1 Produced with Applixware for Linux V. 5.0.1 Kinetic laws, phase-phase expansions, renormalization group, blood coagulation and INR calibration Marcel O. Vlad 1,2,5 , Alexandru D. Corlan 3 , Federico Morán 4 , Rainer Spang 5 , Peter Oefner 5 , and John Ross 1 1 Department of Chemistry, Stanford University, Stanford CA 94305-5080 2 Institute of Mathematical Statistics and Applied Mathematics, Casa Academiei Romane, Calea 13 Septembrie 13, Bucharest, 050711 Romania 3 Cardiology Research Unit, University Emergency Hospital, Romanian Academy of Medical Sciences, 169 Splaiul Independentei, Bucharest 050098, Romania and Department of Enzymology, Institute of Biochemistry of the Romanian Academy, Splaiul Independentei 296, Bucharest 060031, Romania 4 Departamento de Bioquímica y Biología Molecular I, Universidad Complutense Madrid, 28040 Madrid, Spain and Centro de Astrobiologıa (CSIC-INTA), Carretera de Ajalvir, Km 4, 28850 Torrejon de Ardoz, Madrid, Spain 5 Institute of Functional Genomics, University of Regensburg, Josef-Engert Strasse 9, 93053 Regensburg, Germany Abstract We introduce systematic approaches to chemical kinetics based on the use of phase-phase expansions. The approaches follow from the observation that mass action law kinetics displays a linear dependence in a phase-phase (log-log) representation, which is a first order approximation of a regular (or functional) series expansion. For slow processes, such a representation leads to a corrected form of the mass-action law, where the concentrations are replaced by kinetic activities. For fast reactions delay expressions are derived. A generic mechanism is introduced for the occurrence of a generalized mass- action law as a result of self-similar recycling. The approaches are applied to a biological problem of major medical interest, blood coagulation. We show that our self-similar recycling model applied to the first stage of in vitro coagulation reproduces the empirical equations for the International Normalized Ratio calibration, (INR), as well as the Watala, Golanski and Kardas relation (WGK) for dependence of the INR on the concentrations of coagulation factors. Conversely, experimental results, without use of a theoretical model, show that the calibration equation for the INR, combined with the empirical WGK relation, leads to a generalized mass-action type kinetic law for the onset of ‘in vitro’ blood coagulation.