## Group of Applied Mathematics and Computational biology

**The main interest of the group** is to study the function of microdomains in cellular biology and to develop **physical modeling, mathematical analysis, numerical simulations and data analysis**.
Our goal is to identify principles underlying cellular and network function in normal and pathological conditions. For that purpose, in collaboration with experimental groups, we aim to answer basic questions in cellular biology such as what defines trafficking in cells, how synapses regulate their molecular components, how the nucleus is organized, what makes viral particles optimal in trafficking.

### YOU-Tube presentation of the group

**Current projects**

1-**Mathematical Modeling and analysis of cellular processes** developing polymer model, single particle tracking analysis, modeling nuclear organization.

2-**Theory of diffusion in microdomains: ** escape through small opening, analysis of single viral trajectory. Application to cytoplasmic viral trafficking

3-**Studying synaptic transmission and receptor trafficking and dendritic organization:** developing model of synaptic transmission and analysis tools for extracting features in superresolution data. We derive a stochatic model of synaptic current at excitatory synapses and studied the effect of the cleft geometry, receptor trafficking and other factors.

** Applied mathematics and probability**, we develop asymptotic analysis and Brownian simulations, boundary analysis to compute mean first passage time. Applications to chemical reactions in microdomains.

**Other projects in integrated biology** concern sensor cells, such as photoreceptors, where we have recently built a complete model of the single photonresponse to better understand noise in rods and cones. We apply our model to test the effect of various drugs such as viagra which affects the PDE enzyme activity.

**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.

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**Key words**

**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.

**More about our research:**