CHAVES , Madalena

International audience

Biological regulatory networks often give rise to new mathematical problems for which classical methods do not apply. Challenging problems include model assembly or model reduction, network inference, parameter estimation, and control of a system towards a desired state. More recently, questions related to the coupling of basic biochemical...

The mathematical analysis of models for biological systems covers a wide range of challenging problems that include model assembly or model reduction, parameter estimation, or control of a system towards a desired state. Many different formalisms and methodologies can be used to study these problems, but here the focus will be on Boolean and...

The mathematical analysis of dynamical systems covers a wide range of challenging problems related to the time evolution, transient and asymptotic behavior, or regulation and control of physical systems. A large part of my work has been motivated by new mathematical questions arising from biological systems, especially signaling and genetic...

International audience

Circadian clocks form a fundamental mechanism that promotes the correct behavior of many cellular and molecular processes by synchronizing them on a 24 hour period. However, the circadian cycles remain difficult to describe mathematically. To overcome this problem, we first propose a segmentation of the circadian cycle into eight stages based...

Boolean networks with asynchronous updates are a class of logical models particularly well adapted to describe the dynamics of biological networks with uncertain measures. The state space of these models can be described by an asynchronous state transition graph, which represents all the possible exits from every single state, and gives a...

Genetic feedback is one of the mechanisms that enables metabolic adaptations to environmental changes. The stable equilibria of these feedback circuits determine the observable metabolic phenotypes. We consider an unbranched metabolic network with one metabolite acting as a global regulator of enzyme expression. Under switch-like regulation and...

A qualitative method to control piecewise affine differential systems is proposed and explored for application to genetic regulatory networks. This study considers systems whose outputs and inputs are of a qualitative form, well suited to experimental devices: the measurements indicate whether the variables are ``strongly'' or ``weakly''...

To analyze and gain intuition on the mechanisms of complex systems of large dimensions, one strategy is to simplify the model by identifying a reduced system, in the form of a smaller set of variables and interactions that still capture specific properties of the system. For large models of biological networks, the diagram of interactions is...

This paper will discuss the coupling of two oscillators in cyanobacteria. The circadian rhythm of cyanobacteria is thought to be driven by an oscillator based on an ordered sequence of phosphorylations of a protein (KaiC). At the same time, as the cyanobacterial cell grows and divides, the amount of protein KaiC itself is regulated by a...

Boolean networks provide a useful tool to address questions on the structure of large biochemical interactions since they do not require kinetic details and, in addition, a wide range of computational tools and algorithms is available to exactly compute and study the dynamical properties of these models. A recently developed method has shown...

A hierarchy of models, ranging from high to lower levels of abstraction, is proposed to construct "minimal" but predictive and explanatory models of biological systems. Three hierarchical levels will be considered: Boolean networks, piecewise affine differential (PWA) equations, and a class of continuous, ordinary, differential equations'...

The dynamics of the interconnection of two Boolean networks is analyzed directly from the properties of the two individual modules. Motivated by biological systems where multiple timescales are present, we consider asynchronous Boolean networks, whose dynamics can be described by nondeterministic transition graphs. Two new objects are...

The dynamics of Boolean networks can be represented by asynchronous transition graphs, whose attractors describe the system's asymptotic behavior. This paper shows that the attractors of the feedback interconnection of two Boolean modules can be fully identified in terms of crossproducts of the attractors of each module. Based on this...

A qualitative method to control piecewise affine differential systems is proposed and explored for application to genetic regulatory networks. This study considers systems whose outputs and inputs are of a qualitative form, well suited to experimental devices: the measurements indicate whether the variables are "strongly" or "weakly" expressed,...