No abstract

The metaphor of the Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent accessibility of single-cell transcriptomic data has provided new opportunities for quantifying this originally conceptual tool that could offer insight into the gene regulatory networks underlying cellular development. While a number of methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use a simple model to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems, and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data.

The hexosamine biosynthetic pathway (HBP) culminates in the attachment of O-linked β-N-acetylglucosamine (O-GlcNAc) onto serine/threonine residues of target proteins. The HBP is regulated by several modulators, i.e. O-linked β-N-acetylglucosaminyl transferase (OGT) and β-N-acetylglucosaminidase (OGA) catalyze the addition and removal of O-GlcNAc moieties, respectively; while flux is controlled by the rate-limiting enzyme glutamine:fructose-6-phosphate amidotransferase (GFPT), transcribed by two genes, GFPT1 and GFPT2. Since increased HBP flux is glucose-responsive and linked to insulin resistance/type 2 diabetes onset, we hypothesized that diabetic individuals exhibit differential expression of HBP regulatory genes. Volunteers (n = 60; n = 20 Mixed Ancestry, n = 40 Caucasian) were recruited from Stellenbosch and Paarl (Western Cape, South Africa) and classified as control, pre- or diabetic according to fasting plasma glucose and HbA1c levels, respectively. RNA was purified from leukocytes isolated from collected blood samples and OGT, OGA, GFPT1 and GFPT2 expressions determined by quantitative real-time PCR. The data reveal lower OGA expression in diabetic individuals (P < 0.01), while pre- and diabetic subjects displayed attenuated OGT expression vs. controls (P < 0.01 and P < 0.001, respectively). Moreover, GFPT2 expression decreased in pre- and diabetic Caucasians vs. controls (P < 0.05 and P < 0.01, respectively). We also found ethnic differences, i.e. Mixed Ancestry individuals exhibited a 2.4-fold increase in GFPT2 expression vs. Caucasians, despite diagnosis (P < 0.01). Gene expression of HBP regulators differs between diabetic and non-diabetic individuals, together with distinct ethnic-specific gene profiles. Thus differential HBP gene regulation may offer diagnostic utility and provide candidate susceptibility genes for different ethnic groupings.

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation-a physically motivated extension of the chemical Langevin equation- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation - a physically motivated extension of the chemical Langevin equation - to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.