Publications in press or published
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157-U. Dobramysl, D. Holcman, Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows, submitted 2017 |
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156-O. Shukron M. Hauer D. Holcman, Two loci single particle trajectories analysis : constructing a first passage time statistics of local chromatin exploration, Scientific Report 2017 |
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155-O. Shukron D. Holcman, Statistics of randomly cross-linked polymer models to interpret chromatin conformation capture data, Physical Review E 96 (1), 012503 PDF (834.7 ko) |
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154-D. Holcman, Stochastic processes, multiscale modeling and numerical methods for computational cellular biology, Springer 2017 |
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153-N. Hoze D. Holcman, Coagulation-fragmentation with a finite number of particles : models, stochastic analysis and applications to telomere clustering and viral capsid assembly, book chapter 2017 Springer |
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152—D. Holcman J. Reingruber, Modeling and stochastic analysis of the single photon response, book chapter 2017 Springer |
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151-C Guerrier, D Holcman, Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology, Journal of Computational Physics 2017 PDF (2 Mo) |
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150-J. Cartailler, Z. Schuss and D. Holcman, Geometrical effects on nonlinear electrodiffusion in cell physiology, J. of Non linear Science2017. PDF (73.8 ko) |
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We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson’s equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. We find that for a sufficiently high number of charges, they concentrate at the end of the cusp-shaped funnel, which is a singular geometrical effect. We further study the case of charges in a narrow ellipse and inside a corrugated channel. In all cases, the density of charges accumulates near points of local maximum curvature of the boundary. These results can be used in the design of nano-pipettes and help to understand the local voltage changes inside dendrites and axons with heterogenous local geometry.
see also ArXiv
149-J. Cartailler, Z. Schuss and D. Holcman, Effect of the domain geometry on Poisson-Nernst-Planck , Scientific Report 2017 PDF (2.5 Mo) |
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Voltage and charge distributions in cellular microdomains regulate communications, excitability, and signal transduction. We report here new electrical laws in a cell, which follow from a nonlinear electro-diffusion model. These newly discovered relations derive from the geometrical cell-membrane properties, such as membrane curvature, volume, and surface area. These electro-diffusion laws can now be used to predict and interpret voltage distribution in cellular microdomains.
148-MH. Hauer, A. Seeber, V Singh, R Thierry, A Amitai, M. Kryzhanovska, J Eglinger, D Holcman, T Owen-Hughes and SM. Gasser, Histone degradation in response to DNA damage triggers general chromatin decompaction, Nat. Struct. Mol. Bio.Nat Struct Mol Biol. 2017 ;24(2):99-107. PDF (3.3 Mo) |
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147-D. Holcman Z. Schuss, Asymptotics of Singular Perturbations and Mixed BVPs for Elliptic PDEs and their Applications, Springer 2017 |
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144-K. Basnayake, E. Korkotian, D. Holcman Z. Schuss, Extreme statistics and calcium dynamics in spine with ER 2017 |
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141-D. Holcman N.Hoze, Statistical methods for large ensemble of super-resolution stochastic single particle trajectories, Annual Review of Statistics and Aplpications, 2017,4 1-35 |
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Following recent progresses in super-resolution microscopy obtained in the last decade, massive amount of redundant single stochastic trajectories are now available for statistical analysis. Flows of trajectories of molecules or proteins are sampling the cell membrane or its interior at a very high time and space resolution. Several statistical analysis were developed to extract information contained in these data, such as the biophysical parameters of the underlying stochastic motion to reveal the cellular organization. These trajectories can further reveal hidden subcellular organization. We review here the statistical analysis of these trajectories based on the classical Langevin equation, which serves as a model of trajectories. Parametric and non-parametric estimators are constructed by discretizing the stochastic equations and they allow recovering tethering forces, diffusion tensor or membrane organization from measured trajectories, that differ from physical ones by a localization noise. Modeling, data analysis and automatic detection algorithms serve extracting novel biophysical features such as potential wells and other sub-structures, such as rings at an unprecedented spatiotemporal resolution. It is also possible to reconstruct the surface membrane of a biological cell from the statistics of projected random trajectories.
133—U. Dobramysl, D. Holcman, Reconstructing the gradient source position from steady-state fluxes to small receptors 2017, (revision) |
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Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape Time approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level.
125-A. Amitai D. Holcman, Polymer physics of nuclear organization and function, Physics Reports 2017 |
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142-O. Shukron and D. Holcman,Transient chromatin properties revealed by polymer models and stochastic simulations constructed from Chromosomal Capture data, PLOS Computational Biology 13 (4), e1005469 2017 PDF (1.2 Mo) |
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Chromatin organization is probed by chromosomal capture data,from which the encounter probability (EP) between genomic sites is represented in a large matrix. However, this matrix is obtained by averaging the EP over cell population, where diagonal blocks called TADs, contains hidden information about sub-chromatin organization. Our aim here is to elucidate the relationship between TADs structure and gene regulation. For this end, we reconstruct the chromatin dynamics from the EP matrix using polymer model and explore the transient properties, constrained by the statistics of the data. To construct the polymer, we use the EP decay in two steps : first, to account for TADs, we introduce random connectors inside a restricted region defining the TADs. Second, we account for long-range frequent specific genomic interactions in the polymer architecture. Finally, stochastic simulations show that only a small number of randomly placed connectors are required to reproduce the EP of TADs, and allow us to compute the mean first time and the conditional encounter probability of three key genomic sites to meet. These encounter times reveal how chromatin can self-regulate. The present polymer construction is generic and can be used to study steady-state and transient properties of chromatin constrained on 5C data.
http://dx.doi.org/10.1101/065102
and plos
137-A.Amitai, A. Seeber, S. M. Gasser D. Holcman, Statistical polymer simulation distinguishes DNA double-strand break movement due to chromatin expansion and nuclear oscillation, Cell Report 2017 PDF (1.5 Mo) PDF (3.2 Mo) |
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Chromatin is in constant motion within the nucleus, and the time-lapse imaging of single loci by fluorescence microscopy reveals a subdiffusive and spatially constrained dynamics. Standard mean-squared displacement analysis fails to distinguish the different forces that influence chromatin movement. We present an improved timelapse imaging regime that monitors trajectories of tagged DNA loci at a higher temporal resolution than previously reported. We apply a robust statistical analysis that extracts biophysical parameters from the movement. Polymer modeling based on these extracted parameters predicts chromatin expansion near a break and the extrusion of damage from the domain. Both phenomena are confirmed by live imaging of an induced double-strand break in budding yeast. Anomalous exponents of movement allow us to differentiate between extrinsic forces arising from the actin cytoskeleton and intrinsic forces that reflect altered chromatin structure that requires nucleosome remodeling. This paradigm can be applied to single locus trajectories in any species.
