A prediction of mRNA hybridization kinetics based on polypeptide abundances

An oscillating chemical reaction dealt with in this paper is the Brusselator, which is capable of generating a limit cycle oscillation beyond instability point. The rate equations of this reaction scheme are solved by two-time scale method. An evolution criterion is derived for the limit cycle to first order approximation. The time average of entropy change over the period of the limit cycle takes a definite negative value, which is dependent not on the initial conditions but on the external parameters bringing the kinetic behaviour of the system under control. It can be expressed as the product of two quantities. The first, which is kinetic in character, is the areal velocity of the limit cycle. The second, which is thermodynamic in character, is the rotation of anti-symmetric flow with respect to thermodynamic force. It is shown that the latter is equivalent to the irreversible circulation of fluctuation.