Global Density Analysis for an Off-Lattice Agent-Based Model

Yereniuk, Michael A.; Olson, Sarah D.

doi:10.1137/18m1186939

“…In general, continuum models do not make the underlying cell-level processes clear [12]. However, continuum models can be less computationally expensive than discrete models and can be analysed with wellestablished mathematical techniques such as stability analysis [1] and phase plane analysis [18].We are most interested in models that connect the discrete and continuum scales [4,11,26,32,35,46,49] because this allows us to switch between the two spatial scales and take advantage of both.To do so, we focus on a mechanical model and extend the works of Murray et al [28, 29,30,31], Lorenzi et al [23], Baker et al [2], and Murphy et al [27] to a new model for fully heterogeneous populations which experience both proliferation and death. This framework allows us to explore mechanical cell competition, which was not previously possible.This work is structured as follows.…”

mentioning

confidence: 99%

“…We are most interested in models that connect the discrete and continuum scales [4,11,26,32,35,46,49] because this allows us to switch between the two spatial scales and take advantage of both.…”

mentioning

confidence: 99%

Mechanical cell competition in heterogeneous epithelial tissues

Murphy

¹

,

Buenzli

²

,

Baker

³

et al. 2019

Preprint

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Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the discrete model and the new continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage. 1In the emerging field of mechanical cell competition, winner cells compress neighbouring cells promoting tissue crowding and regions of higher density, which leads to cell death [5,21,47], while cell proliferation occurs in regions of lower density [13]. In this work, we focus on mechanical cell competition arising from the coupling of a cell-based model of epithelial tissue mechanics with celllength-dependent proliferation and death mechanisms. We consider mechanical forces to be driven by cell stiffness which is important for cancer progression [41], cancer detection [36], morphogenesis [10], and wound healing [9]. A grand challenge in cell biology is to understand how tissue-level outcomes are related to cell-based mechanisms, especially when experiments are performed by focusing on a single scale, and many cellular processes occur over multiple overlapping timescales [6,48]. Therefore, we apply mathematical modelling with in silico simulations to develop a framework to quantitatively connect cell-level mechanisms with tissue-level outcomes.Many mathematical modelling frameworks, including both discrete models and continuum models, have been used to study cell migration and cell proliferation. In discrete models individual cell properties and inter-cellular interactions can be prescribed [33,34]. However, discrete models often lack macroscopic intuition and can be computationally intensive, especially with proliferation and death included, which are commonly stochastic and require many realizations to understand the average behaviour. Continuum models commonly include proliferation and death through source/sink terms and may require constitutive equations to close the system [3,21,25,39,43]. In general, continuum models do not make the underlying cell-level processes clear [12]. However, continuum models can be less computationally expensive than discrete models and can be analysed with wellestablishe...

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“…We primarily focus on extending the definitions of [22] in the context of when the ABM environment (i.e. bounded region of interest) Ω is a connected, bounded subset of R n .…”

Section: Formalizing Agent-based Modelsmentioning

confidence: 99%

“…In this work, we extend a framework that (i) explicitly allows an agent's location to be continuous or discrete and (ii) provides a clear connection between this positional information and the expected population densities of each (agent) state [22]. This framework requires the update process by which local rules modify agents at each time step to be Markovian in order to simplify later computations.…”

Section: Introductionmentioning

confidence: 99%

“…Our extension of this framework allows for the number of agents to change over time according to an ABM's local rules; as such, our definition of an ABM accommodates a broad set of models actively used in research. We also generalize the computation of a state's "global recurrence rule" (GRR) [22] to calculate changes in population density for that state based on the ABM's local rules and an initial set of model parameters. We present an approach for estimating a state's GRR rather than explicitly calculating it to focus on practical application and provide two case studies of our approach: an ABM based on the Game of Life cellular automaton [6] (which we call "GoL-like") and an ABM developed with experimental data to study early rib development in vertebrates [5].…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Long-term Behavior of Biologically Inspired Agent-based Models

Cruz¹,

Toppen²,

Park³

et al. 2022

Preprint

0

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An agent-based model (ABM) is a computational model in which the local interactions of autonomous agents with each other and with their environment give rise to global properties within a given domain. As the detail and complexity of these models has grown, so too has the computational expense of running several simulations to perform sensitivity analysis and evaluate long-term model behavior. Here, we generalize a framework for mathematically formalizing ABMs to explicitly incorporate features commonly found in biological systems: appearance of agents (birth), removal of agents (death), and locally dependent state changes. We then use our broader framework to extend an approach for estimating long-term behavior without simulations, specifically changes in population densities over time. The approach is probabilistic and relies on treating the discrete, incremental update of an ABM via "time steps" as a Markov process to generate expected values for agents at each time step. As case studies, we apply our extensions to both a simple ABM based on the Game of Life and a published ABM of rib development in vertebrates.

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Mechanical Cell Competition in Heterogeneous Epithelial Tissues

Murphy

¹

,

Buenzli

²

,

Baker

³

et al. 2020

View full text Add to dashboard Cite

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.

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Global Density Analysis for an Off-Lattice Agent-Based Model

Cited by 3 publications

References 42 publications

Mechanical cell competition in heterogeneous epithelial tissues

Mechanical cell competition in heterogeneous epithelial tissues

Estimating the Long-term Behavior of Biologically Inspired Agent-based Models

Mechanical Cell Competition in Heterogeneous Epithelial Tissues

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