TY - JOUR
T1 - Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions
AU - Jin, Wang
AU - Penington, Catherine J.
AU - McCue, Scott W.
AU - Simpson, Matthew J.
PY - 2016/10/7
Y1 - 2016/10/7
N2 - Two-dimensional collective cell migration assays are used to study
cancer and tissue repair. These assays involve combined cell migration
and cell proliferation processes, both of which are modulated by
cell-to-cell crowding. Previous discrete models of collective cell
migration assays involve a nearest-neighbour proliferation mechanism
where crowding effects are incorporated by aborting potential
proliferation events if the randomly chosen target site is occupied.
There are two limitations of this traditional approach: (i) it seems
unreasonable to abort a potential proliferation event based on the
occupancy of a single, randomly chosen target site; and, (ii) the
continuum limit description of this mechanism leads to the standard
logistic growth function, but some experimental evidence suggests that
cells do not always proliferate logistically. Motivated by these
observations, we introduce a generalised proliferation mechanism which
allows non-nearest neighbour proliferation events to take place over a
template of r ≥ 1 concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather
than dealing with the occupancy of a single randomly chosen site.
Analysing the continuum limit description of the stochastic model shows
that the standard logistic source term, λC (1 - C), where λ is the proliferation rate, is generalised to a universal growth function, λC f(C). Comparing the solution of the continuum description with averaged
simulation data indicates that the continuum model performs well for
many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.
AB - Two-dimensional collective cell migration assays are used to study
cancer and tissue repair. These assays involve combined cell migration
and cell proliferation processes, both of which are modulated by
cell-to-cell crowding. Previous discrete models of collective cell
migration assays involve a nearest-neighbour proliferation mechanism
where crowding effects are incorporated by aborting potential
proliferation events if the randomly chosen target site is occupied.
There are two limitations of this traditional approach: (i) it seems
unreasonable to abort a potential proliferation event based on the
occupancy of a single, randomly chosen target site; and, (ii) the
continuum limit description of this mechanism leads to the standard
logistic growth function, but some experimental evidence suggests that
cells do not always proliferate logistically. Motivated by these
observations, we introduce a generalised proliferation mechanism which
allows non-nearest neighbour proliferation events to take place over a
template of r ≥ 1 concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather
than dealing with the occupancy of a single randomly chosen site.
Analysing the continuum limit description of the stochastic model shows
that the standard logistic source term, λC (1 - C), where λ is the proliferation rate, is generalised to a universal growth function, λC f(C). Comparing the solution of the continuum description with averaged
simulation data indicates that the continuum model performs well for
many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.
KW - cell proliferation
KW - cell migration
KW - collective cell migration assay
KW - exclusion process
KW - mean field
KW - logistic growth
KW - generalised logistic growth
UR - http://www.scopus.com/inward/record.url?scp=84994507715&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP140100249
UR - http://purl.org/au-research/grants/arc/FT130100148
U2 - 10.1088/1478-3975/13/5/056003
DO - 10.1088/1478-3975/13/5/056003
M3 - Article
C2 - 27716634
VL - 13
SP - 1
EP - 11
JO - Physical Biology
JF - Physical Biology
SN - 1478-3967
IS - 5
M1 - 056003
ER -