arXiv subjects

D. Holcman

Publications and source records attributed to D. Holcman.

At least 19 recordsLinked to original sources

arXiv2025

Numerical Twin with Two Dimensional Ornstein--Uhlenbeck Processes of Transient Oscillations in EEG signal

Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity as a two-dimensional Ornstein-Uhlenbeck (OU) process with three interpretable parameters: decay rate, mean frequency, and noise amplitude. We develop two complementary estimation strategies. The first fits the power spectral density, amplitude distribution, and autocorrelation to recover OU-parameters. The second segments burst events and performs a statistical match between empirical spindle statistics (duration, amplitude, inter-event interval) and simulated OU output via grid search, resolving parameter degeneracies by including event counts. We extend the framework to multiple frequency bands and piecewise-stationary dynamics to track slow parameter drifts. Applied to electroencephalography (EEG) recorded during general anesthesia, the method identifies OU models that reproduce alpha-spindle (8-12 Hz) morphology and band-limited spectra with low residual error, enabling real-time tracking of state changes that are not apparent from band power alone. This decomposition yields a sparse, interpretable representation of transient oscillations and provides interpretable metrics for brain monitoring.

q-bio.NC↗

arXiv2025

Modeling, Segmenting and Statistics of Transient Spindles via Two-Dimensional Ornstein-Uhlenbeck Dynamics

We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a two-dimensional Ornstein{Uhlenbeck (OU) process with a stable focus, providing a low-dimensional stochastic dynamical system whose trajectories reproduce key morphological features of spindles, including their characteristic rise{decay amplitude envelopes. On the signal processing side, we propose a segmentation procedure based on Empirical Mode Decomposition (EMD) combined with the detection of a central extremum, which isolates single spindle events and yields a collection of oscillatory atoms. This construction enables a systematic statistical analysis of spindle features: we derive empirical laws for the distributions of amplitudes, inter-spindle intervals, and rise/decay durations, and show that these exhibit exponential tails consistent with the underlying OU dynamics. We further extend the model to a pair of weakly coupled OU processes with distinct natural frequencies, generating a stochastic mixture of slow, fast, and mixed spindles in random temporal order. The resulting framework provides a data-driven framework for the analysis of transient oscillations in EEG and, more generally, in nonstationary time series.

q-bio.NC↗

arXiv2024

Segmentation algorithms and modeling of recurrent bursting events in neuronal and glial time series

Long-time series of neuronal recordings are resulting from the activity of connected neuronal networks. Yet how neuronal properties can be extracted remains empirical. We review here the data analysis based on network models to recover physiological parameters from electrophysiological and calcium recordings in neurons and astrocytes. After, we present the recording techniques and activation events, such as burst and interburst and Up and Down states. We then describe time-serie segmentation methods developed to detect and to segment these events. To interpret the statistics extracted from time series, we present computational models of neuronal populations based on synaptic short-term plasticity and After hyperpolarization. We discuss how these models are calibrated so that they can reproduce the statistics observed in the experimental time series. They serve to extract specific parameters by comparing numerical and experimental statistical moment or entire distributions. Finally, we discus cases where calibrated models are used to predict the selective impact of some parameters on the circuit behavior, properties that would otherwise be difficult to dissect experimentally.

q-bio.NC↗

arXiv2020

Extreme escape from a cusp: when does geometry matter for the fastest Brownian particles moving in crowded cellular environments?

We study here the extreme statistics of Brownian particles escaping from a cusp funnel: the fastest Brownian particles among $n$ follow an ensemble of optimal trajectories located near the shortest path from the source to the target. For the time of such first arrivers, we derive an asymptotic formula that differs from the classical narrow escape and dire strait obtained for the mean first passage time. Consequently, when particles are initially distributed at a given distance from a cusp, the fastest do see some properties characterizing the cusp geometry. Therefore, when many particles diffuse around impermeable obstacles, the geometry plays a role in the time to reach a target. In the biological context of cellular transduction with signalling molecules, having to escape such cusp-like domains slows down fast signaling. To conclude, generating multiple copies of the same molecule helps bypass a crowded environment to transmit a molecular signal quickly.

cond-mat.stat-mech↗

arXiv2019

Reconstructing a point source from diffusion fluxes to narrow windows in three dimensions

We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three dimensional half-space or on a sphere. This approach is based on solving the mixed boundary stationary diffusion equation with the Neumann-Green's function and matched asymptotic. We compute the probability fluxes and develop a highly efficient analytical-Brownian numerical scheme. This scheme accelerates the simulation time by avoiding the explicit computation of Brownian trajectories in the infinite domain. Our derived analytical formulas agree with the results obtained from the fast numerical simulation scheme. Using the analytical representation of the particle fluxes, we show how to reconstruct the location of the point source. Furthermore, we investigate the uncertainty in the source reconstruction due to additive fluctuations present in the fluxes. We also study the influence of various window configurations (cluster vs uniform distributions) on recovering the source position.

