Premium
Moments of the probability distribution of moving molecules undergoing reversible isomerization, with applications to experiments
Author(s) -
Mitchell R. M.
Publication year - 1976
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.1976.360150910
Subject(s) - position (finance) , chemistry , isomerization , measure (data warehouse) , mean square , mean field theory , variance (accounting) , square (algebra) , order (exchange) , distribution (mathematics) , thermodynamics , statistical physics , statistics , physics , quantum mechanics , mathematical analysis , mathematics , biochemistry , accounting , business , finance , geometry , database , computer science , economics , catalysis
Exact expressions are obtained for the mean position and the variance about the mean of macromolecules which are moving in an electrostatic or centrifugal field and which, at the same time, are switching back and forth between two isomeric states. Comparison with experiment then yields the forward and backward switching rates. The following special cases are considered: (a) only one species present initially; (b) both species present initially but not in their equilibrium proportions; (c) both species present initially in their equilibrium proportions. It is shown that in the first two cases we need only measure the mean position of all the molecules in order to measure the absolute switching rates k 1 and k 2 . In the third case, however, we must measure the variance (mean‐square deviation) of the position in order to obtain k 1 and k 2 . The first two situations arise when “jumps” (e.g., in temperature or pressure) are made, while the third situation is obtained if the experiment is conducted with the species in chemical equilibrium throughout the experiment.