Interplay between SMAD2 and STAT5A is a critical determinant of IL-17A/IL-17F differential expression.

Interleukins (IL)-17A and F are critical cytokines in anti-microbial immunity but also contribute to auto-immune pathologies. Recent evidence suggests that they may be differentially produced by T-helper (Th) cells, but the underlying mechanisms remain unknown. To address this question, we built a regulatory graph integrating all reported upstream regulators of IL-17A and F, completed by ChIP-seq data analyses. The resulting regulatory graph encompasses 82 components and 136 regulatory links. The graph was then supplemented by logical rules calibrated with original flow cytometry data using naive CD4+ T cells, in conditions inducing IL-17A or IL-17F. The model displays specific stable states corresponding to virtual phenotypes explaining IL-17A and IL-17F differential regulation across eight cytokine stimulatory conditions. Our model analysis points to the transcription factors NFAT2A, STAT5A and SMAD2 as key regulators of the differential expression of IL-17A and IL-17F, with STAT5A controlling IL-17F expression, and an interplay of NFAT2A, STAT5A and SMAD2 controlling IL-17A expression. We experimentally observed that the production of IL-17A was correlated with an increase of SMAD2 transcription, and the expression of IL-17F correlated with an increase of BLIMP-1 transcription, together with an increase of STAT5A expression (mRNA), as predicted by our model. Interestingly, RORγt presumably plays a more determinant role in IL-17A expression as compared to IL-17F expression. In conclusion, we propose the first mechanistic model accounting for the differential expression of IL-17A and F in Th cells, providing a basis to design novel therapeutic interventions in auto-immune and inflammatory diseases.

Contribution of ROS and metabolic status to neonatal and adult CD8+ T cell activation.

In neonatal T cells, a low response to infection contributes to a high incidence of morbidity and mortality of neonates. Here we have evaluated the impact of the cytoplasmic and mitochondrial levels of Reactive Oxygen Species of adult and neonatal CD8+ T cells on their activation potential. We have also constructed a logical model connecting metabolism and ROS with T cell signaling. Our model indicates the interplay between antigen recognition, ROS and metabolic status in T cell responses. This model displays alternative stable states corresponding to different cell fates, i.e. quiescent, activated and anergic states, depending on ROS levels. Stochastic simulations with this model further indicate that differences in ROS status at the cell population level contribute to the lower activation rate of neonatal, compared to adult, CD8+ T cells upon TCR engagement. These results are relevant for neonatal health care. Our model can serve to analyze the impact of metabolic shift during cancer in which, similar to neonatal cells, a high glycolytic rate and low concentrations of glutamine and arginine promote tumor tolerance.

A Quantitative Multivariate Model of Human Dendritic Cell-T Helper Cell Communication.

Cell-cell communication involves a large number of molecular signals that function as words of a complex language whose grammar remains mostly unknown. Here, we describe an integrative approach involving (1) protein-level measurement of multiple communication signals coupled to output responses in receiving cells and (2) mathematical modeling to uncover input-output relationships and interactions between signals. Using human dendritic cell (DC)-T helper (Th) cell communication as a model, we measured 36 DC-derived signals and 17 Th cytokines broadly covering Th diversity in 428 observations. We developed a data-driven, computationally validated model capturing 56 already described and 290 potentially novel mechanisms of Th cell specification. By predicting context-dependent behaviors, we demonstrate a new function for IL-12p70 as an inducer of Th17 in an IL-1 signaling context. This work provides a unique resource to decipher the complex combinatorial rules governing DC-Th cell communication and guide their manipulation for vaccine design and immunotherapies.

Cooperation between T cell receptor and Toll-like receptor 5 signaling for CD4+ T cell activation.

