Sorption kinetics of strontium in porous hydrous ferric oxide aggregates I. The Donnan diffusion model

Sorption of ions by hydrous ferric oxide (HFO) often shows a fast initial sorption reaction followed by a much slower sorption process. The second step is diffusion-controlled and can continue for days or months before equilibrium is reached. In this paper, we demonstrate that the diffusion rate may be explained by electrostatic interactions. The internal and external surfaces of HFO are generally positively charged and therefore repel cations. This can result in extremely low cation concentrations in pores, and therefore a significant reduction in pore diffusion rate. The theory is demonstrated here for sorption of Sr(2+) in HFO aggregates. The ion concentrations in the pore space are calculated using a Donnan model and diffusion is calculated from the Donnan concentration and potential gradients. This diffusion model is compared with nonelectrostatic pore diffusion, which does not take electrostatic interactions into account. The Donnan model predicts very low concentrations of Sr(2+) in the pores and diffusion rates that are up to 8000 times lower than predicted with a nonelectrostatic model.     

Modeling of solvent flow effects in enzyme catalysis under physiological conditions

A stochastic model for the dynamics of enzymatic catalysis in explicit, effective solvents under physiological conditions is presented. Analytically-computed first passage time densities of a diffusing particle in a spherical shell with absorbing boundaries are combined with densities obtained from explicit simulation to obtain the overall probability density for the total reaction cycle time of the enzymatic system. The method is used to investigate the catalytic transfer of a phosphoryl group in a phosphoglycerate kinase-ADP-bis phosphoglycerate system, one of the steps of glycolysis. The direct simulation of the enzyme-substrate binding and reaction is carried out using an elastic network model for the protein, and the solvent motions are described by multiparticle collision dynamics which incorporates hydrodynamic flow effects. Systems where solvent-enzyme coupling occurs through explicit intermolecular interactions, as well as systems where this coupling is taken into account by including the protein and substrate in the multiparticle collision step, are investigated and compared with simulations where hydrodynamic coupling is absent. It is demonstrated that the flow of solvent particles around the enzyme facilitates the large-scale hinge motion of the enzyme with bound substrates, and has a significant impact on the shape of the probability densities and average time scales of substrate binding for substrates near the enzyme, the closure of the enzyme after binding, and the overall time of completion of the cycle.     

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.     

Numerical analysis of surfactant dynamics at air-water interface using the Henry isotherm

This paper focuses on the surfactant behavior at air-water interface, taking into account the diffusion-controlled model together with the Henry isotherm to model the relation between the surface and the subsurface concentrations. The existence and uniqueness of a weak solution is stated. Fully discrete approximations are obtained by using a finite element method and the backward Euler scheme. Error estimates are then proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is derived. Finally, some numerical simulations are presented in order to demonstrate the accuracy of the algorithm and the behavior of the solution.     

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.     

Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions

Molecular-dynamics simulations are presented for the diffusion-controlled bimolecular reaction A+B<==>C in two and three dimensions. The reactants and solvent molecules are modeled as spheres interacting via continuous potential-energy functions. The interaction potential between two reactants contains a deep well that results in a reaction. When the solvent concentration is low and the reactant dynamics is essentially ballistic, the system reaches equilibrium rapidly, and the reaction follows classical kinetics with exponential decay to the equilibrium. When the solvent concentration is high the particles enter the normal diffusion regime quickly and nonclassical behavior is observed, i.e., the reactant concentrations approach equilibrium as t(-d/2) where d is the dimensionality of space. When the reaction well depth is large, however, the reaction becomes irreversible within the simulation time. In this case the reactant concentrations decay as t(-d/4). Interestingly this behavior is also observed at intermediate times for reversible reactions.     

A comprehensive Monte Carlo simulation of styrene atom transfer radical polymerization

<正>An optimized and high-performance Monte Carlo simulation is developed to take thorough account of four different cases of termination in styrene ATRP.According to the simulation results,the bimolecular termination rate constant sharply drops throughout the polymerization when either chain-length dependency of termination rate constant,gel effect,or both together is applied to the simulation.In addition,as expected,the initiator is quickly decomposed at the early stages of the polymerization.The concentration of the catalyst in lower oxidation state decreases at first and then plateaus at higher conversion;furthermore,the steady concentration of M_t~nY/L in the polymerization is the highest when the chain-length-dependent diffusion-controlled termination rate constant is employed in the simulation.The rates of deactivation and chain end degradation reactions are also smaller in this case.Therefore,the fraction of dormant chains is higher throughout the reaction and consequently the portion of dead polymers decreases.Besides,molecular weight increases linearly with conversion;however,when neither gel effect nor chain-length dependency of termination rate constant is considered,the molecular weight deviates from linearity at the end of the reaction.The peak of chain length distribution shifts toward higher molecular weight too during the reaction.Finally,the molecular weight distribution broadens at higher conversion;however, the chain length distribution of polymers produced under conditions of applying chain-length-dependent diffusion-controlled termination rate constant is narrower.     

A new approach for efficient simulation of Coulomb interactions in ionic fluids

We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cutoff distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma-->0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition, we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.     

Reactions on cell membranes: comparison of continuum theory and Brownian dynamics simulations

Biochemical transduction of signals received by living cells typically involves molecular interactions and enzyme-mediated reactions at the cell membrane, a problem that is analogous to reacting species on a catalyst surface or interface. We have developed an efficient Brownian dynamics algorithm that is especially suited for such systems and have compared the simulation results with various continuum theories through prediction of effective enzymatic rate constant values. We specifically consider reaction versus diffusion limitation, the effect of increasing enzyme density, and the spontaneous membrane association/dissociation of enzyme molecules. In all cases, we find the theory and simulations to be in quantitative agreement. This algorithm may be readily adapted for the stochastic simulation of more complex cell signaling systems.     

Investigation of the salting out of methane from aqueous electrolyte solutions using computer simulations

We calculate the excess chemical potential of methane in aqueous electrolyte solutions of NaCl using Monte Carlo computer simulations. In a recent work [Docherty et al. J. Chem. Phys. 2006, 125, 074510], we presented a new potential model for methane in water which is capable of describing accurately the excess chemical potential of methane in pure water over a range of temperatures, a quantity that can be related to the solubility and which is commonly used to study the hydrophobic effect. Here, we use the same potential model for the water-methane interactions and investigate the effect of added salt on the chemical potential of methane in the solution. The methane molecules are modeled as single Lennard-Jones (LJ) interaction sites, and the water molecules are modeled with the TIP4P/2005 model. A correcting factor of chi = 1.07 for the energetic Berthelot (geometric) combining rule of the methane-water interaction is also used, which mimics the polarization of methane in water. We consider NaCl as the salt and treat the ions with the Smith and Dang model (i.e., as charged LJ interaction sites). Ion-water, ion-ion, and ion-methane interactions are treated using Lorentz-Berthelot combining rules. In addition, the Coulombic potential is used to model charge-charge interactions which are calculated using the Ewald sum. We have carried out isobaric-isothermal (NpT) simulations to determine the equilibrium densities of the solutions. The simulation data is in excellent agreement with experimental densities of aqueous NaCl solutions of different concentration. Hydration numbers are also obtained and found to be in agreement with reported data. Canonical (NVT) simulations at the averaged densities are then performed using the Widom test-particle insertion method to obtain the excess chemical potential of methane in the saline solutions. An increase in the chemical potential of methane, corresponding to a salting out effect, is observed when salt is added to the solution. We investigate different concentrations and ion sizes. An overprediction of the salting out effect as compared with experimental data is observed, which we believe is due to the polarizing effect of the ions in the solution, which is not taken into account by the model. We also find a direct correlation between the increase in the chemical potential and the packing fraction of the solution and argue that the main cause of the observed salting out effect (as represented by an increase in the excess chemical potential) is the increase in the packing fraction of the solutions due to the added salt. Together, with this, we put forward an argument toward explaining the anomalous Hofmeister effect of Li(+).     

