Modelling the dynamics of signalling pathways

Canalizing kernel for cell fate determination

The tendency for cell fate to be robust to most perturbations, yet sensitive to certain perturbations raises intriguing questions about the existence of a key path within the underlying molecular network that critically determines distinct cell fates. Reprogramming and trans-differentiation clearly show examples of cell fate change by regulating only a few or even a single molecular switch. However, it is still unknown how to identify such a switch, called a master regulator, and how cell fate is determined by its regulation. Here, we present CAESAR, a computational framework that can systematically identify master regulators and unravel the resulting canalizing kernel, a key substructure of interconnected feedbacks that is critical for cell fate determination. We demonstrate that CAESAR can successfully predict reprogramming factors for de-differentiation into mouse embryonic stem cells and trans-differentiation of hematopoietic stem cells, while unveiling the underlying essential mechanism through the canalizing kernel. CAESAR provides a system-level understanding of how complex molecular networks determine cell fates.

Reducing State Conflicts between Network Motifs Synergistically Enhances Cancer Drug Effects and Overcomes Adaptive Resistance

Inducing apoptosis in cancer cells is a primary goal in anti-cancer therapy, but curing cancer with a single drug is unattainable due to drug resistance. The complex molecular network in cancer cells causes heterogeneous responses to single-target drugs, thereby inducing an adaptive drug response. Here, we showed that targeted drug perturbations can trigger state conflicts between multi-stable motifs within a molecular regulatory network, resulting in heterogeneous drug responses. However, we revealed that properly regulating an interconnecting molecule between these motifs can synergistically minimize the heterogeneous responses and overcome drug resistance. We extracted the essential cellular response dynamics of the Boolean network driven by the target node perturbation and developed an algorithm to identify a synergistic combinatorial target that can reduce heterogeneous drug responses. We validated the proposed approach using exemplary network models and a gastric cancer model from a previous study by showing that the targets identified with our algorithm can better drive the networks to desired states than those with other control theories. Of note, our approach suggests a new synergistic pair of control targets that can increase cancer drug efficacy to overcome adaptive drug resistance.

Deep learning untangles the resistance mechanism of p53 reactivator in lung cancer cells

Tumor suppressor p53 plays a pivotal role in suppressing cancer, so various drugs has been suggested to upregulate its function. However, drug resistance is still the biggest hurdle to be overcome. To address this, we developed a deep learning model called AnoDAN (anomalous gene detection using generative adversarial networks and graph neural networks for overcoming drug resistance) that unravels the hidden resistance mechanisms and identifies a combinatorial target to overcome the resistance. Our findings reveal that the TGF-β signaling pathway, alongside the p53 signaling pathway, mediates the resistance, with THBS1 serving as a core regulatory target in both pathways. Experimental validation in lung cancer cells confirms the effects of THBS1 on responsiveness to a p53 reactivator. We further discovered the positive feedback loop between THBS1 and the TGF-β pathway as the main source of resistance. This study enhances our understanding of p53 regulation and offers insights into overcoming drug resistance.

Normalizing Input-Output Relationships of Cancer Networks for Reversion Therapy

Accumulated genetic alterations in cancer cells distort cellular stimulus-response (or input-output) relationships, resulting in uncontrolled proliferation. However, the complex molecular interaction network within a cell implicates a possibility of restoring such distorted input-output relationships by rewiring the signal flow through controlling hidden molecular switches. Here, a system framework of analyzing cellular input-output relationships in consideration of various genetic alterations and identifying possible molecular switches that can normalize the distorted relationships based on Boolean network modeling and dynamics analysis is presented. Such reversion is demonstrated by the analysis of a number of cancer molecular networks together with a focused case study on bladder cancer with in vitro experiments and patient survival data analysis. The origin of reversibility from an evolutionary point of view based on the redundancy and robustness intrinsically embedded in complex molecular regulatory networks is further discussed.