CD4+ T cells recognize antigens through their T cell receptors (TCRs); however, additional signals involving costimulatory receptors, for example, CD28, are required for proper T cell activation. Alternative costimulatory receptors have been proposed, including members of the Toll-like receptor (TLR) family, such as TLR5 and TLR2. To understand the molecular mechanism underlying a potential costimulatory role for TLR5, we generated detailed molecular maps and logical models for the TCR and TLR5 signaling pathways and a merged model for cross-interactions between the two pathways. Furthermore, we validated the resulting model by analyzing how T cells responded to the activation of these pathways alone or in combination, in terms of the activation of the transcriptional regulators CREB, AP-1 (c-Jun), and NF-κB (p65). Our merged model accurately predicted the experimental results, showing that the activation of TLR5 can play a similar role to that of CD28 activation with respect to AP-1, CREB, and NF-κB activation, thereby providing insights regarding the cross-regulation of these pathways in CD4+ T cells.

On logical bifurcation diagrams.

Bifurcation theory provides a powerful framework to analyze the dynamics of differential systems as a function of specific parameters. Abou-Jaoudé et al. (2009) introduced the concept of logical bifurcation diagrams, an analog of bifurcation diagrams for the logical modeling framework. In this work, we propose a formal definition of this concept. Since logical models are inherently discrete, we use the piecewise differential (PWLD) framework to introduce the underlying bifurcation parameters. Given a regulatory graph, a set of PWLD models is mapped to a set of logical models consistent with this graph, thereby linking continuous changes of bifurcation parameters to sequences of valuations of logical parameters. A logical bifurcation diagram corresponds then to a sequence of valuations of the logical parameters (with their associated set of attractors) consistent with at least one bifurcation diagram of the set of PWLD models. Necessary conditions on logical bifurcation diagrams in the general case, as well as a characterization of these diagrams in the Boolean case, exploiting a partial order between the logical parameters, are provided. We also propose a procedure to determine a logical bifurcation diagram of maximum length, starting from an initial valuation of the logical parameters, in the Boolean case. Finally, we apply our methodology to the analysis of a biological model of the p53-Mdm2 network.

Logical Modeling and Analysis of Cellular Regulatory Networks With GINsim 3.0.

The logical formalism is well adapted to model large cellular networks, in particular when detailed kinetic data are scarce. This tutorial focuses on this well-established qualitative framework. Relying on GINsim (release 3.0), a software implementing this formalism, we guide the reader step by step toward the definition, the analysis and the simulation of a four-node model of the mammalian p53-Mdm2 network.

Logical modeling of lymphoid and myeloid cell specification and transdifferentiation.

Blood cells are derived from a common set of hematopoietic stem cells, which differentiate into more specific progenitors of the myeloid and lymphoid lineages, ultimately leading to differentiated cells. This developmental process is controlled by a complex regulatory network involving cytokines and their receptors, transcription factors, and chromatin remodelers. Using public data and data from our own molecular genetic experiments (quantitative PCR, Western blot, EMSA) or genome-wide assays (RNA-sequencing, ChIP-sequencing), we have assembled a comprehensive regulatory network encompassing the main transcription factors and signaling components involved in myeloid and lymphoid development. Focusing on B-cell and macrophage development, we defined a qualitative dynamical model recapitulating cytokine-induced differentiation of common progenitors, the effect of various reported gene knockdowns, and the reprogramming of pre-B cells into macrophages induced by the ectopic expression of specific transcription factors. The resulting network model can be used as a template for the integration of new hematopoietic differentiation and transdifferentiation data to foster our understanding of lymphoid/myeloid cell-fate decisions.

Formal derivation of qualitative dynamical models from biochemical networks.

