Characterization of local physical field produced by high density gene regulation particles

A mathematical method was introduced to characterize the thermodynamical properties of the biomolecular reaction field composed of high density gene regulating biomolecular particles. The method was originally proposed by Haris and Rice (1959, 1960). The Boltzmann equation was modified by a coarse graining and the pair transition probability was introduced to the kernel of the integral part of the Boltzmann equation. The post collision distribution function was expressed by the local equilibrium distribution function and the perturbation. The perturbed solution was expressed by the Sonine polynomials. The coefficients were given by solving three sets of 8 linear algebraic equations. By these procedures, we derived the transport equations and computed the diffusion coefficient, shear stress and heat flux. The present method is available for characterizing the local biophysical field at high density molecules.