arXiv subjects

Henri Orland

Publications and source records attributed to Henri Orland.

At least 19 recordsLinked to original sources

arXiv2026

Effects of Rim Fluctuations in Classical Nucleation Theory of Virus Capsids

Most spherical viruses exhibit icosahedral symmetry, yet the growth of viral shells remains poorly understood due to the short lifetimes and broad size distribution of assembly intermediates. Classical nucleation theory has been widely applied to describe this process, but it treats the boundary of a growing shell as rigid and structureless. Here, we extend classical nucleation theory by incorporating thermal fluctuations of the capsid rim using both discrete and continuum descriptions. Allowing the rim of a partially formed capsid to undergo small geometric undulations, we show that these fluctuations generate an entropic contribution that renormalizes the effective line tension. As a result, rim fluctuations can either promote or hinder capsid closure, depending on the subunit-subunit binding free energy, temperature, and fluctuation amplitude. We find that fluctuations generally lower the nucleation barrier when the binding free energy is below a threshold value, while for sufficiently strong binding, they can instead raise the barrier by stabilizing incomplete capsids through a finite-size entropy penalty associated with rim closure. By moving beyond the idealized capillarity approximation, our results provide a controlled extension of classical nucleation theory that clarifies how boundary fluctuations influence capsid nucleation and growth.

cond-mat.soft↗

arXiv2025

Realistic Transition Paths for Large Biomolecular Systems: A Langevin Bridge Approach

We introduce a computational framework for generating realistic transition paths between distinct conformations of large bio-molecular systems. The method is built on a stochastic integro-differential formulation derived from the Langevin bridge formalism, which constrains molecular trajectories to reach a prescribed final state within a finite time and yields an efficient low-temperature approximation of the exact bridge equation. To obtain physically meaningful protein transitions, we couple this formulation to a new coarse-grained potential combining a Go-like term that preserves native backbone geometry with a Rouse-type elastic energy term from polymer physics; we refer to the resulting approach as SIDE. We evaluate SIDE on several proteins undergoing large-scale conformational changes and compare its performance with established methods such as MinActionPath and EBDIMS. SIDE generates smooth, low-energy trajectories that maintain molecular geometry and frequently recover experimentally supported intermediate states. Although challenges remain for highly complex motions-largely due to the simplified coarse-grained potential-our results demonstrate that SIDE offers a powerful and computationally efficient strategy for modeling bio-molecular conformational transitions.

q-bio.BM↗

arXiv2025

Schrödinger Bridges for Systems of Interacting Particles

A Schrödinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple Brownian evolution (non-interacting particles). It is related to the problem of entropy-regularized Wasserstein optimal transport. In this article, we generalize Brownian bridges to systems of interacting particles. We derive some equations for the forward and backward single particle ``wave-functions'' which allow to compute the most probable evolution of the single-particle probability between the initial and final distributions.

cond-mat.stat-mech↗

arXiv2024

Frequency-Dependent Conductivity of Concentrated Electrolytes: A Stochastic Density Functional Theory

The response of ionic solutions to time-varying electric fields, quantified by a frequency-dependent conductivity, is essential in many electrochemical applications. Yet, it constitutes a challenging problem due to the combined effect of Coulombic interactions, hydrodynamics, and thermal fluctuations. Here, we study the frequency-dependent conductivity of ionic solutions using a stochastic density functional theory. In the limit of small concentrations, we recover the classical Debye and Falkenhagen (DF) result, predicting an increase in conductivity with field frequency. At higher concentrations, we use a modified Coulomb interaction potential that accounts for the hard-core repulsion between the ions, which was recently employed in the zero-frequency case. Consequently, we extend the DF result to concentrated electrolytes. We discuss experimental and numerical studies and the complexity of observing the DF effect in such setups.

cond-mat.soft↗

arXiv2023

Markov-bridge generation of transition paths and its application to cell-fate choice

