Computation of Diffusion Limited Controlled Actions for Gene Regulating Repressor Particles

Abstract

Temporal changes in association anddissociation kinetics of the repressor –operator reaction were simulated by a computational approach using MATOLABO on the basis of strict mathematical description. The diffusion equation of a repressor particle has been combinedwith arrival probabilities of therepressor particle. Temporal behaviors of the repressor operator complex have been computed by inverting the Laplace transformed equations. The temporal kinetic data of association anddissociation obtained at differentionic strength and at different DNA length were successfully simulated. Those results could be achieved byregulating diffusion constants inmedium on the DNA, a reaction radius of the repressor and a reaction rate per one repressor on the reaction sphere surface, k value. The reported values of association rate constant ka obtained at different ionic strength were also successfully simulated. Amongthe regulated parameters to get these successful simulations, the reaction rate per one particle on the reaction sphere surface, k value has effectiveinfluences on the association anddissociation kinetics particularly those at varying ionic strength that were induced by high KCl condition. By an electro chemical consideration for thechange of k value in combinationwith the screening effects of counter ions around the repressor particle and the DNA molecule, the most effectivefactor seems to be the Coulombrepulsive forces and or Londondispersion forces. The sliding mechanism for facilitated translocation of a repressor protein ona DNA chain can be described by the present mathematical approach which describes the temporal changes in amounts of the species. To achieve such mechanism in varying ionic strength,the secondary changes in the diffusion constants, the reaction radius and the reaction rate per one particle on thereaction sphere surface k value (anelectro chemical factor) seemed to have important roles.