As technological advances allow a better identification of cellular networks, large-scale molecular data are swiftly produced, allowing the construction of large and detailed molecular interaction maps. One approach to unravel the dynamical properties of such complex systems consists in deriving coarse-grained dynamical models from these maps, which would make the salient properties emerge. We present here a method to automatically derive such models, relying on the abstract interpretation framework to formally relate model behaviour at different levels of description. We illustrate our approach on two relevant case studies: the formation of a complex involving a protein adaptor, and a race between two competing biochemical reactions. States and traces of reaction networks are first abstracted by sampling the number of instances of chemical species within a finite set of intervals. We show that the qualitative models induced by this abstraction are too coarse to reproduce properties of interest. We then refine our approach by taking into account additional constraints, the mass invariants and the limiting resources for interval crossing, and by introducing information on the reaction kinetics. The resulting qualitative models are able to capture sophisticated properties of interest, such as a sequestration effect, which arise in the case studies and, more generally, participate in shaping the dynamics of cell signaling and regulatory networks. Our methodology offers new trade-offs between complexity and accuracy, and clarifies the implicit assumptions made in the process of qualitative modelling of biological networks.

Logical Modeling and Dynamical Analysis of Cellular Networks.

The logical (or logic) formalism is increasingly used to model regulatory and signaling networks. Complementing these applications, several groups contributed various methods and tools to support the definition and analysis of logical models. After an introduction to the logical modeling framework and to several of its variants, we review here a number of recent methodological advances to ease the analysis of large and intricate networks. In particular, we survey approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models. To illustrate these developments, we further consider several published logical models for two important biological processes, namely the differentiation of T helper cells and the control of mammalian cell cycle.

Links between topology of the transition graph and limit cycles in a two-dimensional piecewise affine biological model.

A class of piecewise affine differential (PWA) models, initially proposed by Glass and Kauffman (in J Theor Biol 39:103-129, 1973), has been widely used for the modelling and the analysis of biological switch-like systems, such as genetic or neural networks. Its mathematical tractability facilitates the qualitative analysis of dynamical behaviors, in particular periodic phenomena which are of prime importance in biology. Notably, a discrete qualitative description of the dynamics, called the transition graph, can be directly associated to this class of PWA systems. Here we present a study of periodic behaviours (i.e. limit cycles) in a class of two-dimensional piecewise affine biological models. Using concavity and continuity properties of Poincaré maps, we derive structural principles linking the topology of the transition graph to the existence, number and stability of limit cycles. These results notably extend previous works on the investigation of structural principles to the case of unequal and regulated decay rates for the 2-dimensional case. Some numerical examples corresponding to minimal models of biological oscillators are treated to illustrate the use of these structural principles.

Model checking to assess T-helper cell plasticity.

Computational modeling constitutes a crucial step toward the functional understanding of complex cellular networks. In particular, logical modeling has proven suitable for the dynamical analysis of large signaling and transcriptional regulatory networks. In this context, signaling input components are generally meant to convey external stimuli, or environmental cues. In response to such external signals, cells acquire specific gene expression patterns modeled in terms of attractors (e.g., stable states). The capacity for cells to alter or reprogram their differentiated states upon changes in environmental conditions is referred to as cell plasticity. In this article, we present a multivalued logical framework along with computational methods recently developed to efficiently analyze large models. We mainly focus on a symbolic model checking approach to investigate switches between attractors subsequent to changes of input conditions. As a case study, we consider the cellular network regulating the differentiation of T-helper (Th) cells, which orchestrate many physiological and pathological immune responses. To account for novel cellular subtypes, we present an extended version of a published model of Th cell differentiation. We then use symbolic model checking to analyze reachability properties between Th subtypes upon changes of environmental cues. This allows for the construction of a synthetic view of Th cell plasticity in terms of a graph connecting subtypes with arcs labeled by input conditions. Finally, we explore novel strategies enabling specific Th cell polarizing or reprograming events.

The Goodwin model: behind the Hill function.

