Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Individual-based and continuum models of phenotypically heterogeneous
  growing cell populations   Existing studies comparing individual-based models of growing cell
populations and their continuum counterparts have mainly focused on homogeneous
populations, in which all cells have the same phenotypic characteristics.
However, significant intercellular phenotypic variability is commonly observed
in cellular systems. Therefore, we develop here an individual-based model for
the growth of phenotypically heterogeneous cell populations. In this model, the
phenotypic state of each cell is described by a structuring variable that
captures intercellular variability in cell proliferation and migration rates.
The model tracks the spatial evolutionary dynamics of single cells, which
undergo pressure-dependent proliferation, heritable phenotypic changes and
directional movement in response to pressure differentials. We formally show
that the continuum limit of this model comprises a non-local partial
differential equation for the cell population density, which generalises
earlier models of growing cell populations. Results of the individual-based
model illustrate how proliferation-migration tradeoffs shaping the evolution of
single cells can lead to the formation of travelling waves at the population
level where highly-mobile cells locally dominate at the invasive front, while
more-proliferative cells are found at the rear. We demonstrate that there is an
excellent quantitative agreement between these results and the results of
numerical simulations and formal travelling-wave analysis of the continuum
model, when sufficiently large cell numbers are considered. We provide
numerical evidence of scenarios in which the predictions of the two models may
differ due to demographic stochasticity, which cannot be captured by the
continuum model. This indicates the importance of integrating individual-based
and continuum approaches when modelling the growth of phenotypically
heterogeneous cell populations.

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The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th