Simulating sticky particles: A Monte Carlo method to sample a stratification

Brownian dynamics simulations of hard rods in external fields and with contact interactions

We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in contact. It allows one to treat particle interactions in addition to the hard-sphere exclusion as long as the corresponding interaction forces are continuous functions of the particle coordinates. We furthermore develop a treatment of sticky hard spheres as described by Baxter's contact interaction potential.

Thermodynamic stability versus kinetic accessibility: Pareto fronts for programmable self-assembly

A challenge in designing self-assembling building blocks is to ensure the target state is both thermodynamically stable and kinetically accessible. These two objectives are known to be typically in competition, but it is not known how to simultaneously optimize them. We consider this problem through the lens of multi-objective optimization theory: we develop a genetic algorithm to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies. We use a coarse-grained model for the particles' dynamics that allows us to efficiently search over parameters, for systems small enough to be enumerated. For most target states there is a tradeoff when the number of types of particles is small, with medium-weak bonds favouring fast folding, and strong bonds favouring high equilibrium probability. The tradeoff disappears when the number of particle types reaches a value m*, that is usually much less than the total number of particles. This general approach of computing Pareto fronts allows one to identify the minimum number of design parameters to avoid a thermodynamic-kinetic tradeoff. However, we argue, by contrasting our coarse-grained model's predictions with those of Brownian dynamics simulations, that particles with short-ranged isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.

Unfolding of the chromatin fiber driven by overexpression of noninteracting bridging factors

Nuclear molecules control the functional properties of the chromatin fiber by shaping its morphological properties. The biophysical mechanisms controlling how bridging molecules compactify chromatin are a matter of debate. On the one side, bridging molecules could cross-link faraway sites and fold the fiber through the formation of loops. Interacting bridging molecules could also mediate long-range attractions by first tagging different locations of the fiber and then undergoing microphase separation. Using a coarse-grained model and Monte Carlo simulations, we study the conditions leading to compact configurations both for interacting and noninteracting bridging molecules. In the second case, we report on an unfolding transition at high densities of the bridging molecules. We clarify how this transition, which disappears for interacting bridging molecules, is universal and controlled by entropic terms. In general, chains are more compact in the case of interacting bridging molecules because interactions are not valence limited. However, this result is conditional on the ability of our simulation methodology to relax the system toward its ground state. In particular, we clarify how, unless using reaction dynamics that change the length of a loop in a single step, the system is prone to remain trapped in metastable, compact configurations featuring long loops.