Kinetic laws, phase-phase expansions, renormalization group, and INR calibration.
We introduce systematic approaches to chemical kinetics based on the use of phase-phase (log-log) representations of the rate equations. For slow processes, we obtain a corrected form of the mass-action law, where the concentrations are replaced by kinetic activities. For fast reactions, delay expressions are derived. The phase-phase expansion is, in general, applicable to kinetic and transport processes. A mechanism is introduced for the occurrence of a generalized mass-action law as a result of self-similar recycling. We show that our self-similar recycling model applied to prothrombin assays reproduces the empirical equations for the International Normalized Ratio calibration (INR), as well as the Watala, Golanski, and Kardas relation (WGK) for the dependence of the INR on the concentrations of coagulation factors. Conversely, the experimental calibration equation for the INR, combined with the experimental WGK relation, without the use of theoretical models, leads to a generalized mass-action type kinetic law.
Vlad
Marcel O
MO
Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA. marceluc@stanford.edu
Corlan
Alexandru D
AD
Morán
Federico
F
Spang
Rainer
R
Oefner
Peter
P
Ross
John
J
D001681:Biological Assay; D001692:Biological Transport; D002138:Calibration; D003198:Computer Simulation; D007700:Kinetics; D008954:Models, Biological; D011516:Prothrombin / Q000378:metabolism
D011516:Prothrombin