Nanrong Zhao

Diffusion of nanoparticles in semidilute polymer solutions: A mode-coupling theory study

We have proposed a theoretical formalism to study the long-time diffusion behavior of nanoparticles in polymer solutions by using mode-coupling theory (MCT). The non-hydrodynamic part Dmicro of the total diffusion coefficient D is calculated in the MCT framework where the polymer dynamic scattering function Γpp(k, t) in the solution plays an important role. By introducing an approximate summation form for Γpp(k, t), where both limits of short and long length scales are properly accounted for, we can compute Dmicro straightforwardly and investigate explicitly how D depends on the volume fraction ϕ of the polymer solution, the nanoparticle size R, the degree of polymerization N, as well as the entanglement effects. For illustration, we adopt our theoretical approach to analyze the diffusion of gold nanoparticles in semidilute poly(ethylene glycol) (PEG)-water solutions which has been studied in detail experimentally. We find that our theoretical results show very good quantitative agreements with the experimental data in many aspects, such as the strong dependence on ϕ, the large deviation from Stokes-Einstein relation particularly for small particles, as well as the effects of the PEG molecular weight. Such good agreements clearly demonstrate the validity of our MCT framework, which may serve as a good starting point to study many more complex dynamical behaviors associated with polymer solutions.

Kinetics of molecular transitions with dynamic disorder in single-molecule pulling experiments

Macromolecular transitions are subject to large fluctuations of rate constant, termed as dynamic disorder. The individual or intrinsic transition rates and activation free energies can be extracted from single-molecule pulling experiments. Here we present a theoretical framework based on a generalized Langevin equation with fractional Gaussian noise and power-law memory kernel to study the kinetics of macromolecular transitions to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. By using the Kramers rate theory, we have calculated the fluctuating rate constant of molecular transition, as well as the experimentally accessible quantities such as the force-dependent mean lifetime, the rupture force distribution, and the speed-dependent mean rupture force. Particular attention is paid to the discrepancies between the kinetics with and without dynamic disorder. We demonstrate that these discrepancies show strong and nontrivial dependence on the external force or the pulling speed, as well as the barrier height of the potential of mean force. Our results suggest that dynamic disorder is an important factor that should be taken into account properly in accurate interpretations of single-molecule pulling experiments.

Understanding Protein Diffusion in Polymer Solutions: A Hydration with Depletion Model

Understanding the diffusion of proteins in polymer solutions is of ubiquitous importance for modeling processes in vivo. Here, we present a theoretical framework to analyze the decoupling of translational and rotational diffusion of globular proteins in semidilute polymer solutions. The protein is modeled as a spherical particle with an effective hydrodynamic radius, enveloped by a depletion layer. On the basis of the scaling formula of macroscopic viscosity for polymer solutions as well as the mean-field theory for the depletion effect, we specify the space-dependent viscosity profile in the depletion zone. Following the scheme of classical fluid mechanics, the hydrodynamic drag force as well as torque exerted to the protein can be numerically evaluated, which then allows us to obtain the translational and rotational diffusion coefficients. We have applied our model to study the diffusion of proteins in two particular polymer solution systems, i.e., poly(ethylene glycol) (PEG) and dextran. Strikingly, our theoretical results can reproduce the experimental results quantitatively very well, and fully reproduce the decoupling between translational and rotational diffusion observed in the experiments. In addition, our model facilitates insights into how the effective hydrodynamic radius of the protein changes with polymer systems. We found that the effective hydrodynamic radius of proteins in PEG solutions is nearly the same as that in pure water, indicating PEG induces preferential hydration, while, in dextran solutions, it is generally enhanced due to the stronger attractive interaction between protein and dextran molecules.

Distance fluctuation of a single molecule in Lennard-Jones liquid based on generalized Langevin equation and mode coupling theory

Distance fluctuation of a single molecule, modeled as an idealized bead-spring chain, dissolved in a Lennard-Jones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ζ(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t−α, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the bead-to-solvent mass ratio MR, chain spring frequency ω, and the chain length N. Interestingly, the exponent α is robust to be 1/2 against the change of these parameters, although the friction kernel ζ(t) shows nontrivial dependence on time. In addition, we find that the starting time of the p...

Stretching of single poly-ubiquitin molecules revisited: Dynamic disorder in the non-exponential unfolding kinetics

A theoretical framework based on a generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and a power-law memory kernel is presented to describe the non-exponential kinetics of the unfolding of a single poly-ubiquitin molecule under a constant force [T.-L. Kuo, S. Garcia-Manyes, J. Li, I. Barel, H. Lu, B. J. Berne, M. Urbakh, J. Klafter, and J. M. Fernández, Proc. Natl. Acad. Sci. U.S.A. 107, 11336 (2010)]. Such a GLE-fGn strategy is made on the basis that the pulling coordinate variable x undergoes subdiffusion, usually resulting from conformational fluctuations, over a one-dimensional force-modified free-energy surface U(x, F). By using the Kramers rate theory, we have obtained analytical formulae for the time-dependent rate coefficient k(t, F), the survival probability S(t, F) as well as the waiting time distribution function f(t, F) as functions of time t and force F. We find that our results can fit the experimental data of f(t, F) perfectly in the whole time range with a power-law exponent γ = 1/2, the characteristic of typical anomalous subdiffusion. In addition, the fitting of the survival probabilities for different forces facilitates us to reach rather reasonable estimations for intrinsic properties of the system, such as the free-energy barrier and the distance between the native conformation and the transition state conformation along the reaction coordinate, which are in good agreements with molecular dynamics simulations in the literatures. Although static disorder has been implicated in the original work of Kuo et al., our work suggests a sound and plausible alternative interpretation for the non-exponential kinetics in the stretching of poly-ubiquitin molecules, associated with dynamic disorder.

