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David Holcman

Group of Data Modeling, Computational Biology and Predictive Medicine, Applied Mathematics

"Advancing our understanding of complex biological systems and developing medical methods through the integration of mathematical modeling, computational techniques, and data classification. "

Our main interest is to

  • Investigate brain biophysical principles and functions across multiple scales : ranging from cellular to network levels, employing advanced data-driven approaches rooted in biophysical and cellular mechanisms.
  • Utilize modeling and applied mathematics to identify and implement computational principles governing molecular, cellular, and neuronal network organization. This includes analyzing calcium dynamics, voltage in nanodomains, cell migration patterns, communication dynamics, and complex interactions within neural networks.
  • Develop advanced mathematical models, Asymptotics, Data-Driven Analysis, Stochastic Modeling, and Computational PDEs expansion. Designing and deploying algorithms and machine learning techniques for efficient data processing and feature extraction.
  • Quantify and predict the functionality of nano- and micro-domains in cell biology and neurobiology using cutting-edge data science tools. This involves leveraging insights from local structures, biochemical networks, and real-time brain responses to drive medical predictions.

Methods and Expertise : Our expertise lies at the intersection of applied mathematics (stochastic modeling, asymptotic) data science and neuroscience, encompassing data modeling, statistical analysis, machine learning, numerical simulations, and algorithm development. We harness these methodologies to extract valuable insights from diverse datasets, including fluorescence data, super-resolution single-particle trajectories, Hi-C analysis, calcium time series, and EEG databases, driving innovation in understanding brain function and its implications for healthcare.

Clinical applications and Medical predictions :
We developed softwares and methods to study neuronal network activity and predict brain states during anesthesia, coma and tremor. The method relies on time series, such as EEG recorded in the brain. We aim at predicting brain responses few minutes ahead of time based on transient segmentations and pattern identification.

Biography and history

The laboratory was established in 2006 at ENS, following its relocation from the Weizmann Institute. Additionally, the group maintains affiliations with the University of Cambridge and Churchill College (UK).
Over the years, our research endeavors have yielded significant advancements in computational and biophysical theories. Notable contributions include the development of the Narrow Escape Theory (2004) at the intersection between probability theory, simulation and biolophysics, elucidation of polymer physics governing chromatin organization (2010), modeling short-term plasticity responses in neural networks using modeling (2006) , investigation into neuron-glia interaction (2010), and the formulation of Extreme Statistics principles in biology (2017). These results have provided essential frameworks for studying molecular signaling in various cellular contexts, such as neurons, dendritic spines trafficking (2007), and cellular microdomains.

Since 2012, the laboratory has pioneered high-throughput single-particle trajectory analysis and anticipated the potential well organization of dense nanodomains (2012), alongside the discovery of multiple nano-column organization within synapses (2011). Our computational methodologies have been expanded to include hybrid simulations and asymptotic analysis of Partial Differential Equations (PDEs), enabling us to delve into trafficking phenomena across membranes and within organelles like the endoplasmic reticulum, and nucleus organization (post-2018).
Recent advancements include the development of hybrid simulations to investigate cell navigation within the brain (post-2020) and stochastic simulations for studying calcium signaling within spines (2022), as well as during interactions within neuron-glia networks.

Presently, our focus lies in leveraging our expertise to identify neuronal and glial networks (post-2022) and predict brain states during coma and anesthesia (post-2018) utilizing EEG and hemodynamics data using a mix of statistics, real-time algorithms, ML and stochastic predictions.

Past and present Collaborations involved : A. Singer (Princeton university), D. Menassa (Oxford), N. Kubis and D. Longrois (APHP), C. and G. Kaminskii (U. of Cambridge) E. Korkotian (Weizmann), M. Heine (Mainz), K. Tsaneva (Exceter), N. Rouach (College-de-France), J. Paz (UCSF), R. Yuste (Columbia), T. Lagache (Pasteur) and many more.

