Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Motor activity possesses a multiscale regulation that is characterized by fractal activity fluctuations with similar structure across a wide range of timescales spanning minutes to hours. Fractal activity patterns are disturbed in animals after ablating the master circadian pacemaker (suprachiasmatic nucleus, SCN) and in humans with SCN dysfunction as occurs with aging and in dementia, suggesting the crucial role of the circadian system in the multiscale activity regulation. We hypothesized that the normal synchronization between behavioural cycles and the SCN-generated circadian rhythms is required for multiscale activity regulation. To test the hypothesis, we studied activity fluctuations of rats in a simulated shift work protocol that was designed to force animals to be active during the habitual resting phase of the circadian/daily cycle. We found that these animals had gradually decreased mean activity level and reduced 24-h activity rhythm amplitude, indicating disturbed circadian and behavioural cycles. Moreover, these animals had disrupted fractal activity patterns as characterized by more random activity fluctuations at multiple timescales from 4 to 12 h. Intriguingly, these activity disturbances exacerbated when the shift work schedule lasted longer and persisted even in the normal days (without forced activity) following the shift work. The disrupted circadian and fractal patterns resemble those of SCN-lesioned animals and of human patients with dementia, suggesting a detrimental impact of shift work on multiscale activity regulation.     

Modelling the functional roles of synaptic and extra-synaptic γ-aminobutyric acid receptor dynamics in circadian timekeeping

In the suprachiasmatic nucleus (SCN), γ-aminobutyric acid (GABA) is a primary neurotransmitter. GABA can signal through two types of GABA_A receptor subunits, often referred to as synaptic GABA_A (gamma subunit) and extra-synaptic GABA_A (delta subunit). To test the functional roles of these distinct GABA_A in regulating circadian rhythms, we developed a multicellular SCN model where we could separately compare the effects of manipulating GABA neurotransmitter or receptor dynamics. Our model predicted that blocking GABA signalling modestly increased synchrony among circadian cells, consistent with published SCN pharmacology. Conversely, the model predicted that lowering GABA_A receptor density reduced firing rate, circadian cell fraction, amplitude and synchrony among individual neurons. When we tested these predictions, we found that the knockdown of delta GABA_A reduced the amplitude and synchrony of clock gene expression among cells in SCN explants. The model further predicted that increasing gamma GABA_A densities could enhance synchrony, as opposed to increasing delta GABA_A densities. Overall, our model reveals how blocking GABA_A receptors can modestly increase synchrony, while increasing the relative density of gamma over delta subunits can dramatically increase synchrony. We hypothesize that increased gamma GABA_A density in the winter could underlie the tighter phase relationships among SCN cells.     

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.     

Digital clocks: simple Boolean models can quantitatively describe circadian systems

The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day–night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock''s oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate that the ability of logic models to provide a computationally efficient representation of system behaviour could greatly facilitate the reverse-engineering of large-scale biochemical networks.     

Infection dynamics in ecosystems: on the interaction between red and grey squirrels,pox virus,pine martens and trees

Ecological and epidemiological processes and interactions influence each other, positively and negatively, directly and indirectly. The invasion potential of pathogens is influenced by the ecosystem context of their host species’ populations. This extends to the capacity of (multiple) host species to maintain their (common) pathogen and the way pathogen dynamics are influenced by changes in ecosystem composition. This paper exemplifies these interactions and consequences in a study of red and grey squirrel dynamics in the UK. Differences and changes in background habitat and trophic levels above and below the squirrel species lead to different dynamic behaviour in many subtle ways. The range of outcomes of the different interactions shows that one has to be careful when drawing conclusions about the mechanisms and processes involved in explaining observed phenomena concerning pathogens in their natural environment. The dynamic behaviour also shows that planning interventions, for example for conservation purposes, benefits from understanding the complexity of interactions beyond the particular pathogen and its threatened host species.     

Modelling fatigue and the use of fatigue models in work settings

In recent years, theoretical models of the sleep and circadian system developed in laboratory settings have been adapted to predict fatigue and, by inference, performance. This is typically done using the timing of prior sleep and waking or working hours as the primary input and the time course of the predicted variables as the primary output. The aim of these models is to provide employers, unions and regulators with quantitative information on the likely average level of fatigue, or risk, associated with a given pattern of work and sleep with the goal of better managing the risk of fatigue-related errors and accidents/incidents. The first part of this review summarises the variables known to influence workplace fatigue and draws attention to the considerable variability attributable to individual and task variables not included in current models. The second part reviews the current fatigue models described in the scientific and technical literature and classifies them according to whether they predict fatigue directly by using the timing of prior sleep and wake (one-step models) or indirectly by using work schedules to infer an average sleep-wake pattern that is then used to predict fatigue (two-step models). The third part of the review looks at the current use of fatigue models in field settings by organizations and regulators. Given their limitations it is suggested that the current generation of models may be appropriate for use as one element in a fatigue risk management system. The final section of the review looks at the future of these models and recommends a standardised approach for their use as an element of the ‘defenses-in-depth’ approach to fatigue risk management.     

A hybrid multi-stage predictive model for supply chain network collapse recovery analysis: a practical framework for effective supply chain network continuity management

In this paper, we present a multi-stage hybrid model for analysing a supply chain network (SCN) collapse recovery possibility. In the first stage of the model, we analyse the ability of an SCN to fulfil its customers required due date (RDD). As soon as the SCN defaults to timely fulfil their customers RDD, the second stage of the model is triggered to measure the collapse recovery possibility (CRP) of the SCN. Then, we calculate the final collapse recovery possibility (FCRP) of the SCN. Since the operation times, customer demand and external supply of raw material are uncertain, we use fuzzy triangular numbers to estimate the value of foregoing parameters. Consequently, we employ fuzzy program evaluation and review technique (FPERT) to calculate the completion time of SCN operations. In the third stage, for the critical elements of the SCN obtained from FPERT, the SC simulator is developed to provide a dynamic view of the SC and assesses the impact of decisions recommended by the SC fuzzy models on SC performance. Moreover, an empirical example is presented to validate the effectiveness of the proposed model. Finally, we conduct sensitivity analysis on the parameters employed in the model to analyse the behaviour of each parameter.     

Negative feedback self-regulation contributes to robust and high-fidelity transmembrane signal transduction

We present a minimal motif model for transmembrane cell signalling. The model assumes signalling events taking place in spatially distributed nanoclusters regulated by a birth/death dynamics. The combination of these spatio-temporal aspects can be modulated to provide a robust and high-fidelity response behaviour without invoking sophisticated modelling of the signalling process as a sequence of cascade reactions and fine-tuned parameters. Our results show that the fact that the distributed signalling events take place in nanoclusters with a finite lifetime regulated by local production is sufficient to obtain a robust and high-fidelity response.     

Synchronisation mechanisms of circadian rhythms in the suprachiasmatic nucleus

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. Each cell in the SCN contains an autonomous molecular clock, and the SCN is composed of multiple single-cell circadian oscillators. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to create an integrated pacemaker that can govern behavioural and physiological rhythmicity and be reset by environmental light. The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronise to maintain timekeeping activity. To study the synchronisation mechanisms and the circadian rhythm generation, we propose a model based on the structural and functional heterogeneity of the SCN. The model is a heterogeneous network of circadian oscillators in which individual oscillators are self-sustained. The authors show that the dorsomedial region can smooth the periodic light?dark (LD) signal curve and affect its wave form. The authors also study the rhythmic process of the circadian oscillators under the effect of the daily LD cycle, including three courses: information afferent inputs, oscillation and information efferent outputs. The numerical simulations are also given to demonstrate the theoretical results.     

Engineering challenges of BioNEMS: the integration of microfluidics, micro- and nanodevices, models and external control for systems biology

Systems biology, i.e. quantitative, postgenomic, postproteomic, dynamic, multiscale physiology, addresses in an integrative, quantitative manner the shockwave of genetic and proteomic information using computer models that may eventually have 10(6) dynamic variables with non-linear interactions. Historically, single biological measurements are made over minutes, suggesting the challenge of specifying 10(6) model parameters. Except for fluorescence and micro-electrode recordings, most cellular measurements have inadequate bandwidth to discern the time course of critical intracellular biochemical events. Micro-array expression profiles of thousands of genes cannot determine quantitative dynamic cellular signalling and metabolic variables. Major gaps must be bridged between the computational vision and experimental reality. The analysis of cellular signalling dynamics and control requires, first, micro- and nano-instruments that measure simultaneously multiple extracellular and intracellular variables with sufficient bandwidth; secondly, the ability to open existing internal control and signalling loops; thirdly, external BioMEMS micro-actuators that provide high bandwidth feedback and externally addressable intracellular nano-actuators; and, fourthly, real-time, closed-loop, single-cell control algorithms. The unravelling of the nested and coupled nature of cellular control loops requires simultaneous recording of multiple single-cell signatures. Externally controlled nano-actuators, needed to effect changes in the biochemical, mechanical and electrical environment both outside and inside the cell, will provide a major impetus for nanoscience.     

Design principles for phase-splitting behaviour of coupled cellular oscillators: clues from hamsters with 'split' circadian rhythms.

Nonlinear interactions among coupled cellular oscillators are likely to underlie a variety of complex rhythmic behaviours. Here we consider the case of one such behaviour, a doubling of rhythm frequency caused by the spontaneous splitting of a population of synchronized oscillators into two subgroups each oscillating in anti-phase (phase-splitting). An example of biological phase-splitting is the frequency doubling of the circadian locomotor rhythm in hamsters housed in constant light, in which the pacemaker in the suprachiasmatic nucleus (SCN) is reconfigured with its left and right halves oscillating in anti-phase. We apply the theory of coupled phase oscillators to show that stable phase-splitting requires the presence of negative coupling terms, through delayed and/or inhibitory interactions. We also find that the inclusion of real biological constraints (that the SCN contains a finite number of non-identical noisy oscillators) implies the existence of an underlying non-uniform network architecture, in which the population of oscillators must interact through at least two types of connections. We propose that a key design principle for the frequency doubling of a population of biological oscillators is inhomogeneity of oscillator coupling.     

