Probabilistic model of the chain-like structures' translocation through the pore in membrane

• Autorzy: Bartłomiejczyk K.

Identyfikatory

DOI

10.17512/jamcm.2015.4.01

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the analysis of the translocation of the chain-like structures (CLS) through the pore in membrane. It focuses on the so-called passage time and the principal aim is to propose a proper probabilistic model for its distribution. The article starts with some preliminary results concerning stochastic processes. Next, an approximate analytic solution of the considered problem that was received in literature is presented. It is known that the resulting probability distribution of the passage time manifests some important shortcomings. Thus it is important to find a reasonable alternative. It is argued here that the beta Moyal probability distribution can be a good candidate for approximation of the theoretical distribution in various interesting situations. In this paper, two different problems connected with CLS translocation are considered. For both problems the theoretical distributions are known from literature and in both situations the beta Moyal approximations turn out to be very satisfactory.

Słowa kluczowe

EN

Fokker-Planck equation; translocation of chain-like structure; stochastic process; beta Moyal probability distribution

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 4
• Strony: 5--10
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Bartłomiejczyk K.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

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• [4] Polson J.M., Polymer translocation into and out of an ellipsoidal cavity, Journal of Chemical Physics 2015, 142(17), 174903.
• [5] Żurek S., Kośmider M., Drzewiński A., van Leeuwen J.M.J., Translocation of polymers in a lattice model, The European Phys. J. E: Soft Matter and Biological Physics 2012, 35, 47.
• [6] Kosztołowicz T., Lewandowska K.D., Stochastyczny model dyfuzji w układzie membranowym, Metody Matematyczne w Zastosowaniach 2014, 2, 153-174.
• [7] Grzybowski A., Puchała P., Remarks about discrete Young measures and their Monte Carlo simulation, Journal of Applied Mathematics and Computational Mechanics 2015, 14(2), 13-20.
• [8] Grzybowski A.Z., Domański Z., A sequential algorithm with built in tension-propagation mechanism for modeling the chain-like bodies dynamics, arXiv:1312.4206 [cond-mat.soft].
• [9] Cordeiro G.M., Nobre J.S., Pescim R.R., Ortega E.M.M., The beta Moyal: A useful-skew distribution, International Journal of Research and Reviews in Applied Sciences 2012, 10(2), 171-192.