146-A. Amitai, D. Holcman, Search for a TF inside the chromatin 2016. |
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145-A. Amitai, M. Toulouze K. Dubrana, D. Holcman, heterogeneous properties of the chromtain revealed by SPTs, 2016. |
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143-D. Holcman Z. Schuss, First Time to senescence : a new story of time in cell biology 2016 |
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140-J. Yang T. Lagache, D. Heinrich K. Reynaud D. Holcman, Spermatozoa motion in the uterus. |
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139-P. Parutto, N. Hoze. D. Holcman, Novel features hidden in superesolution data. |
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138-D. Holcman Z. Schuss, 100 years after Smoluchowski : stochastic processes in cell biology, J. Phys. A (2016). PDF (3 Mo) |
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136-N.Hoze, J.C Poncer S. Levi D. Holcman, Organization of the perisynaptic space for KCC1 trafficking. |
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135— D. Holcman, La nouvelle physique mathématique en biologie, Gazette des Mathematiques (in French) 2016. PDF (83.7 ko) |
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134-D. Holcman Z. Schuss, New mathematics and physics in life sciences and medicine, Physics Today, 2016. PDF (1.6 Mo) |
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132-N.Hoze, D. Holcman, Stochastic coagulation-fragmentation processes with a finite number of particles and applications, Ann of Applied Probability 2017 |
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131-J. Cartailler T.Kwon, R. Yuste D. Holcman, Nanophysiology of dendritic spines : Electro-diffusion of voltage modulation and conduction |
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130-C. Guerrier D. Holcman, Hybrid Markov-Poissonian model and simulations. Application to calcium dynamics for vesicular release at neuronal synapses, Scientific Report, 2016 PDF (1.4 Mo) |
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Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.
129-D. Holcman Z. Schuss, Stochastic narrow escape, Springer 2015 |
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This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The second part of the book is intended for computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. It includes a summary of output formulas from the mathematical portion of the book and concentrates on their applications in modeling specific problems in theoretical molecular and cellular biology.
Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. This volume reports recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures.
128- Schuss D. Holcman, Dynamics of the telomere length. Mean time to senescence. |
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127 -K. Dao duc, Z. Schuss D. Holcman, Oscillatory Survival Probability : Analytical and Numerical Study of a Non-Poissonian Exit Time, SIAM Multiscale Modeling and Simulations, 2016. |
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126-T. Lagache, C Sieben, T. Meyer, A Hermann, D. Holcman, Stochastic model of endosomal escape of Influenza virus PDF (1.8 Mo) |
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In a large class of viruses, endosomal escape is a fundamental step of infection. Some viruses enter the cytoplasm through an endocytic pathway and subsequently travel through the cytoplasm inside an endosomal compartment. To pursue their fate, viruses have to escape this endosome before being digested by proteases. Although the escape process is fundamental, it is not clearly understood, but following acidification and depending whether the virus is enveloped or naked, endosomal escape is triggered by the conformational changes of glycoproteins or penetration proteins, involved in membrane disruption. To examine the dynamics of escape and determine the role of key parameters, we propose a biophysical model in which we evaluate the time where the penetration proteins are activated and we derive the conformational change kinetics as a function of the pH. Using data on the mean number of bound protons to HA1, a subunit of the influenza hemagglutinin, our analysis agrees with the conformational change kinetics of the hemagglutinin. We further support that only rearrangements of HA1 subunit are pH-dependent and other hemagglutinin subunits rearrangements proceed spontaneously. Finally, we estimate the mean viral escape time from an endosome (around $20\pm 5$ minutes).
124-J. Cartailler, Z. Schuss and D. Holcman, Analysis of the Poisson-Nernst-Planck equation in a ball for modeling the Voltage-Current relation in neurobiological microdomains, Phys D, 2016 2016 PDF (1.1 Mo) |
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123-T. Lagache D. Holcman, Extended Narrow Escape to a composed target and application to viral entry in the nucleus, J. of Stat. Physics, 2016 PDF (691.3 ko) |
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In cellular biology, reaching a target before being degraded or trapped is ubiquitous. An interesting example is given by the virus journey inside the cell cytoplasm : in order to replicate, most viruses have to reach the nucleus before being trapped or degraded. We present here a general approach to estimate the probability and the conditional mean first passage time for such a viral particle to attain safely the nucleus, covered with many (around two thousands) small absorbing pores. Due to this large number of small holes, which defines the limiting scale, any Brownian simulations are very unstable. Our new asymptotic formulas precisely account for this phenomena and allow to quantify the cytoplasmic stage of viral infection. We confirm our analysis with Brownian simulations.
122-D. Holcman, Multiscale modeling, stochastic and asymptotic approaches for analyzing neural networks based on synaptic dynamics, ESAIM : Proceedings and Surveys 47, 36-54 2015. PDF (780.2 ko) |
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How neurons coordinate in complex networks to achieve their function ? Answering this question has relied on experimental approaches such as functional imaging, electrophysiology, mi croscopy imaging, but surprisingly, what is now really missing, to make sense of the data is analytical methods, modeling, complex simulations and analysis. Studying responses of neurons while accounting for their geometrical organization, the details of their connections and specificity remains a challenge. Indeed there are 10^11 of them, connected by 1000 synapses per neuron. It is not clear what is the right modeling and analysis, needed to bridge the multiscales, starting with the release at synapses of thousands of diffusing molecules which ultimately integrates into the network to achieve higher brain function. We discuss here recent progress about modeling and analyzing of small and large neuronal networks. We present neural network equations based on synaptic dynamics. The model is formulated using stochastic differential equations. We focus on the time-response of the network. This time can be analyzed as an exit problem of a stochastic trajectory from the basin of attraction, which presents novel characteristics : the attractor is located very close to the separatrices. This property leads to novel phenomena, manifested by oscillatory peaks of the survival probability. Finally, this report shows how mathematical methods in neuroscience allows a better understanding of neural network.
