## Results and discoveries >2004

### Summary of major result and scientific impacts :

1-**Modeling molecular trafficking in the cytoplasm and on neuronal membrane :** I develop the first theory of modeling receptor trafficking on the surface of neurons [18], developed at UCSF in 2003. With Z. Schuss we derived properties of receptors, diffusing in microdomains from a stochastic approach [33]. This analysis has provided theoretical foundations for the experimental works to quantify aspects of synaptic transmission, obtained by R.Nicoll, R. Malinow.

2-**Narrow escape theory in probability and Partial Differential Equations (PDEs) :** In collaboration with Z.Schuss and A.Singer, we initiated and developed the narrow escape theory [18,28,29,30,40] and the Dire Strait Theory to characterize diffusion in very narrow straits. The theory is now well accepted and used among theoretical physicists and mathematicians.

3-**Phototransduction in rods and cones, data analysis, modeling and simulations** : I developed with his postdoc J. Reingruber, the first model of phototransduction, accounting for the early steps of chemical reactions, the dark noise and the geometrical organization of the photoreceptor outer-segment. The methods are based on homogenization procedure, Markov chain, stochastic analysis, Brownian simulations and allow obtaining novel methods in signal processing. This approach was successfully applied to extract in vivo rate constants for the phosphodiesterase. This model is now used to simulate degenerated photoreceptors [16,23,47,52]. Past Coll. Experimental groups : Korenbrot (UCSF) and G. Fain (UCLA)).

4-**Analysis of dendritic spines, physical modeling and diffusion in narrow domains :** I was one of the first to obtain the laws of diffusion in dendritic spines [17,19,39,71]. Coll. Z. Schuss (Tel Aviv U.), E. Kokotian (Weizmann) M. Segal (Weizmann).

5- **Modeling synaptic organization :** with my PhD students A. Taflia and D. Fresche, we developed complex and complete computational methods and numerical simulations to analyze synaptic transmission : The simulations were used to find that glial cells can penetrate the cleft to modify synaptic transmission and we predicted in 2011 the nanocolumn organization of the synapse, confirmed experimentally in 2016.

6- **Quantifying the early steps of viral infection using stochastic processes and Fokker-Planck equation : ** D. Holcman with his student T. Lagache develop the field of modeling physical virus trafficking at the single particle level in cells and the modeling the early steps of viral infection [35,44,Rev1,75]. Coll. Experimental groups : O. Danos (Necker), A. Herrmann (Berlin). Using stochastic processes, we have proposed that influenza virus buffers the pH in endosomes to delay escape (coll. C.Sieben, EPFL and A. Herrmann, Berlin).

7- **Mathematical Biology of development and morphogenetic gradients : ** In collaboration with A. Prochiantz (College-de-France), I developed in 2007 a theory to study and predict the formation and the precision of boundaries between morphogenetic regions in the brain based on morphogen propagation and stochastic modeling. These boundaries shape the developing tissue. With P. Charnay (ENS) and J.Reingruber, we studied the positive feedback loop of Krox20 activation : they developed a Markov model of DNA, mRNA and protein activations and presented for the first time the phase space. We also show that bistability of the mean field model is actually misleading and Krox20 expression is actually gradual and not bistable (see Bouchara et al, Mol.Sys.Bio 2013). With the group of T. Galli (exp), we were pioneered in the analysis of neurite outgrowth, based on vesicular trafficking and microtubule dynamics.

8-**Search process in the nucleus and nuclear organization : ** With my group (A. Amitai, J. Reingruber, G. Malherbe) in 200, we reported that the search time for a transcription factor in the nucleus is associated with a time in 3 dimensions, different than the time spent on the DNA molecule [Rep3,56,67]. With the experimental work of A. Taddei (Curie), we quantified telomere clustering and provided a novel framework for studying telomere clusters with a few number of particles (with N. Hoze, PhD student). With the group of T. Texeira, and with my PhD student. Daoduc, we computed the length of the shortest telomere and found new statistical laws underlying senescence onset. With K. Dubrana (CEA), we developed novel statistical methods to analyze the search process of a dsDNA break.

9-**Analyze of super-resolution SPT data : ** We developed a novel approach to extract complex features from superresolution data, beyond the diffraction limit. For the first time, we developed with N. Hoze (PhD student) a stochastic method, data analysis and simulations to identify live molecular interactions. Their analysis relies on the Langevin’s equation. Live potential wells can now be extracted from large ensemble of trajectories. We found that excitatory synapses are characterized by large potential wells located at the post-synaptic density. Their nature remains unsolved. We recently work on CaV with M. Heine and found also a nanodomain organization.

10-**Analysis of the Up and Down state in cortical neurons : ** With K. Dao Duc (PhD student), we discovered a new resonance-oscillation in the exit time density function, that allow us to estimate the number of synaptic connection in a neuronal network from the distribution of times in Up-states (coll. A. Konnerth).

11- **Polymer dynamics to study chromatin in confined domains. ** We developed novel approaches to study SPT of chromatin locus (coll. K.Dubrana, S. Gasser, E. Laue,etc..).We developed method s to reconstruct chromatin organization from Chromosomal Capture data.

12- **Reconstructing voltage map from dyes : ** D. Holcman with his student Cartailler developed a novel approach to deconvolve voltage dyes and we used numerical methods to compute the difference of potential between any two points in a dendritic spine. The result were applied to interpret data collected in the Yuste’s lab about voltage in dendritic spines.

13- **EEG analysis and application to prediction of coma outcome and anesthesia in 2018**

D. Holcman with his several students investigated how to re-analyse EEG, extracting novel transient features for classification using Machine-Learning. The results are several patents (submitted) to predict the output of anoxic coma and the depth of anesthesia (a start-up company is in the process of emerging).

14- **Extreme statistics for narrow escape and application to cell biology and neuroscience 2018**

We were able to show for the first time that extreme statistics theory described major events in cell biology and neurobiology. This theory has predicted the organization of receptors on the endoplasmic reticulum. Finally, we have developed a formal theory to show that extreme statics follow deterministic laws that are not physics but statistics.

15-**The semi-classical limit and Partial differential Equations : ** In the field of asymptotic of PDE and analysis on manifolds, Holcman and Kupka have described for the first time in 2001 the semi-classical limit associated with a general non-gradient drift term [12,20,24,31,60] and solve first order PDE on Riemannian manifold, as published from 2001 to 2011. Many results were published prior and sometimes much more general than the ones of N. Anantharaman.

16-**Spectrum of the non-self-adjoint Fokker-Planck operator and escape probability :** D. Holcman in coll. with Z. Schuss obtained recently the exact expression for the spectrum of the Fokker-Planck operator associated to randomly perturbed dynamical system in dimension 2 (with non-concervative drift), a problem which insolved since the discovery of the Fokker-Planck equation more than 100 years ago. With his PhD student K. Dao Duc, they discovered a new resonance-oscillation in the exit time density function. Application is the quantification of the exit time in Up-states observed in certain cortical neuronal dynamics as described by A. Konnerth, B. Sakmann.

17- **Theory of stochastic chemical and mean time to threshold. ** D. Holcman and Z. Schuss have initiated the theory of stochastic chemical reactions in microdomains (in 2005) based on the narrow escape theory. With his PhD student K. Dao Duc, they have computed the mean time that the number of bound molecules reaches a given threshold. Applications are estimates for Long Term Potentiation induction in neurobiology, mRNAs modulation by si RNAs in the nucleus (coll. K. Burrage, Oxford) or estimates of the first open TRP channel in fly photoreceptor. The methods are based two-dimensional Markov chain with zero absorbing boundary conditions.