@article{Koroliouk_Koroliuk_Nicolai_Bisegna_Stella_Rosato_2016, title={A statistical model of macromolecules dynamics for Fluorescence Correlation Spectroscopy data analysis}, volume={4}, url={http://iapress.org/index.php/soic/article/view/20160903}, DOI={10.19139/soic.v4i3.219}, abstractNote={<p class="Style3" style="line-height: 150%; mso-pagination: widow-orphan;"><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">In this paper, we propose a new mathematical model to describe the mechanisms of biological</span></span><span class="FontStyle31"><em><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: IT; mso-fareast-language: EN-US;" lang="IT"> macromolecules interactions</span></em></span><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">. Our model consists of a discrete stationary random sequence given <span style="letter-spacing: 1.5pt;">by</span> a solution of difference stochastic equation, characterized <span style="letter-spacing: 1.5pt;">by a </span>drift predictive component and <span style="letter-spacing: 1.5pt;">by a</span> 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-Einstein</span></span><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">model. In particular, we considered several mix of particles of different diffusion coefficient, respectively: D<sub>1</sub>=10 </span></span><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: Symbol; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-char-type: symbol; mso-symbol-font-family: Symbol;" lang="EN-US">m</span></span><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">m<sup>2</sup>/sec and D<sub>2</sub>=100 </span></span><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: Symbol; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-char-type: symbol; mso-symbol-font-family: Symbol;" lang="EN-US">m</span></span><span class="FontStyle28"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">m<sup>2</sup>/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. </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">Furthermore, when analyzing the data </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: IT; mso-fareast-language: EN-US;" lang="IT">for the </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">mix of particles with different diffusion coefficient, the proposed model parameters </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US"> (regression) and </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US"> </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">(square variance of the stochastic component) have a good discriminative </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: IT; mso-fareast-language: EN-US;" lang="IT">ability </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">for the molar fraction determination.  </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">In this paper, we propose a new mathematical model to describe the mechanisms of biological</span></span><span class="FontStyle31" style="line-height: 150%; font-size: 10px;"><em><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: IT; mso-fareast-language: EN-US;" lang="IT"> macromolecules interactions</span></em></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">. Our model consists of a discrete stationary random sequence given <span style="letter-spacing: 1.5pt;">by</span> a solution of difference stochastic equation, characterized <span style="letter-spacing: 1.5pt;">by a </span>drift predictive component and <span style="letter-spacing: 1.5pt;">by a</span> 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</span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">model. In particular we considered several mix of particles of different diffusion coefficient, respectively: D<sub>1</sub>=10 </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: Symbol; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-char-type: symbol; mso-symbol-font-family: Symbol;" lang="EN-US">m</span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">m<sup>2</sup>/sec and D<sub>2</sub>=100 </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: Symbol; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-char-type: symbol; mso-symbol-font-family: Symbol;" lang="EN-US">m</span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">m<sup>2</sup>/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. </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">Furthermore, when analyzing the data </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: IT; mso-fareast-language: EN-US;" lang="IT">for </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: ’Courier New’; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">mix of particles with different diffusion coefficient, the proposed model parameters </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US"> (regression) and </span></span><span class="FontStyle28" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US"> </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">(square variance of stochastic component) have a good discriminative </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: IT; mso-fareast-language: EN-US;" lang="IT">ability </span></span><span class="FontStyle33" style="line-height: 150%; font-size: 10px;"><span style="font-size: 10.0pt; line-height: 150%; font-family: ’Calibri’,’sans-serif’; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US;" lang="EN-US">for the molar fraction determination. </span></span></p&gt;}, number={3}, journal={Statistics, Optimization & Information Computing}, author={Koroliouk, Dmitri and Koroliuk, Vladimir Semenovich and Nicolai, Eleonora and Bisegna, Paolo and Stella, Lorenzo and Rosato, Nicola}, year={2016}, month={Aug.}, pages={233-242} }