Slow-equilibration approximation in macroscopic approach to studying kinetics at equilibrium.
Macroscopic approach to studying kinetics at equilibrium (MASKE) facilitates measurements of rate constants of formation (k(+)) and dissociation (k(-)) of affinity complexes in the state of chemical equilibrium. MASKE relies on "informational nonequilibrium" created by a nonuniform initial spatial distribution of a label on one of the reactants. In general, finding k(+) and k(-) by MASKE requires fitting experimental label-propagation patterns-dependencies of label concentrations on a coordinate or time-with the simulated label-propagation patterns. Here we introduce a simple fitting-free approach for finding the rate constants in the case of slow equilibration. Slow equilibration means that the characteristic equilibration time of the labeled reactant and labeled complex, t(eq), is much greater than the characteristic separation time of the labeled reactant and labeled complex, t(sep). We developed the mathematics for this approach by solving the differential equations of mass transfer using the assumption of slow equilibration. The approach was then tested and its accuracy was studied by applying it to label-propagation patterns created with the earlier-developed exact solution of the mass-transfer equations. The results proved that the approximate solution was correct. They also showed that k(+) and k(-) can be found with this fitting-free approach with a relative error less than 20% if t(sep) < 0.6t(eq). The practical limitations of our slow-equilibration approximation are discussed.
Department of Chemistry, York University, Toronto, Ontario, Canada.
Leonid T
LT
Cherney
Sergey N
SN
Krylov
D007700:Kinetics; D008956:Models, Chemical