Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

Abstract

We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling 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 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, while 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 .

A novel SEIR-e model for disease transmission and pathogen exposure

“…The posterior distribution captures the relationship between the parameter θ and the observed data, x, while the prior distribution represents prior knowledge about appropriate values for θ. The likelihood represents a belief about x given θ, and is often intractable and costly to compute [38,39]. Approximate Bayesian computation (ABC) methods are a class of likelihood free methods where a simulationbased process replaces the computation of the likelihood [38][39][40].…”

“…The likelihood represents a belief about x given θ, and is often intractable and costly to compute [38,39]. Approximate Bayesian computation (ABC) methods are a class of likelihood free methods where a simulationbased process replaces the computation of the likelihood [38][39][40]. ABC methods are comprehensively reviewed in [38][39][40], so we briefly summarise the key points below.…”

“…The Euclidean distance is commonly used as the discrepancy metric, d(x, x * ) = ||x−x * || 2 . ABC methods result in a sample of parameters from π(θ|d(x, x * ) ≤ ) which is considered a good approximation of π(θ|x) if is sufficiently small [38][39][40]. We use ABC to infer posterior distributions for parameters of the SEIR-e model which correspond to disease transmission, people-people and people-pathogen interactions.…”

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

“…Continuum modelling approaches lack the ability to track individual cells within the growing population, and typically neglect heterogeneity and stochasticity. In comparison, individual-based models (IBMs) allow us to study population dynamics in more detail, by keeping track of all individuals and explicitly capturing heterogeneity and stochasticity [18,19]. Over the last 20 years, as computing power has increased at the same time that experimental imaging resolution has improved, there has been an increasing interest in interpreting tumour spheroid experiments using IBMs [20][21][22][23][24][25], with some studies using these models to focus explicitly on how the balance of cell migration and cell proliferation impacts phenotype selection [26].…”

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

“…However, continuum modelling approaches lack the ability to track individual cells within the growing population, and typically neglect heterogeneity and stochasticity within the population. In comparison, individual-based models (IBMs) allow us to study population dynamics in detail by keeping track of all individuals within the population, as well as explicitly including effects of heterogeneity and stochasticity [19][20][21][22][23]. While some previous IBMs have been developed to describe classical tumour spheroid experiments without FUCCI [24,25], no IBMs have been developed with the specific goal of simulating 4D tumour spheroid experiments with FUCCI.…”