Stochastic modeling of high-molecular substances electrophoresis using the Ornstein-Uhlenbeck process
Journal Title: Комп’ютерне моделювання: аналіз, управління, оптимізація - Year 2018, Vol 2, Issue 2
Abstract
The aim of the work is to develop a statistical model in the form of the Ornstein-Uhlenbeck trend process for describing the electrophoresis of high-molecular substances. The ability of electrophoresis to divide charged biological macromolecules is widely used in scientific research, chemical production and medicine. Despite the use of the molecular-kinetic theory for estimation of the coefficients of the electrophoretic mobility in the form of the stochastic Langevin equation and the Einstein-Smoluchowski relations emerging from it, which takes into account the Brownian motion of particles of the medium, these models remain deterministic. Such models do not allow one to achieve the required accuracy in the description of electrophoresis of high-molecular substances, especially when analyzing their differences. The Ornstein-Uhlenbeck process is the only non-trivial stationary Gaussian Markov process and has the property of returning to the average. This contributed to its use in financial engineering. At present, the Ornstein-Uhlenbeck process has been studied quite deeply and various modifications and generalizations are of interest, in particular the Ornstein-Uhlenbeck trend process. The Ornstein-Uhlenbeck trend process describes a stochastic process that deviates from the deterministic trend and returns to it with a speed proportional to the deviation. Deterministic trend, as a rule, contains several parameters that must be estimated from observational data. In well-known works on modeling the motion of dielectrics, such an estimate is carried out by well-known statistical methods, for example, by method of moments or maximum likelihood estimation. In the case of electrophoresis, we propose to adopt a linear trend with a coefficient proportional to the electrolytic mobility of the substance in a given environment as a deterministic trend. Statistical processing of experimental data makes it possible to obtain parameter estimates, which allows stochastically simulating the process of electrophoresis. The shape of the electrophoresis model has been determined, and methods have been developed for calculating the parameters of the obtained model according to the data of an experiment on the separation of proteins.
Authors and Affiliations
В. І. Олевський, Ю. Б. Олевська
Keywords
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- EP ID EP610389
- DOI 10.32434/2521-6406-2018-4-2-60-64
- Views 134
- Downloads 0
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