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**11 - 16**of**16**### Inferring Reaction Systems from Ordinary Differential Equations

"... In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and prov ..."

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In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation analysis, etc. However, without requiring any in-formation on the reaction kinetics and parameter values, various qualitative analyses can be performed using the structure of the reactions, provided the reactants, products and mod-ifiers of each reaction are precisely defined. In order to apply these structural methods to parametric ODE models, we study a mathematical condition for expressing the consistency between the structure and the kinetics of a reaction, without restricting to Mass Action law kinetics. This condition, satisfied in particular by standard kinetic laws, entails a re-markable property of independence of the influence graph from the kinetics of the reactions. We derive from this study a heuristic algorithm which, given a system of ODEs as input, computes a system of reactions with the same ODE semantics, by inferring well-formed re-actions whenever possible. We show how this strategy is capable of automatically curating the writing of ODE models in SBML, and present some statistics obtained on the model repository biomodels.net.1.

### Complex Functional Rates in the Modeling of Nano Devices (Extended abstract)

, 2013

"... We give an overview of recent work on the rule-based modeling of nano devices. In particular, our experience in the modeling of a nanoscale elevator suggested us to enhance rule-based modeling with complex functional rates that can be used to express rates that depend on the current state of the ent ..."

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We give an overview of recent work on the rule-based modeling of nano devices. In particular, our experience in the modeling of a nanoscale elevator suggested us to enhance rule-based modeling with complex functional rates that can be used to express rates that depend on the current state of the entire complexes in which the reacting molecules reside.

### Structural simplification of chemical reaction networks

, 2015

"... preserving deterministic semantics ..."

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### A Logical Framework for Systems Biology

, 2014

"... We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological systems and temporal properties of their dynamic behaviour. ..."

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We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological systems and temporal properties of their dynamic behaviour. To illustrate our methodology, we consider a model of the P53/Mdm2 DNA-damage repair mechanism. We prove several properties that are important for such a model to satisfy and serve to illustrate the promise of our approach. We formalize the proofs of these properties in the Coq Proof Assistant, with the help of a Lambda Prolog prover for partial automation of the proofs. 1