Exact long-time asymptotics for reversible binding in three dimensions

Simulation of Radiation-Induced DNA Damage and Protection by Histones Using the Code RITRACKS

(1) Background: DNA damage is of great importance in the understanding of the effects of ionizing radiation. Various types of DNA damage can result from exposure to ionizing radiation, with clustered types considered the most important for radiobiological effects. (2) Methods: The code RITRACKS (Relativistic Ion Tracks), a program that simulates stochastic radiation track structures, was used to simulate DNA damage by photons and ions spanning a broad range of linear energy transfer (LET) values. To perform these simulations, the transport code was modified to include cross sections for the interactions of ions or electrons with DNA and amino acids for ionizations, dissociative electron attachment, and elastic collisions. The radiochemistry simulations were performed using a step-by-step algorithm that follows the evolution of all particles in time, including reactions between radicals and DNA structures and amino acids. Furthermore, detailed DNA damage events, such as base pair positions, DNA fragment lengths, and fragment yields, were recorded. (3) Results: We report simulation results using photons and the ions 1H+, 4He2+, 12C6+, 16O8+, and 56Fe26+ at various energies, covering LET values from 0.3 to 164 keV/µm, and performed a comparison with other codes and experimental results. The results show evidence of DNA protection from damage at its points of contacts with histone proteins. (4) Conclusions: RITRACKS can provide a framework for studying DNA damage from a variety of ionizing radiation sources with detailed representations of DNA at the atomic scale, DNA-associated proteins, and resulting DNA damage events and statistics, enabling a broader range of future comparisons with experiments such as those based on DNA sequencing.

Bimolecular multistage diffusion-influenced chemical reactions proceeding from different sites in solutions. I. Rate constants

General matrix algebraic equations for calculating rate constants of multistage diffusion-influenced reactions (involving bimolecular exchange reactions as elementary stages) in liquid solutions that proceed from different active sites in the immediate vicinity of the contact of reactants have been obtained on the basis of the kinematic approximation developed by the authors earlier. The equations make it possible to express rate constants of any multistage multisite bimolecular reaction between non-identical reactants in terms of the defined reaction constants and stationary Green functions averaged over reaction sites and completely determined by molecular motion of reactants or their molecular groups. The asymptotic behavior of these rate constants as they attain their steady-state values on completion of the transient stage is established. It is shown that it coincides with the corresponding exact time asymptote. Calculations are made with some specific two-stage (three-channel) bimolecular reactions as an example.

Reversible Stochastically Gated Diffusion-Influenced Reactions

An approximate but accurate theory is developed for the kinetics of reversible binding of a ligand to a macromolecule when either can stochastically fluctuate between reactive and unreactive conformations. The theory is based on a set of reaction-diffusion equations for the deviations of the pair distributions from their bulk values. The concentrations are shown to satisfy non-Markovian rate equations with memory kernels that are obtained by solving an irreversible geminate (i.e., two-particle) problem. The relaxation to equilibrium is not exponential but rather a power law. In the Markovian limit, the theory reduces to a set of ordinary rate equations with renormalized rate constants.

Green's function for reversible geminate reaction with volume reactivity

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either inverting the Laplace transform numerically or propagating the partial differential equation in the time-domain. We show that integrals of this solution over the reaction sphere agree with previously obtained solutions.

Manifestation of macroscopic correlations in elementary reaction kinetics. I. Irreversible reaction A+A-->product

Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A+A-->product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.

Aging processes in reversible reaction-diffusion systems

Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.

Corrections to the law of mass action and properties of the asymptotic t=∞ state for reversible diffusion-limited reactions

For diffusion-limited reversible A+A<==>B reactions we reexamine two fundamental concepts of classical chemical kinetics-the notion of "chemical equilibrium" and the "law of mass action." We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance mu apart of each other at time moment t, may associate forming a B particle at the rate k+(mu). In turn, any randomly moving B particle may spontaneously dissociate at the rate k-(lambda) into a geminate pair of As "born" at a distance lambda apart of each other. Within a formally exact approach based on Gardiner's Poisson representation method we show that the asymptotic t=infinity state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio k+(mu)k-(mu) does not depend on mu for any mu.

