A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject particular recent interest. This consists random flipping the wake between two asymmetric configurations and believed to contribute pressure drag many bodies. In this study we apply modelling approach recently suggested for axisymmetric bodies by Rigas et al. ( J. Fluid Mech. , vol. 778, 2015, R2) reflectional symmetry-breaking modes rectilinear wake. We demonstrate validity model its Reynolds number...

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

Noise in gene expression is one of the hallmarks life at molecular scale. Here we derive analytical solutions to a set models describing mechanisms underlying transcription DNA into RNA. Our ansatz allows us incorporate effects extrinsic noise---encompassing factors external individual gene---and discuss ramifications for heterogeneity product abundance that has been widely observed single cell data. Crucially, are able show heavy-tailed distributions RNA copy numbers cannot result from...

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into underlying mechanisms experimentally observed behaviour. Waddington's epigenetic landscape has been providing a conceptual framework for processes since its inception. It also allows, however, detailed mathematical quantitative analyses, as can, at least in principle, be related to models dynamical systems. Here we focus on set systems features that intimately linked cell differentiation, by...

Stochastic models are key to understanding the intricate dynamics of gene expression. However, simplest that only account for active and inactive states a fail capture common observations in both prokaryotic eukaryotic organisms. Here, we consider multistate expression generalize canonical Telegraph process capable capturing joint effects transcription factors, heterochromatin state, DNA accessibility (or, prokaryotes, sigma-factor activity) on transcript abundance. We propose two approaches...

Abstract Transcription is fundamentally noisy, leading to significant heterogeneity across bacterial populations. Noise often attributed burstiness, but the underlying mechanisms and their dependence on mode of promotor regulation remain unclear. Here, we measure E. coli single cell mRNA levels for two stress responses that depend sigma factors with different transcription initiation (σ 70 σ 54 ). By fitting a stochastic model observed distributions, show transition from low high expression...

Abstract Noise in gene expression is one of the hallmarks life at molecular scale. Here we derive analytical solutions to a set models describing mechanisms underlying transcription DNA into RNA. Our Ansatz allows us incorporate effects extrinsic noise – encompassing factors external individual and discuss ramifications for heterogeneity product abundance that has been widely observed single cell data. Crucially, are able show heavy-tailed distributions RNA copy numbers cannot result from...

The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing complex problem. In many situations, the dynamics may be described by Langevin equation while constructing landscape comes down to obtaining quasipotential, scalar function that quantifies likelihood reaching each point in state space. this work we provide novel method such extending tool from control theory: sum-of-squares generating Lyapunov functions. Applicable any system...

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

Stochastic models are key to understanding the intricate dynamics of gene expression. But simplest which only account for e.g. active and inactive states a fail capture common observations in both prokaryotic eukaryotic organisms. Here we consider multistate expression generalise canonical Telegraph process, capable capturing joint effects transcription factors, heterochromatin state DNA accessibility (or, prokaryotes, Sigma-factor activity) on transcript abundance. We propose two approaches...

Abstract Models describing the process of stem-cell differentiation are plentiful, and may offer insights into underlying mechanisms experimentally observed behaviour. Waddington’s epigenetic landscape has been providing a conceptual framework for processes since its inception. It also allows, however, detailed mathematical quantitative analyses, as can, at least in principle, be related to models dynamical systems. Here we focus on set systems features that intimately linked cell...

Abstract Phenotypic heterogeneity in clonal bacterial batch cultures is an important adaptive strategy to changing environments, including diazotrophs with the unique capacity convert di-nitrogen into bio-available ammonium. In diazotrophic Klebsiella oxytoca we simultaneously measured mRNA levels of key regulatory ( glnK-amtB, nifLA ) and structural nifHDK operons required for establishing nitrogen fixation, using dual molecule, single cell RNA-FISH. Through stochastic transcription models...

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of systems; however, the molecular origins such and its magnitude are not well understood. Under conditions extreme low-nitrogen stress model diazotroph Klebsiella oxytoca, we found remarkably high nifHDK gene expression, which codes structural genes nitrogenase, one key enzyme global nitrogen cycle. This limited bulk observed nitrogen-fixing capacity population. Using dual-probe, single-cell RNA...