A statistical model of macromolecules dynamics for Fluorescence Correlation Spectroscopy data analysis

Dmitri Koroliouk; Vladimir Semenovich Koroliuk; Eleonora Nicolai; Paolo Bisegna; Lorenzo Stella; Nicola Rosato

doi:10.19139/soic.v4i3.219

Dmitri Koroliouk Institute of Telecommunications and Global Information Space of Ukrainian Acad. Sciences, Kiev, Ukraine
Vladimir Semenovich Koroliuk Institute of Mathematics of Ukrainian Acad. Sciences, Kiev, Ukraine
Eleonora Nicolai Department of Experimental Medicine and Surgery, University of Rome Tor Vergata, 00133 Rome, Italy
Paolo Bisegna Department of Civil Engineering, University of Rome Tor Vergata, 00133 Rome, Italy
Lorenzo Stella Department of Science and Chemical Technology, University of Rome Tor Vergata
Nicola Rosato Department of Experimental Medicine and Surgery, University of Rome Tor Vergata, 00133 Rome, Italy

DOI: https://doi.org/10.19139/soic.v4i3.219

Keywords: FCS, Brownian motion, Discrete Markov diffusion, Protein diffusion

Abstract

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 the mathematical description of collective biological reactions. This paper presents the mathematical model and its verification on a simulated data set, obtained on the basis of the well-known Stokes-Einsteinmodel. In particular, we considered several mix of particles of different diffusion coefficient, respectively: D1=10 mm2/sec and D2=100 mm2/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 the mix of particles with different diffusion coefficient, the proposed model parameters (regression) and (square variance of the stochastic component) have a good discriminative ability for the molar fraction determination. 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-Einsteinmodel. In particular we considered several mix of particles of different diffusion coefficient, respectively: D1=10 mm2/sec and D2=100 mm2/sec. The parameters evaluated by this new mathematical model on simulated data, show good estimation accuracy, in comparison with the a-priori parameters used in the simulations. Furthermore, when analyzing the data for mix of particles with different diffusion coefficient, the proposed model parameters (regression) and (square variance of stochastic component) have a good discriminative ability for the molar fraction determination.

Author Biographies

Dmitri Koroliouk, Institute of Telecommunications and Global Information Space of Ukrainian Acad. Sciences, Kiev, Ukraine

Full Professor,Senior Researcher

Vladimir Semenovich Koroliuk, Institute of Mathematics of Ukrainian Acad. Sciences, Kiev, Ukraine

Full Professor,Academician of Ukrainian Academy of Sciences

Eleonora Nicolai, Department of Experimental Medicine and Surgery, University of Rome Tor Vergata, 00133 Rome, Italy

Researcher

Paolo Bisegna, Department of Civil Engineering, University of Rome Tor Vergata, 00133 Rome, Italy

Full Professor

Lorenzo Stella, Department of Science and Chemical Technology, University of Rome Tor Vergata

Associate ProfessorAssociate Professor

Nicola Rosato, Department of Experimental Medicine and Surgery, University of Rome Tor Vergata, 00133 Rome, Italy

Full Professor

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