Mesoscopic description of solvent effects on polymer dynamics

Solvent effects on polymer dynamics and structure are investigated using a mesoscopic solvent model that accounts for hydrodynamic interactions among the polymer beads. The simulation method combines molecular dynamics of the polymer chain, interacting with the solvent molecules through intermolecular forces, with mesoscopic multiparticle collision dynamics for the solvent molecules. Changes in the intermolecular forces between the polymer beads and mesoscopic solvent molecules are used to vary the solvent conditions from those for good to poor solvents. Polymer collapse and expansion dynamics following changes in solvent conditions are studied for homopolymer and block copolymer solutions. The frictional properties of polymers are also investigated.     

Diffusion behavior of polyelectrolytes in dilute solution: coupling effects of hydrodynamic and Coulomb interactions

The diffusion behavior of polyelectrolytes in dilute salt-free solution is studied through a hybrid mesoscale simulation technique that combines the molecular dynamics method and the multiparticle collision dynamics approach. To elucidate the effects of hydrodynamic interactions (HI), we compare results for hydrodynamic and random solvents. When HI are taken into account, we find that the chain diffusivity decreases initially and then increases gradually with the increasing strength of the Coulomb interaction. By contrast, when HI are switched off, the electrostatic-dependent diffusivity shows three distinct regions, and a plateau of approximately constant diffusivity manifests between two decreasing regions. The findings reveal that the dynamics of polyelectrolytes in dilute solution depend on the coupling effects of hydrodynamic and Coulomb interactions, and that these dynamics can be understood by considering the conformational changes of chains, the counterion condensation, and the dynamics of counterions.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Dynamics of vesicle self-assembly and dissolution

The dynamics of membranes is studied on the basis of a particle-based meshless surface model, which was introduced earlier [Phys. Rev. E 73, 021903 (2006)]. The model describes fluid membranes with bending energy and-in the case of membranes with boundaries-line tension. The effects of hydrodynamic interactions are investigated by comparing Brownian dynamics with a particle-based mesoscale solvent simulation (multiparticle collision dynamics). Particles self-assemble into vesicles via disk-shaped membrane patches. The time evolution of assembly is found to consist of three steps: particle assembly into discoidal clusters, aggregation of clusters into larger membrane patches, and finally vesicle formation. The time dependence of the cluster distribution and the mean cluster size is evaluated and compared with the predictions of Smoluchowski rate equations. On the other hand, when the line tension is suddenly decreased (or the temperature is increased), vesicles dissolve via pore formation in the membrane. Hydrodynamic interactions are found to speed up the dynamics in both cases. Furthermore, hydrodynamics makes vesicle more spherical in the membrane-closure process.     

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

Mesoscopic model for diffusion-influenced reaction dynamics

A hybrid mesoscopic multiparticle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum, and energy so that hydrodynamic effects are fully taken into account. Reactive and nonreactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for large-scale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A + C <==> B + C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction phi of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.     

Dynamics of polymers in a particle-based mesoscopic solvent

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.     

Insight into the role of hydration on protein dynamics

The potential energy surface of a protein is rough. This intrinsic energetic roughness affects diffusion, and hence the kinetics. The dynamics of a system undergoing Brownian motion on this surface in an implicit continuum solvent simulation can be tuned via the frictional drag or collision frequency to be comparable to that of experiments or explicit solvent simulations. We show that the kinetic rate constant for a local rotational isomerization in stochastic simulations with continuum solvent and a collision frequency of 2 ps(-1) is about 10(4) times faster than that in explicit water and experiments. A further increase in the collision frequency to 60 ps(-1) slows down the dynamics, but does not fully compensate for the lack of explicit water. We also show that the addition of explicit water does not only slow down the dynamics by increasing the frictional drag, but also increases the local energetic roughness of the energy landscape by as much as 1.0 kcal/mol.     

Two-particle friction in a mesoscopic solvent

The effects of hydrodynamic interactions on the friction tensors for two particles in solution are studied. The particles have linear dimensions on nanometer scales and are either simple spherical particles interacting with the solvent through repulsive Lennard-Jones forces or are composite cluster particles whose atomic components interact with the solvent through repulsive Lennard-Jones forces. The solvent dynamics is modeled at a mesoscopic level through multiparticle collisions that conserve mass, momentum, and energy. The dependence of the two-particle relative friction tensors on the interparticle separation indicates the importance of hydrodynamic interactions for these nanoparticles.     

