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UPMaBoSS: A Novel Framework for Dynamic Cell Population Modeling
Gautier Stoll, Aurélien Naldi, Vincent Noël, Eric Viara, Emmanuel Barillot, Guido Kroemer, Denis Thieffry and Laurence Calzone
Frontiers in Molecular Biosciences

Mathematical modeling aims at understanding the effects of biological perturbations, suggesting ways to intervene and to reestablish proper cell functioning in diseases such as cancer or in autoimmune disorders. This is a difficult task for obvious reasons: the level of details needed to describe the intra-cellular processes involved, the numerous interactions between cells and cell types, and the complex dynamical properties of such populations where cells die, divide and interact constantly, to cite a few. Another important difficulty comes from the spatial distribution of these cells, their diffusion and motility. All of these aspects cannot be easily resolved in a unique mathematical model or with a unique formalism. To cope with some of these issues, we introduce here a novel framework, UPMaBoSS (for Update Population MaBoSS), dedicated to modeling dynamic populations of interacting cells. We rely on the preexisting tool MaBoSS, which enables probabilistic simulations of cellular networks. A novel software layer is added to account for cell interactions and population dynamics, but without considering the spatial dimension. This modeling approach can be seen as an intermediate step towards more complex spatial descriptions. We illustrate our methodology by means of a case study dealing with TNF-induced cell death. Interestingly, the simulation of cell population dynamics with UPMaBoSS reveals a mechanism of resistance triggered by TNF treatment. Relatively easy to encode, UPMaBoSS simulations require only moderate computational power and execution time. To ease the reproduction of simulations, we provide several Jupyter notebooks that can be accessed within the CoLoMoTo Docker image, which contains all software and models used for this study.

 
PhysiBoSS 2.0: a sustainable integration of stochastic Boolean and agent-based modelling frameworks
Miguel Ponce-de-Leon, Arnau Montagud, Vincent Noel, Gerard Pradas, Annika Meert, Emmanuel Barillot, Laurence Calzone, Alfonso Valencia
Preprint, bioRxiv (2022)

We need to effectively combine the knowledge from surging literature with complex datasets to propose mechanistic models of SARS-CoV-2 infection, improving data interpretation and predicting key targets of intervention. Here, we describe a large-scale community effort to build an open access, interoperable and computable repository of COVID-19 molecular mechanisms. The COVID-19 Disease Map (C19DMap) is a graphical, interactive representation of disease-relevant molecular mechanisms linking many knowledge sources. Notably, it is a computational resource for graph-based analyses and disease modelling. To this end, we established a framework of tools, platforms and guidelines necessary for a multifaceted community of biocurators, domain experts, bioinformaticians and computational biologists. The diagrams of the C19DMap, curated from the literature, are integrated with relevant interaction and text mining databases. We demonstrate the application of network analysis and modelling approaches by concrete examples to highlight new testable hypotheses. This framework helps to find signatures of SARS-CoV-2 predisposition, treatment response or prioritisation of drug candidates. Such an approach may help deal with new waves of COVID-19 or similar pandemics in the long-term perspective.

