Probabilistic kinetic model of slow oxidation of low-density lipoprotein: I. Theory

The microscopic probabilistic model has been introduced to explain the kinetics of very slow oxidation of low-density lipoprotein (LDL) from human plasma. The LDL oxidation, carried out in very unfavorable conditions, is assumed to be initiated by the traces of the transition-metal ions associated with the lipoprotein. The substrates for the metal-ion attack are alpha-tocopherol and the pre-formed lipid hydroperoxide. The theory assumes oscillation of the metal ions and alpha-tocopherol from the oxidized to the reduced states. In this model alpha-tocopherol acts as a pro-oxidant. The entire oxidation process consists of rare bursts of events in individual LDL particles. The reactions within the particles are treated in terms of probabilities of individual active species to participate in a specified reaction. The circular flow of the radical reactions could be visualized as circular flow of microscopic probabilities. The empirical, macroscopic quantities are quantitatively related with the microscopic probabilities, determined by a set of five adjustable parameters. The differential equations describing the initial radical generation rate and the rates of change of concentration of oxygen, hydroperoxide, co-antioxidant and trapped radicals in an LDL system are numerically solved in a finite difference approach.