A comparative study of semi-flexible linear and ring polymer conformational change in an anisotropic environment.

We adopt a Langevin-dynamics based simulation to systematically study the conformational change of a semi-flexible probed polymer in a rod crowding environment. Two topologically different probed polymer types, linear and ring polymers, are specifically considered. Our results unravel the significance of the interplay of probed polymer's semi-flexibility and crowding anisotropy. Firstly, both ring and linear polymers show a non-trivial dimensional change including nonmonotonicity and collapse-swelling crossover as their stiffness increases. Secondly, we modulate rod crowder length to investigate the anisotropic effect. We reveal that the formation of an ordered parallel arrangement of the environment can effectively lead to a remarkable stretching effect on the probed polymer. The coupling between the crowding anisotropy-induced stretching and the polymer stiffness can account for the unusual swelling behavior. Lastly, nonmonotonic swelling and shape change of the ring polymer are analyzed. We find out that the ring polymer is subject to most pronounced swelling at robust stiffness. Moreover, the maximum prolate shape is also observed at the same robust location.

Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems.

A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer. Dependence of probed chain compaction on both crowder size and concentration is investigated explicitly. Particular attention is paid to examining the significant discrepancy in collapse effect associated with the crowder structure. First, we find an opposite compaction behavior in the HS and flexible polymer systems, in consistence with previous simulation and experimental observations. Compaction decreases with HS size while it increases with flexible polymer chain length. The underlying mechanism for such a contradiction is unraveled in terms of a depletion effect. For the HS system, as the crowder size increases, the ability of accommodating the probed chain enhances with a negligible depletion effect and thus results in a reduced compaction, while a polymer crowder system introduces a local depletion effect, responsible for an intensified compaction effect with increasing polymer length. Secondly, we reveal that the anisotropic feature of the rod-like polymer is a crucial factor in compaction. A novel non-monotonous behavior against the polymer length is observed under rod-like polymer crowding, which can be ascribed to the competition between anisotropy-induced stretching and crowding-induced compaction. Lastly, we present a quantitative evaluation of the crowding-induced potential, which provides a scenario for understanding compaction from a microscopic viewpoint. The potential profiles with respect to crowder size demonstrate a consistent tendency with the corresponding collapse behavior. The study in the present work provides a deeper insight into the modeling structure and dynamics of macromolecules in crowded media.

Activity-crowding coupling effect on the diffusion dynamics of a self-propelled particle in polymer solutions.

The anomalous diffusion dynamics of an active particle in polymer solutions is studied based on a Langevin Brownian dynamics simulation. Firstly, the mean-square displacement (MSD) is investigated under various system parameters of active force Fa, probe size σa, polymer volume fraction φ and polymer chain length N. A very novel transition between superdiffusion and subdiffusion is observed with varying Fa and φ, owing to the activity and crowding competition effect. The two anomalous diffusion regimes are identified in the parameter space diagram. The increment of the MSD under activity is examined on intermediate time scales, which manifests a power law relation with the particle's dynamical persistence length L, i.e., ΔMSD = 2Lm, where the exponent m decreases with φ. Secondly, we explicitly evaluate the long-time diffusion coefficients D in a pure solvent and Da in polymer solutions. The dependence of relative diffusivity Da/D on volume fraction φ reproduces the well-known Phillies' equation exp(-κφµ). The fitting parameters show µ≃ 1, but κ apparently increases with activity. More importantly, our simulation justifies a multi-length scaling relation in a very similar form to that for passive probes, depending on simple structural parameters of the probe-polymer system. With the aid of an activation energy model, we find a counterintuitive activity-crowding coupling effect: activity enhances the effective viscosity experienced by the probe and thus strengthens the crowding-induced slowing of diffusion.

Quantifying the protein-protein association rate in polymer solutions: crowding-induced diffusion and energy modifications.

A theoretical framework is developed to study protein-protein association in polymer solutions under diffusion-limited conditions. Starting from the basal association rate, two fundamental aspects concerning macromolecular crowding are particularly taken into account. One is the effect of microviscosity on protein diffusion. The length-scale dependent relations of translational and rotational diffusion coefficients are incorporated. Another is relevant to the crowding-induced effective interaction between the pair of proteins. The resultant energy modifications to the basal association rate are properly introduced, following an instructive classification with increasing crowder size: repulsive interaction dominant, repulsive and attractive interactions competitive, and attractive interaction prevailing. With specific energy modification terms, we are able to investigate the deviations of the association rate from the Stokes-Einstein (SE) behavior (i.e., the linear relationship with respect to the reciprocal of macroviscosity) in a quantitative manner. Our theory is applied to study the association of TEM1-ß-lactamase (TEM) and the ß-lactamase inhibitor protein (BLIP) in polyethylene glycol (PEG) solutions, with varying concentration and polymerization. We explicitly evaluate the relative association rate constant as a function of the solution macroviscosity. The theoretical results demonstrate very good agreement with the experimental data. Moreover, the complicated non-trivial deviations, either positive (slower than SE) or negative (faster than SE), are systematically rationalized. The precise role of energy modifications and the microviscosity effect on diffusion, in particular on rotational diffusion, are clearly unraveled.