121-D Holcman, R Yuste The new nanophysiology : regulation of ionic flow in neuronal subcompartments, Nature Reviews Neuroscience 16 (11), 685-692 PDF (3.3 Mo) |
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Cable theory and the Goldman–Hodgkin–Huxley–Katz models for the propagation of ions and voltage within a neuron have provided a theoretical foundation for electrophysiology and been responsible for many cornerstone advances in neuroscience. However, these theories break down when they are applied to small neuronal compartments, such as dendritic spines, synaptic terminals or small neuronal processes, because they assume spatial and ionic homogeneity. Here we discuss a broader theory that uses the Poisson–Nernst–Planck (PNP) approximation and electrodiffusion to more accurately model the constraints that neuronal nanostructures place on electrical current flow. This extension of traditional cable theory could advance our understanding of the physiology of neuronal nanocompartments.
120-C Guerrier, E Korkotian, D Holcman, Calcium Dynamics in Neuronal Microdomains : Modeling, Stochastic Simulations, and Data Analysis, Encyclopedia of Computational Neuroscience, 486-516 PDF (1.9 Mo) |
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119-C. Guerrier D. Holcman, Brownian search for targets hidden in cusp-like pockets : Progress and Applications, The European Physical Journal Special Topics 223 (14), 3273-3285 2014 PDF (519.4 ko) |
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118-D. Holcman N. Hoze Z. Schuss, Analysis and interpretation of super-resolution single particle trajectories, Biophysical Journal, 2015 PDF (2.6 Mo) |
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117-C. Guerrier D. Holcman, Search Time for a Small Ribbon and Application to Vesicular Release at Neuronal Synapses,Multiscale Modeling & Simulation 2015, Vol. 13, No. 4, pp. 1173-1193 PDF (1.8 Mo) |
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he arrival of a Brownian particle at a narrow cusp located underneath a ball is a model of vesicular release at neuronal synapses, triggered by calcium ions. The asymptotic computation of the arrival time presents several difficulties that can be overcome using conformal mappings and asymptotic analysis of the model equations. Using a regular expansion of the solution of the Laplace equation in the mapped domain, we compute the solution involving both small and large spatial scales. We derive novel asymptotic formulas for Brownian escape through cusps in both two and three dimensions. The range of validity of the asymptotic formulas is challenged by stochastic simulations. Finally, we apply the analysis to estimate the vesicular release probability at presynaptic terminals and, in particular, we suggest that vesicular organization imposes a severe constraint on calcium channel localization : diffusing calcium ions can trigger vesicular release only in a specific range of positions that we provide.
Read More : http://epubs.siam.org/doi/abs/10.11…
116- C. Guerrier, J. Hayes, G. Fortin, D. Holcman, Modeling the PreBotzniger complex, Proc Natl Acad Sci U S A. 2015 Jul 20. pii : 201421997 PDF (3.9 Mo) |
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115- N.Hoze, D. Holcman, Effect of noise on stochastic analysis of superresolution data, Phys. Rev E 2015 PDF (650.7 ko) |
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114-A.Amitai, M toulouze K. Dubrana D. Holcman, Extracting the force field acting on chromatin from an ensemble of tagged locus trajectories,PLoS Comput Biol 11 (8), e1004433 2015 PDF (1.9 Mo) |
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Is it possible to extract tethering forces applied on chromatin from the statistics of a single locus trajectories imaged \textitin vivo ? Chromatin fragments interact with many partners such as the nuclear membrane, other chromosomes or nuclear bodies, but the resulting forces cannot be directly measured in vivo. However, they impact chromatin dynamics and should be reflected in particular in the motion of a single locus. We present here a method based on polymer models and statistics of single trajectories to extract the force characteristics and in particular when they are generated by the gradient of a quadratic potential well. Using numerical simulations of a Rouse polymer and live cell imaging of the MAT-locus located on the yeast \textitSaccharomyces cerevisiae chromosome III, we recover the amplitude and the distance between the observed and the interacting monomer. To conclude, the confined trajectories we observed \textitin vivo reflect local interaction on chromatin.
113- J. Yang, Schuss I. Kupka, D. Holcman, Searching for a small target by spermatozoa in a restricted geometry, J. Math Biology PDF (1.6 Mo) |
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112-K. Dao Duc, P. Parutto, X. Chen ,J. Epzstein, A Konnerth D. Holcman, Peak-Oscillation of the sojourn times in the Up-state of neuronal network, Frontiers Comp. Neuroscience, 2015 PDF (2 Mo) PDF (212.4 ko) |
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Neuronal networks can generate complex patterns of activity that depend on membrane properties of individual neurons as well as on functional synapses. To decipher the impact of synaptic properties and connectivity on neuronal network behavior, we investigate the responses of neuronal ensembles from small (5-30 cells in a restricted sphere) and large (acute hippocampal slice) networks to single electrical stimulation : in both cases, a single stimulus generated a synchronous long-lasting bursting activity. While an initial spike triggered a reverberating network activity that lasted 2-5 seconds for small networks, we found here that it lasted only up to 300 milliseconds in slices. To explain this phenomena present at different scales, we generalize the depression-facilitation model and extracted the network time constants. The model predicts that the reverberation time has a bell shaped relation with the synaptic density, revealing that the bursting time cannot exceed a maximum value. Furthermore, before reaching its maximum, the reverberation time increases sub-linearly with the synaptic density of the network. We conclude that synaptic dynamics and connectivity shape the mean burst duration, a property present at various scales of the networks. Thus bursting reverberation is a property of sufficiently connected neural networks, and can be generated by collective depression and facilitation of underlying functional synapses.
