A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system

A quantitative, physiology-based model of the ascending arousal system is developed, using continuum neuronal population modeling, which involves averaging properties such as firing rates across neurons in each population. The model includes the ventrolateral preoptic area (VLPO), where circadian and homeostatic drives enter the system, the monoaminergic and cholinergic nuclei of the ascending arousal system, and their interconnections. The human sleep-wake cycle is governed by the activities of these nuclei, which modulate the behavioral state of the brain via diffuse neuromodulatory projections. The model parameters are not free since they correspond to physiological observables. Approximate parameter bounds are obtained by requiring consistency with physiological and behavioral measures, and the model replicates the human sleep-wake cycle, with physiologically reasonable voltages and firing rates. Mutual inhibition between the wake-promoting monoaminergic group and sleep-promoting VLPO causes ;;flip-flop' behavior, with most time spent in 2 stable steady states corresponding to wake and sleep, with transitions between them on a timescale of a few minutes. The model predicts hysteresis in the sleep-wake cycle, with a region of bistability of the wake and sleep states. Reducing the monoaminergic-VLPO mutual inhibition results in a smaller hysteresis loop. This makes the model more prone to wake-sleep transitions in both directions and makes the states less distinguishable, as in narcolepsy. The model behavior is robust across the constrained parameter ranges, but with sufficient flexibility to describe a wide range of observed phenomena.     

Quantitative physiologically based modeling of subjective fatigue during sleep deprivation

A quantitative physiologically based model of the sleep-wake switch is used to predict variations in subjective fatigue-related measures during total sleep deprivation. The model includes the mutual inhibition of the sleep-active neurons in the hypothalamic ventrolateral preoptic area (VLPO) and the wake-active monoaminergic brainstem populations (MA), as well as circadian and homeostatic drives. We simulate sleep deprivation by introducing a drive to the MA, which we call wake effort, to maintain the system in a wakeful state. Physiologically this drive is proposed to be afferent from the cortex or the orexin group of the lateral hypothalamus. It is hypothesized that the need to exert this effort to maintain wakefulness at high homeostatic sleep pressure correlates with subjective fatigue levels. The model's output indeed exhibits good agreement with existing clinical time series of subjective fatigue-related measures, supporting this hypothesis. Subjective fatigue, adrenaline, and body temperature variations during two 72 h sleep deprivation protocols are reproduced by the model. By distinguishing a motivation-dependent orexinergic contribution to the wake-effort drive, the model can be extended to interpret variation in performance levels during sleep deprivation in a way that is qualitatively consistent with existing, clinically derived results. The example of sleep deprivation thus demonstrates the ability of physiologically based sleep modeling to predict psychological measures from the underlying physiological interactions that produce them.     

Incorporation of caffeine into a quantitative model of fatigue and sleep

A recent physiologically based model of human sleep is extended to incorporate the effects of caffeine on sleep-wake timing and fatigue. The model includes the sleep-active neurons of the hypothalamic ventrolateral preoptic area (VLPO), the wake-active monoaminergic brainstem populations (MA), their interactions with cholinergic/orexinergic (ACh/Orx) input to MA, and circadian and homeostatic drives. We model two effects of caffeine on the brain due to competitive antagonism of adenosine (Ad): (i) a reduction in the homestatic drive and (ii) an increase in cholinergic activity. By comparing the model output to experimental data, constraints are determined on the parameters that describe the action of caffeine on the brain. In accord with experiment, the ranges of these parameters imply significant variability in caffeine sensitivity between individuals, with caffeine's effectiveness in reducing fatigue being highly dependent on an individual's tolerance, and past caffeine and sleep history. Although there are wide individual differences in caffeine sensitivity and thus in parameter values, once the model is calibrated for an individual it can be used to make quantitative predictions for that individual. A number of applications of the model are examined, using exemplar parameter values, including: (i) quantitative estimation of the sleep loss and the delay to sleep onset after taking caffeine for various doses and times; (ii) an analysis of the system's stable states showing that the wake state during sleep deprivation is stabilized after taking caffeine; and (iii) comparing model output successfully to experimental values of subjective fatigue reported in a total sleep deprivation study examining the reduction of fatigue with caffeine. This model provides a framework for quantitatively assessing optimal strategies for using caffeine, on an individual basis, to maintain performance during sleep deprivation.     