Critical transition and reversion of tumorigenesis

Cancer is caused by the accumulation of genetic alterations and therefore has been historically considered to be irreversible. Intriguingly, several studies have reported that cancer cells can be reversed to be normal cells under certain circumstances. Despite these experimental observations, conceptual and theoretical frameworks that explain these phenomena and enable their exploration in a systematic way are lacking. In this review, we provide an overview of cancer reversion studies and describe recent advancements in systems biological approaches based on attractor landscape analysis. We suggest that the critical transition in tumorigenesis is an important clue for achieving cancer reversion. During tumorigenesis, a critical transition may occur at a tipping point, where cells undergo abrupt changes and reach a new equilibrium state that is determined by complex intracellular regulatory events. We introduce a conceptual framework based on attractor landscapes through which we can investigate the critical transition in tumorigenesis and induce its reversion by combining intracellular molecular perturbation and extracellular signaling controls. Finally, we present a cancer reversion therapy approach that may be a paradigm-changing alternative to current cancer cell-killing therapies.

PRRX1 is a master transcription factor of stromal fibroblasts for myofibroblastic lineage progression

Although stromal fibroblasts play a critical role in cancer progression, their identities remain unclear as they exhibit high heterogeneity and plasticity. Here, a master transcription factor (mTF) constructing core-regulatory circuitry, PRRX1, which determines the fibroblast lineage with a myofibroblastic phenotype, is identified for the fibroblast subgroup. PRRX1 orchestrates the functional drift of fibroblasts into myofibroblastic phenotype via TGF-β signaling by remodeling a super-enhancer landscape. Such reprogrammed fibroblasts have myofibroblastic functions resulting in markedly enhanced tumorigenicity and aggressiveness of cancer. PRRX1 expression in cancer-associated fibroblast (CAF) has an unfavorable prognosis in multiple cancer types. Fibroblast-specific PRRX1 depletion induces long-term and sustained complete remission of chemotherapy-resistant cancer in genetically engineered mice models. This study reveals CAF subpopulations based on super-enhancer profiles including PRRX1. Therefore, mTFs, including PRRX1, provide another opportunity for establishing a hierarchical classification system of fibroblasts and cancer treatment by targeting fibroblasts.

Cancer associated fibroblasts are an important and highly heterogeneous component of the tumor microenvironment. Here the authors identify PRRX1 as a master transcription factor determining a fibroblast lineage with myofibroblastic phenotype, associated with unfavourable prognosis in several cancer types.

A logical network-based drug-screening platform for Alzheimer's disease representing pathological features of human brain organoids

Developing effective drugs for Alzheimer's disease (AD), the most common cause of dementia, has been difficult because of complicated pathogenesis. Here, we report an efficient, network-based drug-screening platform developed by integrating mathematical modeling and the pathological features of AD with human iPSC-derived cerebral organoids (iCOs), including CRISPR-Cas9-edited isogenic lines. We use 1300 organoids from 11 participants to build a high-content screening (HCS) system and test blood-brain barrier-permeable FDA-approved drugs. Our study provides a strategy for precision medicine through the convergence of mathematical modeling and a miniature pathological brain model using iCOs.

Boolean Feedforward Neural Network Modeling of Molecular Regulatory Networks for Cellular State Conversion

The molecular regulatory network (MRN) within a cell determines cellular states and transitions between them. Thus, modeling of MRNs is crucial, but this usually requires extensive analysis of time-series measurements, which is extremely difficult to obtain from biological experiments. However, single-cell measurement data such as single-cell RNA-sequencing databases have recently provided a new insight into resolving this problem by ordering thousands of cells in pseudo-time according to their differential gene expressions. Neural network modeling can be employed by using temporal data as learning data. In contrast, Boolean network modeling of MRNs has a growing interest, as it is a parameter-free logical modeling and thereby robust to noisy data while still capturing essential dynamics of biological networks. In this study, we propose a Boolean feedforward neural network (FFN) modeling by combining neural network and Boolean network modeling approach to reconstruct a practical and useful MRN model from large temporal data. Furthermore, analyzing the reconstructed MRN model can enable us to identify control targets for potential cellular state conversion. Here, we show the usefulness of Boolean FFN modeling by demonstrating its applicability through a toy model and biological networks.

