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Direction-dependent turning leads to anisotropic diffusion and persistence

Part of: Physiological, cellular and medical topics Equations of mathematical physics and other areas of application Miscellaneous applications of functional analysis

Published online by Cambridge University Press:  23 June 2021

N. LOY Open the ORCID record for N. LOY [Opens in a new window] ,
T. HILLEN  and
K. J. PAINTER
N. LOY
Affiliation:
Department of Mathematical Sciences “G.L. Lagrange”, Politecnico di Torino, C.so Duca degli Abruzzi, 24 Torino, Italy emails: [email protected]
T. HILLEN
Affiliation:
Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB, Canada email: [email protected]
K. J. PAINTER
Affiliation:
Interuniversity Department of Regional and Urban Studies and Planning, Politecnico di Torino, Viale Pier Andrea Mattioli, 39, Torino, Italy email: [email protected]
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Abstract

Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains.

Keywords

Cell migrationBoltzmann equationpersistencedirection-dependent turning ratemacroscopic limits

MSC classification

Primary: 35Q92: PDEs in connection with biology and other natural sciences
Secondary: 92C17: Cell movement (chemotaxis, etc.) 46N60: Applications in biology and other sciences 35Q20: Boltzmann equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 4 , August 2022 , pp. 729 - 765
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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