Modeling of a control induced system for product formation in enzyme kinetics

Double substrate enzyme kinetics has a leading role for product quantification and optimization in different chemical and biochemical sectors. Mathematical approach for controlling these reactions in different stages by suitable parameters adds a new dimension in this interdisciplinary field of research. Applying control theoretic approach in the reversible backward stages of double substrate enzymatic model, time economization with regard to product formation is significant. In this article, we formulate a double substrate mathematical model of enzymatic dynamical reaction system with control measures with a view to observe the effect of changes of these measures with respect to the concentration of substrates, enzyme, complexes and finally product. Here, Pontryagin Minimum Principle is used for observing the effect of control measures in the system dynamics with the help of Hamiltonian. We compare the relevant numerical solutions for the substrates, enzyme, complexes and product concentration profile for a specified time interval with respect to control factors.     

Computational Insights into Allosteric Conformational Modulation of P-Glycoprotein by Substrate and Inhibitor Binding

The ATP-binding cassette (ABC) transporter P-glycoprotein (P-gp) is a physiologically essential membrane protein that protects many tissues against xenobiotic molecules, but limits the access of chemotherapeutics into tumor cells, thus contributing to multidrug resistance. The atomic-level mechanism of how substrates and inhibitors differentially affect the ATP hydrolysis by P-gp remains to be elucidated. In this work, atomistic molecular dynamics simulations in an explicit membrane/water environment were performed to explore the effects of substrate and inhibitor binding on the conformational dynamics of P-gp. Distinct differences in conformational changes that mainly occurred in the nucleotide-binding domains (NBDs) were observed from the substrate- and inhibitor-bound simulations. The binding of rhodamine-123 can increase the probability of the formation of an intermediate conformation, in which the NBDs were closer and better aligned, suggesting that substrate binding may prime the transporter for ATP hydrolysis. By contrast, the inhibitor QZ-Leu stabilized NBDs in a much more separated and misaligned conformation, which may result in the deficiency of ATP hydrolysis. The significant differences in conformational modulation of P-gp by substrate and inhibitor binding provided a molecular explanation of how these small molecules exert opposite effects on the ATPase activity. A further structural analysis suggested that the allosteric communication between transmembrane domains (TMDs) and NBDs was primarily mediated by two intracellular coupling helices. Our computational simulations provide not only valuable insights into the transport mechanism of P-gp substrates, but also for the molecular design of P-gp inhibitors.     

Insight into Substrate Preference of Two Chimeric Esterases by Combining Experiment and Molecular Simulation

Better understanding of the relationship between the substrate preference and structural module of esterases is helpful to novel enzyme development. For this purpose, two chimeric esterases AAM7 and PAR, constructed via domain swapping between two ancient thermophilic esterases, were investigated on their molecular simulation(including homology modeling, substrates docking and substrate binding affinity validation) and enzymatic assay(specific activities and activation energies calculating). Our results indicate that the factors contributing to the substrate preference of many enzymes especially the broad-specificity enzymes like esterases are multiple and complicated, the substrate binding domains or binding pockets are important but not the only factor for substrate preference.     

Modeling microscopic swimmers at low Reynolds number

The authors employ three numerical methods to explore the motion of low Reynolds number swimmers, modeling the hydrodynamic interactions by means of the Oseen tensor approximation, lattice Boltzmann simulations, and multiparticle collision dynamics. By applying the methods to a three bead linear swimmer, for which exact results are known, the authors are able to compare and assess the effectiveness of the different approaches. They then propose a new class of low Reynolds number swimmers, generalized three bead swimmers that can change both the length of their arms and the angle between them. Hence they suggest a design for a microstructure capable of moving in three dimensions. They discuss multiple bead, linear microstructures and show that they are highly efficient swimmers. They then turn to consider the swimming motion of elastic filaments. Using multiparticle collision dynamics the authors show that a driven filament behaves in a qualitatively similar way to the micron-scale swimming device recently demonstrated by Dreyfus et al. [Nature (London) 437, 862 (2005)].     

Cooperative motion of spheres arranged in periodic grids between two parallel walls

In this article, we analyze the collective motion of a two-dimensional periodic array of spheres in a slit-pore confined by two parallel planar walls. We determine the friction coefficient of the spheres when all particles move with the same velocity along a particular direction and cooperate with each other in their motion. In order to solve this many-body problem, we use Stokesian dynamics algorithm and resolve multiparticle hydrodynamic interactions in wall-bounded geometry. Apart from particle-particle interactions, we also recognize that the aforementioned collective motion of all particles creates a cumulative effect on the fluid medium. This effect is manifested as either a net induced flow for a periodic pressure field or an additional pressure gradient for quiescent fluid. In our analysis, we focus on both periodic pressure and no-flow conditions. For both cases, the hydrodynamic friction on the translating particles is calculated using our multiparticle Stokesian dynamics simulation. The simulation for the no-flow condition is relatively straightforward-we only need to compute the multiparticle hydrodynamic interactions in quiescent fluid. However, for the periodic pressure condition, the net induced flow dragged by the particles has to be evaluated also. We express this net induced flow in terms of an additional pressure-driven velocity field. We present the hydrodynamic friction as a function of the dimensions of the two-dimensional periodic lattice. For closely packed arrays, the results show a considerable reduction in friction coefficients that usually increase with interparticle distance. Hence, our work renders the theoretical justification for other recent findings that indicate the importance of interparticle mutual cooperation.     