111-D. Holcman N.Hoze, Z. Schuss, Comment, Biophysical Journal 2015 ArXiv PDF (82.5 ko) |
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To recover the long-time behavior and the statistics of molecular tr ajectories from the large number (tens of thousands) of their short fragments, obtained by super-resolution methods at the single molecule level [1, 2], data analysis based on a stochastic model of their non-equilibrium motion is required. Recently, we characterized the local biophysical properties underlying receptor motion based on coarse-grained long-range in teractions, corresponding to attracting potential wells of large sizes [3], as predicted theoretically in [4, 5] (see also [6] for corrals). The purpose of this letter is to point out what was done and not done in [7] on this subject.
arXiv.org > physics > arXiv:1502.00286
110-K Reynaud, Z Schuss, N Rouach, D Holcman, Why so many sperm cells ? Communication Integrative Biology 2015 PDF (94.8 ko) |
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109-K. Dao Duc, D. Cohen M. Segal, N. Rouach D. Holcman, Bursting in neuronal network, PLOS 1, 2015 PDF (109.3 ko) |
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108-K. Dao Duc, J Sibille, N. Rouach, D. Holcman, Potassium regulation through the Kir4.1 channel in astrocyte, consequence for the neural activity, PlOS Computational Biology 2015 PDF (3.1 Mo) |
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107-J. Reingruber D. Holcman, Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting, Seminars in cell & developmental biology 2014 PDF (2.9 Mo) |
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106-N. Hoze D. Holcman, Kinetics of aggregation with a finite number of particles and application to viral capsid assembly, J. Math Bio 2014 PDF (826.7 ko) |
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105-N.Hoze, D. Holcman, Simulations of receptor trafficking in empirical domains and residence time in dendritic spines. 2014 ;107(12):2999-3008. PDF (2.2 Mo) |
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104-D. Holcman Z. Schuss, Oscillatory survival probability and eigenvalues of the non-self adjoint Fokker-Planck operator, SIAM MMS, 2014. PDF (416.6 ko) |
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103-Pannasch U, Freche D, Dallérac G, Ghézali G, Escartin C, Ezan P, Cohen-Salmon M, Benchenane K, Abudara V, Dufour A, Lübke JH, Déglon N, Knott G, Holcman D, Rouach N., Connexin 30 sets synaptic strength by controlling astroglial synapse invasion. Nat Neurosci. 2014 Apr ;17(4):549-58. PDF (2.1 Mo) |
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102-K. Dao Duc, Z. Schuss, D. Holcman, Oscillatory decay of the survival probability of activated diffusion across a limit cycle, Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar ;89(3):030101. PDF (453.2 ko) |
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101-Z. Schuss D. Holcman, Time scale of diffusion in molecular and cellular biology , J. Phys. A : Math. Theor. 47 173001 2014Review PDF (2.8 Mo) |
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100-D. Holcman Z. Schuss, the narrow escape problem, SIAM Review 2013 PDF (1 Mo) |
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99-D. Holcman K. Daoduc, S. Jones, H Byrne, K Burrage, Post-transcriptional regulation in the nucleus and cytoplasm : a study of mean time to threshold (MTT) and narrow escape problem (2013) PDF (769.5 ko) |
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98-N Hozé, D Holcman, Modeling capsid kinetics assembly from the steady state distribution of multi-sizes aggregates, Phys. Lett A 2013 PDF (541.1 ko) |
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97- A. Amitai, D. Holcman, Computing DNA Looping, J. Stat. Phys. 2013 PDF (379.6 ko) |
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96-A. Amitai, D. Holcman, beta-model application to DNA modeling in the nucleus, PRE 88, 052604 2013 PDF (221.7 ko) |
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95— N. Hoze Z. Schuss D. Holcman, Reconstruction of surface and stochastic dynamics from a planar projection of trajectories, SIAM Journal on Imaging Sciences, 6 . 4, 2430–2449. (2013) PDF (601.7 ko) |
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94-Bouchoucha*, Y Reingruber*, J. Le Men, J Gilardi-Hebenstreit*, P, D. Holcman* Charnay*, P Stochastic switching in a feedback loop controls vertebrate hindbrain patterning revision (accepted) Mol. Sys. Biol. 2013 PDF (2.4 Mo) |
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93-K. Daoduc D. Holcman, Computing the length of the shortest telomere in the nucleus, PRL 2013 PDF (303 ko) |
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Telomere length can either be shortened or elongated by an enzyme called telomerase after each cell division. Interestingly, the shortest telomere is involved in controlling the ability of a cell to divide. Yet, its dynamics remains elusive. We present here a stochastic approach where we model this dynamics using a Markov jump process. We solve the forward Fokker-Planck equation to obtain the steady state distribution and the statistical moments of telomere lengths. We focus specifically on the shortest one and we estimate its length difference with the second shortest telomere. After extracting key parameters such as elongation and shortening dynamics from experimental data, we compute the length of telomeres in Yeast and we obtain as possible prediction, the minimum concentration of telomerase required to insure a proper cell division.
