Our main interest is to
- study the function of microdomains in cellular biology
- develop physical modeling, mathematical analysis, numerical simulations and data analysis.
Our goal is to identify principles underlying cellular and network function. For that purpose, in collaboration with experimental groups, we focus on basic questions in cellular biology such as molecular trafficking in cells, synaptic transmission in neurons and principles of nuclear organization.
We develop mathematical multiscale models, statistical methods to treat data, analysis of the model equations and numerical simulations.
See our Youtube presentation of the group:
Watch also this video that summarize our activity in 2014 Youtube 4 minutes summary 2014
!!!!Coming soon 2015!!!! Book: D. Holcman, Z. Schuss Stochastic Narrow Escape
1-Applied mathematics and probability, Mathematical Modeling and analysis.
- We are developing asymptotic methods and Brownian simulations, boundary analysis to compute mean first passage time formulas, with applications to chemical reactions in microdomains.
- We develop polymer simulations and derived polymer looping formula using expansion of eigenvalues in high dimensional space.
- We are developing methods to reconstruct neuronal connectivity from time series using explicit models and computation of the spectrum of the non-self adjoint Fokker- Planck operator. We use oscillation behavior of the escape time for a stochastic process to an unstable limit cycle to reconstruct the mean connectivity underlying Up/down state dynamics.
2-Theory of diffusion in microdomains: we are currently developing a theory to describe the escape through small openings and the analysis of single stochastic trajectory. This approach allows to model and predict some information about the homologous repair process occurring in the nucleus.
3-Synaptic transmission, trafficking and voltage dynamics in dendrites: we are developing model of synaptic transmission and analysis tools for extracting features from superresolution data. Analysis of the Poisson-Nernst-Planck equations allows modeling the voltage dynamics at excitatory synapses and we study the effect of the local geometry.
Other projects in integrative biology concern sensor cells, such as photoreceptors, where we have recently built a complete model of the single photonresponse including dark noise in rods and cones.
In the past, by using asymptotic analysis, we computed the expansion of the mean time for a Brownian molecule to escape through a small hole located on a piece of a cell membrane (Narrow escape problem). This computation defines the forward binding rate of chemical reactions occurring in microdomains.
Fields: Computational Biology, Applied Mathematics, Modeling, Asymptotic analysis, Applied Probability, Partial Differential Equations, Brownian simulations, Mathematical Biology, Computational Neuroscience, Data analysis, Physical Virology, Phototransduction, Polymer Modeling, Data analysis of single particle trajectory, Neuron-glia interactions, Nuclear Organization.
Sub-Fields: Diffusion, Cell Geometry, Brownian Motion, Narrow Escape Time, Dire Strait Time, Asymptotic methods, Mean First Passage Time methods, Markov chains, Aggregation-Dissociation model, conformal methods, WKB expansion, boundary layer analysis, polymer looping, modeling telomere organization, Molecular and Vesicular Trafficking, Synaptic Transmission, numerical Simulations, Early Steps of Viral Infection, Neurite outgrowth. Superresolution data analysis, boundary layer methods, dsDNA break analysis, dendritic spines, modeling calcium dynamics, looping time, synaptic transmission.
More about our research: