in a cell, decision making processes can be significantly affected, compared to a wild-type cell, and the method is able to model and measure such effects. In the TNF—NF-κB pathway, the method computes and reveals changes in false alarm and miss probabilities in A20-deficient cells, caused by cell’s inability to inhibit TNF-induced NF-κB response. In biological terms, a higher false alarm metric in this abnormal TNF signaling system indicates perceiving more cytokine signals which in fact do not exist at the system input, whereas a higher miss metric indicates that it is highly likely to miss signals that actually exist. Overall, this study demonstrates the ability of the developed method for modeling cell decision making errors under normal and abnormal conditions, and in the presence of transduction noise uncertainty. Compared to the previously reported pathway capacity metric, our results suggest that the introduced decision error metrics characterize signaling failures more accurately. This is mainly because while capacity is a useful metric to study information transmission in signaling pathways, it does not capture the overlap between TNF-induced noisy response curves.

Cell continuously receives signals from the surrounding environment and is supposed to make correct decisions, i.e., respond properly to various signals and initiate certain cellular functions. Modeling and quantification of decision making processes in a cell have emerged as important areas of research in recent years. Due to signal transduction noise, cells respond differently to similar inputs, which may result in incorrect cell decisions. Here we develop a novel method for characterization of decision making processes in cells, using statistical signal processing and decision theory concepts. To demonstrate the utility of the method, we apply it to an important signaling pathway that regulates molecules which play key roles in cell survival. Our method reveals that cells can make two types of incorrect decisions, namely, false alarm and miss events. We measure the likelihood of these decisions using single cell experimental data, and demonstrate how these incorrect decisions are related to the signal transduction noise or absence of certain molecular functions. Using our method, decision making errors in other molecular systems can be modeled. Such models are useful for understanding and developing treatments for pathological processes such as inflammation, various cancers and autoimmune diseases.

Single Cell Profiling Using Ionic Liquid Matrix-Enhanced Secondary Ion Mass Spectrometry for Neuronal Cell Type Differentiation

A high-throughput single cell profiling method has been developed for matrix-enhanced-secondary ion mass spectrometry (ME-SIMS) to investigate the lipid profiles of neuronal cells. Populations of cells are dispersed onto the substrate, their locations determined using optical microscopy, and the cell locations used to guide the acquisition of SIMS spectra from the cells. Up to 2,000 cells can be assayed in one experiment at a rate of 6 s per cell. Multiple saturated and unsaturated phosphatidylcholines (PCs) and their fragments are detected and verified with tandem mass spectrometry from individual cells when ionic liquids are employed as a matrix. Optically guided single cell profiling with ME-SIMS is suitable for a range of cell sizes, from Aplysia californica neurons larger than 75 μm to 7-μm rat cerebellar neurons. ME-SIMS analysis followed by t-distributed stochastic neighbor embedding of peaks in the lipid molecular mass range (m/z 700-850) distinguishes several cell types from the rat central nervous system, largely based on the relative proportions of four dominant lipids, PC(32:0), PC(34:1), PC(36:1), and PC(38:5). Furthermore, subpopulations within each cell type are tentatively classified consistent with their endogenous lipid ratios. The results illustrate the efficacy of a new approach to classify single cell populations and subpopulations using SIMS profiling of lipid and metabolite contents. These methods are broadly applicable for high throughput single cell chemical analyses.

An analysis of early-stage IL-2 capture times in populations of T cells diffusively interacting in a confined environment

This numerical analysis examines early-stage Interlukin-2 (IL-2) capture in large populations of secreting T helper (Th) and absorbing T regulatory (Treg) cells in an attempt to provide rational guidelines for when diffusive interactions can affect the Th autocrine cycle, as reflected in capture times. Autocrine and paracrine capture is calculated over a wide range of conditions: the mix of cells in a population; cell size and spacing; antigen activated IL-2 secretion and Th receptor expression rates; receptor dissociation constant; and number of resting Treg receptors. Correlations for quickly estimating IL-2 capture over these conditions are provided. This study suggests that a typical Treg can scavenge a significant amount of IL-2 without affecting autocrine capture by the Th. As a result, Treg influence on autocrine capture is shorter-ranged than previously reported. It is conjectured that high early-stage paracrine relative to autocrine capture leads to faster receptor enhancement for a Treg than a Th. The resulting enhancement time gap is considerably longer and, thus, diffusive suppression more likely, for a weakly- as opposed to strongly-activated Th. The methodology can be extended to later-stage capture to confirm this conjecture and to diffusive interactions in other cell-type populations.

