Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

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Title: Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles
Authors: Carrillo, JA
Colombi, A
Scianna, M
Item Type: Journal Article
Abstract: The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters. The aim of the paper is to demonstrate how the concept of H-stability, deriving from statistical mechanics, can have important implications in this respect. For any given interaction kernel, it in fact allows to a priori predict the regions of the free parameter space that result in stable configurations of the system characterized by a finite and strictly positive minimal interparticle distance, which is fundamental when dealing with biological phenomena. The proposed analytical arguments are indeed able to restrict the range of possible variations of selected model coefficients, whose exact estimate however requires further investigations (e.g., fitting with empirical data), as illustrated in this paper by series of representative simulations dealing with cell colony reorganization, sorting phenomena and zebrafish embryonic development.
Issue Date: 21-Feb-2018
Date of Acceptance: 20-Feb-2018
ISSN: 0022-5193
Publisher: Elsevier
Start Page: 75
End Page: 91
Journal / Book Title: Journal of Theoretical Biology
Volume: 445
Copyright Statement: ©2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: Cell sorting
Cell-cell interactions
Interaction potentials
Nonlocal models
01 Mathematical Sciences
06 Biological Sciences
08 Information And Computing Sciences
Evolutionary Biology
Publication Status: Published
Conference Place: England
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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