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Kinetics of reversible reactions on linear lattices with neighbor effects
Author(s) -
Silberberg A.,
Simha R.
Publication year - 1968
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.1968.360060405
Subject(s) - closure (psychology) , chemistry , k nearest neighbors algorithm , rate equation , lattice (music) , chain (unit) , kinetic energy , statistical physics , reversible reaction , reaction rate , thermodynamics , kinetics , classical mechanics , physics , quantum mechanics , catalysis , computer science , biochemistry , artificial intelligence , economics , acoustics , market economy
As a model for a variety of reaction processes on long chain molecules, for example, helix formation, a kinetic theory on a linear lattice is presented. Each reaction site can undergo reversible transitions between two states (0 and 1) with rates depending on the slate of its nearest neighbors. The system of coupled rate equations for the frequencies of specified runs of 0's and 1's is infinite for an infinite chain. In contrast to the case of irreversible processes, the system cannot, be written down by inspection. A procedure for the systematic derivation of the rate equations is developed which can be programmed on a computer. Explicit expressions for runs up to length four, involving runs up to length five are obtained without recourse to the computer. For the solution of the rate equations a closure must necessarily be imposed, and a possible procedure is pointed out. Furthermore the equilibrium relations following from the model are considered. The well‐known equilibrium results for nearest‐neighbor interactions represent a special case of these equations.