Realizing Cancer Precision Medicine by Integrating Systems Biology and Nanomaterial Engineering

Many clinical trials for cancer precision medicine have yielded unsatisfactory results due to challenges such as drug resistance and low efficacy. Drug resistance is often caused by the complex compensatory regulation within the biomolecular network in a cancer cell. Recently, systems biological studies have modeled and simulated such complex networks to unravel the hidden mechanisms of drug resistance and identify promising new drug targets or combinatorial or sequential treatments for overcoming resistance to anticancer drugs. However, many of the identified targets or treatments present major difficulties for drug development and clinical application. Nanocarriers represent a path forward for developing therapies with these "undruggable" targets or those that require precise combinatorial or sequential application, for which conventional drug delivery mechanisms are unsuitable. Conversely, a challenge in nanomedicine has been low efficacy due to heterogeneity of cancers in patients. This problem can also be resolved through systems biological approaches by identifying personalized targets for individual patients or promoting the drug responses. Therefore, integration of systems biology and nanomaterial engineering will enable the clinical application of cancer precision medicine to overcome both drug resistance of conventional treatments and low efficacy of nanomedicine due to patient heterogeneity.

Feedback analysis identifies a combination target for overcoming adaptive resistance to targeted cancer therapy

Targeted drugs aim to treat cancer by directly inhibiting oncogene activity or oncogenic pathways, but drug resistance frequently emerges. Due to the intricate dynamics of cancer signaling networks, which contain complex feedback regulations, cancer cells can rewire these networks to adapt to and counter the cytotoxic effects of a drug, thereby limiting the efficacy of targeted therapies. To identify a combinatorial drug target that can overcome such a limitation, we developed a Boolean network simulation and analysis framework and applied this approach to a large-scale signaling network of colorectal cancer with integrated genomic information. We discovered Src as a critical combination drug target that can overcome the adaptive resistance to the targeted inhibition of mitogen-activated protein kinase pathway by blocking the essential feedback regulation responsible for resistance. The proposed framework is generic and can be widely used to identify drug targets that can overcome adaptive resistance to targeted therapies.

Combined Positive and Negative Feedback Allows Modulation of Neuronal Oscillation Frequency during Sensory Processing

A key step in sensory information processing involves modulation and integration of neuronal oscillations in disparate frequency bands, a poorly understood process. Here, we investigate how top-down input causes frequency changes in slow oscillations during sensory processing and, in turn, how the slow oscillations are combined with fast oscillations (which encode sensory input). Using experimental connectivity patterns and strengths of interneurons, we develop a system-level model of a neuronal circuit controlling these oscillatory behaviors, allowing us to understand the mechanisms responsible for the observed oscillatory behaviors. Our analysis discovers a circuit capable of producing the observed oscillatory behaviors and finds that a detailed balance in the strength of synaptic connections is the critical determinant to produce such oscillatory behaviors. We not only uncover how disparate frequency bands are modulated and combined but also give insights into the causes of abnormal neuronal activities present in brain disorders.

Signal flow control of complex signaling networks

Complex disease such as cancer is often caused by genetic mutations that eventually alter the signal flow in the intra-cellular signaling network and result in different cell fate. Therefore, it is crucial to identify control targets that can most effectively block such unwanted signal flow. For this purpose, systems biological analysis provides a useful framework, but mathematical modeling of complicated signaling networks requires massive time-series measurements of signaling protein activity levels for accurate estimation of kinetic parameter values or regulatory logics. Here, we present a novel method, called SFC (Signal Flow Control), for identifying control targets without the information of kinetic parameter values or regulatory logics. Our method requires only the structural information of a signaling network and is based on the topological estimation of signal flow through the network. SFC will be particularly useful for a large-scale signaling network to which parameter estimation or inference of regulatory logics is no longer applicable in practice. The identified control targets have significant implication in drug development as they can be putative drug targets.

Minimal intervening control of biomolecular networks leading to a desired cellular state

A cell phenotype can be represented by an attractor state of the underlying molecular regulatory network, to which other network states eventually converge. Here, the set of states converging to each attractor is called its basin of attraction. A central question is how to drive a particular cell state toward a desired attractor with minimal interventions on the network system. We develop a general control framework of complex Boolean networks to provide an answer to this question by identifying control targets on which one-time temporary perturbation can induce a state transition to the boundary of a desired attractor basin. Examples are shown to illustrate the proposed control framework which is also applicable to other types of complex Boolean networks.

