Transition state characteristics during cell differentiation

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington’s epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes—change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions

The route to transcription initiation determines the mode of transcriptional bursting in E. coli

Transcription is fundamentally noisy, leading to significant heterogeneity across bacterial populations. Noise is often attributed to burstiness, but the underlying mechanisms and their dependence on the mode of promotor regulation remain unclear. Here, we measure E. coli single cell mRNA levels for two stress responses that depend on bacterial sigma factors with different mode of transcription initiation (σ70 and σ54). By fitting a stochastic model to the observed mRNA distributions, we show that the transition from low to high expression of the σ70-controlled stress response is regulated via the burst size, while that of the σ54-controlled stress response is regulated via the burst frequency. Therefore, transcription initiation involving σ54 differs from other bacterial systems, and yields bursting kinetics characteristic of eukaryotic systems

Molecular origins of transcriptional heterogeneity in diazotrophic Klebsiella oxytoca.

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of bacterial systems; however, the molecular origins of such heterogeneity and its magnitude are not well understood. Under conditions of extreme low-nitrogen stress in the model diazotroph Klebsiella oxytoca, we found remarkably high heterogeneity of nifHDK gene expression, which codes for the structural genes of nitrogenase, one key enzyme of the global nitrogen cycle. This heterogeneity limited the bulk observed nitrogen-fixing capacity of the population. Using dual-probe, single-cell RNA fluorescent in situ hybridization, we correlated nifHDK expression with that of nifLA and glnK-amtB, which code for the main upstream regulatory components. Through stochastic transcription models and mutual information analysis, we revealed likely molecular origins for heterogeneity in nitrogenase expression. In the wild type and regulatory variants, we found that nifHDK transcription was inherently bursty, but we established that noise propagation through signaling was also significant. The regulatory gene glnK had the highest discernible effect on nifHDK variance, while noise from factors outside the regulatory pathway were negligible. Understanding the basis of inherent heterogeneity of nitrogenase expression and its origins can inform biotechnology strategies seeking to enhance biological nitrogen fixation. Finally, we speculate on potential benefits of diazotrophic heterogeneity in natural soil environments

Extremum seeking to control the amplitude and frequency of a pulsed jet for bluff body drag reduction

Feedback control of fluid flows presents a challenging problem due to nonlinear dynamics and unknown optimal operating conditions. Extremum seeking control presents a suitable method for many flow control situations but involves its own challenges. In this paper we provide a brief analysis of the extremum seeking method, with attention to modifications that we find to be advantageous. In particular, we present an adaptation for optimisation of the frequency of a harmonic input signal, a common scenario for open-loop flow control systems. We then present results from the experimental implementation of our modified method to the open-loop control system of Oxlade et al (2015, J. Fluid Mech., vol. 770), an axisymmetric bluff body wake, forced by a pulsed jet. We find that the system is able to achieve optimal operating conditions in both the amplitude and frequency of the harmonic input signal, and is able to largely reject the disturbances arising from measurements of a highly turbulent flow. We finally show the ability of the extremum seeking system to adapt to changing conditions

theosysbio/gene-expression-models

First release coinciding with publication of JCP article.First release coinciding with publication of JCP article.

Modelling and feedback control of vortex shedding for drag reduction of a turbulent bluff body wake

Three-dimensional bluff body wakes are of key importance due to their relevance to the automotive industry. Such wakes have both large pressure drag and a number of coherent flow structures associated with them. Depending on the geometry, these structures may include both a bistability resulting from a spatial symmetry breaking (SB), and a quasi-periodic vortex shedding. The authors have recently shown that the bistability may be modelled by a Langevin equation and that this model enables the design of a feedback control strategy that efficiently reduces the drag through suppression of asymmetry. In this work the stochastic modelling approach is extended to the vortex shedding, capturing qualitatively both the forced and unforced behaviour. A control strategy is then presented that makes use of the frequency response of the wake, and aims to reduce the measured fluctuations associated with the vortex shedding. The strategy proves to be effective at suppressing fluctuations within specific frequency ranges but, due to amplification of disturbances at other frequencies, is unable to give drag reduction

Diffusive dynamics and stochastic models of turbulent axisymmetric wakes

A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters