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Concentration distribution and spatial moments of moving macromolecules undergoing isomerization
Author(s) -
Killalea M. K.,
McCoy B. J.
Publication year - 1980
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.1980.360191014
Subject(s) - chemistry , isomerization , zeroth law of thermodynamics , hermite polynomials , diffusion , reaction rate constant , distribution function , kinetics , thermodynamics , molecular physics , computational chemistry , mathematical analysis , classical mechanics , physics , mathematics , biochemistry , catalysis
Expressions for zeroth, first, and second spatial moments are obtained for diffusing macromolecules A and B that move due to an external field and undergo reversible isomerization, switching back and forth according to first‐order kinetics. In addition, expressions for third and fourth moments are derived for the special case of equal diffusion coefficients, equal rate constants, and equal but opposite velocities. The initial conditions are arbitrary amounts of A or B concentrated in an infinitesimally narrow region. The moments are computed from derivatives of the Fourier‐transformed concentration profiles of A and B. The moments are used in an expansion in term of Hermite polynomials, the Gram‐Charlier expansion, to construct the concentration profiles of A or B or A and B together. The examples presented show that a few terms of the expansion, for which explicit expressions are given, can give tolerable accuracy if the velocity is not too large and the rate constants and diffusion coefficient are not too small. The expansion can be used to determine when the profiles are unimodal.