 
COVID19 Disease Map, a computational knowledge repository of virus–host interaction mechanisms
Marek Ostaszewski, Anna Niarakis, Alexander Mazein, Inna Kuperstein, Robert Phair, Aurelio Orta‐Resendiz, Vidisha Singh, Sara Sadat Aghamiri, Marcio Luis Acencio, Enrico Glaab, Andreas Ruepp, Gisela Fobo, Corinna Montrone, Barbara Brauner, Goar Frishman, Luis Cristóbal Monraz Gómez, Julia Somers, Matti Hoch, Shailendra Kumar Gupta, Julia Scheel, Hanna Borlinghaus, Tobias Czauderna, Falk Schreiber, Arnau Montagud, Miguel Ponce de Leon, Akira Funahashi, Yusuke Hiki, Noriko Hiroi, Takahiro G Yamada, Andreas Dräger, Alina Renz, Muhammad Naveez, Zsolt Bocskei, Francesco Messina, Daniela Börnigen, Liam Fergusson, Marta Conti, Marius Rameil, Vanessa Nakonecnij, Jakob Vanhoefer, Leonard Schmiester, Muying Wang, Emily E Ackerman, Jason E Shoemaker, Jeremy Zucker, Kristie Oxford, Jeremy Teuton, Ebru Kocakaya, Gökçe Yağmur Summak, Kristina Hanspers, Martina Kutmon, Susan Coort, Lars Eijssen, Friederike Ehrhart, Devasahayam Arokia Balaya Rex, Denise Slenter, Marvin Martens, Nhung Pham, Robin Haw, Bijay Jassal, Lisa Matthews, Marija Orlic‐Milacic, Andrea Senff-Ribeiro, Karen Rothfels, Veronica Shamovsky, Ralf Stephan, Cristoffer Sevilla, Thawfeek Varusai, Jean‐Marie Ravel, Rupsha Fraser, Vera Ortseifen, Silvia Marchesi, Piotr Gawron, Ewa Smula, Laurent Heirendt, Venkata Satagopam, Guanming Wu, Anders Riutta, Martin Golebiewski, Stuart Owen, Carole Goble, Xiaoming Hu, Rupert W Overall, Dieter Maier, Angela Bauch, Benjamin M Gyori, John A Bachman, Carlos Vega, Valentin Grouès, Miguel Vazquez, Pablo Porras, Luana Licata, Marta Iannuccelli, Francesca Sacco, Anastasia Nesterova, Anton Yuryev, Anita de Waard, Denes Turei, Augustin Luna, Ozgun Babur, Sylvain Soliman, Alberto Valdeolivas, Marina Esteban‐Medina, Maria Peña‐Chilet, Kinza Rian, Tomáš Helikar, Bhanwar Lal Puniya, Dezso Modos, Agatha Treveil, Marton Olbei, Bertrand De Meulder, Stephane Ballereau, Aurélien Dugourd, Aurélien Naldi, Vincent Noël, Laurence Calzone, Chris Sander, Emek Demir, Tamas Korcsmaros, Tom C Freeman, Franck Augé, Jacques S Beckmann, Jan Hasenauer, Olaf Wolkenhauer, Egon L Willighagen, Alexander R Pico, Chris T Evelo, Marc E Gillespie, Lincoln D Stein, Henning Hermjakob, Peter D'Eustachio, Julio Saez‐Rodriguez, Joaquin Dopazo, Alfonso Valencia, Hiroaki Kitano, Emmanuel Barillot, Charles Auffray, Rudi Balling, Reinhard Schneider, COVID‐19 Disease Map Community
Molecular systems biology, 17(10), e10387

We need to effectively combine the knowledge from surging literature with complex datasets to propose mechanistic models of SARS-CoV-2 infection, improving data interpretation and predicting key targets of intervention. Here, we describe a large-scale community effort to build an open access, interoperable and computable repository of COVID-19 molecular mechanisms. The COVID-19 Disease Map (C19DMap) is a graphical, interactive representation of disease-relevant molecular mechanisms linking many knowledge sources. Notably, it is a computational resource for graph-based analyses and disease modelling. To this end, we established a framework of tools, platforms and guidelines necessary for a multifaceted community of biocurators, domain experts, bioinformaticians and computational biologists. The diagrams of the C19DMap, curated from the literature, are integrated with relevant interaction and text mining databases. We demonstrate the application of network analysis and modelling approaches by concrete examples to highlight new testable hypotheses. This framework helps to find signatures of SARS-CoV-2 predisposition, treatment response or prioritisation of drug candidates. Such an approach may help deal with new waves of COVID-19 or similar pandemics in the long-term perspective.

 
Setting the basis of best practices and standards for curation and annotation of logical models in biology—highlights of the [BC] 2 2019 CoLoMoTo/SysMod Workshop
Anna Niarakis, Martin Kuiper, Marek Ostaszewski, Rahuman S Malik Sheriff, Cristina Casals-Casas, Denis Thieffry, Tom C Freeman, Paul Thomas, Vasundra Touré, Vincent Noël, Gautier Stoll, Julio Saez-Rodriguez, Aurélien Naldi, Eugenia Oshurko, Ioannis Xenarios, Sylvain Soliman, Claudine Chaouiya, Tomáš Helikar, Laurence Calzone
Briefings in bioinformatics 22.2 (2021): 1848-1859.

