Persistent effects of inertia on diffusion-influenced reactions: Theoretical methods and applications.

The Cattaneo-Vernotte model has been widely studied to take momentum relaxation into account in transport equations. Yet, the effect of reactions on the Cattaneo-Vernotte model has not been fully elucidated. At present, it is unclear how the current density associated with reactions can be expressed in the Cattaneo-Vernotte model.

Inertial dynamic effects on diffusion-influenced reactions: Approach based on the diffusive Cattaneo system.

We investigate the inertial dynamic effects on the kinetics of diffusion-influenced reactions by solving the linear diffusive Cattaneo system with the reaction sink term. Previous analytical studies on the inertial dynamic effects were limited to the bulk recombination reaction with infinite intrinsic reactivity. In the present work, we investigate the combined effects of inertial dynamics and finite reactivity on both bulk and geminate recombination rates.

Interplay of reactive interference and crowding effects in the diffusion-influenced reaction kinetics.

We investigate the interplay of reactive interference and crowding effects in the irreversible diffusion-influenced bimolecular reactions of the type A+B→P+B by using the Brownian dynamics simulation method. It is known that the presence of nonreactive crowding agents retards the reaction rate when the volume fraction of the crowding agents is large enough. On the other hand, a high concentration of B is known to increase the reaction rate more than expected from the mass action law, although the B's may also act as crowders.

Green's function of the Smoluchowski equation with reaction sink: Application to geminate and bulk recombination reactions.

By applying a recently developed solution method for the Fredholm integral equation of the second kind, we obtain an expression for Green's function of the Smoluchowski equation with a reaction sink. The result is applied to obtain accurate analytical expressions for the time-dependent survival probability of a geminate reactant pair and the rate coefficient of the bulk recombination between reactants undergoing diffusive motions under strong Coulomb interactions. The effects of both repulsive and attractive interactions are considered, and the results are compared with the numerical results obtained by solving the equation for the survival probability and the nonequilibrium pair correlation function.

Time-dependent electron transfer rate between geminate ions with strong Coulomb interaction and distance-dependent reactivity.

Previous analytic expressions for the time-dependent rate of diffusion-influenced electron-transfer between geminate ions were obtained for the case when the reaction occurs at a contact separation. By applying a recently developed solution method for the Fredholm integral equation of the second kind, we obtain an accurate analytic expression for the time-dependent electron-transfer rate with the account of the distance-dependent reactivity. We also consider the dependence of the rate on the initial separation between the geminate ions.

Transport dynamics of complex fluids.

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate subdiffusive, and long-time diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a challenging problem. Here, we present a transport equation and its solutions, which yield a unified quantitative explanation of the mean-square displacement (MSD), the non-Gaussian parameter (NGP), and the displacement distribution of complex fluids.

Efficient implementations of analytic energy gradient for mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT).

Analytic energy gradients of individual singlet and triplet states with respect to nuclear coordinates are derived and implemented for the collinear mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT), which eliminates the problematic spin-contamination of SF-TDDFT. Dimensional-transformation matrices for the singlet and triplet response spaces are introduced, simplifying the subsequent derivations. These matrices enable the general forms of MRSF-TDDFT equations to be similar to those of SF-TDDFT, suggesting that the computational overhead of singlet or triplet states for MRSF-TDDFT is nearly identical to that of SF-TDDFT.

New Method for Constant- NPT Molecular Dynamics.

The well-established molecular dynamics simulation methods for constant- NPT ensemble systems such as the Andersen-Nosé-Hoover method and their variants may alter the dynamic properties of the molecules under consideration, because their equations of motion are modified by the coupling with thermostat or barostat. To circumvent this artifact, we propose a new molecular dynamics simulation algorithm, by which only the molecules near the wall of the simulation box are coupled to the thermostat and barostat and the molecules of interest placed in the inner part of the simulation box remain intact. We test the efficiency of our algorithm in attaining the target temperature and pressure and the conformity of the calculated equilibrium and dynamic properties to those of a constant- NPT ensemble system.

Fast Overlap Evaluations for Nonadiabatic Molecular Dynamics Simulations: Applications to SF-TDDFT and TDDFT.

