Related papers: Multistate reversible copolymerization of nonMarko…
The theory of multistate template-directed reversible copolymerization is developed by extending the method based on iterated function systems to matrices, taking into account the possibility of multiple activation states instead of a…
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment…
We investigate theoretically the physics of diffusion-limited intramolecular polymer reactions. The present work completes and goes beyond a previous study [Nat. Chem. 4, 268 (2012)] that showed that the distribution of the polymer…
We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive…
Motivated by a recent work on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer concentration and the other one not.…
The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of…
Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerisation has been studied theoretically in a number of contexts, often by considering a Markov process in…
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…
A co-polycondensation reaction is discussed analytically and by Monte-Carlo simulations where two reactive units compete for reactions with an alternating third reactive unit, whereby irreversible reactions replace bonds which are able to…
Self-assembled linear structures like giant cylindrical micelles or discotic molecules in solution stacked in flexible columns are systems reminiscent of polydisperse polymer solutions.These supramolecular polymers have an equilibrium…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
The non-Markovian nature of polymer motions is accounted for in folding kinetics, using frequency-dependent friction. Folding, like many other problems in the physics of disordered systems, involves barrier crossing on a correlated energy…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
We develop a simple recursive approach to treat reversible condensation polymerization with cyclization. Based upon a minimum set of balance equations, the law of mass action, Gaussian chain statistics, and the assumption of independent…
In this paper, the looping kinetics of a long polymer chain in solution has been investigated by using two state model, where one state represents open chain polymer molecule and the other represents closed chain polymer molecule. The…
Hybrid molecular dynamics/Monte Carlo simulations used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in…
We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the…
We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…