## Results and discoveries >2004

## Summary of significant results and scientific impacts of Holcman’s group :

**1-Modeling molecular trafficking in the cytoplasm and on neuronal membrane : ** At the origin of modeling receptor trafficking on the surface of neuron [18], he developed the theory at UCSF in 2003 with Z. Schuss : they 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 and then observed by light-microscopy by D. Choquet. This work allowed extracting novel biophysical parametes from single particle trajectories recorded in neuronal cells.

**2-Narrow escape theory in applied mathematics :** In collaboration with Z.Schuss and A.Singer, they 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 : ** With J. Reingruber 2006-2013, they developed one 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 method is based on homogenization procedure, Markov chain, stochastic analysis, Brownian simulations and allows obtaining novel understanding of the fast photoresponse. 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]. Coll. Experimental groups : Korenbrot (UCSF), Minke (Jerusalem) and G. Fain (UCLA)).

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

**5- Modeling synaptic transmission with glial protrusions :**With A. Taflia and D. Fresche, they developed (2006-2011) complex and complete computational methods and numerical simulations to analyze synaptic transmission. For the first time, they derived from first principles, an analytical expression for the synaptic current (excitatory) and biophysical models that integrates many sources of noise. Their method allows to study synaptic transmission in normal and pathological conditions and 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 pathologies such as epilepsy [61,62,63]. (coll. N. Rouach, College-de-France). With the group of N. Rouach, they have analyzed how connexin30, a key protein to organize glia cells in network modulates and modifies synaptic transmission, leading to a new function of regulating synaptic transmission by sending protrusions.

**6- Quantifying the early steps of viral infection using stochastic processes and Fokker-Planck equation :** with T. Lagache they initiated modeling of viral 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) B. Dragnea (Indiana). Using jump stochastic processes, they have proposed that influenza virus buffers the pH in endosomes (coll. C.Sieben and A. Herrmann).

7- Mathematical Biology of development and morphogenetic gradients : **–** In collaboration with A. Prochiantz (College-de-France),they developed for the first time 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, they 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. They also show that bistability of the mean field model is actually misleading and Krox20 expression is actually gradual and not bistable.

**–** With the group of T. Galli, they were pioneer in developing a computational approach based on the narrow escape theory to show that dendrite versus axon outgrowth depends on vesicular trafficking and microtubule dynamics and the parameter of MT attachment to the cell membrane.

**8-Search process in the nucleus and nuclear organization : **
**–** With A. Amitai, J. Reingruber, G. Malherbe, they reported in 2007 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 in nanodomains 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, with K. Daoduc, they computed the length of the shortest telomere and found new statistical laws underlying senescence onset.

**–** With K. Dubrana (CEA), and A. Amitai (PhD student), they developed statistical methods to analyze the search process of a dsDNA break.

**–** With M. Hauer, S. Gasser, they develop novel parameter to quantify SPT of single locus trajectories.

**–** With his student O. Shukron, they developed a novel method to reconstruct chromatin organization from HiC data based on a new polymer theory they developed called random cross-linker polymers. They also based dsDNA break based on the search process of polymer.

**–** In Collaboration with the group of E. Laue (U. of Cambridge) and O. Shukron, they discovered two novel scale of chromatin folding using a novel classification of many SPTs trajectories associated with the NurD remodeler complex.

9-A stochastic approach to analyze super-resolution data analysis and novel concept : **–** The mean square displacement analysis of empirical Brownian motion has been applied to extract biophysical information from single particle trajectories.

The group developed novel approaches to extract complex features from super-resolution data, beyond the diffraction limit. For the first time, with N. Hoze (PhD student) they develop a stochastic method, data analysis and simulations to identify live molecular interactions. Their analysis relies on the Langevin’s equation. They show for the first time how to extract potential wells from large ensemble of trajectories. The data were collected by the group of D. Choquet (Bordeaux).

**–** The main result is that excitatory synapses are characterized by large potential wells located at the post-synaptic density. Their nature remains unsolved.

**–** With the group of M. Heine, they recently found in 2020, that high density regions of calcium channels are characterized by potential wells, the energies of which are much reduced compared to the postsynaptic terminal.With P. Parutto, they developed automated analysis of SPTs potential wells and biological network such as reticulum endoplasmic.

**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 solved first order PDE on Riemannian manifolds, a research published from 2001 to 2011.

**11-Spectrum of the non-self-adjoint Fokker-Planck operator and escape probability : **
**–** in coll. with Z. Schuss, they obtained in 2013 an exact expression for the spectrum of the Fokker-Planck operator associated to a randomly perturbed dynamical system in dimension 2 (with non-conservative drift), a problem unsolved since the discovery of the Fokker-Planck equation more than 100 years ago.