Entropy and entropy production of finite chemical reaction systems influenced by Gaussian noise

In this paper we present a stochastic formalism to reveal the meso-statistical significance of the entropy and entropy production of finite chemical reaction systems influenced by the Gaussian noise. As an extension of Shanon entropy a generalized stochastic entropy is introduced without missing any information from both internal and external fluctuations coexisting in this kind of system. An explicit expression of the entropy production valid for the steady state affected by the Gaussian white noise has been obtained. It turns out that the contributions of noise to entropy production of the fluctuations are due to the effect that it intensifies the deviations of the effective probability behavior from the Poisson distribution and the central limit theorem. Meanwhile, a nontrivial shift of the Gibbs’ entropy production is inevitable if the noise is multiplicative. Finally, as an illustration of the Gaussian colored noise, the influence of the Ornstein–Uhlenbeck noise to entropy production is also discusse...

Effects of internal friction on contact formation dynamics of polymer chain

ABSTRACT A theoretical framework is presented to study the contact formation dynamics of polymer chains, in accompany with an electron-transfer quenching. Based on a non-Markovian Smoluchowski equation supplemented with an exponential sink term, we derive the mean time of contact formation under Wilemski–Fixman approximation. Our particular attentions are paid to the effect of internal friction. We find out that internal friction induces a novel fractional viscosity dependence, which will become more remarkable as internal friction increases. Furthermore, we clarify that internal friction inevitably promotes a diffusion-controlled mechanism by slowing the chain relaxation. Finally, we apply our theory to rationalise the experimental investigation for contact formation of a single-stranded DNA. The theoretical results can reproduce the experimental data very well with quite reasonable estimation for the intrinsic parameters. Such good agreements clearly demonstrate the validity of our theory which has appropriately addressed the very role of internal friction to the relevant dynamics.

Polarization induced by external noise in irreversible electrode processes: A stochastic measure of thermodynamic effects driven by external noise in electro-chemical reaction systems

A stochastic thermodynamics of finite electrochemical reaction systems affected by external noise has been established in this article. Based on a general stochastic model of the irreversible electrode processes driven by parameter noise, both the fluctuation and the dissipation in this kind of important physico-chemical system are discussed. It shows that an additional polarization induced by external noise in irreversible electrode processes is inevitable. Furthermore, a perfect formalism to estimate quantitatively both the concentration polarization and the activation polarization induced by a Gaussian white noise in the steady irreversible electrode process has been proposed. It turns out that the order of this noise-driven polarization could arrive at the level as noise intensity even in thermodynamic limit. Some illustrations to calculate the polarizations driven by the additive noise and the multiplicative noise in different cases are also given categorically. The formalism as a stochastic measure of the polarization induced by Gaussian white noise proposed in this article is helpful to further study and utilize generally this electrochemical effect driven by noise in physical chemistry.

Fluctuating bottleneck model studies on kinetics of DNA escape from α-hemolysin nanopores

We have proposed a fluctuation bottleneck (FB) model to investigate the non-exponential kinetics of DNA escape from nanometer-scale pores. The basic idea is that the escape rate is proportional to the fluctuating cross-sectional area of DNA escape channel, the radius r of which undergoes a subdiffusion dynamics subjected to fractional Gaussian noise with power-law memory kernel. Such a FB model facilitates us to obtain the analytical result of the averaged survival probability as a function of time, which can be directly compared to experimental results. Particularly, we have applied our theory to address the escape kinetics of DNA through α-hemolysin nanopores. We find that our theoretical framework can reproduce the experimental results very well in the whole time range with quite reasonable estimation for the intrinsic parameters of the kinetics processes. We believe that FB model has caught some key features regarding the long time kinetics of DNA escape through a nanopore and it might provide a sound starting point to study much wider problems involving anomalous dynamics in confined fluctuating channels.

Understanding chain looping kinetics in polymer solutions: crowding effects of microviscosity and collapse

A theoretical framework based on a generalized Langevin equation with fractional Gaussian noise is presented to describe the looping kinetics of chains in polymer solutions. Particular attention is paid to quantitatively revealing crowding effects on the loop formation rate in terms of microviscosity and collapse. By the aid of empirical relations for these two crowding associated physical quantities, we explicitly investigate the relationship between the looping rate and polymer concentration, the degree of polymerization, and system parameters. According to our analysis, the dependence of the looping rate on the crowder volume fraction exhibits three typical regimes: monotonic decreasing, a non-monotonic trend and monotonic increasing. We reveal that these non-trivial behaviors can be attributed to the competition between the two opposing factors of viscosity-associated inhibition and collapse-induced facilitation of loop formation. We apply our theory to analyze the kinetics of single-stranded DNA hairpin base pairing in polyethylene glycol solutions. The theoretical results can reproduce the experimental data on the closing rate of hairpins quantitatively to a certain degree with reasonable fitting parameters. The unexpected increase of the closing rate upon the addition of increasing amounts of polymer is well rationalised. Such good agreements clearly demonstrate the validity of our theory, appropriately addressing the very role of crowding effects in the relevant kinetics.