Substrate concentration dependence of the diffusion-controlled steady-state rate constant

The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B2*. Comparisons to Brownian dynamics simulations excluding hydrodynamic interactions show excellent agreement up to bulk number densities of B2*rho0 < approximately = 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.     

基于分子动力学模拟提高嗜热磷酸三酯酶样内酯酶非特异性底物活力的理论研究

采用分子动力学模拟和拉伸分子动力学模拟方法, 结合分子力学-广义玻恩表面积(MM-GB/SA)方法进行自由能计算和结构交互指纹分析, 研究了模拟过程中非特异性底物(对氧磷/内酯)分别与嗜热磷酸三酯酶样内酯酶(SsoPox)野生型和突变体(W263F/W263T)结合的构象变化, 分析了Loop8中重要残基Trp263的突变提高SsoPox非特异性底物活力的原因, 发现其能够影响门控残基Phe229的构象变化, 导致活性口袋入口变宽(Phe229与Tyr99之间的距离变大), 使对氧磷和内酯更容易结合到蛋白质的活性位点上; Asp256和Arg223形成盐桥的几率高于野生型(WT)SsoPox, 在Arg223(位于Loop7)的协助下质子更加高效地从活性中心的Asp256(位于Loop8)传递到溶剂中去, 因而能够提高SsoPox水解底物的效率. 通过比较2个野生型复合物的结构稳定性和结合自由能差异, 发现在模拟过程中SsoPox与内酯的复合物体系更加稳定并且具有更低的结合自由能, 有利于SsoPox识别底物并使其埋在活性部位的疏水环境中, 促进氢氧化物亲核进攻底物的亲电中心. 因此, 底物与酶稳定的相互作用可能是SsoPox具有天然内酯酶活性的原因之一.     

A novel algorithm for creating coarse-grained, density dependent implicit solvent models

Implicit solvent simulations are those in which solvent molecules are not explicitly simulated, and the solute-solute interaction potential is modified to compensate for the implicit solvent effect. Implicit solvation is well known in Brownian dynamics of dilute solutions but offers promise to speed up many other types of molecular simulations as well, including studies of proteins and colloids where the local density can vary considerably. This work examines implicit solvent potentials within a more general coarse-graining framework. While a pairwise potential between solute sites is relatively simple and ubiquitous, an additional parametrization based on the local solute concentration has the possibility to increase the accuracy of the simulations with only a marginal increase in computational cost. We describe here a method in which the radial distribution function and excess chemical potential of solute insertion for a system of Lennard-Jones particles are first measured in a fully explicit, all-particle simulation, and then reproduced across a range of solute particle densities in an implicit solvent simulation.     

Mesoscopic dynamics of diffusion-influenced enzyme kinetics

A particle-based mesoscopic model for enzyme kinetics is constructed and used to investigate the influence of diffusion on the reactive dynamics. Enzymes and enzyme-substrate complexes are modeled as finite-size soft spherical particles, while substrate, product, and solvent molecules are point particles. The system is evolved using a hybrid molecular dynamics-multiparticle collision dynamics scheme. Both the nonreactive and reactive dynamics are constructed to satisfy mass, momentum, and energy conservation laws, and reversible reaction steps satisfy detailed balance. Hydrodynamic interactions among the enzymes and complexes are automatically accounted for in the dynamics. Diffusion manifests itself in various ways, notably in power-law behavior in the evolution of the species concentrations. In accord with earlier investigations, regimes where the product production rate exhibits either monotonic or nonmonotonic behavior as a function of time are found. In addition, the species concentrations display both t(-1/2) and t(-3/2) power-law behavior, depending on the dynamical regime under investigation. For high enzyme volume fractions, cooperative effects influence the enzyme kinetics. The time dependent rate coefficient determined from the mass action rate law is computed and shown to depend on the enzyme concentration. Lifetime distributions of substrate molecules newly released in complex dissociation events are determined and shown to have either a power-law form for rebinding to the same enzyme from which they were released or an exponential form for rebinding to different enzymes. The model can be used and extended to explore a variety of issues related concentration effects and diffusion on enzyme kinetics.