The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathematically shown that to obtain limit-cycle oscillations, the Hill coefficient must be larger than 8, a value often considered unrealistic. It is indeed difficult to explain such a high coefficient with simple cooperative dynamics. We present here molecular models of the standard Goodwin model, based on single or multisite phosphorylation/dephosphorylation processes of a transcription factor, which have been previously shown to generate switch-like responses. We show that when the phosphorylation/dephosphorylation processes are fast enough, the limit-cycle obtained with a multisite phosphorylation-based mechanism is in very good quantitative agreement with the oscillations observed in the Goodwin model. Conditions in which the detailed mechanism is well approximated by the Goodwin model are given. A variant of the Goodwin model which displays sharp thresholds and relaxation oscillations is also explained by a double phosphorylation/dephosphorylation-based mechanism through a bistable behavior. These results not only provide rational support for the Goodwin model but also highlight the crucial role of the speed of post-translational processes, whose response curve are usually established at a steady state, in biochemical oscillators.

A theoretical exploration of birhythmicity in the p53-Mdm2 network.

Experimental observations performed in the p53-Mdm2 network, one of the key protein modules involved in the control of proliferation of abnormal cells in mammals, revealed the existence of two frequencies of oscillations of p53 and Mdm2 in irradiated cells depending on the irradiation dose. These observations raised the question of the existence of birhythmicity, i.e. the coexistence of two oscillatory regimes for the same external conditions, in the p53-Mdm2 network which would be at the origin of these two distinct frequencies. A theoretical answer has been recently suggested by Ouattara, Abou-Jaoudé and Kaufman who proposed a 3-dimensional differential model showing birhythmicity to reproduce the two frequencies experimentally observed. The aim of this work is to analyze the mechanisms at the origin of the birhythmic behavior through a theoretical analysis of this differential model. To do so, we reduced this model, in a first step, into a 3-dimensional piecewise linear differential model where the Hill functions have been approximated by step functions, and, in a second step, into a 2-dimensional piecewise linear differential model by setting one autonomous variable as a constant in each domain of the phase space. We find that two features related to the phase space structure of the system are at the origin of the birhythmic behavior: the existence of two embedded cycles in the transition graph of the reduced models; the presence of a bypass in the orbit of the large amplitude oscillatory regime of low frequency. Based on this analysis, an experimental strategy is proposed to test the existence of birhythmicity in the p53-Mdm2 network. From a methodological point of view, this approach greatly facilitates the computational analysis of complex oscillatory behavior and could represent a valuable tool to explore mathematical models of biological rhythms showing sufficiently steep nonlinearities.

How molecular should your molecular model be? On the level of molecular detail required to simulate biological networks in systems and synthetic biology.

The recent advance of genetic studies and the rapid accumulation of molecular data, together with the increasing performance of computers, led researchers to design more and more detailed mathematical models of biological systems. Many modeling approaches rely on ordinary differential equations (ODE) which are based on standard enzyme kinetics. Michaelis-Menten and Hill functions are indeed commonly used in dynamical models in systems and synthetic biology because they provide the necessary nonlinearity to make the dynamics nontrivial (i.e., limit-cycle oscillations or multistability). For most of the systems modeled, the actual molecular mechanism is unknown, and the enzyme equations should be regarded as phenomenological. In this chapter, we discuss the validity and accuracy of these approximations. In particular, we focus on the validity of the Michaelis-Menten function for open systems and on the use of Hill kinetics to describe transcription rates of regulated genes. Our discussion is illustrated by numerical simulations of prototype systems, including the Repressilator (a genetic oscillator) and the Toggle Switch model (a bistable system). We systematically compare the results obtained with the compact version (based on Michaelis-Menten and Hill functions) with its corresponding developed versions (based on "elementary" reaction steps and mass action laws). We also discuss the use of compact approaches to perform stochastic simulations (Gillespie algorithm). On the basis of these results, we argue that using compact models is suitable to model qualitatively biological systems.

From structure to dynamics: frequency tuning in the p53-Mdm2 network. II Differential and stochastic approaches.

