Mathematical models for cell migration with real-time cell cycle dynamics

Vittadello, Sean T.; McCue, Scott W.; Gunasingh, Gency; Haass, Nikolas K.; Simpson, Matthew J.

doi:10.1101/238303

Cited by 14 publications

(33 citation statements)

References 41 publications

(70 reference statements)

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“…As stated previously, formal travelling wave solutions are almost never observed experimentally. Typical scratch assays initial configurations lead to two opposingly-directed fronts, such as the profiles in Figure 2(d), (h), (l) and pshowing the evolution of the Generalised Porous Fisher model for several values of r. Note that, for typical scratch widths, wound closure takes place before travelling waves have an opportunity to form (Jin et al, 2016b;Vittadello et al, 2018). However, the value of r still impacts the wound closure rate and the shape of the moving font.…”

Section: Modelling Cell Populations With Reaction-diffusion Equationsmentioning

confidence: 97%

“…These solutions are of general mathematical interest and have been extensively studied (Harris, 2004;Witelski, 1995). However, since travelling waves only occur as in the long-time limit and require rather special initial conditions, travelling waves are rarely observed experimentally (Jin et al, 2016b;Vittadello et al, 2018). Therefore, we do not consider connecting any kind of travelling wave solutions with experimental data in this work.…”

Section: Modelling Cell Populations With Reaction-diffusion Equationsmentioning

confidence: 99%

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Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology

2019

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Reaction-diffusion models describing the movement, reproduction and death of individuals within a population are key mathematical modelling tools with widespread applications in mathematical biology. A diverse range of such continuum models have been applied in various biological contexts by choosing different flux and source terms in the reaction-diffusion framework. For example, to describe collective spreading of cell populations, the flux term may be chosen to reflect various movement mechanisms, such as random motion (diffusion), adhesion, haptotaxis, chemokinesis and chemotaxis. The choice of flux terms in specific applications, such as wound healing, is usually made heuristically, and rarely is it tested quantitatively against detailed cell density data. More generally, in mathematical biology, the questions of model validation and model selection have not received the same attention as the questions of model development and model analysis. Many studies do not consider model validation or model selection, and those that do often base the selection of the model on residual error criteria after model calibration is performed using nonlinear regression techniques. In this work, we present a model selection case study, in the context of cell invasion, with a very detailed experimental data set. Using Bayesian analysis and information criteria, we demonstrate that model selection and model validation should account for both residual errors and model complexity. These considerations are often overlooked in the mathematical biology literature. The results we present here provide a clear methodology that can be used to guide model selection across a range of applications. Furthermore, the case study we present provides a clear example where neglecting the role of model complexity can give rise to misleading outcomes.

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Section: Modelling Cell Populations With Reaction-diffusion Equationsmentioning

confidence: 97%

Section: Modelling Cell Populations With Reaction-diffusion Equationsmentioning

confidence: 99%

Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology

2019

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“…Previous work has shown that heterogeneity in cell age distribution may still generate logistic growth at the population scale [22]. Other age-structured models have described how the cell age distribution can affect the overall cell population dynamics in scratch assays: the speed with which the cells invade the vacant region [19,44], the efficacy of anti-cancer drugs, particularly phase-specific drugs [5] and the influence of growth factors [6]. Agent-based models have also been considered to study the effect of heterogeneity in cell age distribution on the overall dynamics in in-vitro assays [45,46].…”

Section: Introductionmentioning

confidence: 99%

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

et al. 2019

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Scratch assays are in-vitro methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. Typically, scratch assays are modelled by reaction diffusion equations depicting cell migration by Fickian diffusion and modelling proliferation by a logistic term. In a recent paper (Jin, W. et al. Bull Math Biol (2017)), the authors observed experimentally that during the early stage of the recolonisation process, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The authors did not identify the precise mechanism that causes the disturbance phase but showed that ignoring it can lead to incorrect parameter estimates. The aim of this work is to show that a non-linear age-structured population model can account for the two phases of proliferation in scratch assays. The model consists of an age-structured cell cycle model of a cell population, coupled with an ordinary differential equation describing the resource concentration dynamics in the substrate. The model assumes a resource-dependent cell cycle threshold age, above which cells are able to proliferate. By studying the dynamics of the full system in terms of the subpopulations of cells that can proliferate and the ones that can not, we are able to find conditions under which the model captures the two-phase behaviour. Through numerical simulations we are able

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“…trajectory data is an active area of research (Hywood et al, 2021), but we find using the Simpson et al (2018) model which incorporates cell trajectory data leads to a good outcome.…”

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confidence: 81%

“…The copyright holder for this preprint this version posted April 21, 2021. ; https://doi.org/10.1101/2021.04.20.440712 doi: bioRxiv preprint 2 Data 2D scratch assay experiments are a good screening tool for more complex experimental models, as they are low cost, allow for easy data interpretation and readily allow control of oxygen, nutrients and drug supply (Beaumont et al, 2014;Santiago-Walker et al, 2009). We adopt data from a study conducted by Vittadello et al (2018) where a scratch assay is used to examine melanoma cell proliferation and migration in real time with FUCCI technology. The experiment is initialised by placing a small population of cells and a growth medium in a culture dish (Figure 1 (a)) to create a uniform 2D monolayer of cells.…”

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Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using Approximate Bayesian Computation

Carr

Simpson

Drovandi

2021

Preprint

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We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labeling with proliferation, migration, and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all the parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, whilst difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.

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Mathematical models for cell migration with real-time cell cycle dynamics

Cited by 14 publications

References 41 publications

Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology

Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using Approximate Bayesian Computation

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