Nonlinear dynamics in gene regulation promote robustness and evolvability of gene expression levels

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for the ubiquity of nonlinear dynamics in gene expression networks, and generate useful guidelines for the design of synthetic gene circuits

The current and potential health benefits of the National Health Service Health Check cardiovascular disease prevention programme in England: A microsimulation study.

BACKGROUND: The National Health Service (NHS) Health Check programme was introduced in 2009 in England to systematically assess all adults in midlife for cardiovascular disease risk factors. However, its current benefit and impact on health inequalities are unknown. It is also unclear whether feasible changes in how it is delivered could result in increased benefits. It is one of the first such programmes in the world. We sought to estimate the health benefits and effect on inequalities of the current NHS Health Check programme and the impact of making feasible changes to its implementation. METHODS AND FINDINGS: We developed a microsimulation model to estimate the health benefits (incident ischaemic heart disease, stroke, dementia, and lung cancer) of the NHS Health Check programme in England. We simulated a population of adults in England aged 40-45 years and followed until age 100 years, using data from the Health Survey of England (2009-2012) and the English Longitudinal Study of Aging (1998-2012), to simulate changes in risk factors for simulated individuals over time. We used recent programme data to describe uptake of NHS Health Checks and of 4 associated interventions (statin medication, antihypertensive medication, smoking cessation, and weight management). Estimates of treatment efficacy and adherence were based on trial data. We estimated the benefits of the current NHS Health Check programme compared to a healthcare system without systematic health checks. This counterfactual scenario models the detection and treatment of risk factors that occur within 'routine' primary care. We also explored the impact of making feasible changes to implementation of the programme concerning eligibility, uptake of NHS Health Checks, and uptake of treatments offered through the programme. We estimate that the NHS Health Check programme prevents 390 (95% credible interval 290 to 500) premature deaths before 80 years of age and results in an additional 1,370 (95% credible interval 1,100 to 1,690) people being free of disease (ischaemic heart disease, stroke, dementia, and lung cancer) at age 80 years per million people aged 40-45 years at baseline. Over the life of the cohort (i.e., followed from 40-45 years to 100 years), the changes result in an additional 10,000 (95% credible interval 8,200 to 13,000) quality-adjusted life years (QALYs) and an additional 9,000 (6,900 to 11,300) years of life. This equates to approximately 300 fewer premature deaths and 1,000 more people living free of these diseases each year in England. We estimate that the current programme is increasing QALYs by 3.8 days (95% credible interval 3.0-4.7) per head of population and increasing survival by 3.3 days (2.5-4.1) per head of population over the 60 years of follow-up. The current programme has a greater absolute impact on health for those living in the most deprived areas compared to those living in the least deprived areas (4.4 [2.7-6.5] days of additional quality-adjusted life per head of population versus 2.8 [1.7-4.0] days; 5.1 [3.4-7.1] additional days lived per head of population versus 3.3 [2.1-4.5] days). Making feasible changes to the delivery of the existing programme could result in a sizable increase in the benefit. For example, a strategy that combines extending eligibility to those with preexisting hypertension, extending the upper age of eligibility to 79 years, increasing uptake of health checks by 30%, and increasing treatment rates 2.5-fold amongst eligible patients (i.e., 'maximum potential' scenario) results in at least a 3-fold increase in benefits compared to the current programme (1,360 premature deaths versus 390; 5,100 people free of 1 of the 4 diseases versus 1,370; 37,000 additional QALYs versus 10,000; 33,000 additional years of life versus 9,000). Ensuring those who are assessed and eligible for statins receive statins is a particularly important strategy to increase benefits. Estimates of overall benefit are based on current incidence and management, and future declines in disease incidence or improvements in treatment could alter the actual benefits observed in the long run. We have focused on the cardiovascular element of the NHS Health Check programme. Some important noncardiovascular health outcomes (e.g., chronic obstructive pulmonary disease [COPD] prevention from smoking cessation and cancer prevention from weight loss) and other parts of the programme (e.g., brief interventions to reduce harmful alcohol consumption) have not been modelled. CONCLUSIONS: Our model indicates that the current NHS Health Check programme is contributing to improvements in health and reducing health inequalities. Feasible changes in the organisation of the programme could result in more than a 3-fold increase in health benefits

