## Group of Applied Mathematics and Computational biology

**Our main interest ** is to

- understand the function of nano- and micro- domains in cell biology
- develop physical modeling, mathematical analysis, numerical simulations and data analysis.

Our primary goal is to identify principles and computational rules underlying cell and network functions. We focus on basic questions such as molecular trafficking, synaptic transmission in neurons and nuclear organization.

We develop mathematical multiscale models, statistical methods to analyze data, asymptotics of partial differential equations and numerical simulations.

#### Breaking news of the lab:

P. Parutto is a new PhD student 2015.

A. Amitai moves to MIT in dec 2014 for his posdoc

N. Hoze moves to ETZ in July 2014 for his posdoc

K. Dao duc moves to Berkeley in April 2014 for his posdoc

J. sibile moves to Yale in December 2014 for his posdoc

#### Striking recent publications of the lab:

D. Holcman R. Yuste, The new nanophysiology: Towards nanophysiology: Regulation of ionic flow in neuronal subcompartments, 16, Nat. Rev. Neuroscience 2015.

C. Guerrier, J. Hayes, G. Fortin, D. Holcman, Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics, PNAS, 112(31):9728-33, 2015.

D. Holcman Z. Schuss, New mathematics and physics in life sciences and medicine, Physics Today (to appear soon) 2015.

Dao Duc, D. Holcman, Computing the length of the shortest telomere across cell division, Phys. Rev Lett. 111, 228104 (2013). Spotlight of Exception Research Physics, 6, 129, 2013,

J. Reingruber J. Pahlberg M. Woodroof A. Sampath G. Fain D. Holcman, Detection of of a single photon response in mouse and toad rods, PNAS 110(48):19378-83 (2013).

#### 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**

**!!!!Ready to buy 2015!!!! ** Book: D. Holcman, Z. Schuss Stochastic Narrow Escape

### Some projects

1-**Applied mathematics and probability, Mathematical Modeling and analysis.**

- We are developing asymptotic methods and Brownian simulations, 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 trajectories. This approach allows modeling and predicting 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 tools to extract features from superresolution data. We use the Poisson-Nernst-Planck equations to model the voltage dynamics at excitatory synapses and investigate the role of the local geometry.

**Other projects in integrative biology** concern sensor cells, such as photoreceptors, where we 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:**