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Pierre Illien

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cond-mat.stat-mech cond-mat.soft Biological Physics physics.chem-ph

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preprint2026arXiv

A Brownian dynamics study of liquid-liquid phase separation in multi-scale chromatin networks

In living cells, proteins involved in specialized biochemical functions are often spatially organized within biomolecular condensates. Increasing evidence suggests that some of these condensates, including DNA repair condensates, emerge through liquid-liquid phase separation (LLPS). In the nucleus, however, condensates form within a highly heterogeneous environment composed of chromatin fibers, RNA, and additional protein scaffolds such as PAR chains, all of which may interact with phase-separating proteins. Moreover, condensate formation is frequently associated with specific chromatin conformations; for instance, loop extrusion has been proposed as a mechanism promoting DNA repair condensates. Here, we investigate how the surrounding fibrous environment controls the morphology and spatial organization of phase-separated condensates. Using Brownian dynamics simulations of minimal models combining Lennard-Jones particles with fixed fibrous substrates, we examine the respective roles of local fiber geometry and large-scale network organization, reflecting the multiscale architecture of chromatin. We show that protein-fiber interactions strongly influence droplet positioning relative to the substrate, in a manner analogous to wetting transitions in soft condensed matter systems. Both local geometric constraints and global network organization markedly affect droplet size, morphology, and multiplicity. In addition, large-scale asymmetries in fiber organization can induce robust spatial localization of the dense phase. Our results thus highlight how multiscale structural heterogeneity of the nuclear environment can regulate the emergence and organization of biomolecular condensates.

preprint2026arXiv

Controlling microalgae populations by phototactic memory

Understanding how microorganisms navigate in complex environments is a central question in active matter and biological physics. Phototaxis - the ability to use light as a navigation cue - is a widespread strategy in motile microalgae to optimise photosynthesis and avoid light-induced stress. The microalga Chlamydomonas reinhardtii is a model system for studying this behaviour, where navigation is classically attributed to a photosensitive organelle named eyespot. While this mechanism enables cells to sense the direction of incoming light, their response to light intensity gradients remains less understood. Here we show that structured light landscapes can guide microalgae populations and localise them in defined spatial regions. By analysing single-cell trajectories, we find that cells actively steer relative to the local light gradient, and a comparison with a minimal theoretical model shows that a short-time memory of light exposure acting on the transition between positive and negative phototaxis is necessary to reproduce the observed accumulation. At longer times, we observe a gradual decrease in cell number density within the trapping region, consistent with phototactic adaptation. Beyond controlling population dynamics, our results reveal new aspects of phototactic behaviour, highlighting gradient-aligned steering together with temporal integration as central mechanisms for navigation in structured environments.

preprint2023arXiv

Duality relations in single-file diffusion

Single-file transport, which corresponds to the diffusion of particles that cannot overtake each other in narrow channels, is an important topic in out-of-equilibrium statistical physics. Various microscopic models of single-file systems have been considered, such as the simple exclusion process, which has reached the status of a paradigmatic model. Several different models of single-file diffusion have been shown to be related by a duality relation, which holds either microscopically or only in the hydrodynamic limit of large time and large distances. Here, we show that, within the framework of fluctuating hydrodynamics, these relations are not specific to these models and that, in the hydrodynamic limit, every single-file system can be mapped onto a dual single-file system, which we characterise. This general duality relation allows us to obtain new results for different models, by exploiting the solutions that are available for their dual model.

preprint2022arXiv

Exact closure and solution for spatial correlations in single-file diffusion

Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in 1D, which, despite extensive effort, have however remained elusive, because they involve an infinite hierarchy of equations. Here, for the Symmetric Exclusion Process, a paradigmatic model of single-file diffusion, we break the hierarchy and unveil a closed exact equation satisfied by these correlations, which we solve. Beyond quantifying the correlations, the central role of this key equation as a novel tool for interacting particle systems is further demonstrated by showing that it applies to out-of equilibrium situations, other observables and other representative single-file systems.

preprint2022arXiv

Exact time dependence of the cumulants of a tracer position in a dense lattice gas

We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position -- a regime in which few results are known. The generality of our approach is demonstrated by showing that it goes beyond the case of a symmetric 1D random walk, and covers the important situations of (i) a biased tracer; (ii) comb-like structures; and (iii) $d$-dimensional situations.

