First passage time distribution of chaperone driven polymer translocation through a nanopore: Homopolymer and heteropolymer cases

Translocation, Rejection and Trapping of Polyampholytes

Polyampholytes (PA) are a special class of polymers comprising both positive and negative monomers along their sequence. Most proteins have positive and negative residues and are PAs. Proteins have a well-defined sequence while synthetic PAs have a random charge sequence. We investigated the translocation behavior of random polyampholyte chains through a pore under the action of an electric field by means of Monte Carlo simulations. The simulations incorporated a realistic translocation potential profile along an extended asymmetric pore and translocation was studied for both directions of engagement. The study was conducted from the perspective of statistics for disordered systems. The translocation behavior (translocation vs. rejection) was recorded for all 220 sequences comprised of N = 20 charged monomers. The results were compared with those for 107 random sequences of N = 40 to better demonstrate asymptotic laws. At early times, rejection was mainly controlled by the charge sequence of the head part, but late translocation/rejection was governed by the escape from a trapped state over an antagonistic barrier built up along the sequence. The probability distribution of translocation times from all successful attempts revealed a power-law tail. At finite times, there was a population of trapped sequences that relaxed very slowly (logarithmically) with time. If a subensemble of sequences with prescribed net charge was considered the power-law decay was steeper for a more favorable net charge. Our findings were rationalized by theoretical arguments developed for long chains. We also provided operational criteria for the translocation behavior of a sequence, explaining the selection by the translocation process. From the perspective of protein translocation, our findings can help rationalize the behavior of intrinsically disordered proteins (IDPs), which can be modeled as polyampholytes. Most IDP sequences have a strong net charge favoring translocation. Even for sequences with those large net charges, the translocation times remained very dispersed and the translocation was highly sequence-selective.

Chaperone-driven polymer translocation through nanopore: Spatial distribution and binding energy

Chaperones are binding proteins working as a driving force in biopolymer translocation. They bind to the biopolymer near the pore and prevent its backsliding. Chaperones may have different spatial distributions. Recently, we showed the importance of their spatial distribution in translocation and its effects on the sequence dependency of the translocation time. Here we focus on homopolymers and exponential distribution. Because of the exponential distribution of chaperones, the energy dependency of the translocation time will change. Here we find a minimum in translocation time versus binding effective energy (EBE) curve. The same trend can be seen in the scaling exponent of time versus polymer length, [Formula: see text] ([Formula: see text]), when plotted against EBE. Interestingly in some special cases, e.g. chaperones of size [Formula: see text] and with an exponential distribution rate of [Formula: see text], the minimum even reaches to an amount of less than 1 ([Formula: see text]). We explain the possibility of this rare result. Moreover, based on a theoretical discussion we show that, by taking into account the velocity dependency of the translocation on polymer length, one can truly predict the value of this minimum.

Chaperone-assisted translocation of flexible polymers in three dimensions

Polymer translocation through a nanometer-scale pore assisted by chaperones binding to the polymer is a process encountered in vivo for proteins. Studying the relevant models by computer simulations is computationally demanding. Accordingly, previous studies are either for stiff polymers in three dimensions or flexible polymers in two dimensions. Here, we study chaperone-assisted translocation of flexible polymers in three dimensions using Langevin dynamics. We show that differences in binding mechanisms, more specifically, whether a chaperone can bind to a single site or multiple sites on the polymer, lead to substantial differences in translocation dynamics in three dimensions. We show that the single-binding mode leads to dynamics that is very much like that in the constant-force driven translocation and accordingly mainly determined by tension propagation on the cis side. We obtain β≈1.26 for the exponent for the scaling of the translocation time with polymer length. This fairly low value can be explained by the additional friction due to binding particles. The multiple-site binding leads to translocation the dynamics of which is mainly determined by the trans side. For this process we obtain β≈1.36. This value can be explained by our derivation of β=4/3 for constant-bias translocation, where translocated polymer segments form a globule on the trans side. Our results pave the way for understanding and utilizing chaperone-assisted translocation where variations in microscopic details lead to rich variations in the emerging dynamics.

Translocation of a semiflexible polymer through a nanopore in the presence of attractive binding particles

We study the translocation dynamics of a semiflexible polymer through a nanopore from the cis into the trans compartment containing attractive binding particles (BPs) using the Langevin dynamics simulation in two dimensions. The binding particles accelerate the threading process in two ways: (i) reducing the back-sliding of the translocated monomer, and (ii) providing the pulling force toward the translocation direction. We observe that for certain binding strength (ε_{c}) and concentration (ρ) of the BPs, the translocation is faster than the ideal ratcheting condition as elucidated by Simon, Peskin, and Oster [M. Simon, C. S. Peskin, and G. F. Oster, Proc. Natl. Acad. Sci. USA 89, 3770 (1992)PNASA60027-842410.1073/pnas.89.9.3770]. The asymmetry produced by the BPs at the trans-side leads to similarities of this process to that of a driven translocation with an applied force inside the pore manifested in various physical quantities. Furthermore, we provide an analytic expression for the force experienced by the translocating chain as well as for the scaled mean first passage time (MFPT), for which we observe that for various combinations of N, ε, and ρ the scaled MFPT (〈τ〉/N^{1.5}ρ^{0.8}) collapses onto the same master plot. Based on the analysis of our simulation data, we provide plausible arguments with regard to how the scaling theory of driven translocation can be generalized for such a directed diffusion process by replacing the externally applied force with an effective force.

Polymer translocation: the first two decades and the recent diversification

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.

Dynamics of polymer ejection from capsid

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the ejection times scale with polymer length, τ ∼ N(α). We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) ρ inside the capsid. For very low densities ρ ≤ 0.002 the polymer is only weakly confined by the capsid, and we measure α = 1.33, which is close to α=1.4 obtained for polymer translocation. At intermediate densities the scaling exponents α = 1.25 and 1.21 for ρ = 0.01 and 0.02, respectively. These scalings are in accord with a crude derivation for the lower limit α = 1.2. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, ρ ⪆ 0.25. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.

A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding

Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics, and industrial engineering. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss-Markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary, as measured by its Hölder exponent H. The critical value occurs when the roughness of the boundary equals the roughness of the process, so for diffusive processes the critical value is Hc = 1/2. For smoother boundaries, H > 1/2, the probability density is a continuous function of time. For rougher boundaries, H < 1/2, the probability is concentrated on a Cantor-like set of zero measure: the probability density becomes divergent, almost everywhere either zero or infinity. The critical point Hc = 1/2 corresponds to a widely studied case in the theory of neural coding, in which the external input integrated by a model neuron is a white-noise process, as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs. We argue that this transition corresponds to a sharp boundary between rate codes, in which the neural firing probability varies smoothly, and temporal codes, in which the neuron fires at sharply defined times regardless of the intensity of internal noise.