In Part I of this work, we carried out a logical analysis of a simple model describing the interplay between protein p53, its main negative regulator Mdm2 and DNA damage, and briefly discussed the corresponding differential model (Abou-Jaoudé et al., 2009). This analysis allowed us to reproduce several qualitative features of the kinetics of the p53 response to damage and provided an interpretation of the short and long characteristic periods of oscillation reported by Geva-Zatorsky et al. (2006) depending on the irradiation dose. Starting from this analysis, we focus here on more quantitative aspects of the dynamics of our network and combine the differential description of our system with stochastic simulations which take molecular fluctuations into account. We find that the amplitude of the p53 and Mdm2 oscillations is highly variable (to a degree that depends, however, on the bifurcation properties of the system). In contrast, peak width and timing remain more regular, consistent with the experimental data. Our simulations also show that noise can induce repeated pulses of p53 and Mdm2 that, at low damage, resemble the slow irregular fluctuations observed experimentally. Adding the stochastic dimension in our modeling further allowed us to account for an increase of the fraction of cells oscillating with a high frequency when the irradiation dose increases, as observed by Geva-Zatorsky et al. (2006).

From structure to dynamics: frequency tuning in the p53-Mdm2 network I. Logical approach.

We investigate the dynamical properties of a simple four-variable model describing the interactions between the tumour suppressor protein p53, its main negative regulator Mdm2 and DNA damage, a model inspired by the work of Ciliberto et al. [2005. Steady states and oscillations in the p53/Mdm2 network. Cell Cycle 4(3), 488-493]. Its core consists of an antagonist circuit between p53 and nuclear Mdm2 embedded in a three-element negative circuit involving p53, cytoplasmic and nuclear Mdm2. A major concern has been to develop an integrated approach in which various types of descriptions complement each other. Here we present the logical analysis of our network and briefly discuss the corresponding differential model. Introducing the new notion of "logical bifurcation diagrams", we show that the essential qualitative dynamical properties of our network can be summarized by a small number of bifurcation scenarios, which can be understood in terms of the balance between the positive and negative circuits of the core network. The model displays a wide variety of behaviours depending on the level of damage, the efficiency of damage repair and, importantly, the DNA-binding affinity and transcriptional activity of p53, which are both stress- and cell-type specific. Our results qualitatively account for several experimental observations such as p53 pulses after irradiation, failure to respond to irradiation, shifts in the frequency of the oscillations, or rapid dampening of the oscillations in a cell population. They also suggest a great variability of behaviour from cell to cell and between different cell-types on the basis of different post-translational modifications and transactivation properties of p53. Finally, our differential analysis provides an interpretation of the high and low frequency oscillations observed by Geva-Zatorsky et al. [2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033] depending on the irradiation dose. A more detailed analysis of our differential model as well as its stochastic analysis will be developed in a next paper.

A theoretical radiobiological assessment of the influence of radionuclide half-life on tumor response in targeted radiotherapy when a constant kidney toxicity is maintained.

The potential of targeted radionuclide therapy may be limited if the antibody affinity to the tumor is relatively low and if significant normal tissue damage occurs while the tumor is sterilized. One way to increase the efficiency of the antibody-radionuclide complex might be to use knowledge of the radiobiological processes to select a near-optimal radionuclide half-life. In this paper, the role of physical half-life in targeted radiotherapy optimization is investigated using the linear quadratic (LQ) radiobiological model in conjunction with a range of radiobiological parameters relevant to the tumor. Five radionuclides ((211)At, (90)Y, (131)I, (86)Rb, and (114m)In) were selected, providing a half-life range from 0.3-49.5 days. The dose-limiting organ was assumed to be the kidney, with a simple fractional link between the initial (extrapolated) dose-rate to the tumor and the initial dose-rate to the kidney. The results suggest that short-lived radionuclides (half-life in the range of 1-10 days) have an advantage over medium- and long-lived radionuclides. Furthermore, for very rapid tumor uptake (uptake half-time of a few hours), very short-lived radionuclides (half-life of less than 1 day) could be efficiently employed. Ultimately, however, treatment outcome (in terms of tumor cell kill) is limited by the antibody affinity to the tumor.