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Recent Mathematical Models of Axonal Transport

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Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

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Abstract

An axon is a long thin projection of a neuron that allows for rapid electrochemical communications with other cells over long distances. Axonal transport refers to the stochastic, bidirectional movement of organelles and proteins along cytoskeletal polymers inside an axon, powered by molecular motor proteins. The movement from the cell body to the axon terminal is called anterograde transport and the movement in the opposite direction is called retrograde transport. Axonal transport is a vital process for the axon to survive and maintain its regular shape. Mathematical models have been developed to help understand how cargoes are transported inside an axon and how impairment of axonal transport affects cargo distribution. In this chapter, we review recent mathematical models of axonal transport and discuss open problems in this area.

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Acknowledgements

This research was supported by US NSF DMS 1312966 and US NSF CAREER Award 1553637. CX was also supported by the Mathematical Biosciences Institute as a long-term visitor.

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  1. Department of Mathematics, Ohio State University, Columbus, OH, USA

    Chuan Xue

  2. Biophysics Graduate Program, Ohio State University, Columbus, OH, USA

    Gregory Jameson

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Correspondence to Chuan Xue .

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    David Holcman

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Xue, C., Jameson, G. (2017). Recent Mathematical Models of Axonal Transport. In: Holcman, D. (eds) Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-62627-7_12

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