## Results and discoveries >2004

### Summary of major result and scientific impacts :

1-**Modeling molecular trafficking in the cytoplasm and on neuronal membrane :** D. Holcman and Z. Schuss are at the origin of the field of modeling receptor trafficking on the surface of neuron [18], developed at UCSF in 2003. With Z. Schuss they derived properties of receptor 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 and observed by light-microscopy. Holcman’s work allows extracting information from single particle tracking in neuronal cells. Coll. Experimental group : D.Choquet (Bordeaux).

2-**Narrow escape theory in probability and Partial Differential Equations ** (PDEs) : In collaboration with Z.Schuss and A.Singer, D. Holcman initiated and developed the narrow escape theory [18,28,29,30,40] and recently with Z. Schuss, the Dire strait theory to characterize diffusion in very narrow straits. The theory is now well accepted and used among theoretical physicists and mathematicians. The methods are asymptotic of PDEs, boundary layer analysis, conformal mapping, matched asymptotics, WKB expansions.

3-**Phototransduction in rods and cones, data analysis, modeling and simulations :** D. Holcman has 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 simulation and allowed to obtained novel methods in signal processing to analyze in vivo rate constants (for phosphodiesterase). This model is now used to simulated degenerated photoreceptors [16,23,47,52]. Coll. Experimental groups : Korenbrot (UCSF), Minke (Jerusalem) and G. Fain (UCLA)).

4-**Analysis of dendritic spines, physical modeling and diffusion in narrow domains :** D. Holcman was pioneer in deriving and obtaining the laws of diffusion in dendritic spines [17,19,39,71]. Coll. Z. Schuss (Tel Aviv U.), E. Kokotian (Weizmann) M. Segal (Weizmann).

5- **Studying synaptic transmission :** Recently, D. Holcman and his PhD students A. Taflia and D. Fresche have developed complex and complete computational methods and numerical simulations to analyze synaptic transmission. His group has for the first time derived from first principles, an analytical expression for the synaptic current (excitatory) and biophysical models that integrate many sources of noise. The result is to study synaptic transmission in normal and pathological conditions and to study the role of key parameters such the geometry, location of vesicle or receptor trafficking, organization of the PSD in synaptic transmission modulation. The simulations are now used to study transmission for certain pathology such as epilepsy [61,62,63]. (coll. N. Rouach (College-de-France)). With the group of N. Rouach, they have understood how connexin30, a molecule present in glia cells modulates and modifies synaptic transmission, leading to a new function.

6- **Quantifying the early steps of viral infection using stochastic processes and Fokker-Planck equation : ** D. Holcman with his students T. Lagache and G. Malherbe have initiated 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 (NYU), B. Dragnea ( Indiana). Using jump process modeling, they have discovered how influenza virus buffers the pH in endosomes.

7- **Mathematical Biology of development and morphogenetic gradients :** In collaboration with A. Prochiantz (College-de-France), D. Holcman developed for the first time in 2007 a theory to study and predict the formation and precision of boundaries between morphogenetic regions in the brain based on stochastic modeling, which shape the developing tissue. With P. Charnay ( ENS), D. Holcman and his posdoc J.Reingruber studied the positive feedback loop of Krox20 activation : they developed a now Markov model of DNA, mRNA and protein activations and presented for the first time the phase space and show that the bistability of the mean field model is actually misleading and Krox20 expression is actually gradual and not bistable (recent publication in Mol.Sys.Bio). In addition, with the group of T. Galli, they were pioneer in analyzing the neurite outgrowth based on vesicular trafficking and microtubule dynamics, leading to a new to study vesicular trafficking.

8-**Search process in the nucleus and nuclear organization :** Holcman’s with his group (A. Amitai, J. Reingruber, G. Malherbe) were the first in 2007 to report 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]. In addition, with the experimental work of A. Taddei (Curie), they have quantified telomere clustering and provided a novel framework for studying telomere clusters with a few number of particles (N. Hoze). With the group of T. Texeira, D. Holcman with his student K. Daoduc, they compute the length of the shortest telomere and found new statistical laws to understand senescence onset. With K. Dubrana (CEA), D. Holcman with his student A. Amitai, they developed novel statistical methods to analysis the search of a DNA break.

9- **A stochastic approach to analyze supperresolution data analysis and novel concept :** despite 40 years of extensive used of the mean square displacement to analyze empirical Brownian motion, a novel approach was necessary to extract biophysical features from supperresolution data, beyond the diffraction limit. For the first time, D. Holcman’s with his PhD student N. Hoze developed a stochastic method, data analysis and simulations to identify live molecular interactions. Their analysis relies on using Langevin equation to extract live potential well from large ensemble of trajectories. This work was in collaboration with D. Choquet (Bordeaux). We found new potential wells at the post-synpatic density.

10-**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.

11-**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.

12-** Statistical physics and asymptotic analysis of transient polymer dynamics in confined domains.** D. Holcman with his student A. Amitai have recently developed novel approaches to estimate the mean time for a polymer to loop in free and confined domain using asymptotic analysis of the first eingenvalue of the Laplace operator in large dimensional space. They applied their analysis to reveal for the first time the degree of confinement of a locus in the cell nucleus from Chromosomal Capture Technic.

13- **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.