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Lecture 2021-2022

Multiscale modeling, analysis and simulations for data science : from molecular to system neuroscience

David Holcman
Wednesday. 17h20-20h00.

NEW Starting date : second week of October : wed 13th

WHERE "316" : third floor-teaching unit—ENS 46 rue d’Ulm, 75005 Paris
Class common to : Sorbonne University- PSL-ENS : Applied Math/Statistical physics/ Computer science/Computational Biology
On site Classes

General description : The class aims at describing modern modeling in neuroscience from the molecular, cellular to the Brain level with medical application.
We will start by introducing stochastic models to analyze large amount of single particle trajectories obtained by superresolution microscopy. We will present mean-field models of neurons, synapses, glial cells, calcium dynamics, learning and memory and extraction of motifs from time series.
The class continues with modeling and analysis of neural network, bursting modeling, model of recurrent bursting in electrophysiology traces and Up-Down state.
Finally, we will introduce Model-Machine-learning method to predict Brain behavior from EEG time series : applications to coma and anesthesia

The goal of the class : is to present modeling approach, stochastics analysis, signal processing and analysis to extract predictive features based on physiology. The class is ideal for engineers, mathematicians, physicists, theoretical chemists or computer scientists.
This class (in english) will use the Holcman’s Cambridge lecture and e-class presented in and Youtube channel
contact : david.holcman chez


A-Part I
1. Stochastic processes, Fokker-Planck equation, MFPT.
2. Recovering a stochastic process from noisy trajectories : application for the reconstruction of synaptic membrane and cellular organelle network : case of the endoplasmic reticulum.
3. Reconstruction for high-density regions, potential wells analysis, based on density statistics and vector field reconstruction. Introduction to the vector field index.
4. Statistical multiscale estimators, MLE, vector field approach, hybrid algorithm to analyze single particle trajectories. Ex. of calcium channels, calreticulin, AMPAR, NMDA, Gly,..receptors :

B-Part I
1. Exit problem and boundary layer for linear PDE and Mean First Passage Time Equations.
2. Small hole theory : search for a small target : application to neuronal signaling
3. Extreme statistics and redundancy principle to study rare events.
4. Diffusion in the cleft+ method of simulations. Calcium dynamics in a dendritic spine.
5. Fast simulations of rare events.
6. Model of vesicular release and calcium in the pre-synaptic terminal. Diffusion in microdomains : Molecular and vesicular trafficking. Hybrid (Markov and mass-action) model of reaction-diffusion.
7. Model of reconstruction a source for growth-cone from diffusion flux to receptors.
8. Modeling synaptic transmission and plasticity. Model of the synaptic current.
9. ER-network : concept of active Graph and interpreting photo-activation data.

B-Part II :
1. Modeling well connected neuronal network based on synaptic facilitation-depression using low dimensional mean-field model and stochastic dynamical systems.
2. Stochastic analysis of
a. Bursting
b. Up-Down states, computing the distribution of time in the Up-state by studying the non-selfadjoint Fokker-Planck and the full spectrum.
3. Large-scale model of Neuron-glia interactions.
4. Model of electro-diffusion based on Poisson-Nernst-Planck model, asymptotic and singularities, simulations. Electro-neutrality in nano-domain. Computation of the voltage using Comsol.
5. Deconvolution of time series (voltage dyes).

C-Part III :
EEG analysis. Power sprectrum, model of alpha band, spectral analysis, spectrogram. Relation between EEG and neuronal network.
Machine learning classification, feature extractions. Segmentation of suppression, detection of artifact : applications to Coma, anesthesia and sleep.

Evaluation : small projects( 40h, 2 page reports, 20 minutes oral presentations).

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 2018
 Schuss, Z., Theory and Applications of Stochastic Processes (Hardback, 2009) Springer ; 1st Edition. (December 21, 2009)

Basics :
D. Holcman Z. Schuss, 100 years after Smoluchowski : stochastic processes in cell biology, J. Phys. A (2016).
Z. Schuss D. Holcman, The dire strait time, SIAM Multicale Modeling and simulations, 2012.
D. Holcman Z. Schuss, the Narrow Escape Problem, SIAM Rev 56 no. 2, 213–257, 2014.
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).
Z. Schuss, Brownian Dynamics at Boundaries and Interfaces, Springer series on Applied Mathematics Sciences, vol.186 (2013).
Advanced :
• D. Holcman N.Hoze, Statistical methods of short super-resolution stochastic single trajectories analysis, Annual Review of Statistics and Its Application, 4, 1-35 (2017).
• Z Schuss, K Basnayake, D Holcman, Redundancy principle and the role of extreme statistics in molecular and cellular biology, Physics of life reviews 28, 52-79 (2019)
• N Rouach, KD Duc, J Sibille, D. Holcman, ionic fluxes regulated neurons and astrocytes. Dynamics of ion fluxes between neurons, astrocytes and the extracellular space during neurotransmission, Opera Medica et Physiologica 4 (1), 1-18, 2018.
• J Cartailler, P Parutto, C Touchard, F Vallée, D Holcman, Alpha rhythm collapse predicts iso-electric suppressions during anesthesia, Communications biology 2 (1), 1-10 2019.