We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master equation for Markov bridges, which exhibits the original transition rates scaled by a time-dependent factor. Trajectories can then be generated using a refined version of the Gillespie algorithm. We illustrate the benefits of our method by sampling trajectories in the Müller-Brown potential. This allows us to generate transition paths which would otherwise be obtained at a high computational cost with standard Kinetic Monte Carlo methods because commitment to a transition path is essentially a rare event. We then apply our method to a single-cell RNA sequencing dataset from mouse pancreatic cells to investigate the cell differentiation pathways of endocrine-cell precursors. By sampling Markov bridges for a specific differentiation pathway we obtain a time-resolved dynamics that can reveal features such as cell types which behave as bottlenecks. The ensemble of trajectories also gives information about the fluctuations around the most likely path. For example, we quantify the statistical weights of different branches in the differentiation pathway to alpha cells.

cond-mat.stat-mech↗

arXiv2023

Conductivity of Concentrated Electrolytes

The conductivity of ionic solutions is arguably their most important trait, being widely used in electrochemical, biochemical, and environmental applications. The Debye-Hückel-Onsager theory successfully predicts the conductivity at very low ionic concentrations of up to a few millimolars, but there is no well-established theory applicable at higher concentrations. We study the conductivity of ionic solutions using a stochastic density functional theory, paired with a modified Coulomb interaction that accounts for the hard-core repulsion between the ions. The modified potential suppresses unphysical, short-range electrostatic interactions, which are present in the Debye-Hückel-Onsager theory. Our results for the conductivity show very good agreement with experimental data up to 3 molars, without any fit parameters. We provide a compact expression for the conductivity, accompanied by a simple analytical approximation.

cond-mat.soft↗

arXiv2022

Conductance of concentrated electrolytes: multivalency and the Wien effect

The electric conductivity of ionic solutions is well understood at low ionic concentrations of up to a few millimolar but becomes difficult to unravel at higher concentrations that are still common in nature and technological applications. A model for the conductivity at high concentrations was recently put forth for monovalent electrolytes at low electric fields. The model relies on applying a stochastic density-functional theory and using a modified electrostatic pair-potential that suppresses unphysical, short-range electrostatic interactions. Here, we extend the theory to multivalent ions as well as to high electric fields where a deviation from Ohm's law known as the Wien effect occurs. Our results are in good agreement with experiments and recent simulations.

cond-mat.soft↗

arXiv2022

Dielectric Constant of Ionic Solutions: Combined Effects of Correlations and Excluded Volume

The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper we study two such possible sources: long-range Coulombic correlations and solvent excluded volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. We show that both correlations and excluded volume are required in order to capture the important features of the dielectric behavior. For highly polar solvents, such as water, the dielectric constant is given by the product of the solvent volume fraction and a concentration-dependent susceptibility per volume fraction. The available solvent volume decreases as function of ionic strength due the increasing volume fraction of ions. A similar decrease occurs for the susceptibility due to correlations between the ions and solvent, reducing the dielectric response even further. Our predictions for the dielectric constant fit well with experiments for a wide range of concentrations for different salts in different temperatures, using a single fit parameter related to the ion size.

cond-mat.stat-mech↗

arXiv2022

Sampling constrained stochastic trajectories using Brownian bridges

We present a new method to sample conditioned trajectories of a system evolving under Langevin dynamics, based on Brownian bridges. The trajectories are conditioned to end at a certain point (or in a certain region) in space. The bridge equations can be recast exactly in the form of a non linear stochastic integro-differential equation. This equation can be very well approximated when the trajectories are closely bundled together in space, i.e. at low temperature, or for transition paths. The approximate equation can be solved iteratively, using a fixed point method. We discuss how to choose the initial trajectories and show some examples of the performance of this method on some simple problems. The method allows to generate conditioned trajectories with a high accuracy.

math-ph↗

arXiv2021

Generating stochastic trajectories with global dynamical constraints

We propose a method to exactly generate Brownian paths $x_c(t)$ that are constrained to return to the origin at some future time $t_f$, with a given fixed area $A_f = \int_0^{t_f}dt\, x_c(t)$ under their trajectory. We derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that encodes the constraint. Finally, we generalise our method to other types of dynamical constraints such as a fixed occupation time on the positive axis $T_f=\int_0^{t_f}dt\, Θ\left[x_c(t)\right]$ or a fixed generalised quadratic area $\mathcal{A}_f=\int_0^{t_f}dt \,x_c^2(t)$.

