The effects of time-varying temperature on delays in genetic networks

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.

Guidelines for designing the antithetic feedback motif

Integral feedback control is commonly used in mechanical and electrical systems to achieve zero steady-state error following an external disturbance. Equivalently, in biological systems, a property known as robust perfect adaptation guarantees robustness to environmental perturbations and return to the pre-disturbance state. Previously, Briat et al proposed a biomolecular design for integral feedback control (robust perfect adaptation) called the antithetic feedback motif. The antithetic feedback controller uses the sequestration binding reaction of two biochemical species to record the integral of the error between the current and the desired output of the network it controls. The antithetic feedback motif has been successfully built using synthetic components in vivo in Escherichia coli and Saccharomyces cerevisiae cells. However, these previous synthetic implementations of antithetic feedback have not produced perfect integral feedback control due to the degradation and dilution of the two controller species. Furthermore, previous theoretical results have cautioned that integral control can only be achieved under stability conditions that not all antithetic feedback motifs necessarily fulfill. In this paper, we study how to design antithetic feedback motifs that simultaneously achieve good stability and small steady-state error properties, even as the controller species are degraded and diluted. We provide simple tuning guidelines to achieve flexible and practical synthetic biological implementations of antithetic feedback control. We use several tools and metrics from control theory to design antithetic feedback networks, paving the path for the systematic design of synthetic biological controllers.

Investigating the dynamics of microbial consortia in spatially structured environments

The spatial organization of microbial communities arises from a complex interplay of biotic and abiotic interactions, and is a major determinant of ecosystem functions. Here we design a microfluidic platform to investigate how the spatial arrangement of microbes impacts gene expression and growth. We elucidate key biochemical parameters that dictate the mapping between spatial positioning and gene expression patterns. We show that distance can establish a low-pass filter to periodic inputs and can enhance the fidelity of information processing. Positive and negative feedback can play disparate roles in the synchronization and robustness of a genetic oscillator distributed between two strains to spatial separation. Quantification of growth and metabolite release in an amino-acid auxotroph community demonstrates that the interaction network and stability of the community are highly sensitive to temporal perturbations and spatial arrangements. In sum, our microfluidic platform can quantify spatiotemporal parameters influencing diffusion-mediated interactions in microbial consortia.

Bayesian inference of distributed time delay in transcriptional and translational regulation

MOTIVATION

Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks.

RESULTS

We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy.

AVAILABILITY AND IMPLEMENTATION

Accompanying code in R is available at https://github.com/cbskust/DDE_BD.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.