Multiscale-linking simulation of irreversible colloidal deposition in the presence of DLVO interactions

An efficient multiscale-linking algorithm, based on the self-consistent integration of Brownian dynamics simulation of particle trajectories with the solution of the continuum-level conservation equation for particle concentration subject to an adaptive Neumann boundary condition that accounts for the blocking effect of deposition, is developed. The algorithm has been already validated in the case of deposition of noninteracting hard spheres [R.V. Magan, R. Sureshkumar, Multiscale Model. Simul. 2 (2004) 475]. In this study, the above algorithm is extended to incorporate particle interactions modeled by the DLVO theory. The simulations are used to identify a time scale at which the deposition process transitions from a power-law to an asymptotic regime. Detailed characterization of the two regimes is provided for a wide range of ionic strength, particle surface charge density, bulk volume fraction, and substrate potential values. The radial distribution functions obtained for various ionic strengths can be collapsed into a master curve when the radial distance is normalized with respect to a characteristic length scale of inter-particle repulsion. Moreover, simulation results suggest a rescaled, uniformly valid soft random sequential adsorption (RSA) model. Simulation results for the kinetics and monolayers structure compare favorably with experimental data, without the use of adjustable parameters. Comparison with other dynamic simulation techniques shows that while their predictions are qualitatively similar, notable quantitative differences exist especially for small ionic strengths.     

Efficient solvent boundary potential for hybrid potential simulations

A common challenge in computational biophysics is to obtain statistical properties similar to those of an infinite bulk system from simulations of a system of finite size. In this work we describe a computationally efficient algorithm for performing hybrid quantum chemical/molecular mechanical (QC/MM) calculations with a solvent boundary potential. The system is partitioned into a QC region within which catalytic reactions occur, a spherical region with explicit solvent that envelops the quantum region and is treated with a MM model, and the surrounding bulk solvent that is treated implicitly by the boundary potential. The latter is constructed to reproduce the solvation free energy of a finite number of atoms embedded inside a low-dielectric sphere with variable radius, and takes into account electrostatic and van der Waals interactions between the implicit solvent and the QC and MM atoms in the central region. The method was implemented in the simulation program pDynamo and tested by examining elementary steps in the reaction mechanisms of two enzymes, citrate synthase and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated with the method and those obtained by previous experimental and computational studies. Directions in which the utility of the method can be further improved are discussed.     

A modified model of diffusion-controlled reactions

The treatment used for diffusion-controlled reactions is extended to the case when the final jumplike step of the reagent approach differs essentially from the preceding diffusion. In terms of the model proposed it is possible to take into account, in a simple way, chemical inhomogeneity of the reagents when the in-cage reaction rate depends on the pair state (for example, on the molecular orientation). In this connection the reaction can be controlled either by the reagent intrusion into the solvation shell of the partner, or by the in-cage relaxation.     

COAST: Controllable approximative stochastic reaction algorithm

We present an approximative algorithm for stochastic simulations of chemical reaction systems, called COAST, based on three different modeling levels: for small numbers of particles an exact stochastic model; for intermediate numbers an approximative, but computationally more efficient stochastic model based on discrete Gaussian distributions; and for large numbers the deterministic reaction kinetics. In every simulation time step, the subdivision of the reaction channels into the three different modeling levels is done automatically, where all approximations applied can be controlled by a single error parameter for which an appropriate value can easily be found. Test simulations show that the results of COAST simulations agree well with the outcomes of exact algorithms; however, the asymptotic run times of COAST are asymptotically proportional to smaller powers of the particle numbers than exact algorithms.     

Diffusion-controlled reaction. VI. Radiation graft polymerization of styrene to polyethylene

The radiation graft polymerization of styrene to polyethylene was studied under diffusion-controlled conditions of radiation intensity I, monomer concentration M₁, and polymer sample thickness L. The results of the present study together with previous work under diffusion-free conditions verify our theoretical model for the diffusion-controlled reaction. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The order of dependence of grafting rate on radiation intensity for diffusion-controlled reaction is one-half that for diffusion-free reaction. Diffusion control leads to a decrease in the order of dependence of grafting rate on monomer concentration. The decrease is greater than theoretically predicted; possible reasons for this effect are described.     