The fast accumulation of biological data calls for their integration, analysis and exploitation through more systematic approaches. The generation of novel, relevant hypotheses from this enormous quantity of data remains challenging. Logical models have long been used to answer a variety of questions regarding the dynamical behaviours of regulatory networks. As the number of published logical models increases, there is a pressing need for systematic model annotation, referencing and curation in community-supported and standardised formats. This article summarises the key topics and future directions of a meeting entitled ‘Annotation and curation of computational models in biology’, organised as part of the 2019 [BC]2 conference. The purpose of the meeting was to develop and drive forward a plan towards the standardised annotation of logical models, review and connect various ongoing projects of experts from different communities involved in the modelling and annotation of molecular biological entities, interactions, pathways and models. This article defines a roadmap towards the annotation and curation of logical models, including milestones for best practices and minimum standard requirements.

 
Personalized logical models to investigate cancer response to BRAF treatments in melanomas and colorectal cancers
Jonas Béal, Lorenzo Pantolini, Vincent Noël, Emmanuel Barillot, Laurence Calzone
PLOS Computational Biology 17.1 (2021): e1007900.

The study of response to cancer treatments has benefited greatly from the contribution of different omics data but their interpretation is sometimes difficult. Some mathematical models based on prior biological knowledge of signaling pathways facilitate this interpretation but often require fitting of their parameters using perturbation data. We propose a more qualitative mechanistic approach, based on logical formalism and on the sole mapping and interpretation of omics data, and able to recover differences in sensitivity to gene inhibition without model training. This approach is showcased by the study of BRAF inhibition in patients with melanomas and colorectal cancers who experience significant differences in sensitivity despite similar omics profiles. We first gather information from literature and build a logical model summarizing the regulatory network of the mitogen-activated protein kinase (MAPK) pathway surrounding BRAF, with factors involved in the BRAF inhibition resistance mechanisms. The relevance of this model is verified by automatically assessing that it qualitatively reproduces response or resistance behaviors identified in the literature. Data from over 100 melanoma and colorectal cancer cell lines are then used to validate the model’s ability to explain differences in sensitivity. This generic model is transformed into personalized cell line-specific logical models by integrating the omics information of the cell lines as constraints of the model. The use of mutations alone allows personalized models to correlate significantly with experimental sensitivities to BRAF inhibition, both from drug and CRISPR targeting, and even better with the joint use of mutations and RNA, supporting multi-omics mechanistic models. A comparison of these untrained models with learning approaches highlights similarities in interpretation and complementarity depending on the size of the datasets. This parsimonious pipeline, which can easily be extended to other biological questions, makes it possible to explore the mechanistic causes of the response to treatment, on an individualized basis.

 
WebMaBoSS: A Web Interface for Simulating Boolean Models Stochastically
Vincent Noël, Marco Ruscone, Gautier Stoll, Eric Viara, Andrei Zinovyev, Emmanuel Barillot, Laurence Calzone
Frontiers in molecular biosciences 8 (2021).

WebMaBoSS is an easy-to-use web interface for conversion, storage, simulation and analysis of Boolean models that allows to get insight from these models without any specific knowledge of modeling or coding. It relies on an existing software, MaBoSS, which simulates Boolean models using a stochastic approach: it applies continuous time Markov processes over the Boolean network. It was initially built to fill the gap between Boolean and continuous formalisms, i.e., providing semi-quantitative results using a simple representation with a minimum number of parameters to fit. The goal of WebMaBoSS is to simplify the use and the analysis of Boolean models coping with two main issues: 1) the simulation of Boolean models of intracellular processes with MaBoSS, or any modeling tool, may appear as non-intuitive for non-experts; 2) the simulation of already-published models available in current model databases (e.g., Cell Collective, BioModels) may require some extra steps to ensure compatibility with modeling tools such as MaBoSS. With WebMaBoSS, new models can be created or imported directly from existing databases. They can then be simulated, modified and stored in personal folders. Model simulations are performed easily, results visualized interactively, and figures can be exported in a preferred format. Extensive model analyses such as mutant screening or parameter sensitivity can also be performed. For all these tasks, results are stored and can be subsequently filtered to look for specific outputs. This web interface can be accessed at the address: https://maboss.curie.fr/webmaboss/ and deployed locally using docker. This application is open-source under LGPL license, and available at https://github.com/sysbio-curie/WebMaBoSS.