92-D. Holcman, Unraveling novel features hidden in superresolution microscopy data. Commun Integr Biol. 2013 ;6(3):e23893. doi : 10.4161/cib.23893. PDF (86.6 ko) |
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91-A. Amitai and D. Holcman, Diffusing Polymers in Confined Microdomains and Estimation of Chromosomal Territory Sizes from Chromosome Capture Data Phys. Rev. Lett. 110, 248105 (2013) PDF (316.3 ko) |
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90-Xu Z, Dao Duc K, Holcman D, Teixeira MT, The Length of the Shortest Telomere as the Major Determinant of the Onset of Replicative Senescence.Genetics. 2013 PDF (2.5 Mo) |
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89-D. Holcman Z. Schuss, Control of flux by narrow passages and hidden targets in cellular biology, Phys Progr. Report 2013 Jul ;76(7):074601. doi : 10.1088/0034-4885/76/7/074601. PDF (3.4 Mo) |
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88-Reingruber J, Pahlberg J, Woodruff ML, Sampath AP, Fain GL, Holcman D., Detection of single photons by toad and mouse rods, Proc Natl Acad Sci U S A. 2013 ;110(48):19378-83. PDF (1.1 Mb) |
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87-N. Hoze A. M. Ruault, C. Amoroso , A. Taddei D. Holcman, Spatial telomere organization and clustering in yeast S. Cerevisiae nucleus is generated by a random dynamics of aggregation-dissociation, Mol biol. Cell 2013 PDF (4.6 Mo) |
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86- K. Dao Duc, D. Holcman, Using default constraints of the spindle assembly checkpoint to estimate the associated chemical rates, BMC Biophysics ;5(1):1. 2012 PDF (870.6 ko) |
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Default activation of the spindle assembly checkpoint provides severe constraints on the underlying biochemical activation rates : on one hand, the cell cannot divide before all chromosomes are aligned, but on the other hand, when they are ready, the separation is quite fast, lasting a few minutes. Our purpose is to use these opposed constraints to estimate the associated chemical rates. RESULTS :
To analyze the above constraints, we develop a markovian model to describe the dynamics of Cdc20 molecules. We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached. CONCLUSIONS :
By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.
85-N. Hoze, D. Nair, J.B. Sibarita, E. Hosy, C. Sieben, S. Manley, A. Herrmann, D. Choquet, and D. Holcman, Heterogeneity of receptor trafficking and molecular interactions revealed by super-resolution analysis of live cell imaging, PNAS Oct, 2012 PDF (1.6 Mo) |
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84-A. Amitai, I. Kupka and D. Holcman,Computation of the Mean First-Encounter Time Between the Ends of a Polymer Chain, Phys. Rev. Lett. 109, 108302 (2012) PDF (256.2 ko) |
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83-A. Amitai I. Kupka D. Holcman, mean time for a polymer to loop. SIAM Multiscale analysis, 10, No. 2, pp. 612–632 (2012) PDF (1.2 Mo) |
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We present a new approach to investigating the dynamics of loop formation in a very crude polymer model and estimate the mean first time for the two ends to meet. This time depends on the number of monomers N. We obtain analytical formulas when N = 3,4 in dimension two and an asymptotic formula when N is large. Our analysis is confirmed by stochastic simulations.
82-D. Holcman Z. Schuss, The dire strait time, SIAM Multiscale Modeling and simulations, 10(4), 1204–1231. (28 pages) 2012 PDF (895.9 ko) |
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81-D. Fresche, CY Lee, N. Rouach, D. Holcman, Synaptic transmission in neurological disorders dissected by a quantitative approach, 5-5, 1-5, Communicative & Integrative Biology (2012)0 PDF (745.9 ko) |
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78- K. Dao Duc, D. Holcman : Using default constraints of the spindle assembly checkpoints to estimate the associate chemical rates, BMC Biophysics 2012 |
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80- T. Lagache, O. Danos, D. Holcman, Modeling the endosomal step of non-enveloped viruses in cell infection, Biophys J. 2012 ;102(5):980-9. PDF (463.9 ko) |
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79-. Amitai, C. Amuroso, A. Ziskind, D. Holcman, Encounter dynamics of a small target by a polymer diffusing in a confined domain, J.Chem. Phys. 137, 244906 (2012) ; PDF (1005.6 ko) |
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78-D. Holcman Z. Schuss, Brownian needle in dire straits: Stochastic motion of a rod in very confined narrow domains, Phys. Rev. E 85, 010103(R) (2012) 2012. PDF (245.5 kb) |
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77-N. Hoze, D. Holcman, Coagulation–fragmentation for a finite number of particles and application to telomere clustering in the yeast nucleus, Physics Letters A,Volume 376, 6–7, 845–849, 2012. PDF (656.4 ko) |
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76- O. Stettler, R. L. Joshi, J. Reingruber, D. Holcman, C. Bouillot, A. Prochiantz, K. L. Moya : Extracellular Engrailed potentiates EphrinA5 via a novel signalling mechanism involving ATP and the adenosine A1 receptor, Development. 2012 ;139(1):215-24. PDF (2 Mo) |
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75-D. Holcman N. Hoze Z.schuss, Narrow escape through a funnel and effective diffusion on a crowded membrane, PRE, 001900 (2011)2011 PDF (471.5 ko) |
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74-D. Holcman Z. Schuss, Diffusion laws in dendritic spines, J. Math. Neuroscience 2011. PDF (922.1 kb) |
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Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically consist of a relatively large head connected to the dendritic shaft by a narrow cylindrical neck. The surface of the head is connected smoothly by a funnel or non-smoothly to the narrow neck, whose end absorbs the particles at the dendrite. We demonstrate here how the geometry of the neuronal spine can control di®usion and ultimately synaptic processes. We show that the mean residence time of a Brownian particle, such as an ion or molecule inside the spine, and of a receptor on its membrane, prior to absorption at the dendritic shaft depends strongly on the curvature of the connection of the spine head to the neck and on the neck’s length. The analytical results solve the narrow escape problem for domains with long narrow necks.