Deciphering the expression dynamics of ANGPTL8 associated regulatory network in insulin resistance using formal modelling approaches

ANGPTL8 is a recently identified novel hormone which regulates both glucose and lipid metabolism. The increase in ANGPTL8 during compensatory insulin resistance has been recently reported to improve glucose tolerance and a part of cytoprotective metabolic circuit. However, the exact signalling entities and dynamics involved in this process have remained elusive. Therefore, the current study was conducted with a specific aim to model the regulation of ANGPTL8 with emphasis on its role in improving glucose tolerance during insulin resistance. The main contribution of this study is the construction of a discrete model (based on kinetic logic of René Thomas) and its equivalent Stochastic Petri Net model of ANGPTL8 associated Biological Regulatory Network (BRN) which can predict its dynamic behaviours. The predicted results of these models are in‐line with the previous experimental observations and provide comprehensive insights into the signalling dynamics of ANGPTL8 associated BRN. The authors’ results support the hypothesis that ANGPTL8 plays an important role in supplementing the insulin signalling pathway during insulin resistance and its loss can aggravate the pathogenic process by quickly leading towards Diabetes Mellitus. The results of this study have potential therapeutic implications for treatment of Diabetes Mellitus and are suggestive of its potential as a glucose‐lowering agent.Inspec keywords: molecular biophysics, biomembranes, diseases, stochastic processes, biochemistry, patient treatment, Petri nets, genetics, sugar, cellular biophysics, biology computingOther keywords: ANGPTL8 associated regulatory network, formal modelling approaches, lipid metabolism, compensatory insulin resistance, glucose tolerance, equivalent Stochastic Petri Net model, ANGPTL8 associated BRN     

Regulatory principles and experimental approaches to the circadian control of starch turnover

In many plants, starch is synthesized during the day and degraded during the night to avoid carbohydrate starvation in darkness. The circadian clock participates in a dynamic adjustment of starch turnover to changing environmental condition through unknown mechanisms. We used mathematical modelling to explore the possible scenarios for the control of starch turnover by the molecular components of the plant circadian clock. Several classes of plausible models were capable of describing the starch dynamics observed in a range of clock mutant plants and light conditions, including discriminating circadian protocols. Three example models of these classes are studied in detail, differing in several important ways. First, the clock components directly responsible for regulating starch degradation are different in each model. Second, the intermediate species in the pathway may play either an activating or inhibiting role on starch degradation. Third, the system may include a light-dependent interaction between the clock and downstream processes. Finally, the clock may be involved in the regulation of starch synthesis. We discuss the differences among the models’ predictions for diel starch profiles and the properties of the circadian regulators. These suggest additional experiments to elucidate the pathway structure, avoid confounding results and identify the molecular components involved.     

Macrophage interactions with modified material surfaces

An understanding of the biological response at material surfaces is a key biomaterials research area. Inflammation, tissue repair and regeneration are hallmarks of this response. Macrophages are long-lived and versatile cells and have a pivotal role at surfaces of implanted medical devices. The present review provides an update on macrophage behaviour at material surfaces. The interactions between cells and material surfaces are dynamic processes which require additional experimental models with different degrees of environmental complexity. It is concluded that both modifications of material surface properties and cellular signalling pathways will provide strategies for optimising the performance of biomedical devices.     

Modelling excitable cells using cycle-linear hybrid automata

Cycle-linear hybrid automata (CLHAs), a new model of excitable cells that efficiently and accurately captures action-potential morphology and other typical excitable-cell characteristics such as refractoriness and restitution, is introduced. Hybrid automata combine discrete transition graphs with continuous dynamics and emerge in a natural way during the (piecewise) approximation process of any nonlinear system. CLHAs are a new form of hybrid automata that exhibit linear behaviour on a per-cycle basis but whose overall behaviour is appropriately nonlinear. To motivate the need for this modelling formalism, first it is shown how to recast two recently proposed models of excitable cells as hybrid automata: the piecewise-linear model of Biktashev and the nonlinear model of Fenton-Karma. Both of these models were designed to efficiently approximate excitable-cell behaviour. We then show that the CLHA closely mimics the behaviour of several classical highly nonlinear models of excitable cells, thereby retaining the simplicity of Biktashev's model without sacrificing the expressiveness of Fenton-Karma. CLHAs are not restricted to excitable cells; they can be used to capture the behaviour of a wide class of dynamic systems that exhibit some level of periodicity plus adaptation.     

On methods for studying stochastic disease dynamics.

Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters.