Scott H. Northrup

Brownian dynamics simulation of diffusion-influenced bimolecular reactions

A method is developed and tested for extracting diffusion‐controlled rate constants for condensed phase bimolecular reactions from Brownian dynamics trajectory simulations. This method will be useful when highly detailed model systems are employed, such as those required to explore the complicated range of interactions between enzymes and their substrates. The method is verified by comparing with exact analytical results for simple cases of spheres with uniform reactivity subject to various centrosymmetric Coulombic and Oseen slip hydrodynamic interactions. The utility of the method is illustrated for more complicated cases involving anisotropic reactivity and rotational diffusion.

The stable states picture of chemical reactions. I. Formulation for rate constants and initial condition effects

The stable states picture (SSP) of chemical reactions is used to derive flux time correlation function (tcf) formulas for reaction rate constants. These formulas, which apply to both gas phase and condensed phase reactions, are interpreted in terms of the flux out of an internally equilibrated stable reactant and the ensuing irreversible flux into a stable product. The determination of the rate constants by dynamics in an intermediate region lying between these stable states is illustrated for a simple model of barrier crossing in liquids. Generalized rate constant expressions which hold when internal nonequilibrium in the stable states is important are derived and discussed. The SSP approach is also used to derive tcf expressions for short time initial condition effects which carry information on reactive dynamics beyond that contained in rate constants. As an illustration, it is shown how the SSP formulation provides a starting point for the resolution of primary and secondary recombination in liquid st...

Stochastically gated diffusion‐influenced reactions

The theory of diffusion‐influenced reactions is extended to cases where the reactivity of the species fluctuates in time (e.g., the accessibility of a binding site of a protein is modulated by a gate). The opening and closing of the gate is assumed to be a stationary Markov process [i.e., it is described by the kinetic scheme (open) a⇄b (closed)]. When the reaction is described by suitable boundary conditions, by solving the appropriate reaction‐diffusion equations, it is shown that the stochastically gated association rate constant (kSG) is given by k−1SG=k−1∞ + [a−1 b(a+b)κu(a+b)]−1, where κu(s) is the Laplace transform of the time‐dependent rate constant of the ungated problem and k∞ is the corresponding steady‐state rate constant. The limits when the relaxation time for gate fluctuations is larger or smaller than the characteristic time for diffusion are considered. The relation to previous work is discussed. The theory is applied to three models: (i) a gated sphere, (ii) a gated disk on an infinite...

Short range caging effects for reactions in solution. I. Reaction rate constants and short range caging picture

The effects of short range solvent structure and short range dynamical correlations are investigated for the steady state rate constant k for solution reactions influenced by diffusion. The description is in terms of a Smoluchowski equation describing relative motion of two molecules in an outer spatial translational region, supplemented by a sink term that accounts for dynamics in an inner reaction zone. In the outer region, solvent structural effects are included by a potential of mean force, which exhibits a short range well and barrier combination leading to ’’potential caging.’’ Outer region short range dynamical correlations are included via a separation‐dependent diffusion coefficient, leading to ’’dynamical caging’’ as relative motion is showed at small separations. These two short range effects are neglected in standard diffusion treatments. We find that k is only modestly influenced by the above short range effects. In order to expose short range structure and correlation influence in a more sen...

Molecular dynamics of ferrocytochrome c: Magnitude and anisotropy of atomic displacements

Abstract Two computer simulations of the atomic motion in tuna ferrocytochrome c have been carried out. The average structures and the structural correlations of the magnitudes of the atomic position fluctuations are in substantial agreement with recent X-ray diffraction results, particularly for the protein interior. The simulations show, however, that the atomic displacements are quite anisotropic. The degree of anisotropy and the preferred directions of atomic displacement exhibit correlations with structural features of the protein.

Diffusion‐controlled reactions: A variational formula for the optimum reaction coordinate

The preferred path for a diffusion‐controlled reaction depends, in general, upon global properties of the potential surface and the frictional resistance to motion upon this surface. A variational formula for this path is derived. The corresponding Euler–Lagrange equations are examined for two important special cases.

Reactive dynamics for diffusive barrier crossing

A theory is presented for intramolecular reactions A?B regarded as potential barrier crossing between two stable states A and B in the large friction limit. This limit, in which dynamics are governed by spatial diffusion in the potential, is an important example of extreme deviation from transition state theory predictions. Our theory expresses the full reaction rate constants in terms of simpler contributions: (a) the barrier rate constants and (b) the internal rate constants. The former depend solely on dynamics near the barrier top and govern the rate when stable state internal equilibrium is maintained. The latter depend solely on internal equilibration dynamics in the stable states A and B (defined away from the barrier top). The internal rate constants correct the barrier rate constants for stable state internal nonequilibrium effects. These two contributions are discussed in dynamical terms in some detail. Our theoretical rate constants are evaluated and compared with the rate constants observed by...

Experimental and theoretical analysis of the interaction between cytochromec and cytochromeb5

Experimental and theoretical investigation of the interaction of cytochromec and cytochromeb5 performed over nearly twenty years has produced considerable insight into the manner in which these proteins recognize and bind to each other. The results of these studies and the experimental and theoretical strategies that have been developed to achieve these results have significant implications for understanding the behavior of similar complexes formed by more complex and less-well characterized electron transfer proteins. The current review provides a comprehensive summary and critical evaluation of the literature on which the current status of our understanding of the interaction of cytochromec and cytochromeb5 is based. The general issues related to the study of electron transfer complexes of this type are discussed and some new directions for future investigation of such systems are considered.

Coupling of translational and reactive dynamics for a Fokker–Planck model

The coupling of translational and reactive dynamics is investigated for a Fokker–Planck description of relative particle motion in a solvent. A division into inner and outer relative coordinate spatial regions separated by a boundary layer is made. The inner region is characterized by a deep potential well associated with bound, or reacted, particles and a potential barrier. The outer zone is characterized by less rapidly varying forces which include solvent structural effects. With this division, a Fokker–Planck source equation for unreacted particles is derived. The source in this equation incorporates the complete inner region dynamics involving both reactive and nonreactive trajectories. This equation is then reduced via projection operator techniques to a spatial Smoluchowski source equation for unreacted particles in the outer region for the case of slow reaction. Validity conditions involving velocity relaxation are given. The sources here include both inner region short range repulsive effects and...

Extended Brownian dynamics of diffusion controlled reactions

The Brownian dynamics simulation method of Northrup et al. is extended so that dynamical trajectories can be initiated with the reactants in close proximity to one another. A more general analysis is presented which shows that this procedure is exact in cases where the first‐time encounter flux to the more proximal starting surface is isotropic, such as cases where interparticle forces are centrosymmetric, but is approximate otherwise. Diffusion controlled rate constants for three model systems obtained by this procedure are compared with analytic results or with exact rate constants derived from simulations following the original Northrup procedure. Agreement is good to excellent in all cases considered. The extended method is expected to be of considerable practical importance in systems with highly anisotropic reactivity where it is computationally inefficient to obtain rate constants by the original method.