73-C Ribrault J. Reingruber, N. Ziv, D. Holcman, A. Triller, Syntaxin1A diffusion reveals transient and local SNARE interactions, J. Neuroscience Nov 30 ;31(48):17590-17602.(2011) |
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72-A. Biess E. Korkotian D. Holcman, Barriers to diffusion in dendrites and estimation of calcium spread following synaptic inputs, PLoS Comp Biology (2011), 7(10), e1002182 2011 PDF (3.1 Mb) |
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The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as D_cyto/D_water = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5\mu m). Full paper
71-U Pannasch, L Vargova, J. Reingruber, P Ezan, C Giaume, D. Holcman,E Sykova, N. Rouach, Astroglial networks scale synaptic activity and plasticity, PNAS 108(20):8467-72. 2011 PDF (1.1 Mo) |
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70- J. Reingruber, D. Holcman : The Narrow Escape problem in a flat cylindrical microdomain, SIAM Multicale Modeling and Simulations, 2011 PDF (957.8 ko) |
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D. Holcman Z. Schuss, Kinetics of Non-Arrhenius reactions. |
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69-D. Fresche, U. Pannasch, N. Rouach D. Holcman, Synapse geometry and receptor dynamics modulate synaptic strength, PloS1 (6)10,e25122 2011 PDF (2.5 Mo) |
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Synaptic transmission relies on several processes, such as the location of a released vesicle, the number and type of receptors, trafficking between the postsynaptic density (PSD) and extrasynaptic compartment, as well as the synapse organization. To study the impact of these parameters on excitatory synaptic transmission, we present a computational model for the fast AMPA-receptor mediated synaptic current. We show that in addition to the vesicular release probability, due to variations in their release locations and the AMPAR distribution, the postsynaptic current amplitude has a large variance, making a synapse an intrinsic unreliable device. We use our model to examine our experimental data recorded from CA1 mice hippocampal slices to study the differences between mEPSC and evoked EPSC variance. The synaptic current but not the coefficient of variation is maximal when the active zone where vesicles are released is apposed to the PSD. Moreover, we find that for certain type of synapses, receptor trafficking can affect the magnitude of synaptic depression. Finally, we demonstrate that perisynaptic microdomains located outside the PSD impacts synaptic transmission by regulating the number of desensitized receptors and their trafficking to the PSD. We conclude that geometrical modifications, reorganization of the PSD or perisynaptic microdomains modulate synaptic strength, as the mechanisms underlying long-term plasticity.
68-A. Taflia D. Holcman, Estimating the Synaptic Current in a Multiconductance AMPA Receptor Model c transmission,Biophys J. 101(4):781-92.2011 PDF (476.1 ko) |
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67-J. Reingruber D. Holcman, Transcription factor search for a DNA promoter in a three-state model, PRE short com 000900(R) (2011) PDF (455.9 ko) |
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66-C. Amoruso T. Lagache D. Holcman, Modeling the early steps of cytoplasmic trafficking in viral infection and gene delivery (in press) SIAM of Applied Math PDF (491.8 ko) |
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Gene delivery of nucleic acid to the cell nucleus is a fundamental step of gene therapy. To better evaluate what modeling approaches can bring to the field of drug and gene delivery, we propose to review here some of these modelings, focusing at the particular stage of plasmid DNA or virus cytoplasmic trafficking. A challenging question is to quantify the success of these limiting steps. This review is divided into two main parts : first, we present some modeling and simulations of plasmid trafficking and the limiting phase of DNA-polycation escape from an endosome, while in the second part, we discuss virus cytoplasmic trafficking. This latest modelings can be used to analyze the success of viral escape from endosomes, to quantify the early step of viral-cell infection and to propose new simulation tools to design new synthetic vectors using hybrid-viruses.
65-S. Vakeroudis, M. Yor, D. Holcman : The Mean First Rotation Time of a planar polymer, J. Stat. Phys,143, 6/June 2011, p. 1074-1095.2011 PDF (396.5 ko) |
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We estimate here the mean first time, called the mean rotation time (MRT), for a planar polymer to wind around a point. The polymer is modeled as a collection of n rods, each of them parameterized by a Brownian angle. We are led to study the sum of i.i.d. exponentials with a one dimensional Brownian motion in the argument. We find that the free end of the polymer satisfies a novel stochastic equation with nonlinear time function. Finally, we obtain an asymptotic formula for the MRT, and the leading order term depends on the square root of n and, interestingly, weakly on the initial configuration. Our analytical results are confirmed by Brownian simulations.
64-Bouzigues C, Holcman D, Dahan M., A Mechanism for the Polarity Formation of Chemoreceptors at the Growth Cone Membrane for Gradient Amplification during Directional Sensing,PLoS One. 2010, 22 ;5(2):e9243 PDF PLos1Bouzigues (601.8 ko) |
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63-G. Malherbe D. Holcman, Stochastic modeling of gene activation and application to cell regulation, J. Th.Bio 2010. PDF (728.1 ko) |
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62-D. Holcman I. Kupka , Some questions in computational cellular biology, 2010, J. Fixed Point th. Appl. PDF holcman-kupka (2.6 Mo) |
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61-K. Dao Duc D. Holcman, Threshold activation for stochastic chemical reactions in microdomains, PRE 1, 81,2010. PDF ProofPRE2010-2 (338 ko) |
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60-C. Giaume, A. Koulakoff, L. Roux, D. Holcman and N. Rouach, Astroglial connexin-mediated networks:a step further in neuroglial interactions, Nat. Rev. Neuroscience, 11(2):87-99. Fev 2010. PDF Reviewnrn2757 (3.2 Mo) |
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59-J. Reinbruber D. Holcman, Narrow escape for a stochastically gated Brownian ligand, J. Cond. Matt, 22 2010 PDF reingruberHolcman_GNET_JCondMat2010 (426.3 ko) |
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58-G. Malherbe D. Holcman, Search for a DNA target site in the nucleus, Phys. Lett. A. 374,3,2010, 466-471 PDF PLA19339 (450 ko) |
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57-D. Holcman, Computational challenges in synaptic transmission, AMS Contemporary Mathematics : Proceedings of the Conference on Imaging Microstructures : Mathematical and Computational Challenges, Edited by H. Ammari and H. Kang. 2009 PDF Ammari-review (2.6 Mo) |
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56-T. Lagache E. Dauty D. Holcman, Physical principles and models describing intracellular virus particle dynamics, Current Opinion in Microbiology, 12,4 (2009). PDF REview-Physical12 (266.9 ko) PDF PDFfile-LDH-currOpi (770 ko) |
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Modeling in cellular biology benefits greatly from quantitative analyses that arise from the theory of diffusion and chemical reactions. Recent progress in single particle imaging enables the visualization of viral trajectories evolving in the cytoplasm. Biophysical models and mathematical analysis have been developed to unravel the complexity of single viral trajectories. We review here models of active motion of viruses along the cytoskeleton as well as their diffusion. We present resent efforts to estimate global trafficking properties, such as the probability and the mean time for a viral particle to reach a small nuclear pore. However, most signaling pathways involved in controlling viral motion remain undescribed and should be the goal of future modeling efforts.
