Non-Markovian polymer reaction kinetics

Abstract

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.

Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions

“…In section II, we recall briefly some important results of the Zimm model. In section III, we show how to adapt the recent non-Markovian theory [18,23,28] of cyclization kinetics to the Zimm model. We compare the numerical solution of the model to both Brownian dynamics simulations and to the results of a Wilemski-Fixman approach.…”

“…On the theoretical level, various approaches have been proposed to quantify the kinetics of polymer closure [13][14][15][16][17][18][19][20][21][22]. An important step has been provided by Wilemski and Fixman [13,14], who made a local equilibrium assumption, thereby replacing the non-Markovian problem by an effective Markovian approach.…”

“…However, a non-Markovian description of the closure kinetics has not been considered so far. The first goal consists in describing these effects by adapting a theory proposed recently [18,23,28], which was so far restricted to the case of flexible and semi-flexible free draining chains. One could expect that the treatment of pre-averaged interactions is not valid for the problem of chain closure, since interactions averaged over equilibrium configurations could differ from the actual (non-preaveraged) interactions for closed chains, which could then play an important role for the contact kinetics.…”

“…Recent works have improved these approaches in the case of the Rouse chain (i.e. flexible without hydrodynamic interactions) by introducing several methods: (i) a refined way to take into account the memory of the initial configurations [16], (ii) an exact formal iterative resolution scheme in one dimension [17], (iii) a strong localized perturbation analysis [21], and (iv) an approach based on the calculation of the distribution of chain configurations at the instant of cyclization [18,[23][24][25], which has a strong influence on the contact kinetics.…”

Enhanced Quantum Transport in Multiplex Networks

“…This definition can be applied for both, incoherent and coherent processes, where the latter needs some adjustment, see below. For diffusive processes such as random walks, MFPTs have been calculated, e.g., for polymer reaction kinetics [11] or confined systems [12], see [13] for an overview of different applications.…”