Systems analysis identifies potential target genes to overcome cetuximab resistance in colorectal cancer cells

Cetuximab (CTX), a monoclonal antibody against epidermal growth factor receptor, is being widely used for colorectal cancer (CRC) with wild-type (WT) KRAS. However, its responsiveness is still very limited and WT KRAS is not enough to indicate such responsiveness. Here, by analyzing the gene expression data of CRC patients treated with CTX monotherapy, we have identified DUSP4, ETV5, GNB5, NT5E, and PHLDA1 as potential targets to overcome CTX resistance. We found that knockdown of any of these five genes can increase CTX sensitivity in KRAS WT cells. Interestingly, we further found that GNB5 knockdown can increase CTX sensitivity even for KRAS mutant cells. We unraveled that GNB5 overexpression contributes to CTX resistance by modulating the Akt signaling pathway from experiments and mathematical simulation. Overall, these results indicate that GNB5 might be a promising target for combination therapy with CTX irrespective of KRAS mutation.

The Hidden Control Architecture of Complex Brain Networks

The brain controls various cognitive functions in a robust and efficient way. What is the control architecture of brain networks that enables such robust and optimal control? Is this brain control architecture distinct from that of other complex networks? Here, we developed a framework to delineate a control architecture of a complex network that is compatible with the behavior of the network and applied the framework to structural brain networks and other complex networks. As a result, we revealed that the brain networks have a distributed and overlapping control architecture governed by a small number of control nodes, which may be responsible for the robust and efficient brain functions. Moreover, our artificial network evolution analysis showed that the distributed and overlapping control architecture of the brain network emerges when it evolves toward increasing both robustness and efficiency.

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We develop a framework to delineate the control architecture of brain networks

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The control architecture of brain networks is compared with other complex networks

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Brain networks have a distributed and overlapping control architecture

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Robust and efficient brain functions might be rooted in its control architecture

Pancreatic Beta Cell G-Protein Coupled Receptors and Second Messenger Interactions: A Systems Biology Computational Analysis

Insulin secretory in pancreatic beta-cells responses to nutrient stimuli and hormonal modulators include multiple messengers and signaling pathways with complex interdependencies. Here we present a computational model that incorporates recent data on glucose metabolism, plasma membrane potential, G-protein-coupled-receptors (GPCR), cytoplasmic and endoplasmic reticulum calcium dynamics, cAMP and phospholipase C pathways that regulate interactions between second messengers in pancreatic beta-cells. The values of key model parameters were inferred from published experimental data. The model gives a reasonable fit to important aspects of experimentally measured metabolic and second messenger concentrations and provides a framework for analyzing the role of metabolic, hormones and neurotransmitters changes on insulin secretion. Our analysis of the dynamic data provides support for the hypothesis that activation of Ca²⁺-dependent adenylyl cyclases play a critical role in modulating the effects of glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP) and catecholamines. The regulatory properties of adenylyl cyclase isoforms determine fluctuations in cytoplasmic cAMP concentration and reveal a synergistic action of glucose, GLP-1 and GIP on insulin secretion. On the other hand, the regulatory properties of phospholipase C isoforms determine the interaction of glucose, acetylcholine and free fatty acids (FFA) (that act through the FFA receptors) on insulin secretion. We found that a combination of GPCR agonists activating different messenger pathways can stimulate insulin secretion more effectively than a combination of GPCR agonists for a single pathway. This analysis also suggests that the activators of GLP-1, GIP and FFA receptors may have a relatively low risk of hypoglycemia in fasting conditions whereas an activator of muscarinic receptors can increase this risk. This computational analysis demonstrates that study of second messenger pathway interactions will improve understanding of critical regulatory sites, how different GPCRs interact and pharmacological targets for modulating insulin secretion in type 2 diabetes.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

