Models, measurement and inference in epithelial tissue dynamics

Maclaren, Oliver J.; Byrne, Helen M.; Fletcher, Alexander G.; Maini, Philip K.

doi:10.3934/mbe.2015.12.1321

Cited by 17 publications

(18 citation statements)

References 83 publications

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“…Bayesian methods have been demonstrated to provide a powerful framework for the design of experiments, model selection and parameter estimation, especially in the life sciences [15,34,86,91,92,138,143,145]. Given observations, Y obs , and a biochemical reaction network model parameterised by the M × 1 real-valued vector of kinetic parameters, θ = [k 1 , k 2 , .…”

Section: Bayesian Inferencementioning

confidence: 99%

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Warne

Baker

Simpson

2019

J. R. Soc. Interface.

112

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Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab ® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

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Section: Bayesian Inferencementioning

confidence: 99%

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Warne

Baker

Simpson

2019

J. R. Soc. Interface.

112

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“…interdisciplinary approach involving experimental measurements, mathematical and 591 computational modelling, and statistical quantification of uncertainties. While a 592 diverse range of mathematical models have been constructed for epithelial cell and 593 tissue dynamics (reviewed in [58,59,[73][74][75]), from compartment models to 594 individual-based models to continuum models, we lack consistent and reproducible 595 frameworks for comparing models representing conjectured biological mechanisms 596 both to each other and to experimental data (for an overview, see our review [49]).…”

Section: Figure 12mentioning

confidence: 99%

“…180 This enabled samples to be drawn from both prior predictive and prior parameter 181 models, in the usual way (see e.g. [17,49] and the Computational methods section 182 below). In particular, the prior predictive distribution was used in its usual form 183 y ∼ (y) = ∫ (y| (k)) (k) k (2) which incorporates the aforementioned deterministic link between a given sample of 184 process parameters and the output process variable, L = (k).…”

mentioning

confidence: 99%

“…Our structural assumptions mean that the information gained is represented in updates of the parameter model while the process and measurement models maintain the same form. Modified from [49], which was based on [50].…”

mentioning

confidence: 99%

“…Equations of this (and 321 similar) form have been derived before, also based on continuous approximations to 322 discrete master equations (e.g. [54][55][56][57] also contain similar ideas; [49] gives additional 323 references).…”

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confidence: 99%

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A hierarchical Bayesian framework for understanding the spatiotemporal dynamics of the intestinal epithelium

Maclaren

Parker

et al. 2016

Preprint

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Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cellular migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and 1/42 interpret them using mathematical models, we develop a probabilistic, hierarchical framework. This framework provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine drawing reliable conclusions -uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. This allows the incorporation of features of both continuum tissue models and discrete cellular models. We perform model checks on both in-sample and out-of-sample datasets and use these checks to illustrate how to test possible model improvements and assess the robustness of our conclusions. This allows us to consider -and ultimately decide against -the need to retain finite-cell-size effects to explain a small misfit appearing in one set of long-time, out-of-sample predictions. Our approach leads us to conclude, for the present set of experiments, that a primarily proliferation-driven model is adequate for predictions over most time-scales. We describe each stage of our framework in detail, and hope that the present work may also serve as a guide for other applications of the hierarchical approach to problems in computational and systems biology more generally. Author SummaryThe intestinal epithelium serves as an important model system for studying the dynamics and regulation of multicellular populations. It is characterised by rapid rates of self-renewal and repair; failure of the regulation of these processes is thought to explain, in part, why many tumours occur in the intestinal and similar epithelial tissues. These features have led to a large amount of work on estimating rate parameters in the intestine. There still remain, however, large gaps between the raw data collected, the experimental interpretation of these data, and speculative mechanistic models for underlying processes. In our view hierarchical statistical modelling provides an ideal, but currently underutilised, method to begin to bridge these gaps. This approach makes essential use of the distinction between 2/42 'measurement', 'process' and 'parameter' models, giving an explicit framework for combining experimental data and mechanistic modelling in the presence of multiple sources of uncertainty. As we illustrate, the hie...

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Tissue Regeneration Processing and Mimicking

Oktay,

Durasi

et al. 2023

Stem Cell Biology and Regenerative Medicine

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Models, measurement and inference in epithelial tissue dynamics

Cited by 17 publications

References 83 publications

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

A hierarchical Bayesian framework for understanding the spatiotemporal dynamics of the intestinal epithelium

Tissue Regeneration Processing and Mimicking

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