Breaking news of the lab :

  • May 2024 : Congradulation for Kanishka Phillips’ prize of 100kUS.
  • Dec 20 2023 : our new State-chart representation to map the brain in stable states during anesthesia in collaboration with the group of J. Paz (UCSF) : see V. Loison et al Neuroimage
  • Sept 29 2023 : our new algorithm on SPT classification has just appeared in Nature Struc. and molecular Biology, in Collaboration with the group of E. Laue, S. Basu. D. Klenerman and D.Heinrich from Cambridge.
  • P. Parutto, previous PhD student of the lab, was elected in 2023 Byfellow of the Churchill college, Cambridge, UK.
  • The project on neurophiology and anesthesia was awarded an ANR grant 2023.
  • Our novel method to analyse single particle trajectory in Cell Reports Methods (October 2022) *Cover page
  • French Newspaper "le Monde" (April 2022) popularize the concept of predictive anesthesia and the real-time algorithm to predict brain sensitivity developed by C. Sun in the lab.
  • Cover page on exteme statistics with switching European J. of physics B

Striking recent peer reviewed publications of the lab :

T. Perochon, Z. Krsnik, T. Lagache, D.A. Menassa D. Holcman, Spatiotemporal mapping of human microglia during brain development with advanced spatial statistics assisted by deep-learning, 2023.

S. Basu, O. Shukron et al, Live-cell 3D single-molecule tracking reveals how NuRD modulates enhancer dynamics, Nature Struct. Mol. Biology, 2023

Chang LH, Ghosh S, Papale A, Luppino JM, Miranda M, Piras V, Degrouard J, Edouard J, Poncelet M, Lecouvreur N, Bloyer S, Leforestier A, Joyce EF, Holcman D, Noordermeer D. Multi-feature clustering of CTCF binding creates robustness for loop extrusion blocking and Topologically Associating Domain boundaries.Nat Commun. 2023

Mc Hugh J, Makarchuk S, Mozheiko D, Fernandez-Villegas A, Kaminski Schierle GS, Kaminski CF, Keyser UF, Holcman* D, Rouach* N. Diversity of dynamic voltage patterns in neuronal dendrites revealed by nanopipette electrophysiology. Nanoscale. 2023 Jul 27 ;15(29):12245-12254. doi : 10.1039/d2nr03475a.

P Parutto, J Heck, M Lu, C Kaminski, E Avezov, M Heine, D Holcman, High-throughput super-resolution single-particle trajectory analysis reconstructs organelle dynamics and membrane reorganization, Cell reports methods 2 (8), 100277 2022

U Dobramysl, D Holcman, Computational methods and diffusion theory in triangulation sensing to model neuronal navigation, Reports on Progress in Physics 2022.

Basnayake, K., Mazaud, D., Kushnireva, L., Bemelmans, A., Rouach, N., Korkotian, E., & Holcman, D. (2021). Nanoscale molecular architecture controls calcium diffusion and ER replenishment in dendritic spines, Science Advances 7(38), eabh1376. >

U Dobramysl, D Holcman, Triangulation Sensing to Determine the Gradient Source from Diffusing Particles to Small Cell Receptors, Physical Review Letters 125 (14), 148102. 2020

Youtube presentation of the group :


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

 Predicting Brain state from EEG during Anesthesia. We are developing methods to analyse EEG and predict the Brain states.

 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 are developing asymptotic and simulations methods to compute the voltage in nanodomains.

 Synaptic transmission, trafficking and voltage dynamics in dendrites : we are developing models 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 build model of the single photonresponse including dark noise in rods and cones with Juergen Reingruber.

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 (See WIKI)). This computation defines the forward binding rate of chemical reactions occurring in microdomains.


Fields : Computational Methods, Data analysis, Neuroscience, Real-time algorithms, Brain simulations, Mathematical Biology, Statistical Biophysics, Predictive Medicine, Applied Mathematics, Model-Machine-Learning, Asymptotic Analysis, Applied Probability, EEG analysis, Deconvolution methods, Electrophysiological time series, Coma, Anesthesia, Brain analysis, Polymer Modeling, Neuron-glia interactions, microdomains, Nuclear Organization.

Sub-Fields :
Diffusion, stochastic modeling, Data Geometry, Partial Differential Equations, Brownian simulations, Brownian Motion, Narrow Escape Time, Dire Strait Time, Asymptotic methods, Mean First Passage Times, Markov chains, Extreme statistics, Hybrid simulations, Statistical methods, Wavelet decomposition, Analysis of single particle trajectory, Stochatic simulations, Aggregation-Dissociation model, Conformal methods, WKB expansion, boundary layer analysis, polymer looping, modeling telomere organization, Molecular and Vesicular Trafficking, Synaptic Transmission, Numerical methods, Early Steps of Viral Infection, Neurite outgrowth, Super-resolution data analysis, boundary layer methods, dsDNA break, dendritic spines, modeling calcium dynamics, looping time, synaptic transmission.

More about our research :
More about our past research in french :

copyrights@David Holcman, free to use with appropriate reference.