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Kinetic models with non-local sensing determining cell polarization and speed according to independent cues

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Abstract

Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics. We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.

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Acknowledgements

This work was partially supported by Istituto Nazionale di Alta Matematica, Ministry of Education, Universities and Research, through the “MIUR grant Dipartimenti di Eccellenza 2018-2022”, Project no. E11G18000350001 and Compagnia San Paolo that finances NL Ph.D. scholarship.

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  1. Department of Mathematical Sciences “G. L. Lagrange”, Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    Nadia Loy & Luigi Preziosi

  2. Department of Mathematics “G. Peano”, Via Carlo Alberto 10, 10123, Turin, Italy

    Nadia Loy

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  1. Nadia Loy
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  2. Luigi Preziosi
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Correspondence to Luigi Preziosi.

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Loy, N., Preziosi, L. Kinetic models with non-local sensing determining cell polarization and speed according to independent cues. J. Math. Biol. 80, 373–421 (2020). https://doi.org/10.1007/s00285-019-01411-x

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