Inferring extrinsic noise from single-cell gene expression data using approximate Bayesian computation.

BACKGROUND: Gene expression is known to be an intrinsically stochastic process which can involve single-digit numbers of mRNA molecules in a cell at any given time. The modelling of such processes calls for the use of exact stochastic simulation methods, most notably the Gillespie algorithm. However, this stochasticity, also termed "intrinsic noise", does not account for all the variability between genetically identical cells growing in a homogeneous environment. Despite substantial experimental efforts, determining appropriate model parameters continues to be a challenge. Methods based on approximate Bayesian computation can be used to obtain posterior parameter distributions given the observed data. However, such inference procedures require large numbers of simulations of the model and exact stochastic simulation is computationally costly. In this work we focus on the specific case of trying to infer model parameters describing reaction rates and extrinsic noise on the basis of measurements of molecule numbers in individual cells at a given time point. RESULTS: To make the problem computationally tractable we develop an exact, model-specific, stochastic simulation algorithm for the commonly used two-state model of gene expression. This algorithm relies on certain assumptions and favourable properties of the model to forgo the simulation of the whole temporal trajectory of protein numbers in the system, instead returning only the number of protein and mRNA molecules present in the system at a specified time point. The computational gain is proportional to the number of protein molecules created in the system and becomes significant for systems involving hundreds or thousands of protein molecules. CONCLUSIONS: We employ this simulation algorithm with approximate Bayesian computation to jointly infer the model's rate and noise parameters from published gene expression data. Our analysis indicates that for most genes the extrinsic contributions to noise will be small to moderate but certainly are non-negligible

A Bayesian semi-parametric model for thermal proteome profiling.

Funder: Wellcome TrustThe thermal stability of proteins can be altered when they interact with small molecules, other biomolecules or are subject to post-translation modifications. Thus monitoring the thermal stability of proteins under various cellular perturbations can provide insights into protein function, as well as potentially determine drug targets and off-targets. Thermal proteome profiling is a highly multiplexed mass-spectrommetry method for monitoring the melting behaviour of thousands of proteins in a single experiment. In essence, thermal proteome profiling assumes that proteins denature upon heating and hence become insoluble. Thus, by tracking the relative solubility of proteins at sequentially increasing temperatures, one can report on the thermal stability of a protein. Standard thermodynamics predicts a sigmoidal relationship between temperature and relative solubility and this is the basis of current robust statistical procedures. However, current methods do not model deviations from this behaviour and they do not quantify uncertainty in the melting profiles. To overcome these challenges, we propose the application of Bayesian functional data analysis tools which allow complex temperature-solubility behaviours. Our methods have improved sensitivity over the state-of-the art, identify new drug-protein associations and have less restrictive assumptions than current approaches. Our methods allows for comprehensive analysis of proteins that deviate from the predicted sigmoid behaviour and we uncover potentially biphasic phenomena with a series of published datasets

Maternal Obesity Induced by Diet in Rats Permanently Influences Central Processes Regulating Food Intake in Offspring

Hypothalamic systems which regulate appetite may be permanently modified during early development. We have previously reported hyperphagia and increased adiposity in the adult offspring of rodents fed an obesogenic diet prior to and throughout pregnancy and lactation. We now report that offspring of obese (OffOb) rats display an amplified and prolonged neonatal leptin surge, which is accompanied by elevated leptin mRNA expression in their abdominal white adipose tissue. At postnatal Day 30, before the onset of hyperphagia in these animals, serum leptin is normal, but leptin-induced appetite suppression and phosphorylation of STAT3 in the arcuate nucleus (ARC) are attenuated; the level of AgRP-immunoreactivity in the hypothalamic paraventricular nucleus (PVH), which derives from neurones in the ARC and is developmentally dependent on leptin, is also diminished. We hypothesise that prolonged release of abnormally high levels of leptin by neonatal OffOb rats leads to leptin resistance and permanently affects hypothalamic functions involving the ARC and PVH. Such effects may underlie the developmental programming of hyperphagia and obesity in these rats

Yield determination of maize hybrids under limited irrigation

Hybrid adoption, irrigation, and planting density are important factors for maize (Zea mays L.) production in semiarid regions. For this study, a 2-yr field experiment was conducted in the Texas High Plains to investigate maize yield determination, seasonal evapotranspiration (ETc), and water-use efficiency (WUE) under limited irrigation. Two hybrids (N74R, a conventional hybrid, and N75H, a drought-tolerant (DT) hybrid) were planted at three water regimes (I100, I75, and I50, referring to 100%, 75%, and 50% of the evapotranspiration requirement) and three planting densities (PD 6, PD 8, and PD 10, referring to 6, 8, and 10 seeds m−2). At I50, drought stress reduced grain yield by 4.78 t/ha for the conventional hybrid but only 4.22 t/ha for the DT hybrid, when compared to I100. Although ETc decreased at I75 and I50, the highest WUE was found at I75. The DT hybrid did not yield more than the conventional hybrid but had greater yield stability at lower water regimes and extracted less soil water. Drought decreased biomass, harvest index, and kernel weight but did not affect kernel number. Higher planting densities increased biomass and kernel number but decreased kernel weight. Kernel number and kernel weight of the conventional hybrid were more sensitive to planting density than the DT hybrid. These data demonstrated that limited irrigation at I75 is an effective way to save water and maintain the maize yield in semiarid areas, and that DT hybrid shows a greater yield stability to plant density under water stress

Results of the 2016 Indianapolis Biodiversity Survey, Marion County, Indiana

Surprising biodiversity can be found in cities, but urban habitats are understudied. We report on a bioblitz conducted primarily within a 24-hr period on September 16 and 17, 2016 in Indianapolis, Indiana, USA. The event focused on stretches of three waterways and their associated riparian habitat: Fall Creek (20.6 ha; 51 acres), Pleasant Run (23.5 ha; 58 acres), and Pogue’s Run (27.1 ha; 67 acres). Over 75 scientists, naturalists, students, and citizen volunteers comprised 14 different taxonomic teams. Five hundred ninety taxa were documented despite the rainy conditions. A brief summary of the methods and findings are presented here. Detailed maps of survey locations and inventory results are available on the Indiana Academy of Science website (https://www.indianaacademyofscience.org/)

Multivariate moment closure techniques for stochastic kinetic models.

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs

Accelerating Bayesian hierarchical clustering of time series data with a randomised algorithm

We live in an era of abundant data. This has necessitated the development of new and innovative statistical algorithms to get the most from experimental data. For example, faster algorithms make practical the analysis of larger genomic data sets, allowing us to extend the utility of cutting-edge statistical methods. We present a randomised algorithm that accelerates the clustering of time series data using the Bayesian Hierarchical Clustering (BHC) statistical method. BHC is a general method for clustering any discretely sampled time series data. In this paper we focus on a particular application to microarray gene expression data. We define and analyse the randomised algorithm, before presenting results on both synthetic and real biological data sets. We show that the randomised algorithm leads to substantial gains in speed with minimal loss in clustering quality. The randomised time series BHC algorithm is available as part of the R package BHC, which is available for download from Bioconductor (version 2.10 and above) via http://bioconductor.org/packages/2.10/bioc/html/BHC.html. We have also made available a set of R scripts which can be used to reproduce the analyses carried out in this paper. These are available from the following URL. https://sites.google.com/site/randomisedbhc/