Overcoming barriers in trajectory space: mechanism and kinetics of rare events via Wang-Landau enhanced transition path sampling

Thermal properties of knotted block copolymer rings with charged monomers subjected to short-range interactions

The thermal properties of coarse-grained knotted copolymer rings fluctuating in a highly screening solution are investigated on a simple cubic lattice using the Wang-Landau Monte Carlo algorithm. The rings contain two kinds of monomers A and B with opposite charges that are subjected to short-range interactions. In view of possible applications in medicine and the construction of intelligent materials, it is shown that the behavior of copolymer rings can be tuned by changing both their monomer configuration and topology. We find several phase transitions depending on the monomer distribution. They include the expansion and collapse of the knotted polymer as well as rearrangements leading to metastable states. The temperatures at which these phase transitions are occurring and other features can be tuned by changing the topology of the system. The processes underlying the observed transitions are identified. In knots formed by diblock copolymers, two different classes of behaviors are detected depending on whether there is an excess of monomers of one kind or not. Moreover, we find that the most stable compact states are formed by copolymers in which units of two A monomers are alternated by units of two B monomers. Remarkably, these compact states are in a lamellar phase. The transition from the lamellar to the expanded state produces in the specific heat capacity a narrow and high peak that is centered at temperatures that are much higher than those of the peaks observed in all other monomer distributions.

Pathways to self-organization: Crystallization via nucleation and growth

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In this article, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.

Relating sequence encoded information to form and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) showcase the importance of conformational plasticity and heterogeneity in protein function. We summarize recent advances that connect information encoded in IDP sequences to their conformational properties and functions. We focus on insights obtained through a combination of atomistic simulations and biophysical measurements that are synthesized into a coherent framework using polymer physics theories.

Absolute transition rates for rare events from dynamical decoupling of reaction variables

We introduce a new approach to evaluate transition rates for rare events in complex many-particle systems. Building on a path-integral representation of transition probabilities for Markov processes, the rate is first expressed in terms of a free energy in the transition-path ensemble. We then define an auxiliary process where a suitably defined reaction variable is dynamically decoupled from all the others, whose dynamics is left unchanged. For this system the transition rates coincide with those of a unidimensional process whose only coordinate is the reaction variable. The free-energy difference between the auxiliary and the physical transition-path ensembles is finally evaluated using standard techniques. The efficiency of this method is deemed to be optimal because the physical and auxiliary dynamics differ by one degree of freedom only at any system size. Our method is demonstrated numerically on a simple model of Lennard-Jones particles ruled by the overdamped Langevin equation.