A Model of Anomalous Chain Translocation Dynamics

Crowding induced switching of polymer translocation by the amalgamation of entropy and osmotic pressure

The translocation of polymers is omnipresent in inherently crowded biological systems. We investigate the dynamics of polymer translocation through a pore in free and crowded environments using Langevin dynamics simulation. We observed a location-dependent translocation rate of monomers showcasing counterintuitive behavior in stark contrast to the bead velocity along the polymer backbone. The free energy calculation of asymmetrically placed polymers indicates a critical number of segments to direct receiver-side translocation. For one-sided crowding, we have identified a critical crowding size revealing a nonzero probability of translocation toward the crowded-side. Moreover, we have observed that shifting the polymer toward the crowded-side compensates for one-sided crowding, yielding an equal probability akin to a crowder-free system. In two-sided crowding, a slight variation in crowder size and packing fraction induces a polymer to switch its translocation direction. These conspicuous yet counter-intuitive phenomena are rationalized by minimalistic theoretical arguments based on osmotic pressure and radial entropic forces.

CRISPR-Cas9 Genome Interrogation: A Facilitated Subdiffusive Target Search Strategy

The functional application of RNA-guided CRISPR-associated Cas9 protein, a bacterial immune system-based protein complex, via which in vivo, highly specific, and well-regulated, gene-editing processes are being monitored at an unprecedented level, has led to remarkable progress in genetic engineering and technology. The complicated in vivo process of genome interrogation followed by gene editing by the Cas9 complex was recently reported by Knight et al. (Science, 2015, 350, 823-826) using an elegant single-particle tracking method, aided by the two-photon fluorescence correlation spectroscopic technique. In contrast to the usually observed fast target-searching and protein-binding events in biophysical systems, an interesting slow genome-interrogation process by the RNA-guided CRISPR-Cas9 system through a crowded chromatin environment of a mammalian cell has been revealed in Knight et al.'s study. Motivated by this experiment, in this paper, we provide a generalized theoretical framework to capture this particular target-searching mechanism of the CRISPR-Cas9 protein complex. We show that an analysis on the basis of 3D subdiffusion under a cylindrical volume, created by several nonspecific off-target interactions from the DNA strands, can capture the essential details of the process. Moreover, on the basis of this model, we quantify the dynamics of this process and estimate the survival probability, first passage time, and the intensity correlation function of the tagged proteins of the experiment. The results from our theoretical predictions are found to be consistent with the experimental observations, and hence, seem to provide a plausible microscopic picture of the process.

Dynamics of Disordered Proteins under Confinement: Memory Effects and Internal Friction

Many proteins are disordered under physiological conditions. How efficiently they can search for their cellular targets and how fast they can fold upon target binding is determined by their intrinsic dynamics, which have thus attracted much recent attention. Experiments and molecular simulations show that the inherent reconfiguration timescale for unfolded proteins has a solvent friction component and an internal friction component, and the microscopic origin of the latter, along with its proper mathematical description, has been a topic of considerable debate. Internal friction varies across different proteins of comparable length and increases with decreasing denaturant concentration, showing that it depends on how compact the protein is. Here we report on a systematic atomistic simulation study of how confinement, which induces a more compact unfolded state, affects dynamics and friction in disordered peptides. We find that the average reconfiguration timescales increase exponentially as the peptide's spatial dimensions are reduced; at the same time, confinement broadens the spectrum of relaxation timescales exhibited by the peptide. There are two important implications of this broadening: First, it limits applicability of the common Rouse and Zimm models with internal friction, as those models attempt to capture internal friction effects by introducing a single internal friction timescale. Second, the long-tailed distribution of relaxation times leads to anomalous diffusion effects in the dynamics of intramolecular distances. Analysis and interpretation of experimental signals from various measurements that probe intramolecular protein dynamics (such as single-molecule fluorescence correlation spectroscopy and single-molecule force spectroscopy) rely on the assumption of diffusive dynamics along the distances being probed; hence, our results suggest the need for more general models allowing for anomalous diffusion effects.

Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding

Recent single-molecule experiments probed transition paths of biomolecular folding and, in particular, measured the time biomolecules spend while crossing their free energy barriers. A surprising finding from these studies is that the transition barriers crossed by transition paths, as inferred from experimentally observed transition path times, are often lower than the independently determined free energy barriers. Here we explore memory effects leading to anomalous diffusion as a possible origin of this discrepancy. Our analysis of several molecular dynamics trajectories shows that the dynamics of common reaction coordinates used to describe protein folding is subdiffusive, at least at sufficiently short times. We capture this effect using a one-dimensional fractional Brownian motion (FBM) model, in which the system undergoes a subdiffusive process in the presence of a potential of mean force, and show that this model yields much broader distributions of transition path times with stretched exponential long-time tails. Without any adjustable parameters, these distributions agree well with the transition path times computed directly from protein trajectories. We further discuss how the FBM model can be tested experimentally.

Subdiffusion in hair bundle dynamics: the role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. [Proc. Natl. Acad. Sci. U.S.A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link.

Fractional Brownian motion approach to polymer translocation: the governing equation of motion

We suggest a governing equation that describes the process of polymer-chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time t after the process has begun, and (ii) a subdiffusive increase of the distribution variance Δ(t) with elapsed time Δ(t)∝t(α). The latter quantity measures the mean-squared number s of polymer segments that have passed through the pore Δ(t)=([s(t)-s(t=0)](2)), and is known to grow with an anomalous diffusion exponent α<1. Our main assumption [i.e., a Gaussian distribution of the translocation velocity v(t)] and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation, which we performed in 3D. We also numerically confirm the predictions made recently that the exponent α changes from 0.91 to 0.55 to 0.91 for short-, intermediate-, and long-time regimes, respectively.