55-D. Holcman I. Kupka, The probability of an encounter of two Brownian particles before escape, J. Phys A 2009 PDF kupkaholcmanProofJPyhsA (175 ko) |
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We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis. Finally, we discuss some applications to the probability that a double strand DNA break repairs in confined environments.
54-T. Lagache, E. Dauty, D. Holcman, Toward a quantitative analysis of virus and plasmid trafficking in cells, PRE, 79,1,2009 PDF (416.5 kb) |
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53-J. Reingruber and D. Holcman, Diffusion in narrow domains and application to phototransduction, Phys Rev E 79, 030904 (2009). PDF ReingruberHolcman_PRE2009 (138.9 ko) |
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52-J. Reingruber D. Holcman, The Gated Narrow Escape Time for Molecular Signaling, PRL 103, 148102 (2009) PDF GNET_PRL2009 (289.5 ko) |
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51-J. Reingruber, E. Abad, D. Holcman : Narrow escape time to a structured target located on the boundary of a microdomain, J Chem Phys. 130, 094909 (2009). PDF ReingruberAbadHolcman_JCP2009 (162.6 ko) |
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50-K. Tsaneva, A. Burgo, T. Galli, D. Holcman, Quantifying neurite growth mediated by interactions between secretory vesicles, microtubules and actin networks, Biophysical Journal, 2009 PDF (1.9 Mb) |
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49-D. Holcman A. Singer, Z. Schuss, Narrow escape and leakage of Brownian particles. PRE 78:051111 (2008). PDF PRE-leakage (132.7 kb) |
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Questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem. The determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the Neumann Green’s function for the Laplacian in a 3-D domain with a Dirac mass on the boundary. In addition to the usual 3-D Coulomb singularity, this Green’s function also has an additional weaker logarithmic singularity. By calculating the coefficient of this logarithmic singularity, we calculate the second term in the asymptotic expansion of the narrow escape time and in the expansion of the principal eigenvalue of the Laplace equation with mixed Dirichlet-Neumann boundary conditions, with small Dirichlet and large Neumann parts. We also determine the leakage flux of Brownian particles that diffuse from a source to an absorbing target on a reflecting boundary of a domain, if a small perforation is made in the reflecting boundary.
48-J. Reingruber D. Holcman, Estimating the rate constant of cGMP hydrolysis by activated phosphodiesterase in photoreceptors, J. Chem. Phys. 129, 145102 (2008). PDF (301 ko) |
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47-T. Lagache D. Holcman, Quantifying intermittent transport in cell cytoplasm, Phys. Rev. E 77, 030901(R) (2008) PDF (184.4 kb) |
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46-Z, Schuss, D. Holcman, The first eigenvalue of Laplace operator with small holes, J. Phys A. (2008). PDF (214.4 kb) |
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45-Z, Schuss, D. Holcman, small hole through a cluster of receptors, Phys Lett. A. (2008). PDF (259.8 kb) |
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44-D. Holcman I. Kupka, Semi-classical limit of the first eigenfunction and concentration on the recurrent sets of a dynamical system, to appear in Forum Math 2009. PDF Blow_up_lim_cy-Final (426 kb) |
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43-J. Reingruber D. Holcman, The dynamics of phosphodiesterase activation in rods and cones, Biophysical Journal 94, 1954 (2008). PDF (443.2 kb) |
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42- T. Lagarche D. Holcman, Effective motion of a virus trafficking inside a biological cell, accepted in SIAM. PDF (380.8 kb) |
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41- D. Holcman, V Kasatkin A. Prochiantz, Formation of morphogenetic gradients during early development, J. Th. Bio, 2007 PDF (654.7 kb) |
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40- Singer Z, Schuss, D. Holcman, Partially Reflected Diffusion, SIAM of Applied Math PDF (161.2 kb) PDF (263.1 kb) |
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39-Z. Schuss, A. Singer, D. Holcman Narrow Escape: Theory and Applications to Cellular Microdomains, Proc. Nat. Acad. Sci. 2007 PDF (494.8 kb) |
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38-A. Taflia D. Holcman, Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary. Chem Phys. 2007;126(23):234107. PDF (235.9 kb) |
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37-A. Biess E.Korkotian D. Holcman, Diffusion through a dendritic spine neck; 76,1 PRE PDF (303.6 kb) |
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36- D. Holcman, Modeling viral DNA trafficking in a biological cell, Journal Stat. Physics 2007 10.1007/s10955-007-9282-4 PDF (400.9 kb) |
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35- V. Kasatkin Prochiantz A D. Holcman A. , Stability of boundaries between neighboring morphogenetic regions, Bull. Math. Bio.2007. PDF BMAB9246_Author (357.2 kb) |
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Generation of morphogenetic gradients during early development is a fundamental step of positional signaling, which ultimately results in patterning and cell specialization. Based on morphogen propagation from cells to cells, we have presented a biophysical model where gradients and boundaries between different morphogenetic regions can be generated. In that theory, morphogens are transcription factors which induce their own activation and at the same time propagate in the cell ensemble.
Because random perturbations of a gradient can affect the precise location of the boundary between two morphogenetic regions, we propose to analyze here these fluctuations. In particular, we derive a precise expression for the variance of the boundary location as a function of the variance of the perturbation. We also analyze a variant version of the biophysical model of morphogenetic gradients in which morphogens can form dimers. As a result, gradients are smoother and borders are much sharper.