Modeling Signaling Networks to Advance New Cancer Therapies

Cell signaling pathways control cells' responses to their environment through an intricate network of proteins and small molecules partitioned by intracellular structures, such as the cytoskeleton and nucleus. Our understanding of these pathways has been revised recently with the advent of more advanced experimental techniques; no longer are signaling pathways viewed as linear cascades of information flowing from membrane-bound receptors to the nucleus. Instead, such pathways must be understood in the context of networks, and studying such networks requires an integration of computational and experimental approaches. This understanding is becoming more important in designing novel therapies for diseases such as cancer. Using the MAPK (mitogen-activated protein kinase) and PI3K (class I phosphoinositide-3' kinase) pathways as case studies of cellular signaling, we give an overview of these pathways and their functions. We then describe, using a number of case studies, how computational modeling has aided in understanding these pathways' deregulation in cancer, and how such understanding can be used to optimally tailor current therapies or help design new therapies against cancer.

A model for aryl hydrocarbon receptor-activated gene expression shows potency and efficacy changes and predicts squelching due to competition for transcription co-activators

A stochastic model of nuclear receptor-mediated transcription was developed based on activation of the aryl hydrocarbon receptor (AHR) by 2,3,7,8-tetrachlorodibenzodioxin (TCDD) and subsequent binding the activated AHR to xenobiotic response elements (XREs) on DNA. The model was based on effects observed in cells lines commonly used as in vitro experimental systems. Following ligand binding, the AHR moves into the cell nucleus and forms a heterodimer with the aryl hydrocarbon nuclear translocator (ARNT). In the model, a requirement for binding to DNA is that a generic coregulatory protein is subsequently bound to the AHR-ARNT dimer. Varying the amount of coregulator available within the nucleus altered both the potency and efficacy of TCDD for inducing for transcription of CYP1A1 mRNA, a commonly used marker for activation of the AHR. Lowering the amount of available cofactor slightly increased the EC50 for the transcriptional response without changing the efficacy or maximal response. Further reduction in the amount of cofactor reduced the efficacy and produced non-monotonic dose-response curves (NMDRCs) at higher ligand concentrations. The shapes of these NMDRCs were reminiscent of the phenomenon of squelching. Resource limitations for transcriptional machinery are becoming apparent in eukaryotic cells. Within single cells, nuclear receptor-mediated gene expression appears to be a stochastic process; however, intercellular communication and other aspects of tissue coordination may represent a compensatory process to maintain an organism’s ability to respond on a phenotypic level to various stimuli within an inconstant environment.

Quantitative analysis of receptor tyrosine kinase-effector coupling at functionally relevant stimulus levels

A major goal of current signaling research is to develop a quantitative understanding of how receptor activation is coupled to downstream signaling events and to functional cellular responses. Here, we measure how activation of the RET receptor tyrosine kinase on mouse neuroblastoma cells by the neurotrophin artemin (ART) is quantitatively coupled to key downstream effectors. We show that the efficiency of RET coupling to ERK and Akt depends strongly on ART concentration, and it is highest at the low (∼100 pM) ART levels required for neurite outgrowth. Quantitative discrimination between ERK and Akt pathway signaling similarly is highest at this low ART concentration. Stimulation of the cells with 100 pM ART activated RET at the rate of ∼10 molecules/cell/min, leading at 5-10 min to a transient peak of ∼150 phospho-ERK (pERK) molecules and ∼50 pAkt molecules per pRET, after which time the levels of these two signaling effectors fell by 25-50% while the pRET levels continued to slowly rise. Kinetic experiments showed that signaling effectors in different pathways respond to RET activation with different lag times, such that the balance of signal flux among the different pathways evolves over time. Our results illustrate that measurements using high, super-physiological growth factor levels can be misleading about quantitative features of receptor signaling. We propose a quantitative model describing how receptor-effector coupling efficiency links signal amplification to signal sensitization between receptor and effector, thereby providing insight into design principles underlying how receptors and their associated signaling machinery decode an extracellular signal to trigger a functional cellular outcome.

Deciphering the mechanism behind Fibroblast Growth Factor (FGF) induced biphasic signal-response profiles

BACKGROUND

The Fibroblast Growth Factor (FGF) pathway is driving various aspects of cellular responses in both normal and malignant cells. One interesting characteristic of this pathway is the biphasic nature of the cellular response to some FGF ligands like FGF2. Specifically, it has been shown that phenotypic behaviors controlled by FGF signaling, like migration and growth, reach maximal levels in response to intermediate concentrations, while high levels of FGF2 elicit weak responses. The mechanisms leading to the observed biphasic response remains unexplained.

