Abstract
Motivated by the recent experimental observations on clustering of motor proteins on microtubule filament, we study an open system of two parallel totally asymmetric simple exclusion processes under asymmetric coupling conditions, which incorporates the mutual interaction with the surrounding environment through Langmuir Kinetics (LK) in both the lanes. In the modified LK, the attachment and detachment rates depends on the configuration of nearest neighboring sites. We analyse the model within the framework of continuum mean-field theory and the phase diagrams along with density profiles are obtained using boundary layer analysis. The effect of mutual interactions on the phase diagram for two different situations of attachment and detachment (LK) rates is discussed. Under the symmetric LK dynamics, the topological structure of the phase diagram remains similar to the one in without mutual interaction; while for the antisymmetric case, after a certain critical value of attractive/repulsive mutual attraction, significant changes are found in the qualitative nature of phase diagram. Moreover, it is shown that the type of mutual interaction affects the dynamic properties of motor proteins. The theoretical findings are examined by extensive Monte-Carlo simulations.
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Celis-Garza, D., Teimouri, H., Kolomeisky, A.B.: Correlations and symmetry of interactions influence collective dynamics of molecular motors. J. Stat. Mech. 2015(4), P04013 (2015)
Chandel, S., Chaudhuri, A., Muhuri, S.: Collective transport of weakly interacting molecular motors with Langmuir kinetics. EPL (Europhys. Lett.) 110(1), 18002 (2015)
Chowdhury, D.: Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist’s perspective. Phys. Rep. 529(1), 1–197 (2013)
Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329(4), 199–329 (2000)
Derrida, B., Evans, M., Hakim, V., Pasquier, V.: Exact solution of a 1D asymmetric exclusion model using a matrix formulation. J. Phys. A 26(7), 1493 (1993)
Dhiman, I., Gupta, A.K.: Effect of coupling strength on a two-lane partially asymmetric coupled totally asymmetric simple exclusion process with Langmuir kinetics. Phys. Rev. E 90(1), 012114 (2014)
Evans, M., Juhasz, R., Santen, L.: Shock formation in an exclusion process with creation and annihilation. Phys. Rev. E 68(2), 026117 (2003)
Frey, E., Parmeggiani, A., Franosch, T.: Collective phenomena in intracellular processes. Genome Inform. 15(1), 46–55 (2004)
Gupta, A.K., Dhiman, I.: Asymmetric coupling in two-lane simple exclusion processes with Langmuir kinetics: phase diagrams and boundary layers. Phys. Rev. E 89(2), 022131 (2014)
Howard, J.: Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Sunderland (2001)
Howard, J., Clark, R.: Mechanics of motor proteins and the cytoskeleton. Appl. Mech. Rev. 55, 39 (2002)
Jiang, R., Hu, M.B., Wu, Y.H., Wu, Q.S.: Weak and strong coupling in a two-lane asymmetric exclusion process. Phys. Rev. E 77(4), 041128 (2008)
Jiang, R., Wang, R., Wu, Q.S.: Two-lane totally asymmetric exclusion processes with particle creation and annihilation. Physica A 375(1), 247–256 (2007)
Katz, S., Lebowitz, J.L., Spohn, H.: Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors. J. Stat. Phys. 34(3–4), 497–537 (1984)
Kolomeisky, A.B.: Motor proteins and molecular motors: how to operate machines at the nanoscale. J. Phys. 25(46), 463101 (2013)
Kolomeisky, A.B., Schütz, G.M., Kolomeisky, E.B., Straley, J.P.: Phase diagram of one-dimensional driven lattice gases with open boundaries. J. Phys. A 31(33), 6911 (1998)
Krug, J.: Boundary-induced phase transitions in driven diffusive systems. Phys. Rev. Lett. 67(14), 1882 (1991)
