Cell density and cell size dynamics during in vitro tissue growth experiments: Implications for mathematical models of collective cell behaviour

et al. 2017

Preprint

Cell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K ≥ 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak.In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.

Section: Introductionmentioning

confidence: 99%

Continuum approximations for lattice-free multi-species models of collective cell migration

Matsiaka

Penington

et al. 2017

Preprint

“…The first experiment, shown in Figure 1(a), is often referred to as a growth-to-confluence assay. Here we observe a population of cells seeded, initially at low density, as the cells move and proliferate and the population increases in number to eventually occupy the whole domain under observation [5,8]. The second experiment we consider is shown in Figure 1(b), and is often referred to as a scratch assay.…”

Section: Experimental Designmentioning

confidence: 99%

The impact of experimental design choices on parameter inference for models of growing cell colonies

Parker

Simpson

2017

Preprint

Self Cite

To better understand development, repair and disease progression it is useful to quantify the behaviour of proliferative and motile cell populations as they grow and expand to fill their local environment. Inferring parameters associated with mechanistic models of cell colony growth using quantitative data collected from carefully designed experiments provides a natural means to elucidate the relative contributions of various processes to the growth of the colony. In this work we explore how experimental design impacts our ability to infer parameters for simple models of the growth of proliferative and motile cell populations. We adopt a Bayesian approach, which allows us to characterise the uncertainty associated with estimates of the model parameters. Our results suggest that experimental designs that incorporate initial spatial heterogeneities in cell positions facilitate parameter inference without the requirement of cell tracking, whilst designs that involve uniform initial placement of cells require cell tracking for accurate parameter inference. As cell tracking is an experimental bottleneck in many studies of this type, our recommendations for experimental design provide for significant potential time and cost savings in the analysis of cell colony growth.

“…Since we work with an off-lattice discrete framework, each agent is allowed to move in any direction on a continuous domain. This off-lattice approach is more realistic than a simpler lattice-based model where the locations of agents are restricted to an artificial lattice structure [18,44,45,42,46].…”

Section: Discrete Stochastic Modelmentioning

confidence: 99%

Mechanistic and experimental models of cell migration reveal the importance of intercellular interactions in cell invasion

Matisaka

Shah

et al. 2018

Preprint

Self Cite

Moving fronts of cells are essential for development, repair and disease progression. Therefore, understanding and quantifying the details of the mechanisms that drive the movement of cell fronts is of wide interest. Quantitatively identifying the role of intercellular interactions, and in particular the role of cell pushing, remains an open question. Indeed, perhaps the most common continuum mathematical idealization of moving cell fronts is to treat the population of cells, either implicitly or explicitly, as a population of point particles undergoing a random walk that neglects intercellular interactions. In this work, we report a combined experimental-modelling approach showing that intercellular interactions contribute significantly to the spatial spreading of a population of cells. We use a novel experimental data set with PC-3 prostate cancer cells that have been pretreated with Mitomycin-C to suppress proliferation. This allows us to experimentally separate the effects of cell migration from cell proliferation, thereby enabling us to focus on the migration process in detail as the population of cells recolonizes an initially-vacant region in a series of two-dimensional experiments. We quantitatively model the experiments using a stochastic modelling framework, based on Langevin dynamics, which explicitly incorporates random motility and various intercellular forces including: (i) long range attraction (adhesion); and (ii) finite size effects that drive short range repulsion (pushing). Quantitatively comparing the ability of this model to describe the experimentally observed population-level behaviour provides us with quantitative insight into the roles of random motility and intercellular interactions. To quantify the mechanisms at play, we calibrate the stochastic model to match experimental cell density profiles to obtain estimates of cell diffusivity, D, and the amplitude of intercellular forces, f 0 . Our analysis shows that taking a standard modelling approach which ignores intercellular forces provides a poor match to the experimental data whereas incorporating intercellular forces, including short-range pushing and longer range attraction, leads to a faithful representation of the experimental observations. These results demonstrate a significant role for intercellular interactions in cell invasion.1 Author summaryMoving cell fronts are routinely observed in various physiological processes, such as wound healing, malignant invasion and embryonic morphogenesis. We explore the effects of a previously overlooked mechanism that contributes to population-level front movement: pushing. Our framework is flexible and incorporates range of reasonable biological phenomena, such as random motility, cell-to-cell adhesion, and pushing. We find that neglecting finite size effects and intercellular forces, such as cell pushing, reduces our ability to mimic and predict our experimental observations.