Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions.

BACKGROUND: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. METHODS: Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. RESULTS: The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model's structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. CONCLUSIONS: Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.

Distinct and conserved transcriptomic changes during nematode-induced giant cell development in tomato compared with Arabidopsis: a functional role for gene repression.

Root-knot nematodes (RKNs) induce giant cells (GCs) from root vascular cells inside the galls. Accompanying molecular changes as a function of infection time and across different species, and their functional impact, are still poorly understood. Thus, the transcriptomes of tomato galls and laser capture microdissected (LCM) GCs over the course of parasitism were compared with those of Arabidopsis, and functional analysis of a repressed gene was performed. Microarray hybridization with RNA from galls and LCM GCs, infection-reproduction tests and quantitative reverse transcription-polymerase chain reaction (qRT-PCR) transcriptional profiles in susceptible and resistant (Mi-1) lines were performed in tomato. Tomato GC-induced genes include some possibly contributing to the epigenetic control of GC identity. GC-repressed genes are conserved between tomato and Arabidopsis, notably those involved in lignin deposition. However, genes related to the regulation of gene expression diverge, suggesting that diverse transcriptional regulators mediate common responses leading to GC formation in different plant species. TPX1, a cell wall peroxidase specifically involved in lignification, was strongly repressed in GCs/galls, but induced in a nearly isogenic Mi-1 resistant line on nematode infection. TPX1 overexpression in susceptible plants hindered nematode reproduction and GC expansion. Time-course and cross-species comparisons of gall and GC transcriptomes provide novel insights pointing to the relevance of gene repression during RKN establishment.