Heterogeneous kinetics of the loop formation of a single polymer chain in crowded and disordered media

Attractive crowding effect on passive and active polymer looping kinetics

Loop formation in complex environments is crucially important to many biological processes in life. In the present work, we adopt three-dimensional Langevin dynamics simulations to investigate passive and active polymer looping kinetics in crowded media featuring polymer-crowder attraction. We find polymers undergo a remarkable coil-globule-coil transition, highlighted by a marked change in the Flory scaling exponent of the gyration radius. Meanwhile, looping time as a function of the crowder's volume fraction demonstrates an apparent non-monotonic alteration. A small number of crowders induce a compact structure, which largely facilitates the looping process. While a large number of crowders heavily impede end-to-end diffusion, looping kinetics is greatly inhibited. For a self-propelled chain, we find that the attractive crowding triggers an unusual activity effect on looping kinetics. Once a globular state is formed, activity takes an effort to open the chain from the compact structure, leading to an unexpected activity-induced inhibition of looping. If the chain maintains a coil state, the dominant role of activity is to enhance diffusivity and, thus, speed up looping kinetics. The novel conformational change and looping kinetics of both passive and active polymers in the presence of attractive crowding highlight a rather distinct scenario that has no analogy in a repulsive crowding counterpart. The underlying mechanism enriches our understanding of the crucial role of attractive interactions in modulating polymer structure and dynamics.

Polymer looping kinetics in active heterogeneous environments

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Comparative study of polymer looping kinetics in passive and active environments

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

History-dependent nonequilibrium conformations of a highly confined polymer globule in a sphere

Chromatin undergoes condensation-decondensation processes repeatedly during its cell lifetime. The spatial organization of chromatin in nucleus resembles the fractal globule, of which structure significantly differs from an equilibrium polymer globule. There have been efforts to develop a polymer globule model to describe the fractal globulelike structure of tightly packed chromatin in nucleus. However, the transition pathway of a polymer toward a globular state has been often ignored. Because biological systems are intrinsically in nonequilibrium states, the transition pathway that the chromatin would take before reaching the densely packaged globule should be of importance. In this study, by employing a simple polymer model and Langevin dynamics simulations, we investigate the conformational transition of a single polymer from a swollen coil to a compact globule. We aim to elucidate the effect of transition pathways on the final globular structure. We show that a fast collapse induces a nonequilibrium structure even without a specific intramolecular interaction and that its relaxation toward an equilibrium globule is extremely slow. Due to a strong confinement, the fractal globule never relaxes into an equilibrium state during our simulations such that the globular structure becomes dependent on the transition pathway.