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Class 2018-19

Stochastic analysis, asymptotic of Partial Differential Equation, application to Big Data in molecular and cellular dynamics and neuroscience

David Holcman
WHEN : Nov2018-Jan 2019
Tue. 5pm-8pm
Starting date : Tue Nov 06 2018
WHERE "Salle Conference" : 46 rue d’Ulm, 75005 Paris
Youtube class google

General description : A large amount of data are now generated in molecular and cellular biology using recent techniques such as superresolution microscopy for trajectories of single molecular particles, chromosomal capture, leading to matrix of millions by millions about the mean distances between any two locus on the chromatin. Other examples are multi-electrode array to record signal from 10 000 electrodes. How to make sense of such signals and extract information ?

The goal of the class is to present modeling and recent mathematical analysis, used to explain and extract features hidden in large data. The first part of the class will be based on stochastic analysis and partial differential equations and statistical physics. In the second part, we will focus on several applications such as the nucleus organization, synapses and neural networks in neuroscience.

This class (in english) is based on the Holcman’s Cambridge lecture and e-class presented in and YoutubeAutomatic word wrap
contact : david.holcman at
Part I

 Stochastic processes, Fokker-Planck equation, jump processManual word wrap
 Recovering a stochastic from noisy trajectories (formula Feller+Hoze PRE 2015)Manual word wrap
 Short time asymptotics Dim 1 and nManual word wrap
 Escape for the fastest particle dim 1 (result in dimension 3)Manual word wrap
 Exit problem and boundary layer for linear PDE for Mean First Passage Time Equations.

Small hole theory : search for a small target.

• Two holes and manyAutomatic word wrap
• Direstrait Automatic word wrap
• Non-selfadjoint Fokker-Planck and the full spectrum Automatic word wrap
• External Greens’function.Application to sensingAutomatic word wrap
• Dim 2 and 3Automatic word wrap
• Hybrid simulations (stochastic analytical)

Model of electro-diffusion, asymptotic and singularities.

• General model : gap junction, channels, pumps, glial cell neurons and interactionsAutomatic word wrap
• Ball PNPAutomatic word wrap
• Cusp funnel, dim 2 and 3.Automatic word wrap
• Injection of a current.

Deconvolution of time series (voltage dye)

• Causal signal Automatic word wrap
• Electro-diffusion with PNP

Introduction to projection of microscopy data. New Nonlinear PDE. Application to superresolution data analysis.

Nucleus organization:Automatic word wrap
• HI-CAutomatic word wrap
• Modeling polymer dynamics using Rouse modelAutomatic word wrap
• RLC-polymer model and statistical propertiesAutomatic word wrap
• Looping timeAutomatic word wrap
• Search for a target
Part II and III

Synaptic transmission and plasticity. Automatic word wrap
• Model of the current. synaptic current. Automatic word wrap
• Modeling synaptic transmission : homogenization of the Robin constant for small cluster a receptor. Automatic word wrap
• Modeling synaptic transmission, synaptic weight. Automatic word wrap
• Diffusion in the Synaptic cleft.

Diffusion in microdomains :

• Calcium dynamics in a dendritic spine. Automatic word wrap
• Molecular and vesicular trafficking. Automatic word wrap
• Hybrid (Markov and mass-action) model of reaction-diffusion.

Analysis of nucleus organization. Automatic word wrap
• Search time (asymptotic formula) for modeling DNA break repair. Automatic word wrap
• Recurrent time of 2 telomeres, Automatic word wrap
• dissociation time from a cluster. Asymptotic estimations.

Aggregation-dissociation with a finite number of particles in confined microdomains. Application to Virus assembly and telomere organization. Automatic word wrap
Evaluation : small projects.
References :

D. Holcman Z. Schuss, Stochastic Narrow Escape : theory and applications, Springer 2015

D. Holcman, Z. Schuss, Asymptotics of Singular Perturbations and Mixed Boundary Value Problems for Elliptic Partial Differential Equations, and their applications, Springer (in press) 2017
Basics :

Z. Schuss D. Holcman, The dire strait time, SIAM Multicale Modeling and simulations, 2012.Automatic word wrap
D. Holcman Z. Schuss, the Narrow Escape Problem, SIAM Rev 56 no. 2, 213–257 2014Automatic word wrap
D. Holcman, Z. Schuss Control of flux by narrow passages and hidden targets in cellular biology, Reports on Progress in Physics 76 (7):074601. (2013).Automatic word wrap
Z. Schuss, Brownian Dynamics at Boundaries and Interfaces, Springer series on Applied Mathematics Sciences, vol.186 (2013). Automatic word wrap
Schuss, Z., Theory and Applications of Stochastic Processes (Hardback, 2009) Springer ; 1st Edition. (December 21, 2009)
Advanced :

• N.Hoze, N. Deepak, E. Hosy, C. Sieben, S. Manley, A. Herrmann, JB Sibarita, D. Choquet, D. Holcman, Stochastic analysis of receptor trajectories from superresolution data, PNAS doi:10.1073/pnas.1204589109 2012.Automatic word wrap
• N. Hoze Z. Schuss D. Holcman, Reconstruction of surface and stochastic dynamics from a planar projection of trajectories, SIAM Journal on Imaging Sciences 2013Automatic word wrap
• Z. Schuss D. Holcman, The dire strait time, SIAM Multicale Modeling and simulations, 2012.Automatic word wrap
• 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, 2013Automatic word wrap
• D. Coombs and R. Straube M Ward Diffusion on a Sphere with Localized Traps : Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points (SIAM J. Appl. Math., Vol. 70, No. 1, (2009), pp. 302-332.) Automatic word wrap
• S. Pillay, A. Peirce, and T. Kolokolnikov, M. Ward, An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems : Part I : Two-Dimensional Domains (SIAM Multiscale Modeling and Simulation, (March 2009), 28 pages.)