Swapping in lattice-based cell migration models

Shahzeb Raja Noureen; Jennifer P. Owen; Richard L Mort; Christian A. Yates

doi:10.1103/PhysRevE.107.044402

Swapping in lattice-based cell migration models

Shahzeb Raja Noureen, Jennifer P. Owen, Richard L Mort, Christian A. Yates

Lancaster University

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Abstract

Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can `swap' its position with another agent in its neighbourhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyse the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.

Original language	English
Article number	044402
Journal	Physical Review E
Volume	107
Early online date	27 Apr 2023
DOIs	https://doi.org/10.1103/PhysRevE.107.044402
Publication status	Published - 30 Apr 2023

Bibliographical note

Shahzeb Raja Noureen is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1. This research made use of the Balena High Performance Computing (HPC) Service at the University of Bath. The images in Figure 1 were taken by Dr. Matthew Ford (Centre for Research in Reproduction and Development, McGill, Canada). Richard Mort was supported by North West Cancer
Research (NWCR Grant CR1132) and the NC3Rs (NC3Rs grant NC/T002328/1). We would like to thank the members of Christian Yates’ mathematical biology reading group for constructive and helpful comments on a preprint of this paper. Finally, we would like to thank Fraser Waters for his help in managing some of the code related to this project.

Funding

S.R.N. is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the Project No. EP/S022945/1. This research made use of the Balena High Performance Computing (HPC) Service at the University of Bath. The images in Fig. were taken by Dr. Matthew Ford (Centre for Research in Reproduction and Development, McGill, Canada). R.M. was supported by North West Cancer Research (NWCR Grant No. CR1132) and the NC3Rs (NC3Rs Grant No. NC/T002328/1). We thank the members of Christian A. Yates' mathematical biology journal club for constructive and helpful comments on a preprint of this paper. Finally, we thank Fraser Waters for his help in managing some of the code related to this project.

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10.1103/PhysRevE.107.044402

author_accepted_msAccepted author manuscript, 4.89 MBLicence: CC BY

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title = "Swapping in lattice-based cell migration models",

abstract = "Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can `swap' its position with another agent in its neighbourhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyse the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.",

author = "{Raja Noureen}, Shahzeb and Owen, {Jennifer P.} and Mort, {Richard L} and Yates, {Christian A.}",

note = "Shahzeb Raja Noureen is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1. This research made use of the Balena High Performance Computing (HPC) Service at the University of Bath. The images in Figure 1 were taken by Dr. Matthew Ford (Centre for Research in Reproduction and Development, McGill, Canada). Richard Mort was supported by North West Cancer Research (NWCR Grant CR1132) and the NC3Rs (NC3Rs grant NC/T002328/1). We would like to thank the members of Christian Yates{\textquoteright} mathematical biology reading group for constructive and helpful comments on a preprint of this paper. Finally, we would like to thank Fraser Waters for his help in managing some of the code related to this project.",

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N2 - Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can `swap' its position with another agent in its neighbourhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyse the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.

AB - Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can `swap' its position with another agent in its neighbourhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyse the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.

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Swapping in lattice-based cell migration models

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