Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching

Abstract

A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10−7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.

Bayesian Emulation and History Matching of JUNE

“…Hence it is vital to define a clear statistical model describing the difference between the epidemiological model, f (x), and the observed data denoted as the vector z. While more complex statistical models are available [13], here we describe a simple but powerful version that has been successfully used in a variety of scientific disciplines, for example climate, cosmology, oil reservoirs, epidemiology and systems biology [1,8,17,46,48,49].…”

Bayesian emulation and history matching ofJUNE

“…Hence, it is vital to define a clear statistical model describing the difference between the epidemiological model, ffalse(xfalse), and the observed data denoted as the vector z. While more complex statistical models are available [20], here, we describe a simple but powerful version that has been successfully used in a variety of scientific disciplines, for example climate, cosmology, oil reservoirs, epidemiology and systems biology [2–5,10,21].…”

Efficient Emulation of Computer Models Utilising Multiple Known Boundaries of Differing Dimensions

“…The model takes an input vector of 45 rate parameters (k 1 , k 1a , k 2 , ...), although we will be interested in a subset of 38 of them, as discussed in Appendix E, and returns an output vector of 18 chemical concentrations ([Auxin], [X], [P LSp], ...). This Arabidopsis model has been successfully emulated in the literature in the context of history matching [38,21].…”

“…See [13,14] for discussion of the benefits of using a Bayes linear approach, and [36,21] for its benefits within a computer model setting.…”