Levine, E., Willmann, R.: Spontaneous symmetry breaking in a non-conserving two-species driven model. J. Phys. A 37(10), 3333 (2004)
MacDonald, C.T., Gibbs, J.H., Pipkin, A.C.: Kinetics of biopolymerization on nucleic acid templates. Biopolymers 6(1), 1–25 (1968)
Mirin, N., Kolomeisky, A.B.: Effect of detachments in asymmetric simple exclusion processes. J. Stat. Phys. 110(3–6), 811–823 (2003)
Mukherji, S., Mishra, V.: Bulk and surface transitions in asymmetric simple exclusion process: impact on boundary layers. Phys. Rev. E 74(1), 011116 (2006)
Neri, I., Kern, N., Parmeggiani, A.: Exclusion processes on networks as models for cytoskeletal transport. New J. Phys. 15(8), 085005 (2013)
Parmeggiani, A., Franosch, T., Frey, E.: Phase coexistence in driven one-dimensional transport. Phys. Rev. Lett. 90(8), 086601 (2003)
Parmeggiani, A., Franosch, T., Frey, E.: Totally asymmetric simple exclusion process with Langmuir kinetics. Phys. Rev. E 70(4), 046101 (2004)
Popkov, V., Rákos, A., Willmann, R.D., Kolomeisky, A.B., Schütz, G.M.: Localization of shocks in driven diffusive systems without particle number conservation. Phys. Rev. E 67(6), 066117 (2003)
Popkov, V., Schütz, G.M.: Steady-state selection in driven diffusive systems with open boundaries. EPL (Europhys. Lett.) 48(3), 257 (1999)
Privman, V.: Nonequilibrium Statistical Mechanics in One Dimension. Cambridge University Press, Cambridge (2005)
Pronina, E., Kolomeisky, A.B.: Two-channel totally asymmetric simple exclusion processes. J. Phys. A 37(42), 9907 (2004)
Pronina, E., Kolomeisky, A.B.: Asymmetric coupling in two-channel simple exclusion processes. Physica A 372(1), 12–21 (2006)
Roos, W.H., Campàs, O., Montel, F., Woehlke, G., Spatz, J.P., Bassereau, P., Cappello, G.: Dynamic kinesin-1 clustering on microtubules due to mutually attractive interactions. Phys. Biol. 5(4), 046004 (2008)
Schütz, G., Domany, E.: Phase transitions in an exactly soluble one-dimensional exclusion process. J. Stat. Phys. 72(1–2), 277–296 (1993)
Seitz, A., Surrey, T.: Processive movement of single kinesins on crowded microtubules visualized using quantum dots. EMBO J. 25(2), 267–277 (2006)
Sopasakis, A., Katsoulakis, M.A.: Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics. SIAM J. Appl. Math. 66(3), 921–944 (2006)
Teimouri, H., Kolomeisky, A.B., Mehrabiani, K.: Theoretical analysis of dynamic processes for interacting molecular motors. J. Phys. A 48(6), 065001 (2015)
Toroczkai, Z., Zia, R.: A model for electrophoresis of polymers with impurities: exact distribution for a steady state. Phys. Lett. A 217(2), 97–103 (1996)
Vilfan, A., Frey, E., Schwabl, F., Thormählen, M., Song, Y.H., Mandelkow, E.: Dynamics and cooperativity of microtubule decoration by the motor protein kinesin. J. Mol. Biol. 312(5), 1011–1026 (2001)
Vuijk, H., Rens, R., Vahabi, M., MacKintosh, F., Sharma, A.: Driven diffusive systems with mutually interactive Langmuir kinetics. Phys. Rev. E 91(3), 032143 (2015)
Wang, R., Jiang, R., Liu, M., Liu, J., Wu, Q.S.: Effects of Langmuir kinetics on two-lane totally asymmetric exclusion processes of molecular motor traffic. Int. J. Mod. Phys. C 18(09), 1483–1496 (2007)
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The author gratefully acknowledges the financial support from the Department of Science and Technology (DST), Government of India.
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Gupta, A.K. Collective Dynamics on a Two-Lane Asymmetrically Coupled TASEP with Mutually Interactive Langmuir Kinetics. J Stat Phys 162, 1571–1586 (2016). https://doi.org/10.1007/s10955-016-1463-6
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DOI: https://doi.org/10.1007/s10955-016-1463-6