A statistical model of macromolecules dynamics for fluorescence correlation spectroscopy data analysis

In this paper we propose a new mathematical model to describe the mechanisms of biological macromolecules interactions. Our model consists of a discrete stationary random sequence given by a solution of difference stochastic equation, characterized by a drift predictive component and by a diffusion term. The relative statistical estimations are very simple and effective, promising to be a good tool for mathematical description of collective biological reactions. This paper presents the mathematical model and its verification on simulated data set, obtained on the basis of the well-known Stokes-Einstein model. In particular we considered several mix of particles of different diffusion coefficient, respectively: D1 = 10µm2 /sec and D2 = 100µm2 /sec. The parameters evaluated by this new mathematical model on simulated data, show good estimation accuracy, in comparison with the prior parameters used in the simulations. Furthermore, when analyzing the data for mix of particles with different diffusion coefficient, the proposed model parameters V (regression) and σ 2 (square variance of stochastic component) have a good discriminative ability for the molar fraction determination.