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Madalena Chaves

Analysis of genetic networks through piecewise linear systems and Boolean models

Dynamics of signal transduction pathways (continuous nonlinear systems - ODEs)

Stability analysis and observer design for a class of nonlinear systems

ColAge

‣ Operational interactions (with L. Tournier):
Boolean models often provide a good characterization of the qualitative dynamics of genetic networks. The state space of a Boolean model is finite, and its dynamics are fully described by an asynchronous transition graph. From the analysis of this graph, we identify families of operational interactions, that is, groups of interactions which are responsible for a given dynamical behaviour of the system. See application to the apoptosis network.

‣ Apoptosis and the NFkB pathway (with T. Eissing, F. Allgower):
Apoptosis is a form of programed cell death which enables the organism to remove unwanted or damaged cells. This is an essential biological function in a healthy living organism. The complex Nuclear Factor kB pathway interacts with the caspase cascade at the heart of apoptosis. I have worked on a Boolean model to study apoptosis regulation by the NFkB pathway. This is a system that exhibits bistability.

‣ Segment polarity genes network in Drosophila (with R. Albert, E.D. Sontag, A. Sengupta):
These are the genes responsible for establishing the anterior-posterior polarity of segments in the embryo of the fruit fly. I have been working on the analysis of a Boolean model of the segment polarity network, introducing asynchronous updating rules, and other methods that allow a more realistic analysis of discrete models with respect to the time scales of the various regulatory processes (transcription, translation, or post-translational modifications). One can also study the effect of cell division on the robustness of the network.
For the continuous model of the segment polarity network proposed by von Dassow et. al., we have fully characterized the feasible parameter space, as a hierarchy of intervals.

‣ Gene expression regulates signaling (with I. Ndiaye, J.-L. Gouze):
Many signaling pathways eventually trigger transcription of groups of genes. But, conversely, the signaling pathway may be regulated by gene expression patterns. We propose a simple model for such a regulatory mechanism, exploring the idea that the dynamics of a signal transduction pathway is must faster than the dynamics of gene transcription/translation.

‣ Receptor-ligand interactions (with E.D. Sontag, R. Dinerstein):
The binding of a ligand to a cell receptor triggers a sequence of biochemical reactions, that ultimately lead to a cell response (such as contraction, motility, proliferation). I am interested in the modeling of various stages in this process, from receptor-ligand binding, to cascades of protein activation, to cell signaling in the form of changes in the levels of cytosolic calcium, cAMP,... One of the goals would be to obtain validated models that help us in predicting and controlling the response of the cell to given stimulus.

‣ Zero-deficiency chemical networks are a class of nonlinear systems which model general biochemical networks with mass-action kinetics. The formalism was first introduced and studied by M. Feinberg, F. Horn and R. Jackson.
In my thesis I designed globablly asymptotically convergent observers for this class of systems, where other standard observers (eg. Kalman filters) may fail.

Recently, I have extended the analysis of zero-deficiency networks to the case of time-dependent kinetic parameters - these are interpreted as inputs into the system. Such system satisfies an input-to-state stability (ISS) property, which guarantees robustness with respect to small perturbations in the kinetic parameters, such as temperature fluctuations, or various external factors and stimuli.