Fast overlap integral algorithms for the spin-flip time-dependent density functional theory (SF-TDDFT) and the linear response (LR)-TDDFT were proposed on the basis of determinant factorization (DF) and the truncated Leibnitz formula (TLF). These in turn allow efficient computation of nonadiabatic coupling terms (NACTs) in nonadiabatic molecular dynamics simulations. The TLF(0), TLF(1), and TLF(2) were proposed according to the truncation order.

Eliminating spin-contamination of spin-flip time dependent density functional theory within linear response formalism by the use of zeroth-order mixed-reference (MR) reduced density matrix.

The use of the mixed reference (MR) reduced density matrix, which combines reduced density matrices of the = +1 and -1 triplet-ground states, is proposed in the context of the collinear spin-flip-time-dependent density functional theory (SF-TDDFT) methodology. The time-dependent Kohn-Sham equation with the mixed state is solved by the use of spinor-like open-shell orbitals within the linear response formalism, which enables to generate additional configurations in the realm of TD-DFT. The resulting MR-SF-TDDFT computational scheme has several advantages before the conventional collinear SF-TDDFT.

Effects of external electric field and anisotropic long-range reactivity on charge separation probability.

We consider the effects of external electric field and anisotropic long-range reactivity on the recombination dynamics of a geminate charge pair. A closed-form analytic expression for the ultimate separation probability of the pair is presented. In previous theories, analytic expressions for the separation probability were obtained only for the case where the recombination reaction can be assumed to occur at a contact separation.

Concentration effects on the rates of irreversible diffusion-influenced reactions.

We formulate a new theory of the effects of like-particle interactions on the irreversible diffusion-influenced bimolecular reactions of the type A + B → P + B by considering the evolution equation of the triplet ABB number density field explicitly. The solution to the evolution equation is aided by a recently proposed method for solving the Fredholm integral equation of the second kind. We evaluate the theory by comparing its predictions with the results of extensive computer simulations.

An accurate expression for the rates of diffusion-influenced bimolecular reactions with long-range reactivity.

By using the recently developed method for solving the Fredholm integral equations of the second kind, we derive a very accurate expression for the steady-state rate constant of diffusion-influenced bimolecular reactions involving long-range reactivity. We consider the general case in which the reactants interact via an arbitrary central potential and hydrodynamic interaction. The rate expression becomes exact in the two opposite limits of small and large reactivity, and also performs very well in the intermediate regime.

Internal Diffusion-Controlled Enzyme Reaction: The Acetylcholinesterase Kinetics.

Acetylcholinesterase is an enzyme with a very high turnover rate; it quenches the neurotransmitter, acetylcholine, at the synapse. We have investigated the kinetics of the enzyme reaction by calculating the diffusion rate of the substrate molecule along an active site channel inside the enzyme from atomic-level molecular dynamics simulations. In contrast to the previous works, we have found that the internal substrate diffusion is the determinant of the acetylcholinesterase kinetics in the low substrate concentration limit.

Effects of the interaction potential and hydrodynamic interaction on the diffusion-influenced reaction rates.

Recently, we proposed an accurate analytic expression for the diffusive propagator of a pair of particles under a central interaction potential and hydrodynamic interaction, and derived the rate expressions for fully diffusion-controlled geminate and bimolecular reactions. In this work, we present a still more accurate propagator expression, and extend the theory to the partially diffusion-controlled cases with various types of interaction potentials, including the screened Coulomb potential and the potential of mean force due to solvation. We evaluate the accuracies of our theory and other competing theories against exact numerical results.

Zwanzig-Mori equation for the time-dependent pair distribution function.

We develop a microscopic theoretical framework for the time-dependent pair distribution function starting from the Liouville equation. An exact Zwanzig-Mori equation of motion for the time-dependent pair distribution function is derived based on the projection-operator formalism. It is demonstrated that, under the Markovian approximation, our equation reduces to the so-called telegraph equation that includes the potential of mean force acting between the pair particles.

Communication: Propagator for diffusive dynamics of an interacting molecular pair.

We introduce a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach leads to a divergent perturbation series solution. By using the method, we obtain an accurate expression of the propagator for diffusive dynamics of a pair of particles interacting via an arbitrary central potential and hydrodynamic interaction.