A data-driven, mathematical model of mammalian cell cycle regulation

Few of >150 published cell cycle modeling efforts use significant levels of data for tuning and validation. This reflects the difficultly to generate correlated quantitative data, and it points out a critical uncertainty in modeling efforts. To develop a data-driven model of cell cycle regulation, we used contiguous, dynamic measurements over two time scales (minutes and hours) calculated from static multiparametric cytometry data. The approach provided expression profiles of cyclin A2, cyclin B1, and phospho-S10-histone H3. The model was built by integrating and modifying two previously published models such that the model outputs for cyclins A and B fit cyclin expression measurements and the activation of B cyclin/Cdk1 coincided with phosphorylation of histone H3. The model depends on Cdh1-regulated cyclin degradation during G1, regulation of B cyclin/Cdk1 activity by cyclin A/Cdk via Wee1, and transcriptional control of the mitotic cyclins that reflects some of the current literature. We introduced autocatalytic transcription of E2F, E2F regulated transcription of cyclin B, Cdc20/Cdh1 mediated E2F degradation, enhanced transcription of mitotic cyclins during late S/early G2 phase, and the sustained synthesis of cyclin B during mitosis. These features produced a model with good correlation between state variable output and real measurements. Since the method of data generation is extensible, this model can be continually modified based on new correlated, quantitative data.

Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices

Abstract

Simulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.

CCCTC-binding factor mediates effects of glucose on beta cell survival

OBJECTIVES

Pancreatic islet β-cell survival is paramount for regulation of insulin activity and for maintaining glucose homeostasis. Recently, Pax6 has been shown to be essential for many vital functions in β-cells, although many molecular mechanisms of its homeostasis in β-cells remain unclear. The present study investigates novel effects of glucose- and insulin-induced CCCTC-binding factor (CTCF) activity on Pax6 gene expression as well as for subsequent effects of insulin-activated signalling pathways, on β-cell proliferation.

MATERIALS AND METHODS

Pancreatic β-TC-1-6 cells were cultured in DMEM and stimulated with high concentrations of glucose (5-125 mm); cell viability was assessed by MTT assay. Effects of CTCF on Pax6 were evaluated in the high glucose-induced environment and CTCF/Erk-suppressed cells, by promoter reporter and western blotting analyses.

RESULTS

Increases in glucose and insulin concentrations upregulated CTCF and consequently downregulated Pax6 in β-cell survival and proliferation. Knocking-down CTCF directly affected Pax6 transcription through CTCF binding and blocked the response to glucose. Altered Erk activity mediated effects of CTCF on controlling Pax6 expression, which partially regulated β-cell proliferation.

CONCLUSIONS

CTCF functioned as a molecular mediator between insulin-induced upstream Erk signalling and Pax6 expression in these pancreatic β-cells. This pathway may contribute to regulation of β-cell survival and proliferation.

A protein turnover signaling motif controls the stimulus-sensitivity of stress response pathways

Stimulus-induced perturbations from the steady state are a hallmark of signal transduction. In some signaling modules, the steady state is characterized by rapid synthesis and degradation of signaling proteins. Conspicuous among these are the p53 tumor suppressor, its negative regulator Mdm2, and the negative feedback regulator of NFκB, IκBα. We investigated the physiological importance of this turnover, or flux, using a computational method that allows flux to be systematically altered independently of the steady state protein abundances. Applying our method to a prototypical signaling module, we show that flux can precisely control the dynamic response to perturbation. Next, we applied our method to experimentally validated models of p53 and NFκB signaling. We find that high p53 flux is required for oscillations in response to a saturating dose of ionizing radiation (IR). In contrast, high flux of Mdm2 is not required for oscillations but preserves p53 sensitivity to sub-saturating doses of IR. In the NFκB system, degradation of NFκB-bound IκB by the IκB kinase (IKK) is required for activation in response to TNF, while high IKK-independent degradation prevents spurious activation in response to metabolic stress or low doses of TNF. Our work identifies flux pairs with opposing functional effects as a signaling motif that controls the stimulus-sensitivity of the p53 and NFκB stress-response pathways, and may constitute a general design principle in signaling pathways.