Addition of a non-photic component to a light-based mathematical model of the human circadian pacemaker

Mathematical models have become vital to the study of many biological processes in humans due to the complexity of the physiological mechanisms underlying these processes and systems. While our current mathematical representation of the human circadian pacemaker has proven useful in many experimental situations, it uses as input only a direct effect of light on the circadian pacemaker. Although light (a photic stimulus) has been shown to be the primary synchronizer of the circadian pacemaker across a number of species, studies in both animals and humans have confirmed the existence of non-photic effects that also contribute to phase shifting and entrainment. We modified our light-based circadian mathematical model to reflect evidence from these studies that the sleep-wake cycle and/or associated behaviors have a non-photic effect on the circadian pacemaker. In our representation, the sleep-wake cycle and its associated behaviors provides a non-photic drive on the circadian pacemaker that acts both independently and concomitantly with light stimuli. Further experiments are required to validate fully our model and to understand the exact effect of the sleep-wake cycle as a non-photic stimulus for the human circadian pacemaker.     

Sleep and cortical temperature in the Djungarian hamster under baseline conditions and after sleep deprivation

The Djungarian hamster (Phodopus sungorus) is a markedly photoperiodic rodent which exhibits daily torpor under short photoperiod. Normative data were obtained on vigilance states, electroencephalogram (EEG) power spectra (0.25–25.0 Hz), and cortical temperature (T_CRT) under a 168 h light-dark schedule, in 7 Djungarian hamsters for 2 baseline days, 4 h sleep deprivation (SD) and 20 h recovery.During the baseline days total sleep time amounted to 59% of recording time, 67% in the light period and 43% in the dark period. The 4 h SD induced a small increase in the amount of non-rapid eye movement (NREM) sleep and a marked increase in EEG slow-wave activity (SWA; mean power density 0.75–4.0 Hz) within NREM sleep in the first hours of recovery. T_CRT was lower in the light period than in the dark period. It decreased at transitions from either waking or rapid eye movement (REM) sleep to NREM sleep, and increased at the transition from NREM sleep to waking or REM sleep. After SD, T_CRT was lower in all vigilance states.In conclusion, the sleep-wake pattern, EEG spectrum, and time course of T_CRT in the Djungarian hamster are similar to other nocturnal rodents. Also in the Djungarian hamster the time course of SWA seems to reflect a homeostatically regulated process as was formulated in the two-process model of sleep regulation.Abbreviations EEG electroencephalogram - EMG electromyogram - N NREM sleep - NREM non-rapid eye movement - R REM sleep - REM rapid eye movement - SD sleep deprivation - SWA slow-wave activity - T_CRT cortical temperature - TST total sleep time - VS vigilance state - W waking     

Time-of-Day Mediates the Influences of Extended Wake and Sleep Restriction on Simulated Driving

Although a nonlinear time-of-day and prior wake interaction on performance has been well documented, two recent studies have aimed to incorporate the influences of sleep restriction into this paradigm. Through the use of sleep-restricted forced desynchrony protocols, both studies reported a time-of-day?×?sleep restriction interaction, as well as a time-of-day?×?prior wake?×?sleep dose three-way interaction. The current study aimed to investigate these interactions on simulated driving performance, a more complex task with ecological validity for the problem of fatigued driving. The driving performance of 41 male participants (mean?±?SD: 22.8 ±2.2 yrs) was assessed on a 10-min simulated driving task with the standard deviation of lateral position (SDLAT) measured. Using a between-group design, participants were subjected to either a control condition of 9.33?h of sleep/18.66?h of wake, a moderate sleep-restriction (SR) condition of 7?h of sleep/21?h of wake, or a severe SR condition of 4.66?h of sleep/23.33?h of wake. In each condition, participants were tested at 2.5-h intervals after waking across 7?×?28-h d of forced desynchrony. Driving sessions occurred at nine doses of prior wake, within six divisions of the circadian cycle based on core body temperature (CBT). Mixed-models analyses of variance (ANOVAs) revealed significant main effects of time-of-day, prior wake, sleep debt, and sleep dose on SDLAT. Additionally, significant two-way interactions of time-of-day?×?prior wake and time-of-day?×?sleep debt, as well as significant three-way interactions of time-of-day?×?prior wake?×?sleep debt and time-of-day?×?sleep debt?×?sleep dose were observed. Although limitations such as the presence of practice effects and large standard errors are noted, the study concludes with three findings. The main effects demonstrate that extending wake, reducing sleep, and driving at poor times of day all significantly impair driving performance at an individual level. In addition to this, combining either extended wake or a sleep debt with the early morning hours greatly decreases driving performance. Finally, operating under the influence of a reduced sleep dose can greatly decrease performance at all times of the day. (Author correspondence: raymond.matthews@unisa.edu.au)     

