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Kinetic laws, phase-phase expansions, renormalization group, and INR calibration.
Marcel Ovidiu Vlad MO,
Alexandru Dan Corlan,
Federico Morán,
Reiner Spang,
Peter Oefner P,
John Ross,
Proc Natl Acad Sci U S A. 106(16):6465-70, 2009
ABSTRACT
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.
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