Bayesian hierarchical modelling for inferring genetic interactions in yeast

Hierarchical Bayesian models of transcriptional and translational regulation processes with delays

MOTIVATION

Simultaneous recordings of gene network dynamics across large populations have revealed that cell characteristics vary considerably even in clonal lines. Inferring the variability of parameters that determine gene dynamics is key to understanding cellular behavior. However, this is complicated by the fact that the outcomes and effects of many reactions are not observable directly. Unobserved reactions can be replaced with time delays to reduce model dimensionality and simplify inference. However, the resulting models are non-Markovian, and require the development of new inference techniques.

RESULTS

We propose a non-Markovian, hierarchical Bayesian inference framework for quantifying the variability of cellular processes within and across cells in a population. We illustrate our approach using a delayed birth-death process. In general, a distributed delay model, rather than a popular fixed delay model, is needed for inference, even if only mean reaction delays are of interest. Using in silico and experimental data we show that the proposed hierarchical framework is robust and leads to improved estimates compared to its non-hierarchical counterpart. We apply our method to data obtained using time-lapse microscopy and infer the parameters that describe the dynamics of protein production at the single cell and population level. The mean delays in protein production are larger than previously reported, have a coefficient of variation of around 0.2 across the population, and are not strongly correlated with protein production or growth rates.

AVAILABILITY AND IMPLEMENTATION

Accompanying code in Python is available at https://github.com/mvcortez/Bayesian-Inference.

CONTACT

kresimir.josic@gmail.com or jaekkim@kaist.ac.kr or cbskust@korea.ac.kr.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A Bayesian non-parametric mixed-effects model of microbial growth curves

Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth.

Design considerations and analysis planning of a phase 2a proof of concept study in rheumatoid arthritis in the presence of possible non-monotonicity

Background

It is important to quantify the dose response for a drug in phase 2a clinical trials so the optimal doses can then be selected for subsequent late phase trials. In a phase 2a clinical trial of new lead drug being developed for the treatment of rheumatoid arthritis (RA), a U-shaped dose response curve was observed. In the light of this result further research was undertaken to design an efficient phase 2a proof of concept (PoC) trial for a follow-on compound using the lessons learnt from the lead compound.

Methods

The planned analysis for the Phase 2a trial for GSK123456 was a Bayesian Emax model which assumes the dose-response relationship follows a monotonic sigmoid “S” shaped curve. This model was found to be suboptimal to model the U-shaped dose response observed in the data from this trial and alternatives approaches were needed to be considered for the next compound for which a Normal dynamic linear model (NDLM) is proposed. This paper compares the statistical properties of the Bayesian Emax model and NDLM model and both models are evaluated using simulation in the context of adaptive Phase 2a PoC design under a variety of assumed dose response curves: linear, Emax model, U-shaped model, and flat response.

Results

It is shown that the NDLM method is flexible and can handle a wide variety of dose-responses, including monotonic and non-monotonic relationships. In comparison to the NDLM model the Emax model excelled with higher probability of selecting ED90 and smaller average sample size, when the true dose response followed Emax like curve. In addition, the type I error, probability of incorrectly concluding a drug may work when it does not, is inflated with the Bayesian NDLM model in all scenarios which would represent a development risk to pharmaceutical company.

The bias, which is the difference between the estimated effect from the Emax and NDLM models and the simulated value, is comparable if the true dose response follows a placebo like curve, an Emax like curve, or log linear shape curve under fixed dose allocation, no adaptive allocation, half adaptive and adaptive scenarios. The bias though is significantly increased for the Emax model if the true dose response follows a U-shaped curve.

Conclusions

In most cases the Bayesian Emax model works effectively and efficiently, with low bias and good probability of success in case of monotonic dose response. However, if there is a belief that the dose response could be non-monotonic then the NDLM is the superior model to assess the dose response.

Electronic supplementary material

The online version of this article (10.1186/s12874-017-0416-3) contains supplementary material, which is available to authorized users.

Automated inference procedure for the determination of cell growth parameters

The growth rate and carrying capacity of a cell population are key to the characterization of the population's viability and to the quantification of its responses to perturbations such as drug treatments. Accurate estimation of these parameters necessitates careful analysis. Here, we present a rigorous mathematical approach for the robust analysis of cell count data, in which all the experimental stages of the cell counting process are investigated in detail with the machinery of Bayesian probability theory. We advance a flexible theoretical framework that permits accurate estimates of the growth parameters of cell populations and of the logical correlations between them. Moreover, our approach naturally produces an objective metric of avoidable experimental error, which may be tracked over time in a laboratory to detect instrumentation failures or lapses in protocol. We apply our method to the analysis of cell count data in the context of a logistic growth model by means of a user-friendly computer program that automates this analysis, and present some samples of its output. Finally, we note that a traditional least squares fit can provide misleading estimates of parameter values, because it ignores available information with regard to the way in which the data have actually been collected.