cond-mat.stat-mech↗

arXiv2021

Simultaneous identification of multiple binding sites in proteins: A statistical mechanics approach

We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions between charges are controlled by electrostatics, while hydrophobic interactions are modeled with a Yukawa potential. We impose steric constraints by assuming that the system is represented on a cubic lattice. We also assume incompressibility, i.e. all sites of the lattice are occupied. This model, which we refer to as the Hydrophobic Dipolar Poisson Boltzmann Langevin (HDPBL) model, leads to a system of two equations whose solutions give the water dipole, salt, and hydrophobic molecule densities, all of them in the presence of the others in a self-consistent way. We use those to study the organization of the ions, co-solvent and solvent molecules around proteins. In particular, peaks of densities are expected to reveal, simultaneously, the presence of compatible binding sites of different kinds on a protein. We have tested and validated the ability of HDPBL to detect pockets in proteins that bind to hydrophobic ligands, polar ligands and charged small probes as well as to characterize the environment of membrane proteins.

physics.bio-ph↗

arXiv2020

A polymer model for the quantitative reconstruction of 3d chromosome architecture from Hi-C and GAM data

It is widely believed that the folding of the chromosome in the nucleus has a major effect on genetic expression. For example co-regulated genes in several species have been shown to colocalize in space despite being far away on the DNA sequence. In this manuscript, we present a new method to model the three-dimensional structure of the chromosome in live cells, based on DNA-DNA interactions measured in high-throughput chromosome conformation capture experiments (Hi-C) and genome architecture mapping experiments (GAM). Our approach incorporates a polymer model, and directly uses the contact probabilities measured in Hi-C and GAM experiments rather than estimates of average distances between genomic loci. Specifically, we model the chromosome as a Gaussian polymer with harmonic interactions and extract the coupling coefficients best reproducing the experimental contact probabilities. In contrast to existing methods, we give an exact expression of the contact probabilities at thermodynamic equilibrium. The Gaussian effective model (GEM) reconstructed with our method reproduces experimental contacts with high accuracy. We also show how Brownian Dynamics simulations of our reconstructed GEM can be used to study chromatin organization, and possibly give some clue about its dynamics.

q-bio.QM↗

arXiv2020

Multicanonical Monte Carlo Ensemble Growth Algorithm

We present a novel Ensemble Monte Carlo Growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by re-weighting with a Boltzmann factor. The algorithm we present combines two approaches: the first is the Monte Carlo ensemble growth method, where a "population" of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.

cond-mat.stat-mech↗

arXiv2017

Self Consistent Field Theory of Virus Assembly

The Ground State Dominance Approximation(GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.

physics.bio-ph↗

arXiv2017

RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses

Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood. We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction. We also observe a first order transition and kink profile as a function of RNA length. All these transitions could explain the different RNA profiles observed inside viral shells.

physics.bio-ph↗

arXiv2017

Efficient sampling of knotting-unknotting pathways for semiflexible Gaussian chains

We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any knotted state. Our method allows the generation of statistically independent paths in a computationally efficient manner. We show that these conditioned paths can be exactly generated by a set of local stochastic differential equations. The method is used to analyze the transition routes between various knots in crossable filamentous structures, thus mimicking topological reconnections occurring in soft matter systems or those introduced in DNA by topoisomerase enzymes. We find that the average number of crossings, writhe and unknotting number are not necessarily monotonic in time and that more complex topologies than the initial and final ones can be visited along the route.

cond-mat.soft↗

arXiv2016

Conditioned Langevin Dynamics enables efficient sampling of transition paths

We propose a novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$ under a given potential $U(x)$. These paths are sampled with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a local Stochastic Partial Differential Equation (SPDE). This equation cannot be solved in general. We present several approximations that are valid either in the low temperature regime or in the presence of barrier crossing. We show that this method warrants the generation of statistically independent transition paths. It is computationally very efficient. We illustrate the method on the two dimensional Mueller potential as well as on the Mexican hat potential.

cond-mat.stat-mech↗

arXiv2016

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump, and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm, as well as the ionic profiles are used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally-measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.

cond-mat.soft↗