## 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, softwares and data analysis.
- Develop predictive methods for medical applications.

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 recently moved to applied science: fertility and sperm motion in the uterus and the prediction of brain vascular accidents.

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

#### Breaking news of the lab:

May 2017 The narrow escape theory has inspired the FARGO TV series

May 2017: Schuss’80 celebrated in Akko, see

.

Two new books to appear in 2017:

- 1-D. Holcman Z. Schuss, Asymptotics of Singular Perturbations and Mixed BVPs for Elliptic PDEs and their Applications, Applied Mathematics Springer 2017.

- 2-D. Holcman, Stochastic processes, multiscale modeling and numerical methods for computational cellular biology, (collective reviews) Springer.

Thibault Lagache, former PhD is now associate researcher at Columbia University, NY 2017.

We congradulate Juergen Reingruber for his HDR Dec 5 2016.

Marzhieh and Jing got married last year: we wish them a lot of happiness. 2016.

A. Biess (postdoc in 2007) became an Assistant Professor at Ben Gourion University

D. Holcman was elected in 2015 French Governmental Fellow of the Churchill College in Cambridge, UK.

G. Guerrier moved to UBC (Vancouver) in Oct 2016 for a postdoc .

P. Parutto is a new PhD student 2015.

A. Amitai moved to MIT in dec 2014 for his postdoc.

D. Holcman became a fellow of the Churchill College Cambridge in 2014.

N. Hoze moved to ETZ in July 2014 for his postdoc.

K. Dao duc moved to Berkeley in April 2014 for his postdoc.

J. Sibille moved to Yale in December 2014 for his postdoc.

#### Striking recent publications of the lab:

Amitai A, Holcman D, Polymer physics of nuclear organization and function, Physics Report, 2017.

Amitai A, Seeber A, Gasser SM, Holcman D, Visualization of Chromatin Decompaction and Break Site Extrusion as Predicted by Statistical Polymer Modeling of Single-Locus Trajectories. Cell Rep. 2017;18(5):1200-1214.

D Holcman, N Hozé, Statistical Methods of Short Super-Resolution Stochastic Single Trajectories Analysis, Annual Review of Statistics and Its Application 4 (1) 2017.

D. Holcman Z. Schuss, New mathematics and physics in life sciences and medicine, Physics Today, 2016.

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.

#### 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

### How to join the lab?

1-at the master level: enroll in our class that belongs to Master 2 of Paris VI (Applied mathematics) or interdisciplinary Master at ENS (Imalys)

2- at a PhD level: you must have spent 6 months of training period in the lab.

3- at a postdoc level: physicists, mathematicians, computer scientists are welcome to apply.

4- at a senior level: we are 3 senior researchers. Please contact D. Holcman

### 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:**