The effect of hydrodynamic interactions on nanoparticle diffusion in polymer solutions: a multiparticle collision dynamics study.

The diffusion of nanoparticles (NPs) in polymer solutions is studied by a combination of a mesoscale simulation method, multiparticle collision dynamics (MPCD), and molecular dynamics (MD) simulations. We investigate the long-time diffusion coefficient D as well as the subdiffusive behavior in the intermediate time region. The dependencies of both D and subdiffusion factor α on NP size and polymer concentration, respectively, are explicitly calculated. Particular attention is paid to the role of hydrodynamic interaction (HI) in the NP diffusion dynamics. Our simulation results show that the long-time diffusion coefficients satisfy perfectly the scaling relation found by experimental observations. Meanwhile, the subdiffusive factor decreases with the increase in polymer concentration but is of little relevance to the NP size. By parallel simulations with and without HI, we reveal that HI will generally enhance D, while the enhancement effect is non-monotonous with increasing polymer concentration, and it becomes most pronounced at semidilute concentrations. With the aid of a scaling law based on the diffusive activation energy model, we understand that HI affects diffusion through decreasing the diffusive activation energy on the one hand while increasing the effective diffusion size on the other. In addition, HI will certainly influence the subdiffusive behavior of the NP, leading to a larger subdiffusion exponent.

A new scaling for the rotational diffusion of molecular probes in polymer solutions.

In the present work, we propose a new scaling form for the rotational diffusion coefficient of molecular probes in semi-dilute polymer solutions, based on a theoretical study. The mean-field theory for depletion effect and semi-empirical scaling equation for the macroscopic viscosity of polymer solutions are properly incorporated to specify the space-dependent concentration and viscosity profiles in the vicinity of the probe surface. Following the scheme of classical fluid mechanics, we numerically evaluate the shear torque exerted on the probes, which then allows us to further calculate the rotational diffusion coefficient Dr. Particular attention is given to the scaling behavior of the retardation factor Rrot ≡ D/Dr with D being the diffusion coefficient in pure solvent. We find that Rrot has little relevance to the macroscopic viscosity of the polymer solution, while it can be well featured by the characteristic length scale rh/δ, i.e. the ratio between the hydrodynamic radius of the probe rh and the depletion thickness δ. Correspondingly, we obtain a novel scaling form for the rotational retardation factor, following Rrot = exp[a(rh/δ)b] with rather robust parameters of a ≃ 0.51 and b ≃ 0.56. We apply the theory to an extensive calculation for various probes in specific polymer solutions of poly(ethylene glycol) (PEG) and dextran. Our theoretical results show good agreements with the experimental data, and clearly demonstrate the validity of the new scaling form. In addition, the difference of the scaling behavior between translational and rotational diffusions is clarified, from which we conclude that the depletion effect plays a more significant role on the local rotational diffusion rather than the long-range translation diffusion.

Probing the reactivity of microhydrated α-nucleophile in the anionic gas-phase S(N)2 reaction.

To probe the kinetic performance of microsolvated α-nucleophile, the G2(+)M calculations were carried out for the gas-phase S(N)2 reactions of monohydrated and dihydrated α-oxy-nucleophiles XO(-)(H2O)(n = 1,2) (X = HO, CH3O, F, Cl, Br), and α-sulfur-nucleophile, HSS(-)(H2O)(n = 1,2), toward CH3Cl. We compared the reactivities of hydrated α-nucleophiles to those of hydrated normal nucleophiles. Our calculations show that the α-effect of monohydrated and dihydrated α-oxy-nucleophiles will become weaker than those of unhydrated ones if we apply a plot of activation barrier as a function of anion basicity. Whereas the enhanced reactivity of monohydrated and dihydrated ROO(-) (R = H, Me) could be observed if compared them with the specific normal nucleophiles, RO(-) (R = H, Me). This phenomena can not be seen in the comparisons of XO(-)(H2O)(n = 1,2) (X = F, Cl, Br) with ClC2H4O(-)(H2O)(n = 1,2), a normal nucleophile with similar gas basicity to XO(-)(H2O)(n = 1,2). These results have been carefully analyzed by natural bond orbital theory and activation strain model. Meanwhile, the relationships between activation barriers with reaction energies and the ionization energies of α-nucleophile are also discussed.

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 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.