Kinetics and thermodynamics of living copolymerization processes

Abstract

Theoretical advances are reported on the kinetics and thermodynamics of free and template-directed living copolymerizations. Until recently, the kinetic theory of these processes had only been established in the fully irreversible regime, in which the attachment rates are only considered. However, the entropy production is infinite in this regime and the approach to thermodynamic equilibrium cannot be investigated. For this purpose, the detachment rates should also be included. Inspite of this complication, the kinetics can be exactly solved in the regimes of steady growth and depolymerization. In this way, analytical expressions are obtained for the mean growth velocity, the statistical properties of the copolymer sequences, as well as the thermodynamic entropy production. The results apply to DNA replication, transcription and translation, allowing us to understand important aspects of molecular evolution.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Insights into Error Control Mechanisms in Biological Processes: Copolymerization and Enzyme-Kinetics Revisited

“…This scheme can also represent the free copolymerization process that does not rely on a template and is mainly used in industrial systems. 5,6,39 Based on the assumption that a copolymer sequence can be described as a first-order Markov chain, various theoretical methods, such as Kruger's approach and Gaspard's method, can be applied to reduce the original set of kinetic equations for the terminal model into the closed set of steady-state equations. 11,13,14 Below, we describe one such truncation method based on a Markov-chain approximation, named as steady-state copolymerization method, described in ref 15.…”

“…Copolymerization is a process of chemically combining distinct monomer species to form polymer molecules. 1−4 Copolymerization processes can be classified into two categories: free copolymerization 5,6 and templated copolymerization that uses a template to control the distribution of produced sequences. Many biological information phenomena ranging from replication to translation rely on the templated copolymerization processes.…”

“…Copolymerization is a process of chemically combining distinct monomer species to form polymer molecules. − Copolymerization processes can be classified into two categories: free copolymerization , and templated copolymerization that uses a template to control the distribution of produced sequences. Many biological information phenomena ranging from replication to translation rely on the templated copolymerization processes. − For instance, during DNA replication, different monomer nucleotides, either cognate or noncognate, are added sequentially to the growing DNA strand, following the sequence of the template DNA. , Therefore, the fidelity of the information processing can be understood by investigating the templated copolymerization kinetics.…”

Bridging the gaps at the physics–chemistry–biology interface

“…Without conventional theoretical understanding of the structural characteristics of the system under investigation, we lack the principles by means of which to guide the optimal acquisition of data which we would expect to be forthcoming in any experimental design activity. The article provides a logical introduction to the multiplicity of research topics discussed in the following papers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], which report findings spanning the full gamut of domains from physics and chemistry to biology. The first five research articles [3][4][5][6][7] address issues associated with the development and implementation of a range of methodologies for handling multiscale problems in molecular and condensed matter physics as well as fluid dynamics.…”

“…The following two articles [8,9] consider multiscale situations arising in polymer and materials chemistry. The final eight articles [10][11][12][13][14][15][16][17] deal with the most complex and challenging aspects of multiscale modelling at the physics-chemistry-biology interface. The papers address problems which span many biologically relevant scales of organization, from the molecular and genomic levels through cellular to organ and organism levels.…”