Research and current projects
Cell geometrical coding : modeling Electrodiffusions
Due to small the nanometric scale and the charge-voltage interaction, the in vivo current-voltage (I-V) conversion, which is a key component of synaptic transmission remains difficult to study in particular in cell protrusions. We are developing modeling and simulations of electro-diffusion to compute the I-V relation so that we can predict how geometrical parameters are encoding synaptic memory.
EEG- predictive medecine, Modeling-statistics of time series in electrophysiology
It remains difficult to anticipate brain sensitivity especially following covid lockdown that has affected a generation of students, but also during coma, General Anesthesia. We developed predictive tools to interpret the ElectroEncephaloGram (EEG). In a series of efforts to predict the depth of the brain, we have been developing :
1-Network modeling approaches, coarse-grained n-dimensional Ornstein-Ulhenbeck processes, revealing key parameters.
2-Signal processing based on wavelets, spectrogram and spectral decomposition, segmentation to extract time-frequency statistics in real-time.
3-Statistical approaches and Machine-Learning to classify patients into 12 classes.
This approach allows to generate a state-chart representation of the brain and to quantify the transitions between brain profound states using control theory and viterbi algorithm.
Rare events in cell biology : theory of extreme statistics and application to cellular microdomains, trafficking in the ER
We recently develop novel algorithm to simulate fast diffusion events that we applied to model cell navigation in the brain.
The physics of cell nucleus organization, polymer physics and stochastic processes
Organization and dynamics of chromatin in the cell nucleus remains unclear. Two ensembles of data are accessible : many stochastic single particle trajectories (SPTs) of a DNA locus and the Hi-C distribution of contact frequencies across cell populations : We are developing algorithms to recovered the geometrical organization of the DNA from these two ensemble of data.
We recently explored the possible organization of phase separated domains (PSDs) that are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression.
We derived properties of PSDs derived from polymer models. Increasing the number of cross-linkers generate a polymer condensation, preventing the access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we estimated the mean residence and first escaping times. Finally, by computing the mean square displacement of single particle trajectories, we can reconstruct the properties of PSDs in term of a continuum range of anomalous exponents. To conclude, PSDs can result from a condensed chromatin, where the number of cross-linkers control the molecular access.
Stochastic and Statistics of Super-resolution single particles trajectories
Collaboration for the experimental part : D. Ron, Cambridge UK and M. Heine (Magdeburg). A large number of single particle trajectories (SPTs) can now be recorded directly by super-resolution microscopy in cellular environment. The exploration of this environment at an unprecedented nanometer scale opened a new area of science (Nobel 2014 in chemistry). Although the intracellular dynamics can be explored by flows of trajectories, their analysis and interpretation remain a difficult task, because in most cases, the nature of the physical motion and of the local environment, in which trajectories are acquired, are unknown.
Such analysis involves several steps : deconvolution of the signal, physical models to interpret the recorded motion, derivation of optimal estimators of physical parameters, asymptotic analysis of the model equations to explore the parameter space, simulations of the model stochastic equations on a long time scale, and the extraction of features hidden in the data.
Our aim is to develop a new theoretical tools to data analysis of SPTs, based on physical models of molecular diffusion and electro-diffusion, to develop singular perturbation methods for the asymptotic analysis of the model equations and multiscale stochastic simulations for the extraction of information from nano- to micro-cellular compartments.
We are applying the methods to the study of two- and three-dimensional motion of proteins, channels, and chromatin loci in their respectively native sub-cellular environment. This allow to probe precisely the pre- and post-synaptic terminals of neuronal cells, the refined endoplasmic reticulum network, made of connected narrow tubes, the cell nucleus, and more. Although these sub-compartments are not physically related, still, the theoretical modeling involved is related and can be used to confirm the broad applicability of the proposed approach.
The output of this research is new models, analysis, simulations methods, and algorithms for the extraction of information from large data of SPTs, which can reveal hidden structures below the diffraction limit of the recording apparatus. The representation of big data in concise geometry, by extracting underlying structures, such as high dimensional manifolds, is a key to the extraction of new features. The proposed approach is expected to the emergence of new physical concepts and theoretical methods for the understanding of basic cell properties.