34- D Holcman- C. Pugh, Boundary between complete and compact manifolds, Indiana Journal of Math. PDF (188 kb) |
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33- D. Holcman A.Triller, Modeling synaptic dynamics and receptor trafficking, Biophysical Journal 2006 Jul 14 PDF (236.7 kb) |
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32- D. Holcman I. Kupka, Singular perturbation for the first eigenfunction and blow up analysis, Forum Math May 2006 PDF (520.8 kb) |
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31- D. Holcman M.Tsodyks, Emergence of Up and Down states in cortical neurons, PloS Computational biology 2006 PDF (859.5 kb) |
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30- A. Singer Z, Schuss, D. Holcman, B. Eisenberg, Narrow Escape, J. of Stat. Phys. 2006 PDF (192.5 kb) |
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29- A. Singer Z, Schuss, D. Holcman, Narrow Escape II (in press) J. of Stat. Phys. PDF (170.9 kb) |
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28- A. Singer Z, Schuss, D. Holcman, Narrow Escape III, J. of Stat. Phys. PDF (155.4 kb) |
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26- E. Bart S. Bao D. Holcman, Modeling the spontaneous activity of the auditory cortex, Journal of Computational Neuroscience 19 (3): 357-378 2005 PDF (1.3 Mb) |
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24- D. Holcman J. Korenbrot, The limit of photoreceptor sensitivity: molecular mechanisms of dark noise in retinal cones, J Gen Physiol. 2005 Jun;125(6):641-60. PDF (375.9 kb) |
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20- D. Holcman, E. Korkotian, M. Segal, Calcium dynamic in dendritic spine, modeling and experiments. Review, Cell Calcium 2005 May;37(5):467-75. PDF (1 Mb) |
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23- D. Holcman, Z. Schuss, Stochastic Chemical Reactions in Micro-domains. Journal of Chemical Physics 122,1, 2005 PDF (371.4 kb) PDF (581.1 kb) |
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22- D. Holcman Z. Schuss, Modeling Calcium Dynamics in Dendritic Spines, SIAM of Applied Math 65 (2005), no. 3, 1006—1026. PDF (361.4 kb) |
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21- D. Holcman I. Kupka, Perturbation Methods and First Order Differential Equations on Riemannian Manifolds, Quarterly Journal of Mathematics 56, 1,65—93 (2005). PDF (409.2 kb) |
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27- David Holcman, Avi Marchewka, and Zeev Schuss : Survival probability of diffusion with trapping in cellular neurobiology, Phys. Rev. E, 72, 031910 (2005) PDF (118.5 kb) |
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25- D. Holcman, I. Kupka, Concentration of the first eigenfunction for a second order elliptic operator, C.R.A.S Serie I-2005 - Volume 341 - Numéro 4 p243-246 |
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18- D. Holcman, Z. Schuss, Escape through a small opening: receptor trafficking in a synaptic membrane, J. of Statistical Physics 117, 5/6 Dec. (2004)p 191-230. PDF (256.5 kb) |
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17- D. Holcman, Z. Schuss, E. Korkotian, Calcium dynamic in dendritic spines and spine motility, Biophysical Journal 87:81-91 (2004) PDF (485.4 kb) |
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16- D. Holcman J. Korenbrot, Longitudinal diffusion in retinal rod and cone outer segment cytoplasm: the consequence of cell structure, Biophysical Journal 86:2566-2582 (2004) PDF (333.3 kb) |
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19- E. Korkotian D. Holcman, M. Segal, Dynamic Regulation of Spine-Dendrite Coupling in Cultured Hippocampal Neurons, Euro J. of Neuroscience, Nov; 20(10):2649-63. 2004. PDF (1008.2 kb) |
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15- D.Holcman M.Margaliot, Stability Analysis of Switched Homogeneous Systems in the plane, SIAM J. of Control, 41 (2002), no. 5, 1609—1625. PDF (215.2 kb) PDF (215.2 kb) |
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14- P. Greiner D. Holcman Y. Kannai, Wave Kernel related to second order operators, Duke Mathematical Journal, 114 (2002), no. 2, 329—386.. PostScript (1 Mb) |
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12- D. Holcman I. Kupka, Singular Perturbation and first order PDE on manifolds. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), no. 5, 465—470. PDF (131.4 kb) |
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13- D. Holcman, Prescribed Scalar Curvature problem on Complete manifolds, J. Math. Pures Appl. (9) 80 (2001), no. 2, 223—244.et Appl. 2001. |
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11- D. Holcman E. Humbert, Poincare-Sobolev inequality on manifolds with boundary, Math. Z. 237 (2001), no. 4, 669—695 |
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10- D. Holcman, Solutions nodales d’EDP non lineaires sur les varietes non localement conformément plates, Paris 2000, Comment. Math. Helv. 76 (2001), no. 3, 373—387 PDF (231.8 kb) |
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9- D. Holcman, Nonlinear PDE with vector fields, J. Anal. Math. 81 (2000), 111—137. |
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8- D. Holcman, Influence de la masse sur les solutions nodales d’EDP non lineaires, Bull. Sci. Math. 124 (2000), no. 5, 385—414 |
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7- Barrie J.M., Holcman D., Freeman W.J., Statistical evaluation of clusters derived by nonlinear mapping of EEG spatial patterns, Journal of Neuroscience Methods august(90) 1999 p87-95. |
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6- D. Holcman, On the mass of manifolds with boundary, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1191—1196 |
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5- D.Holcman, EDP non lineaires avec champ de vecteurs, Compt. Rend. Acad. Sci. Paris, 329 (1999), no. 10, 871—876. |
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4- D. Holcman, Prescribed Scalar Curvature problem on Complete manifolds, Compt. Acad. Sci Serie I,t 328, 1999. p 321-326 |
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3- D.Holcman, Solutions nodales sur les varietes Riemanniennes, J. of Funct. Analys., 1999,Vol. 26, p219-245. |
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2- D. Holcman, Solutions nodales sur les varietes riemanniennes a bord, Compt. Rend. Acad. Sci. Paris, t.326, Serie I, 1998, p1321-1324. |
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1- D. Holcman, Solutions nodales sur les varietes Riemanniennes compactes, Compt. Rend. Acad. Sci. Paris, 1998,t. 326, Série I, p1205-1208 |
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