Stochastic and Statistics of Super-resolution single particles trajectories

Collaboration (D. Ron and E. Avezov, Cambridge UK).

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.