preprint2021arXiv

Microscopic theory for the diffusion of an active particle in a crowded environment

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean-field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.

preprint2020arXiv

Cooperatively enhanced reactivity and 'stabilitaxis' of dissociating oligomeric proteins

Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer them a functional advantage with respect to non-dissociating proteins. In uniform environments with position-independent association-dissociation, we find that enhanced diffusion in the monomeric state coupled to reassociation into the functional oligomeric form leads to enhanced reactivity with distant targets. In non-uniform environments with position-dependent association-dissociation, caused e.g. by spatial gradients of an inhibiting chemical, we find that dissociating proteins generically tend to accumulate in regions where they are most stable, a process that we term 'stabilitaxis'.

preprint2020arXiv

Speed-Dispersion Induced Alignment : a 1D model inspired by swimming droplets experiments

We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensates, leaving large regions with very low density. A careful examination of the interactions between two "colliding" droplets demonstrates that local alignment takes place as a result of the interplay between the dispersion of their speeds and the absence of Galilean invariance. Inspired by these observations, we propose a minimalistic 1D model of active particles reproducing such dynamical rules and, combining analytical arguments and numerical evidences, we show that the model exhibits a transition to collective motion in 1D for a large range of values of the control parameters. Condensation takes place as a transient phenomena which tremendously slows down the dynamics, before the system eventually settles into a homogeneous aligned phase.

preprint2016arXiv

Propagators of random walks on comb lattices of arbitrary dimension

We study diffusion on comb lattices of arbitrary dimension. Relying on the loopless structure of these lattices and using first-passage properties, we obtain exact and explicit formulae for the Laplace transforms of the propagators associated to nearest-neighbour random walks in both cases where either the first or the last point of the random walk is on the backbone of the lattice, and where the two extremities are arbitrarily chosen. As an application, we compute the mean-square displacement of a random walker on a comb of arbitrary dimension. We also propose an alternative and consistent approach of the problem using a master equation description, and obtain simple and generic expressions of the propagators. This method is more general and is extended to study the propagators of random walks on more complex comb-like structures. In particular, we study the case of a two-dimensional comb lattice with teeth of finite length.

preprint2015arXiv

Distribution of the position of a driven tracer in a hardcore lattice gas

We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the TP position and the bath configuration and resorting to a mean-field-type approximation, we presented a computation of the fluctuations of the TP position in a previous publication [Phys. Rev. E \textbf{87}, 032164 (2013)]. Counterintuitively, on a one-dimensional lattice, the diffusion coefficient of the TP was shown to be a non-monotonic function of the density of bath particles, and reaches a maximum for a nonzero value of the density. Here, we: (i) give the details of this computation and offer a physical insight into the understanding of the non-monotonicity of the diffusion coefficient; (ii) extend the mean-field-type approximation to decouple higher-order correlation functions, and obtain the evolution equation satisfied by the cumulant generating function of the position of the TP, valid in any space dimension. In the particular case of a one-dimensional lattice, we solve this equation and obtain the probability distribution of the TP position. We show that the position rescaled by its fluctuations is asymptotically distributed accordingly to a Gaussian distribution in the long-time limit.

preprint2013arXiv

Geometry-induced superdiffusion in driven crowded systems

Recent Molecular Dynamics simulations of glass-forming liquids revealed superdiffusive fluctuations associated with the position of a tracer particle (TP) driven by an external force. Such anomalous response, whose mechanism remains elusive, has been observed up to now only in systems close to their glass transition, suggesting that this could be one of its hallmarks. Here, we show that the presence of superdiffusion is in actual fact much more general, provided that the system is crowded and geometrically confined. We present and solve analytically a minimal model consisting of a driven TP in a dense, crowded medium in which the motion of particles is mediated by the diffusion of packing defects, called vacancies. For such non glass-forming systems, our analysis predicts a long-lived superdiffusion which ultimately crosses over to giant diffusive behavior. We find that this trait is present in confined geometries, for example long capillaries and stripes, and emerges as a universal response of crowded environments to an external force. These findings are confirmed by numerical simulations of systems as varied as lattice-gases, dense liquids and granular fluids.