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Modelling Collective Cytoskeletal Transport and Intracellular Traffic

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The Impact of Applications on Mathematics

Part of the book series: Mathematics for Industry ((MFI,volume 1))

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Abstract

Biological cells require active fluxes of matter to maintain their internal organization and perform multiple tasks to live. In particular they rely on cytoskeletal transport driven by motor proteins, ATP-fueled molecular engines, for delivering vesicles and biochemically active cargoes inside the cytoplasm. Experimental progress allows nowadays quantitative studies describing intracellular transport phenomena down to the nanometric scale of single molecules. Theoretical approaches face the challenge of modelling the multiscale, out-of-equilibrium and non-linear properties of cytoskeletal transport: from the mechanochemical complexity of a single molecular motor up to the collective transport on cellular scales. We will present some of our recent progress in building a generic modelling scheme for cytoskeletal transport based on lattice gas models called “exclusion processes”. Interesting new properties arise from the emergence of density inhomogeneities of particles along the network of one dimensional lattices. Moreover, understanding these processes on networks can provide important hints for other fundamental and applied problems such as vehicular, pedestrian and data traffic, or ultimately for technological and biomedical applications.

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Notes

  1. 1.

    The typical energy scale is \(1~k_BT \sim 4\times 10^{-21}~\mathrm{J}\) with \(k_B \simeq 1,38 \times 10^{-23}~\mathrm{J}/\mathrm{K}\) is the Boltzmann constant and \(T \simeq 300~\mathrm{K}\) is the absolute temperature in Kelvin units.

  2. 2.

    Note that in TASEP-LK such a condition is relaxed since particles can enter and leave the system at any site due to the binding/unbinding Langmuir process.

  3. 3.

    In the effective rates \(\alpha _{v,eff}\) and \(\beta _{v,eff}\) we keep the explicit dependence on the jump rate \(p\).

  4. 4.

    A detailed analysis, for large values of the connectivity can be found in the supplementary material of ref. [11].

  5. 5.

    The current distribution \(W(j_s)\) remains monomodal (see the inset in Fig. 5) since the current is globally invariant under the particle-hole symmetry.

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Acknowledgments

The authors thank the European Molecular Biology Organization (EMBO), the Centre National de la Recherche Scientifique (CNRS), the National Agency for Research (ANR), the Program of Laboratory of Excellence (LabEx) NUMEV and the Scientific Council of the University of Montpellier 2 for the financial support obtained during these years. We acknowledge the interesting discussions we had on these topics in these years with A. Abrieu, C. Appert, P. Arndt, B. Bassetti, P. Benetatos, M. Bornens, C. Braun-Breton, S. Camalet, G. Cappello, L. Ciandrini, M. Cosentino-Lagomarsino, N. Crampe, O. Dauloudet, S. Diez, J. Dorignac, A. Dunn, B. Embley, M. Evans, T. Franosch F. Geniet, J. Howard, K. Kroy, J.F. Joanny, F. Jülicher, K. Kruse, C. Leduc, M. Lefranc, V. Lorman, P. Malgaretti, K. Mallick, P. Montcourrier, B. Mulder, I. Pagonabarraga, A. Parmeggiani, P. Pierobon, J. Prost, O. Radulescu, A. Raguin, C.M. Romano, E. Sackmann, J. Santos, K. Sasaki, C.F. Schmidt, G.M. Schütz, K. Sekimoto, J. Spudich, F. Turci, C. Vanderzande and M. Wakayama. N.K. and A.P. would like to thank B. Embley for his contribution in the study of TASEP on small networks. In particular, A.P. specially thanks E. Frey for the opportunity to work on exclusion processes for motor protein transport and for the many important and insightful discussions they had on the topic, together with T. Franosch, some years ago.

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Authors and Affiliations

  1. L2C, UMR 5221 CNRS, Université Montpellier 2, Pl. E. Bataillon, 34095, Montpellier Cedex 5, France

    Andrea Parmeggiani, Izaak Neri & Norbert Kern

  2. DIMNP, UMR 5235 CNRS, Université Montpellier 2 et Montpellier 1, Montpellier Cedex 5, France

    Andrea Parmeggiani

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  1. Andrea Parmeggiani
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Editors and Affiliations

  1. Institute for Mathematics and Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama

  2. CSIRO (Commonwealth Scientific and Industrial Research Organisation), Canberra, Aust Capital Terr, Australia

    Robert S. Anderssen

  3. School of Mathematical Sciences, Fudan University, Shanghai, China

    Jin Cheng

  4. Kyushu University, Fukuoka, Japan

    Yasuhide Fukumoto

  5. Institute of Natural and Mathematical Sciences, Massey University, Palmerston North, Auckland, New Zealand

    Robert McKibbin

  6. Institute of Mathematics, Free University of Berlin, Berlin, Germany

    Konrad Polthier

  7. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  8. Department of Mathematics, National University of Singapore, Singapore, Singapur, Singapore

    Kim-Chuan Toh

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Parmeggiani, A., Neri, I., Kern, N. (2014). Modelling Collective Cytoskeletal Transport and Intracellular Traffic. In: Wakayama, M., et al. The Impact of Applications on Mathematics. Mathematics for Industry, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54907-9_1

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