Kinetics of collision-induced reactions between hard-sphere reactants.

We investigate the reaction kinetics of hard-sphere reactants that undergo reaction upon collision. When the reaction probability at a given collision is unity, the Noyes rate theory provides an exact expression of the rate coefficient. For the general case with the reaction probability less than unity, Noyes assumed that successive recollision times between a tagged pair of reactants are decorrelated.

A rigorous foundation of the diffusion-influenced bimolecular reaction kinetics.

We formulate a general theory of the diffusion-influenced kinetics of irreversible bimolecular reactions occurring in the low concentration limit. Starting from the classical Liouville equation for the reactants and explicit solvent molecules, a formally exact expression for the bimolecular reaction rate coefficient is derived; the structures of reactant molecules and the sink functions may be arbitrarily complicated. The present theoretical formulation shows clearly how the well-known Noyes and Wilemski-Fixman rate theories are related and can be improved in a systematic manner.

Diffusion-influenced reactions involving a reactant with two active sites.

We consider the kinetics of diffusion-influenced reactions which involve a reactant species that can be modeled as a sphere with two reactive patches located on its surface at an arbitrary angular distance. An approximate analytic expression for the rate coefficient is derived based on the Wilemski-Fixman-Weiss decoupling approximation and a multivariable Padé approximation. The accuracy of the rate expression is evaluated against computer simulations as well as an exact analytic expression available for a special case.

Excluded volume effects on the intrachain reaction kinetics.

On the basis of the recently developed optimized Rouse-Zimm theory of chain polymers with excluded volume interactions, we calculate the long-time first-order rate constant k(1) for end-to-end cyclization of linear chain polymers. We first find that the optimized Rouse-Zimm theory provides the longest chain relaxation times tau(1) of excluded volume chains that are in excellent agreement with the available Brownian dynamics simulation results. In the free-draining limit, the cyclization rate is diffusion-controlled and k(1) is inversely proportional to tau(1), and the k(1) values calculated using the Wilemski-Fixman rate theory are in good agreement with Brownian dynamics simulation results.

Nanosecond molecular dynamics simulations of Cdc25B and its complex with a 1,4-naphthoquinone inhibitor: implications for rational inhibitor design.

Cdc25 phosphatases have been considered as attractive drug targets for anticancer therapies due to the correlation of their overexpression with a wide variety of cancers. To gain insight into designing new potent inhibitors, we investigate the dynamic properties of Cdc25B and its complex with a 1,4-naphtoquinone inhibitor NSC 95397 by means of molecular dynamics simulations in aqueous solution. It is shown from the calculated dynamic properties that the malleability of the residues 530-532 residing at the start of C-terminal region around the active site should be responsible for the catalytic action of Cdc25B.

Theory of non-Markovian rate processes.

Starting from a multidimensional reaction kinetic equation with a general time evolution operator and a reaction sink function K, we derive formally exact expressions for the survival probability, reaction time distribution, and mean reaction time by using the projection operator technique. These rate expressions are given in the rational function form, with the irreducible memory function Omegairr as the key ingredient. This approach has an advantage over the direct perturbation approaches that use the reaction term as the small parameter, in that Omegairr has a structure that can be perturbatively treated with (K - K) as the small parameter.

Mean first passage time for the contact between the ends of a chain polymer.

We investigate the first passage times for the contact between the ends of a Rouse chain, whose initial separation is greater than a predefined contact distance, sigma, and equilibrium-distributed. An approximate analytic expression for the mean first passage time is obtained and compared with the results of previous theories and Brownian dynamics simulations. We find that the results of the present theory are in better agreement with Brownian dynamics simulation results than those of previously reported theories.

Critical assessment of the automated AutoDock as a new docking tool for virtual screening.

A major problem in virtual screening concerns the accuracy of the binding free energy between a target protein and a putative ligand. Here we report an example supporting the outperformance of the AutoDock scoring function in virtual screening in comparison to the other popular docking programs. The original AutoDock program is in itself inefficient to be used in virtual screening because the grids of interaction energy have to be calculated for each putative ligand in chemical database.