## Group of Applied Mathematics and Computational biology

**The main interest of the group** 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, nuclear organization, early step of viral infection.

For that purpose, we develop mathematical multiscale models, statistical average methods, asymptotic analysis of equations and stochastic simulations.

See our Youtube presentation of the group:

### YOU-Tube presentation

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**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

### Current projects

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 also analyze polymer looping using expansion of eigenvalues in high dimensional space.
- The explicit computation of the spectrum of the non-self adjoint Fokker- Planck operator reveals the oscillation behavior of the escape time for a stochastic process to an unstable limit cycle .

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 the nuclear organization.

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.
Poisson-Nernst-Planck equations allows modeling the voltage dynamics at excitatory synapses and studied 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.

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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, dendritic spines, modeling calcium dynamics, looping time, synaptic transmission.

**More about our research:**