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Class 2020-21

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

David Holcman


Wednesday. 17h30-20h30.

Starting date: October 7th

NOTE: Wednesday 14: ZOOM only

WHERE "Salle Conference": ENS 46 rue d’Ulm, 75005 Paris
Class common to: Sorbonne University- PSL-ENS: Computer science/Applied Math/Computational Biology
onlineClass: Zoom

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
contact: david.holcman at

A-Introduction PDF of the class —> Here

B-Part I

  • Stochastic processes, Fokker-Planck equation
  • Recovering a stochastic process from noisy trajectories: application to the reconstruction of synapses and cellular organels.
  • Exit problem and boundary layer for linear PDE and Mean First Passage Time Equations.
  • Small hole theory: search for a small target: application to neuronal signaling
  • Extreme statistics and redundancy principle to study rare events.
  • Diffusion in the cleft+ method of simulations. Calcium dynamics in a dendritic spine.
  • Fast simulations of rare events.
  • 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.
  • Model of reconstruction a source for growth-cone from diffusion flux to receptors.
  • Modeling synaptic transmission and plasticity. Model of the synaptic current.

C-Part II and III:

  • Analytical method of single particle trajectories analysis for calcium channel, calreticulin, AMPAR, NMDA, Gly,..receptors: Model of reconstruction for high-density regions, potential wells analysis, based on density statistics and vector field reconstruction. Introduction to the vector field index.
  • ER-network: concept of active Graph and interpreting photo-activation data.
  • Model facilitation-depression, Bursting and Up-Down states, distribution of time in the Up-state by studying the non-selfadjoint Fokker-Planck and the full spectrum.
  • Large-scale model of Neuron-glia interactions.
  • Model of electro-diffusion, asymptotic and singularities, simulations. Electro-neutrality.
  • Deconvolution of time series (voltage dyes).
  • EEG analysis. Band spectral analysis.
  • Machine learning classification, feature extractions. Applications to Coma, Anesthesia and sleep.
    Evaluation : small projects( 40h,2 page reports, 20 minutes oral presentations).

 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).
• 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.