Rotational and spin viscosities of water: Application to nanofluidics

In this paper we evaluate the rotational viscosity and the two spin viscosities for liquid water using equilibrium molecular dynamics. Water is modeled via the flexible SPC/Fw model where the Coulomb interactions are calculated via the Wolf method which enables the long simulation times required. We find that the rotational viscosity is independent of the temperature in the range from 284 to 319 K. The two spin viscosities, on the other hand, decrease with increasing temperature and are found to be two orders of magnitude larger than that estimated by Bonthuis et al. [Phys. Rev. Lett. 103, 144503 (2009)] We apply the results from molecular dynamics simulations to the extended Navier-Stokes equations that include the coupling between intrinsic angular momentum and linear momentum. For a flow driven by an external field the coupling will reduce the flow rate significantly for nanoscale geometries. The coupling also enables conversion of rotational electrical energy into fluid linear momentum and we find that in order to obtain measurable flow rates the electrical field strength must be in the order of 0.1?MV?m(-1) and rotate with a frequency of more than 100 MHz.     

Numerical simulations of the polymerization reaction of deuterated diacetylene 2,4‐hexadiynylene bis(p‐toluenesulfonate) crystal

In this paper, we developed two types of programs in order to simulate the polymerization reaction of a fully deuterated crystal of diacetylene 2,4‐hexadiynylene bis(p‐toluenesulfonate) (pTS‐D). The first simulation is based on a modification of Baughman's model, a classical model for simulating the polymerization of diacetylene crystals. The agreement between the simulated and experimental results concerning the reaction kinetics is satisfactory. With this simulation algorithm, we take into account the experimental observation that the polymerization of pTS‐H and pTS‐D crystals is really a random process of formation of polymer chains along the crystallographic axis b . The second simulation is based on the Monte Carlo method, which permits not only to simulate the kinetics of the reaction, but also the chain‐length distribution in the hydrogenated and deuterated compounds. These two types of simulations were already developed for the hydrogenated crystal of diacetylene, named pTS‐H. Two main modifications are applied in the case of pTS‐D for taking into account experimental results: in the first the rate constants of chain‐terminating microscopic processes are different in pTS‐H and pTS‐D which must be considered. The second modification concerns the evolution of the lattice deformation during the course of polymerization. The experimental variation of the b parameter as a function of polymer content X in pTS‐D is different from that in pTS‐H; this result is important to consider when calculating the activation energy of the initiation and propagation microscopic processes.     

Simulations of remote mutants of dihydrofolate reductase reveal the nature of a network of residues coupled to hydride transfer

Recent experimental and theoretical studies have proposed that enzymes involve networks of coupled residues throughout the protein that participate in motions accompanying chemical barrier crossing. Here, we have examined portions of a proposed network in dihydrofolate reductase (DHFR) using quantum mechanics/molecular mechanics simulations. The simulations use a hybrid quantum mechanics‐molecular mechanics approach with a recently developed semiempirical AM1‐SRP Hamiltonian that provides accurate results for this reaction. The simulations reproduce experimentally determined catalytic rates for the wild type and distant mutants of E. coli DHFR, underscoring the accuracy of the simulation protocol. Additionally, the simulations provide detailed insight into how residues remote from the active site affect the catalyzed chemistry, through changes in the thermally averaged properties along the reaction coordinate. The mutations do not greatly affect the structure of the transition state near the bond activation, but we observe differences somewhat removed from the point of C? H cleavage that affect the rate. The mutations have global effects on the thermally averaged structure that propagate throughout the enzyme and the current simulations highlight several interactions that appear to be particularly important. © 2014 Wiley Periodicals, Inc.     

Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions

We investigate a generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface. The exact solution of the relevant mixed boundary-value problem was found for different ratios of the intrinsic rate constants. The results obtained may be used to test numerical programs that describe diffusion-controlled reactions in real systems of particles with anisotropic reactivity.