 
Exact solving and sensitivity analysis of stochastic continuous time Boolean models
Mihály Koltai, Vincent Noël, Andrei Zinovyev, Laurence Calzone, Emmanuel Barillot
BMC bioinformatics 21.1 (2020): 1-22.

Background: Solutions to stochastic Boolean models are usually estimated by Monte Carlo simulations, but as the state space of these models can be enormous, there is an inherent uncertainty about the accuracy of Monte Carlo estimates and whether simulations have reached all attractors. Moreover, these models have timescale parameters (transition rates) that the probability values of stationary solutions depend on in complex ways, raising the necessity of parameter sensitivity analysis. We address these two issues by an exact calculation method for this class of models. Results: We show that the stationary probability values of the attractors of stochastic (asynchronous) continuous time Boolean models can be exactly calculated. The calculation does not require Monte Carlo simulations, instead it uses graph theoretical and matrix calculation methods previously applied in the context of chemical kinetics. In this version of the asynchronous updating framework the states of a logical model define a continuous time Markov chain and for a given initial condition the stationary solution is fully defined by the right and left nullspace of the master equation’s kinetic matrix. We use topological sorting of the state transition graph and the dependencies between the nullspaces and the kinetic matrix to derive the stationary solution without simulations. We apply this calculation to several published Boolean models to analyze the under-explored question of the effect of transition rates on the stationary solutions and show they can be sensitive to parameter changes. The analysis distinguishes processes robust or, alternatively, sensitive to parameter values, providing both methodological and biological insights. Conclusion: Up to an intermediate size (the biggest model analyzed is 23 nodes) stochastic Boolean models can be efficiently solved by an exact matrix method, without using Monte Carlo simulations. Sensitivity analysis with respect to the model’s timescale parameters often reveals a small subset of all parameters that primarily determine the stationary probability of attractor states.

 
Synthesis and Simulation of Ensembles of Boolean Networks for Cell Fate Decision
Stéphanie Chevalier, Vincent Noël, Laurence Calzone, Andrei Zinovyev, Loïc Paulevé
International Conference on Computational Methods in Systems Biology, pp. 193-209

The construction of models of biological networks from prior knowledge and experimental data often leads to a multitude of candidate models. Devising a single model from them can require arbitrary choices, which may lead to strong biases in subsequent predictions. We introduce here a methodology for a) synthesizing Boolean model ensembles satisfying a set of biologically relevant constraints and b) reasoning on the dynamics of the ensembles of models. The synthesis is performed using Answer-Set Programming, extending prior work to account for solution diversity and universal constraints on reachable fixed points, enabling an accurate specification of desired dynamics. The sampled models are then simulated and the results are aggregated through averaging or can be analyzed as a multi-dimensional distribution. We illustrate our approach on a previously published Boolean model of a molecular network regulating the cell fate decisions in cancer progression. It appears that the ensemble-based approach to Boolean modelling brings new insights on the variability of synergistic interacting mutations effect concerning propensity of a cancer cell to metastasize.