Eukaryotic cells constantly synthesize new proteins and degrade old ones. While most proteins are degraded within 24 hours of being synthesized, some proteins are short-lived and exist for only minutes. Using mathematical models, we asked how rapid turnover, or flux, of signaling proteins might regulate the activation of two well-known transcription factors, p53 and NFκB. p53 is a cell cycle regulator that is activated in response to DNA damage, for example, due to ionizing radiation. NFκB is a regulator of immunity and responds to inflammatory signals like the macrophage-secreted cytokine, TNF. Both p53 and NFκB are controlled by at least one flux whose effect on activation is positive and one whose effect is negative. For p53 these are the turnover of p53 and Mdm2, respectively. For NFκB they are the TNF-dependent and -independent turnover of the NFκB inhibitor, IκB. We find that juxtaposition of a positive and negative flux allows for precise tuning of the sensitivity of these transcription factors to different environmental signals. Our results therefore suggest that rapid synthesis and degradation of signaling proteins, though energetically wasteful, may be a common mechanism by which eukaryotic cells regulate their sensitivity to environmental stimuli.

Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models

The steady states of cells affect their response to perturbation. Indeed, diagnostic markers for predicting the response to therapeutic perturbation are often based on steady state measurements. In spite of this, no method exists to systematically characterize the relationship between steady state and response. Mathematical models are established tools for studying cellular responses, but characterizing their relationship to the steady state requires that it have a parametric, or analytical, expression. For some models, this expression can be derived by the King-Altman method. However, King-Altman requires that no substrate act as an enzyme, and is therefore not applicable to most models of signal transduction. For this reason we developed py-substitution, a simple but general method for deriving analytical expressions for the steady states of mass action models. Where the King-Altman method is applicable, we show that py-substitution yields an equivalent expression, and at comparable efficiency. We use py-substitution to study the relationship between steady state and sensitivity to the anti-cancer drug candidate, dulanermin (recombinant human TRAIL). First, we use py-substitution to derive an analytical expression for the steady state of a published model of TRAIL-induced apoptosis. Next, we show that the amount of TRAIL required for cell death is sensitive to the steady state concentrations of procaspase 8 and its negative regulator, Bar, but not the other procaspase molecules. This suggests that activation of caspase 8 is a critical point in the death decision process. Finally, we show that changes in the threshold at which TRAIL results in cell death is not always equivalent to changes in the time of death, as is commonly assumed. Our work demonstrates that an analytical expression is a powerful tool for identifying steady state determinants of the cellular response to perturbation. All code is available at http://signalingsystems.ucsd.edu/models-and-code/ or as supplementary material accompanying this paper.

Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions

The numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.

Dynamic regulation of Tgf-B signaling by Tif1γ: a computational approach

TIF1γ (Transcriptional Intermediary Factor 1 γ) has been implicated in Smad-dependent signaling by Transforming Growth Factor beta (TGF-β). Paradoxically, TIF1γ functions both as a transcriptional repressor or as an alternative transcription factor that promotes TGF-β signaling. Using ordinary differential-equation models, we have investigated the effect of TIF1γ on the dynamics of TGF-β signaling. An integrative model that includes the formation of transient TIF1γ-Smad2-Smad4 ternary complexes is the only one that can account for TGF-β signaling compatible with the different observations reported for TIF1γ. In addition, our model predicts that varying TIF1γ/Smad4 ratios play a critical role in the modulation of the transcriptional signal induced by TGF-β, especially for short stimulation times that mediate higher threshold responses. Chromatin immunoprecipitation analyses and quantification of the expression of TGF-β target genes as a function TIF1γ/Smad4 ratios fully validate this hypothesis. Our integrative model, which successfully unifies the seemingly opposite roles of TIF1γ, also reveals how changing TIF1γ/Smad4 ratios affect the cellular response to stimulation by TGF-β, accounting for a highly graded determination of cell fate.

A framework for modeling the relationship between cellular steady-state and stimulus-responsiveness

In cell signaling systems, the abundances of signaling molecules are generally thought to determine the response to stimulation. However, the kinetics of molecular processes, for example receptor trafficking and protein turnover, may also play an important role. Few studies have systematically examined this relationship between the resting state and stimulus-responsiveness. Fewer still have investigated the relative contribution of steady-state concentrations and reaction kinetics. Here we describe a mathematical framework for modeling the resting state of signaling systems. Among other things, this framework allows steady-state concentration measurements to be used in parameterizing kinetic models, and enables comprehensive characterization of the relationship between the resting state and the cellular response to stimulation.