cond-mat.stat-mech↗

arXiv2018

Electrical transient laws in neuronal microdomains based on electro-diffusion

The current-voltage (I-V) conversion characterizes the physiology of cellular microdomains and reflects cellular communication, excitability, and electrical transduction. Yet deriving such I-V laws remains a major challenge in most cellular microdomains due to their small sizes and the difficulty of accessing voltage with a high nanometer precision. We present here novel analytical relations derived for different numbers of ionic species inside a neuronal micro/nano-domains, such as dendritic spines. When a steady-state current is injected, we find a large deviation from the classical Ohm's law, showing that the spine neck resistance is insuficent to characterize electrical properties. For a constricted spine neck, modeled by a hyperboloid, we obtain a new I-V law that illustrates the consequences of narrow passages on electrical conduction. Finally, during a fast current transient, the local voltage is modulated by the distance between activated voltage-gated channels. To conclude, electro-diffusion laws can now be used to interpret voltage distribution in neuronal microdomains.

q-bio.NC↗

arXiv2017

Voltage laws for three-dimensional microdomains with cusp-shaped funnels derived from Poisson-Nernst-Planck equations

We study the electro-diffusion properties of a domain containing a cusp-shaped structure in three dimensions when one ionic specie is dominant. The mathematical problem consists in solving the steady-state Poisson-Nernst-Planck (PNP) equation with an integral constraint for the number of charges. A non-homogeneous Neumann boundary condition is imposed on the boundary. We construct an asymptotic approximation for certain singular limits that agree with numerical simulations. Finally, we analyse the consequences of non-homogeneous surface charge density. We conclude that the geometry of cusp-shaped domains influences the voltage profile, specifically inside the cusp structure. The main results are summarized in the form of new three-dimensional electrostatic laws for non-electroneutral electrolytes. We discuss applications to dendritic spines in neuroscience.

q-bio.NC↗

arXiv2015

Poisson-Nernst-Planck equations in a ball

The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratu-type equation with the difference that the boundary condition is Neumann, not Dirichlet and there a minus sign in the exponent of the exponential term. The entire boundary is impermeable to the ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct a steady radial solution and find that the potential is maximal in the center and decreases toward the boundary. We study the limit of large charge in dimension 1,2 and 3. For the case of a small absorbing window in the sphere, we find the escape rate of an ion from the steady density.

physics.class-ph↗

arXiv2015

Analysis of single particle trajectories: when things go wrong

To recover the long-time behavior and the statistics of molecular trajectories from the large number (tens of thousands) of their short fragments, obtained by super-resolution methods at the single molecule level, 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 interactions, corresponding to attracting potential wells of large sizes. The purpose of this letter is to discuss optimal estimators and show what happens when thing goes wrong.

physics.bio-ph↗

arXiv2014

Oscillatory Survival Probability: Analytical, Numerical Study for oscillatory narrow escape and applications to neural network dynamics

We study the escape of Brownian motion from the domain of attraction $Ω$ of a stable focus with a strong drift. The boundary $\partial Ω$ of $Ω$ is an unstable limit cycle of the drift and the focus is very close to the limit cycle. We find a new phenomenon of oscillatory decay of the peaks of the survival probability of the Brownian motion in $Ω$. We compute explicitly the complex-valued second eigenvalue $λ_2(Ω$) of the Fokker-Planck operator with Dirichlet boundary conditions and show that it is responsible for the peaks. Specifically, we demonstrate that the dominant oscillation frequency equals $1/{\mathfrak{I}}m\{λ_2(Ω)\}$ and is independent of the relative noise strength. We apply the analysis to a canonical system and compare the density of exit points on $\partial Ω$ to that obtained from stochastic simulations. We find that this density is concentrated in a small portion of the boundary, thus rendering the exit a narrow escape problem. Unlike the case in the classical activated escape problem, the principal eigenvalue does not necessarily decay exponentially as the relative noise strength decays. The oscillatory narrow escape problem arises in a mathematical model of neural networks with synaptic depression. We identify oscillation peaks in the density of the time the network spends in a specific state. This observation explains the oscillations of stochastic trajectories around a focus prior to escape and also the non-Poissonian escape times. This phenomenon has been observed and reported in the neural network literature.

math.AP↗

arXiv2014

Why so many sperm cells?