 
Dynamical Boolean Modeling of Immunogenic Cell Death
Andrea Checcoli, Jonathan G Pol, Aurelien Naldi, Vincent Noël, Emmanuel Barillot, Guido Kroemer, Denis Thieffry, Laurence Calzone, Gautier Stoll
Frontiers in Physiology

As opposed to the standard tolerogenic apoptosis, immunogenic cell death (ICD) constitutes a type of cellular demise that elicits an adaptive immune response. ICD has been characterized in malignant cells following cytotoxic interventions, such as chemotherapy or radiotherapy. Briefly, ICD of cancer cells releases some stress/danger signals that attract and activate dendritic cells (DCs). The latter can then engulf and cross-present tumor antigens to T lymphocytes, thus priming a cancer-specific immunity. This series of reactions works as a positive feedback loop where the antitumor immunity further improves the therapeutic efficacy by targeting cancer cells spared by the cytotoxic agent. However, not all chemotherapeutic drugs currently approved for cancer treatment are able to stimulate bona fide ICD: some commonly used agents, such as cisplatin or 5-fluorouracil, are unable to activate all features of ICD. Therefore, a better characterization of the process could help identify some gene or protein candidates to target pharmacologically and suggest combinations of drugs that would favor/increase antitumor immune response. To this end, we have built a mathematical model of the major cell types that intervene in ICD, namely cancer cells, DCs, CD8+ and CD4+ T cells. Our model not only integrates intracellular mechanisms within each individual cell entity, but also incorporates intercellular communications between them. The resulting cell population model recapitulates key features of the dynamics of ICD after an initial treatment, in particular the time-dependent size of the different cell types. The model is based on a discrete Boolean formalism and is simulated by means of a software tool, UPMaBoSS, which performs stochastic simulations with continuous time, considering the dynamics of the system at the cell population level with appropriate timing of events, and accounting for death and division of each cell type. With this model, the time scales of some of the processes involved in ICD, which are challenging to measure experimentally, have been predicted. In addition, our model analysis led to the identification of actionable targets for boosting ICD-induced antitumor response. All computational analyses and results are compiled in interactive notebooks which cover the presentation of the network structure, model simulations, and parameter sensitivity analyses.

 
Fibroblast Growth Factor 2 lethally sensitizes cancer cells to stress‐targeted therapeutic inhibitors
Matheus H Dias, Cecília S Fonseca, Julianna D Zeidler, Layra L Albuquerque, Marcelo S da Silva, Eduardo Cararo‐Lopes, Marcelo S Reis, Vincent Noël, Edmilson O Dos Santos, Ian A Prior, Hugo A Armelin
Molecular oncology

In malignant transformation, cellular stress-response pathways are dynamically mobilized to counterbalance oncogenic activity, keeping cancer cells viable. Therapeutic disruption of this vulnerable homeostasis might change the outcome of many human cancers, particularly those for which no effective therapy is available. Here, we report the use of fibroblast growth factor 2 (FGF2) to demonstrate that further mitogenic activation disrupts cellular homeostasis and strongly sensitizes cancer cells to stress-targeted therapeutic inhibitors. We show that FGF2 enhanced replication and proteotoxic stresses in a K-Ras-driven murine cancer cell model, and combinations of FGF2 and proteasome or DNA damage response-checkpoint inhibitors triggered cell death. CRISPR/Cas9-mediated K-Ras depletion suppressed the malignant phenotype and prevented these synergic toxicities in these murine cells. Moreover, in a panel of human Ewing's sarcoma family tumor cells, sublethal concentrations of bortezomib (proteasome inhibitor) or VE-821 (ATR inhibitor) induced cell death when combined with FGF2. Sustained MAPK-ERK1/2 overactivation induced by FGF2 appears to underlie these synthetic lethalities, as late pharmacological inhibition of this pathway restored cell homeostasis and prevented these described synergies. Our results highlight how mitotic signaling pathways which are frequently overridden in malignant transformation might be exploited to disrupt the robustness of cancer cells, ultimately sensitizing them to stress-targeted therapies. This approach provides a new therapeutic rationale for human cancers, with important implications for tumors still lacking effective treatment, and for those that frequently relapse after treatment with available therapies.

 
An interdisciplinary approach for designing of kinetic models of the Ras/MAPK signaling pathway
Marcelo S. Reis, Vincent Noël, Matheus H.S. Dias, Layra L. Albuquerque, Amanda S. Guimarães, Lulu Wu, Junior Barrera and Hugo A. Armelin.
Kinase Signaling Networks, Methods in Molecular Biology, vol. 1636, chap. 28

We present in this article a methodology for designing kinetic models of molecular signaling networks, which was exemplarily applied for modeling one of the Ras/MAPK signaling pathways in the mouse Y1 adrenocortical cell line. The methodology is interdisciplinary, that is, it was developed in a way that both dry and wet lab teams worked together along the whole modeling process.