RESULTS

A combination of experiments and computational modeling was used to understand the mechanism behind the observed biphasic signaling responses. FGF signaling involves a tertiary surface interaction that we captured with a computational model based on Ordinary Differential Equations (ODEs). It accounts for FGF2 binding to FGF receptors (FGFRs) and heparan sulfate glycosaminoglycans (HSGAGs), followed by receptor-phosphorylation, activation of the FRS2 adapter protein and the Ras-Raf signaling cascade. Quantitative protein assays were used to measure the dynamics of phosphorylated ERK (pERK) in response to a wide range of FGF2 ligand concentrations on a fine-grained time scale for the squamous cell lung cancer cell line H1703. We developed a novel approach combining Particle Swarm Optimization (PSO) and feature-based constraints in the objective function to calibrate the computational model to the experimental data. The model is validated using a series of extracellular and intracellular perturbation experiments. We demonstrate that in silico model predictions are in accordance with the observed in vitro results.

CONCLUSIONS

Using a combined approach of computational modeling and experiments we found that competition between binding of the ligand FGF2 to HSGAG and FGF receptor leads to the biphasic response. At low to intermediate concentrations of FGF2 there are sufficient free FGF receptors available for the FGF2-HSGAG complex to enable the formation of the trimeric signaling unit. At high ligand concentrations the ligand binding sites of the receptor become saturated and the trimeric signaling unit cannot be formed. This insight into the pathway is an important consideration for the pharmacological inhibition of this pathway.

Influence of the microenvironment on cell fate determination and migration

Several critical cell functions are influenced not only by internal cellular machinery but also by external mechanical and biochemical cues from the surrounding microenvironment. Slight changes to the microenvironment can result in dramatic changes to the cell's phenotype; for example, a change in the nutrients or pH of a tumor microenvironment can result in increased tumor metastasis. While cellular fate and the regulators of cell fate have been studied in detail for several decades now, our understanding of the extracellular regulators remains qualitative and far from comprehensive. In this review, we discuss the microenvironment influence on cell fate in terms of adhesion, migration, and differentiation and focus on both developments in experimental and computation tools to analyze cellular fate.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

Exhaustively characterizing feasible logic models of a signaling network using Answer Set Programming

MOTIVATION

Logic modeling is a useful tool to study signal transduction across multiple pathways. Logic models can be generated by training a network containing the prior knowledge to phospho-proteomics data. The training can be performed using stochastic optimization procedures, but these are unable to guarantee a global optima or to report the complete family of feasible models. This, however, is essential to provide precise insight in the mechanisms underlaying signal transduction and generate reliable predictions.

RESULTS

We propose the use of Answer Set Programming to explore exhaustively the space of feasible logic models. Toward this end, we have developed caspo, an open-source Python package that provides a powerful platform to learn and characterize logic models by leveraging the rich modeling language and solving technologies of Answer Set Programming. We illustrate the usefulness of caspo by revisiting a model of pro-growth and inflammatory pathways in liver cells. We show that, if experimental error is taken into account, there are thousands (11 700) of models compatible with the data. Despite the large number, we can extract structural features from the models, such as links that are always (or never) present or modules that appear in a mutual exclusive fashion. To further characterize this family of models, we investigate the input-output behavior of the models. We find 91 behaviors across the 11 700 models and we suggest new experiments to discriminate among them. Our results underscore the importance of characterizing in a global and exhaustive manner the family of feasible models, with important implications for experimental design.

AVAILABILITY

caspo is freely available for download (license GPLv3) and as a web service at http://caspo.genouest.org/.

SUPPLEMENTARY INFORMATION

Supplementary materials are available at Bioinformatics online.

CONTACT

santiago.videla@irisa.fr.

Diversity training for signal transduction: leveraging cell-to-cell variability to dissect cellular signaling, differentiation and death

Populations of 'identical' cells are rarely truly identical. Even when in the same state of differentiation, isogenic cells may vary in expression of key signaling regulators, activate signal transduction at different thresholds, and consequently respond heterogeneously to a given stimulus. Here, we review how new experimental and analytical techniques are suited to connect these different levels of variability, quantitatively mapping the effects of cell-to-cell variability on cellular decision-making. In particular, we summarize how this helps classify signaling regulators according to the impact of their variability on biological functions. We further discuss how variability can also be leveraged to shed light on the molecular mechanisms regulating cellular signaling, from the individual cell to the population of cells as a whole.