A key limiting step in fertility is the search for the oocyte by spermatozoa. Initially, there are tens of millions of sperm cells, but a single one will make it to the oocyte. This may be one of the most severe selection processes designed by evolution, whose role is yet to be understood. Why is it that such a huge redundancy is required and what does that mean for the search process? we propose to discuss here these questions and consequently a new line of interdisciplinary research needed to find possible answers.

q-bio.CB↗

arXiv2014

Residence times of receptors in dendritic spines analyzed by simulations in empirical domains

Analysis of high-density superresolution imaging of receptors reveal the organization of dendrites at the nano-scale resolution. We present here simulations in empirical live cell images, which allows converting local information extracted from short range trajectories into simulations of long range trajectories. Based on these empirical simulations, we compute the residence time of an AMPA receptor (AMPAR) in dendritic spines that accounts for receptors local interactions and geometrical organization. We report here that depending on the type of the spine, the residence time varies from one to five minutes. Moreover, we show that there exists transient organized structures, previously described as potential wells that can regulate the trafficking of AMPARs to dendritic spines.

q-bio.SC↗

arXiv2013

Oscillatory decay of the survival probability of activated diffusion across a limit cycle

Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary oscillations can be discerned in the survival probability. We show that these oscillations are due to complex-valued higher order eigenvalues of the Fokker-Planck operator, which we compute explicitly in the limit of small noise. We also show that in this limit the period of the oscillations is the winding number of the activated stochastic process. These peak probability oscillations are not related to stochastic resonance and should be detectable in planar dynamical systems with the topology described here.

math-ph↗

arXiv2013

Potential wells for AMPA receptors organized in ring nanodomains

By combining high-density super-resolution imaging with a novel stochastic analysis, we report here a peculiar nano-structure organization revealed by the density function of individual AMPA receptors moving on the surface of cultured hippocampal dendrites. High density regions of hundreds of nanometers for the trajectories are associated with local molecular assembly generated by direct molecular interactions due to physical potential wells. We found here that for some of these regions, the potential wells are organized in ring structures. We could find up to 3 wells in a single ring. Inside a ring receptors move in a small band the width of which is of hundreds of nanometers. In addition, rings are transient structures and can be observed for tens of minutes. Potential wells located in a ring are also transient and the position of their peaks can shift with time. We conclude that these rings can trap receptors in a unique geometrical structure contributing to shape receptor trafficking, a process that sustains synaptic transmission and plasticity.

q-bio.SC↗

arXiv2013

Encounter dynamics of a small target by a polymer diffusing in a confined domain

We study the first passage time for a polymer, that we call the narrow encounter time (NETP), to reach a small target located on the surface of a microdomain. The polymer is modeled as a Freely Joint Chain (beads connected by springs with a resting non zero length) and we use Brownian simulations to study two cases: when (i) any of the monomer or (ii) only one can be absorbed at the target window. Interestingly, we find that {in the first case} the NETP is an increasing function of the polymer length until a critical length, after which it decreases. Moreover, in the long polymer regime, we identified an exponential scaling law for the NETP as a function of the polymer length. {In the second case, the position of the absorbed monomer along the polymer chain strongly influences the NETP}. Our analysis can be applied to estimate the mean first time of a DNA fragment to a small target in the chromatin structure or for mRNA to find a small target.

cond-mat.soft↗

arXiv2008

Narrow escape and leakage of Brownian particles

Questions of flux regulation in biological cells raise renewed interest in the narrow escape problem. The often inadequate expansions of the narrow escape time are due to a not so well known fact that the boundary singularity of Green's function for Poisson's equation with Neumann and mixed Dirichlet-Neumann boundary conditions in three-dimensions contains a logarithmic singularity. Using this fact, we find the second term in the 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 find 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.

math-ph↗

arXiv2008

Quantifying intermittent transport in cell cytoplasm

Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of intermittent dynamics, where the motion of a particle, such as a virus, alternates between pure Brownian and directed movement along microtubules. In this communication, we estimate the mean time for particle to attach to a microtubule network. This computation leads to a coarse grained equation of the intermittent motion in radial and cylindrical geometries. Finally, by using the degradation activity inside the cytoplasm, we obtain refined asymptotic estimations for the probability and the mean time a virus reaches a small nuclear pore.

q-bio.QM↗

arXiv2007

The search kinetics of a target inside the cell nucleus

The mean time required by a transcription factor (TF) or an enzyme to find a target in the nucleus is of prime importance for the initialization of transcription, gene activation or the start of DNA repair. We obtain new estimates for the mean search time when the TF or enzyme, confined to the cell nucleus, can switch from a one dimensional motion along the DNA and a free Brownian regime inside the crowded nucleus. We give analytical expressions for the mean time the particle stays bound to the DNA, $τ_{DNA}$, and the mean time it diffuses freely, $τ_{free}$. Contrary to previous results but in agreement with experimental data, we find a factor $τ_{DNA} \approx 3.7 τ_{free}$ for the Lac-I TF. The formula obtained for the time required to bind to a target site is found to be coherent with observed data. We also conclude that a higher DNA density leads to a more efficient search process.

q-bio.BM↗