 
Glyceraldehyde 3-Phosphate Dehydrogenase-Telomere Association Correlates with Redox Status in Trypanosoma cruzi
Ricardo Pariona-Llanos, Raphael Souza Pavani, Marcelo Reis, Vincent Noel, Ariel Mariano Silber, Hugo Aguirre Armelin, Maria Isabel Nogueira Cano, Maria Carolina Elias
Plos one

Glyceraldehyde 3-phosphate dehydrogenase (GAPDH) is a classical metabolic enzyme involved in energy production and plays a role in additional nuclear functions, including transcriptional control, recognition of misincorporated nucleotides in DNA and maintenance of telomere structure. Here, we show that the recombinant protein T. cruzi GAPDH (rTcGAPDH) binds single-stranded telomeric DNA. We demonstrate that the binding of GAPDH to telomeric DNA correlates with the balance between oxidized and reduced forms of nicotinamide adenine dinucleotides (NAD+/NADH). We observed that GAPDH-telomere association and NAD+/NADH balance changed throughout the T. cruzi life cycle. For example, in replicative epimastigote forms of T. cruzi, which show similar intracellular concentrations of NAD+ and NADH, GAPDH binds to telomeric DNA in vivo and this binding activity is inhibited by exogenous NAD+. In contrast, in the T. cruzi non-proliferative trypomastigote forms, which show higher NAD+ concentration, GAPDH was absent from telomeres. In addition, NAD+ abolishes physical interaction between recombinant GAPDH and synthetic telomere oligonucleotide in a cell free system, mimicking exogenous NAD+ that reduces GAPDH-telomere interaction in vivo. We propose that the balance in the NAD+/NADH ratio during T. cruzi life cycle homeostatically regulates GAPDH telomere association, suggesting that in trypanosomes redox status locally modulates GAPDH association with telomeric DNA.

 
A hybrid mammalian cell cycle model
V. Noël, S. Vakulenko, O. Radulescu
Electronic Proceedings in Theoretical Computer Science 125 : 68-83, HSB 2013, Taormina

Hybrid modeling provides an effective solution to cope with multiple time scales dynamics in systems biology. Among the applications of this method, one of the most important is the cell cycle regulation. The machinery of the cell cycle, leading to cell division and proliferation, combines slow growth, spatio-temporal re-organisation of the cell, and rapid changes of regulatory proteins concentrations induced by post-translational modifications. The advancement through the cell cycle comprises a well defined sequence of stages, separated by checkpoint transitions. The combination of continuous and discrete changes justifies hybrid modelling approaches to cell cycle dynamics. We present a piecewise-smooth version of a mammalian cell cycle model, obtained by hybridization from a smooth biochemical model. The approximate hybridization scheme, leading to simplified reaction rates and binary event location functions, is based on learning from a training set of trajectories of the smooth model. We discuss several learning strategies for the parameters of the hybrid model.

 
Modèles réduits et hybrides de réseaux de réactions biochimiques: applications à la modélisation du cycle cellulaire
V. Noël
Thèse de doctorat. Université Rennes 1.

La modélisation des systèmes biologiques, particulièrement à l'échelle moléculaire, est une problématique nouvelle, issue de l'apport des techniques à haut débit. Le défi en modélisation mathématique est de pouvoir analyser le comportement de ces systèmes dynamiques de très grande dimension. L'enjeu est de taille, car la compréhension du fonctionnement normal et pathologique des cellules au niveau moléculaire, ouvre la voie aux thérapies ciblés pour des maladies systémiques telles que le cancer. Pour s'affranchir des problèmes liés à l'imprécision des valeurs des paramètres, cette thèse propose de travailler avec des ordres, plutôt qu'avec des valeurs précises de paramètres. Ceci conduit naturellement à l'utilisation de l'analyse tropicale pour obtenir des modèles réduits et hybrides. Ces développements ouvrent des nouvelles perspectives sur le plan mathématique, concernant l'étude de systèmes dynamiques. Cette étude propose quelques résultats concernant la tropicalisation des systèmes d'équations différentielles. Une autre partie de la thèse est consacrée à l'étude numérique des systèmes hybrides. La question ici est comment construire un modèle hybride qui reproduit un comportement expérimental donné, aussi comment identifier un modèle hybride à partir de séries temporelles. Cette thèse propose un algorithme original d'identification. Cet algorithme sépare le problème en deux sous-problèmes, notamment l'identification des paramètres des modes et l'identification des paramètres de commande des modes. Des applications à relativement grande échelle sont abordées par cette approche, notamment un modèle de cycle cellulaire chez les mammifères.