Self-organisation of auxin transport in plant cells

The phytohormone auxin plays a key role in many plant developmental processes. Its polar cell-to-cell transport is linked to and dependent on auxin efflux transporters and their polar localisation in cell membranes. This relies on feedback loops between auxin and its transport on many levels. Hypotheses brought forward in auxin biology, trying to elucidate the nature of these feedbacks, such as the canalisation hypothesis, depend on mechanisms by which auxin transport is established and maintained on specific routes through tissues. Auxin transport canalisation is based on a proposed feedback between auxin flux and auxin transport polarisation, with the result that auxin transport is directed by the strength of auxin fluxes. Despite this phenomenon being well described in biology, its underlying mechanisms are largely unknown. Many of them are occurring at the cell level, justifying a focus on cells in elucidating the nature of this feedback. In this thesis, computational modelling of self-organising mechanisms potentially leading to such phenomena at a cell level has been accomplished. While many auxin transport models are already available at tissue and whole plant scales, such a single cell model is a novel contribution. With the main focus on auxin/proton interactions grounded on the results of biological experiments, a feedback by which auxin influences its own transport by the activation of plasma membrane-bound proton pumps is described. In simulations, it is shown to lead to increased allocation of auxin in cells as well as to enhancement of all auxin transport fluxes over the membrane, and in due course to the establishment of canalisation-type polarisation patterns, without polarised transporter localisation. The results point towards a functional redundancy of polarisation in auxin transport and lead to hypotheses on differential energisation of auxin transporters, which may play a role in auxin transport polarisation events

Relating the Bipolar Spectrum to Dysregulation of Behavioural Activation: A Perspective from Dynamical Modelling

<div><p>Bipolar Disorders affect a substantial minority of the population and result in significant personal, social and economic costs. Understanding of the causes of, and consequently the most effective interventions for, this condition is an area requiring development. Drawing upon theories of Bipolar Disorder that propose the condition to be underpinned by dysregulation of systems governing behavioural activation or approach motivation, we present a mathematical model of the regulation of behavioural activation. The model is informed by non-linear, dynamical principles and as such proposes that the transition from “non-bipolar” to “bipolar” diagnostic status corresponds to a switch from mono- to multistability of behavioural activation level, rather than an increase in oscillation of mood. Consistent with descriptions of the behavioural activation or approach system in the literature, auto-activation and auto-inhibitory feedback is inherent within our model. Comparison between our model and empirical, observational data reveals that by increasing the non-linearity dimension in our model, important features of Bipolar Spectrum disorders are reproduced. Analysis from stochastic simulation of the system reveals the role of noise in behavioural activation regulation and indicates that an increase of nonlinearity promotes noise to jump scales from small fluctuations of activation levels to longer lasting, but less variable episodes. We conclude that further research is required to relate parameters of our model to key behavioural and biological variables observed in Bipolar Disorder.</p></div

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels

<div><p>Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for the ubiquity of nonlinear dynamics in gene expression networks, and generate useful guidelines for the design of synthetic gene circuits.</p></div

Robustness, evolvability, noise and expression levels for genotypes that are robust and evolvable.

<p>The relationships between sensitivity-based robustness, evolvability computed using 1-mutant neighbors, noise and gene expression levels in circuit I, when only monostable genotypes are considered. Genotypes from the set of genotypes characterized by high robustness and evolvability ((<i>E</i> × <i>R</i>) > 0.1, cf. Figure B in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153295#pone.0153295.s001" target="_blank">S1 File</a>) are drawn in red to compare their positions with respect to different measure combinations. (a): The robustness-evolvability relationship of the G-P mapping. (b): Scaled intrinsic noise versus robustness. (c): The relationship between scaled intrinsic noise and evolvability. (d): Gene expression levels at steady state () plotted against scaled intrinsic noise.</p

Nonlinearity creates regions presenting sudden changes in phenotype with small changes in genotype.

<p>Expression level as a function of the composite parameters <i>α</i> and <i>K</i> for the G-P mappings of circuit I obtained with <i>N</i> = 1 (panel a) and <i>N</i> = 2 (panel b). The product, (<i>E</i> × <i>R</i>), of evolvability computed for large scale perturbations (1-mutant neighbors) and sensitivity-based robustness is color-coded, with blue indicating a negative E/R correlation and red indicating the region of high robustness and evolvability (cf. Figure B in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153295#pone.0153295.s001" target="_blank">S1 File</a>).</p

Robustness and evolvability in G-P mappings.

<p>G-P mappings of circuit I (a-c) and circuit II (d-f), showing the density of genotypes on the map. Three different combinations of robustness/evolvability measures are shown in each case. The first column (a and d) shows the relationship between sensitivity-based robustness and scaled intrinsic noise (small mutational effects); the second column (b and e) shows sensitivity-based robustness against evolvability computed using 1-mutant neighbors, represented by 40% parameter perturbations on average (small mutational effects versus large mutational effects); the third column (c and f) shows robustness against evolvability when both are computed using 10% parameter perturbations (large mutational effects). Red colors indicate areas on the G-P mapping that are highly populated by genotypes.</p