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Mathematical Medicine and Biology 2005 22(1):1-14; doi:10.1093/imammb/dqh018
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© The Author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

Optimality principle and determination of kinetic constants for biochemical reactions

Kirill V. Tyurin * and Michael A. Khanin §

Mathematical Modelling Laboratory, Centre for Theoretical Problems of Physico-Chemical Pharmacology, Russian Academy of Sciences, Moscow 123060, Marshal Konev Str. 16/34, Russia  *

An optimality principle is applied to determine kinetic constants for biochemical (enzymatic and second-order) reactions involved in a physiological system, a minimum protein consumption criterion being adopted. A direct optimization problem is to determine optimal zymogen concentrations. An ‘inverse’ optimization problem is also considered; this problem is to determine the kinetic constants for the biochemical reactions involved in a physiological system such that the optimal and observed zymogen and procofactor concentrations coincide. In solving an ‘inverse’ optimization problem we assume that the scheme of biochemical reactions and zymogen and procofactor concentrations are known. Good agreement is observed between the model results for the extrinsic blood coagulation pathway and relevant biochemical data.

The proposed method is also applicable to determining kinetic constants for other physiological biochemical-reaction systems.

Keywords: kinetic constant determination; clotting factor activation; inverse optimization problem

Received on 8 June 2002. revised on 28 June 2004.

* Email: kvt{at}aha.ru

§ Email: khanin{at}softel.ru


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