 
Tropicalization and Tropical equilibration for chemical kinetics
V. Noël, D. Grigoriev, S. Vakulenko, O. Radulescu
In Press, AMS Contemporary Mathematics, Tropical 2012, Moscow

Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated terms, find a natural formulation in tropical analysis and can be used for model reduction.

 
Reduction of dynamical biochemical reaction networks in computational biology
O. Radulescu, A. N. Gorban, A. Zinovyev, V. Noël
Frontiers in Genetics 3, 131

Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. s. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques.

 
Hybrid models of the cell cycle molecular machinery
V. Noël, D. Grigoriev, S. Vakulenko, O. Radulescu
Electronic Proceedings in Theoretical Computer Science 92 : 88-105, HSB 2012, Newcastle

Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off some molecular interactions, simulating cell progression through a series of functioning modes. The advancement through the cell cycle is the archetype of such an organized sequence of events. We present an approach, inspired from tropical geometry ideas, allowing to reduce, hybridize and analyse cell cycle models consisting of polynomial or rational ordinary differential equations.

 
Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models
V. Noël, D. Grigoriev, S. Vakulenko, O. Radulescu
Electronic Notes in Theoretical Computer Science 284, pp. 75-91, SASB 2011, Venezia

We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the cell cycle. We also propose a practical recipe for detecting quasi-equilibrium QE reactions and quasi-steady state QSS species in biochemical models with rational rate functions and use this recipe for model reduction. Interestingly, the QE/QSS invariant manifold of the smooth model and the reduced dynamics along this manifold can be put into correspondence to the tropical variety of the hybridization and to sliding modes along this variety, respectively.

 
Algorithm for Identification of Piecewise Smooth Hybrid Systems : Application to Eukaryotic Cell Cycle Regulation
V. Noël, S. Vakulenko, O. Radulescu
Lecture Notes in Computer Science 6833, pp. 225-236, WABI 2011, Saakbrücken

We discuss piecewise smooth hybrid systems as models for regulatory networks in molecular biology. These systems involve both continuous and discrete variables. The discrete variables allow to switch on and off some of the molecular interactions in the model of the biological system. Piecewise smooth hybrid models are well adapted to approximate the dynamics of multiscale dissipative systems that occur in molecular biology. We show how to produce such models by a top down approach that use biological knowledge for a guided choice of important variables and interactions. Then we propose an algorithm for fitting parameters of the piecewise smooth models from data. We illustrate some of the possibilities of this approach by proposing hybrid versions of eukaryotic cell cycle regulation.

 
Piecewise smooth hybrid systems as models for networks in molecular biology
V. Noël, S. Vakulenko, O. Radulescu
Proceedings of JOBIM 2010, p57-62, Montpellier

We discuss piecewise smooth hybrid systems as models for regulatory networks in molecular biology. These systems involve both continuous and discrete variables. In the context of gene networks, the discrete variables allow to switch on and off some of the molecular interactions in the model of the biological system. Piecewise smooth hybrid models are well adapted to approximate the dynamics of multiscale dissipative systems that occur in molecular biology. We show how to produce such models by a top down approach that use biological knowledge for a guided choice of important variables and interactions. Then we propose an algorithm for fitting parameters of the piecewise smooth models from data. We illustrate some of the possibilities of this approach by proposing a minimal piecewise smooth model for the cell cycle