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Mathematical model of self-organizing and adaptable intracellular transport network K.A. Novikov1, A.N. Gratchev2, J.G. Kzhyshkowska3, O.A. Melnichenko4, A.A. Romanyukha
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Moscow State University, Russian Federation, konst.novikov@gmail.com

Institute of Cancerogenesis, N.N. Blokhin Cancer Research Center, RAMS, Russian Federation, Moscow

alexei.gratchev@gmail.com
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Moscow Research Institute of General Pathology and Pathophysiology, Russian Federation, julia.kzhyshkowska@googlemail.com

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Novartis Pharma LLC, Russian Federation, Moscow olesya.melnichenko@gmail.com Institute of Numerical Mathematics Russian Academy of Sciences Russian Federation, Moscow eburg@inm.ras.ru

Last decade invest igat ions proved the importance of microtubules in viral entry into cell, atherosclerosis development , cancer therapy and nervous system diseases. Our aim is to reconstruct mechanisms that form intracellular transport network capable of adapt ive changes of cellular metabo lic state. We constructed a mathemat ical model of intracellular microtubular transport system self-organizat ion and cargo transfer, which is an extensio n of the model o f microtubule self-organizat ion in melanophores [1]. Our model is a co mbinat ion of two coupled blocks: agent-based and cont inuous ones. Agent-based block direct ly simulate individual microtubule dynamics: nucleat ion (new microtubule birth), polymerizat ion, depo lymerizatio n and death. Individual microtubule end dynamics and stabilizat ion factors result in transport network format ion and this process is called self-organizat ion. The general feature of transport network is defined by localizat ion of nucleat ion centers and membrane, which microtubule plus-ends are stabilized on. Cont inuous block embodied by partial different ial equat ion describing cargo transfer alo ng microtubule network, init ial and boundary condit io ns that describe endocytosis (positive flux) or zero flux through the cell membrane. The model was implemented with finite vo lumes method and direct simulat ions.

We simulated the experiment on intracellular endosome transport described in [2] and obtained the patterns similar to the original experiment that are posit ive correlat ion between total number of endosomes and mean distance from nucleus to endosomes, negative correlat ion between mean endoso me size and total number of endosomes, negat ive correlat ion between mean endoso me size and mean distance fro m nucleus. However, the mechanism o f endosome size dynamics has been studied insufficient ly. Thus we included an assumpt ion of cont inuous endosome size decrease . This assumption is based on a funct iona l link between endosome size and its distance fro m nucleus [2]. We also obtained general shape o f milt isect ion transport network with symmetric microtubule spat ial distribut ion. We currently consider the factors that influence microtubule stabilit y and growth direct ion cho ice. These factors result in preferable directions of microtubules in transport network in the living cell. 1. E. N. Cytrynbaum, V. Rodionov, A. Mogilner (2004) Computational model o f dynein-dependent self-organization of microtubule asters, Journal of Cell Science, 117: 13811397. 2. C. Collinet et al. (2010) Systems survey o f endoc ytosis by mult iparametric image analys is, Nature, 464:243249 3. K.A. Novikov, A.N. Gratchev, J.G. Kzhyshkowska, O.A. Melnichenko, A.A. Romanyukha (submitted to publication) Mathemat ical model o f intracellular vesicular transport over tubulin cytoskeleton, Mathematical Models and Computer Simulations.