caa a22 4500 605519471 CHVBK 20210128100730.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s11009-013-9372-5 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9372-5 A Quasi Random Walk to Model a Biological Transport Process [Elektronische Daten] [Peter Keller, Sylvie Rœlly, Angelo Valleriani] Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V. Springer Science+Business Media New York, 2013 Molecular motor nationallicence Kinesin V nationallicence Birth-and-death process nationallicence Markov Chain nationallicence Quasi Random Walk nationallicence Keller Peter School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, EH9 3JZ, Edinburgh, Scotland aut Rœlly Sylvie Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany aut Valleriani Angelo Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Abteilung Theorie & Bio-Systeme, Wissenschaftspark Potsdam-Golm, 14424, Potsdam, Germany aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 125-137 1387-5841 17:1<125 2015 17 11009 https://doi.org/10.1007/s11009-013-9372-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9372-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Keller Peter School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, EH9 3JZ, Edinburgh, Scotland aut NATIONALLICENCE 700 1- Rœlly Sylvie Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany aut NATIONALLICENCE 700 1- Valleriani Angelo Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Abteilung Theorie & Bio-Systeme, Wissenschaftspark Potsdam-Golm, 14424, Potsdam, Germany aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 125-137 1387-5841 17:1<125 2015 17 11009