**–** With his K. Dao Duc (PhD student), they discovered a new resonance-oscillation in the exit time density function. This phenomenon allows quantifying the exit time in Up-states, observed in certain cortical neuronal dynamics as described by the physiology groups D. Ferster, A. Konnerth and 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 domains. This approach is based on asymptotic analysis of the first eingenvalue of the Laplace operator in high 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 data.

**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 K. Dao Duc (PhD student), they have computed the mean time that the number of bound molecules reaches a given threshold. Applications are : estimating the probability of Long-Term Potentiation induction in neurobiology, mRNAs modulation by siRNAs in the nucleus (coll. K. Burrage, Oxford) or computing the first time for the first TRP channel to open in fly photoreceptor. The methods are based on two-dimensional Markov chains with zero absorbing boundary conditions.

With his postdoc A. Papale, they recently extend this approach to define the memory of chromatin organization.

**14- Asymptotic of PNP in bounded domain with cusp geometry for non electoneutrality in 2016.**

With J. Cartailler, they developed a novel approach to solve the Poissoin-Nernst-Planck equation in bounded domains and computed the difference of potential between any two points, when there is no electro-neutrality. This analysis is based on a new de-singularization method and matched asymptotic analysis.

The result was applied to interpret data collected in the Yuste’s lab about voltage in dendritic spine. A deconvolution of time series was also used. This research was disseminated in high profile journals of several disciplines (neuroscience, applied math, statistical physics, chemical physics, etc...).

Recently in coll. with I.M. Sokolov, they studied global but non-local electroneutrality of electrolyte to study how far an electrical field can penetrate inside the ionic solution.

**14- EEG analysis and applications to predict coma outcome and depth of anesthesia.**

With several students of the group, they developed novel method mixing signal processing and Machine-Learning to obtain a predictive analysis of EEG, extracting also novel transient features. The results are used to predict the output of anoxic coma and the depth of anesthesia (Patent with Pr. N. Kubis).

**–** With J. Cartailler, they developed a novel method to predict the sensitivity of anesthesia after 10 minutes.

**–** They also develop a statistical analysis of EEG parameter to predict post-anesthetic complications.

**–** With M. Dora, PhD in the lab, they developed a novel feedback control approach to guarantee an optimal anesthesia.

**15- Extreme statistics for narrow escape and application to cell biology and neuroscience.**

With K. Basnyake, they developed Extreme Narrow escape, which is a theory to compute the first time that the first random particle finds a target. They obtain the first asymptotic formula to compute the mean time for the fastest. They developed the general theory of redundancy about the role of many copies of the same particle to understand how the time scale in cell biology signalling can be so fast. This theory has predicted the organization of receptors on the endoplasmic reticulum, coll. with E. Korkotian. Finally, this theory shows that many laws of signalling are well described by extreme statistics.

**16-Reconstruction of the flow in the Endoplasmic reticulum and predicting the mode of propagation. **

With P. Parutto, they developed a novel analysis to reconstruct the ER flow from the analysis of many redundant SPTs. They discover a novel model of propagation that correlated with the ER organization in tubule and nodes. With his PhD M. Dora, D. Holcman they developed a new model of the ER based on graph theory showing that the material propagates in packets, due to the alternant flow inside the tubules.

**17-How the Spine-apparatus is refilled and depleted in calcium during learning and memory.** With K. Bansyake, they proposed a new mechanism of ER refilling based on store operated calcium entry and Er depletion based on extreme statistics of the first ions to reach the base of a dendritic spine.

**18-How a cell can sense its environment and triangulate the position of a source releasing Brownian particles :**

In coll with U. Dubrasmyl postdoc at Cambridge, they developed novel fast hybrid stochastic-analytical simulation and the analytical theory to study the flow of Brownian particles to a target in an open space, without the need to simulating trajectory except in small neighborhood of the sensing cell. This theory is called triangulation sensing and is based on narrow escape. The theory explains how a cell with several receptors can triangulate the position of a source. This theory is used to analyze how neuron migrate toward their target in the developing Brain.

**19-Emergency COVID-19 research efforts 2020 :**
**–** They developed a novel rate model to study the progression of the disease across the population structured by age.
**–** They used the narrow escape theory to compute the probability and the time of infection between an infected and susceptible located in the same room under various conditions, with and without masks.
**–** They developed a novel platform to analyze the EEG of coma patient to grade the severity of the coma.

**20-Sperm motility in the context of fertility : modeling and data analysis. **
**–** In collaboration with his postdoc J. Yang and Pr. D.Heinrich from Leiden, they developed a novel approach based on the trajectories of the first sperm to arrive to the ovule to define the time scale of fertilization in Uterus. With the group of D.Heinrich, they discovered novel form of sperm diffraction around round obstacles using micro-chambers.