Elementary Steps in Excited-State Proton Transfer

The absorption of a photon by a hydroxy-aromatic photoacid triggers a cascade of events contributing to the overall phenomenon of intermolecular excited-state proton transfer. The fundamental steps involved were studied over the last 20 years using a combination of theoretical and experimental techniques. They are surveyed in this sequel in sequential order, from fast to slow. The excitation triggers an intramolecular charge transfer to the ring system, which is more prominent for the anionic base than the acid. The charge redistribution, in turn, triggers changes in hydrogen-bond strengths that set the stage for the proton-transfer step itself. This step is strongly influenced by the solvent, resulting in unusual dependence of the dissociation rate coefficient on water content, temperature, and isotopic substitution. The photolyzed proton can diffuse in the aqueous solution in a mechanism that involves collective changes in hydrogen-bonding. On longer times, it may recombine adiabatically with the excited base or quench it. The theory for these diffusion-influenced geminate reactions has been developed, showing nice agreement with experiment. Finally, the effect of inert salts, bases, and acids on these reactions is analyzed.

Chaperone-assisted translocation

We investigate the translocation of a stiff polymer through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind reversibly to the polymer on both sides of the membrane. A bound chaperone covers one (univalent binding) or many (multivalent binding) binding sites. Assuming that the diffusion of the chaperones is fast compared to the rate of translocation we describe the process by a one-dimensional master equation. We expand previous models by a detailed study of the effective force in the master equation, which is obtained by the appropriate statistical mechanical average over the chaperone states. The dependence of the force on the degree of valency (the number of binding sites occupied by a chaperone) is studied in detail. We obtain finite size corrections (to the thermodynamical expression for the force), which, for univalent binding, can be expressed analytically. We finally investigate the mean velocity for translocation as a function of chaperone binding strength and size. For both univalent and multivalent binding simple results are obtained for the case of a sufficiently long translocating polymer.

Scaling law in target-hunting processes

We study a hunting process for a target, in which the hunter tracks the goal by smelling odors it emits. The odor intensity is supposed to decrease with the diffusion distance. The Monte Carlo experiment is carried out on a two-dimensional square lattice. Having no idea of the location of the target, the hunter determines its moves only by random attempts in each direction. By sorting the searching time in each simulation and introducing a variable x to reflect the sequence of searching times, we obtain a curve with a wide plateau, indicating the most probable time of successfully finding the target. The simulations reveal a scaling law for the searching time versus the distance to the position of the target. The scaling exponent depends on the sensitivity of the hunter. Our model may be a prototype in studying such searching processes as various food-foraging behaviors of wild animals.

Target problem on small-world networks

In this work we focus on reactions on small-world networks (SWN's), disordered graphs of much recent interest. We study the target problem, since it allows an exact solution on regular lattices. On SWN's we find that the decay of the targets (for which we extend the formalism to disordered lattices) is again related to S(n), the mean number of distinct sites visited in n steps, although the S(n) vs n dependence changes here drastically in going from regular linear chains to their SWN.

Long-time tails in the kinetics of reversible bimolecular reactions

A new approach is developed to study the relaxation of concentrations to equilibrium in reversible bimolecular reactions. For A+B <==> C, a general analytic expression is derived for the amplitude of the power law (t(-d/2)) asymptotics for arbitrary diffusion coefficients and concentrations of the reactants. Our formalism is based on the analysis of the time correlation functions describing the equilibrium fluctuations of the concentrations. This powerful and simple procedure can be readily used to study other bimolecular reactions such as A+B <==> C+D.

Rigorous derivation of the long-time asymptotics for reversible binding

Using an iterative solution in Laplace-Fourier space, we supply a rigorous mathematical proof for the long-time asymptotics of reversible binding in one dimension. The asymptotic power law and its concentration dependent prefactor result from diffusional and many-body effects which, unlike for the corresponding irreversible reaction and in classical chemical kinetics, play a dominant role in shaping the approach to equilibrium.