A model investigation of the impact of ventilation-perfusion mismatch on oxygenation during apnea in preterm infants

Ventilation-perfusion (V/Q) mismatch is a prominent feature of preterm infants and adults with lung disease. V/Q mismatch is known to cause arterial hypoxemia under steady-state conditions, and has been proposed as the cause of rapid arterial oxygen desaturation during apnea. However, there is little evidence to support a role for V/Q mismatch in the dynamic changes in arterial oxygenation that occur during apnea. Using a mathematical model, we quantified the effect of V/Q mismatch on the rate of desaturation during apnea to ascertain whether it could lead to rates of up to 10% s^-1 as observed in preterm infants. We used a lung-body model for the preterm infant that incorporated 50 parallel alveolar-capillary units that were ventilated and perfused with the severity of V/Q mismatch (σ) defined conventionally according to σ=S.D. of the distribution of V/Q ratios. Average desaturation rate 10 s from apnea onset was strongly elevated with worsening V/Q mismatch as a result of an earlier desaturation of low V/Q units compared with high V/Q units. However, V/Q mismatch had little impact after apnea onset, with peak desaturation rate only substantially increased if mismatching caused a lowered resting arterial O₂ saturation. In conclusion, V/Q mismatch causes a more immediate onset of desaturation during apnea, and therefore places preterm infants and adults with lung disease at risk of hypoxemic dips. However, V/Q mismatch does not accelerate desaturation rate beyond apnea onset and cannot, therefore, explain the rapid desaturation observed during recurrent apnea in preterm infants.     

Dynamics of macromolecular populations: a mathematical model of the quantitative changes of RNA in the silkgland during the last larval instar.

The quantitative changes of RNA in the silkgland of Bombyx mori have been studied during the last larval instar by using a mathematical model (Volterra-Kostitzin model). This model can be associated with a global mechanism including synthesis and degradative processes. The numerical and statistical methods used for model analysis are described in an appendix. Thus we have compared the accumulation of total RNA (essentially ribosomal) after a treatment (juvenile hormone) and between several strains. The importance of the degradative factor is denoted to explain the observed differences, whereas the synthesis rates remain relatively stable. The last observation may lead us to an interpretation of the molecular effect of a selection to increase silk production : rather than an increase of the productivity of cellular machinery, the degradative process has been limited.     

simBio: a Java package for the development of detailed cell models

Quantitative dynamic computer models, which integrate a variety of molecular functions into a cell model, provide a powerful tool to create and test working hypotheses. We have developed a new modeling tool, the simBio package (freely available from http://www.sim-bio.org/), which can be used for constructing cell models, such as cardiac cells (the Kyoto model from Matsuoka et al., 2003, 2004a, b, the LRd model from Faber and Rudy, 2000, and the Noble 98 model from Noble et al., 1998), epithelial cells (Strieter et al., 1990) and pancreatic β cells (Magnus and Keizer, 1998). The simBio package is written in Java, uses XML and can solve ordinary differential equations. In an attempt to mimic biological functional structures, a cell model is, in simBio, composed of independent functional modules called Reactors, such as ion channels and the sarcoplasmic reticulum, and dynamic variables called Nodes, such as ion concentrations. The interactions between Reactors and Nodes are described by the graph theory and the resulting graph represents a blueprint of an intricate cellular system. Reactors are prepared in a hierarchical order, in analogy to the biological classification. Each Reactor can be composed or improved independently, and can easily be reused for different models. This way of building models, through the combination of various modules, is enabled through the use of object-oriented programming concepts. Thus, simBio is a straightforward system for the creation of a variety of cell models on a common database of functional modules.     

Approaching mathematical model of the immune network based DNA Strand Displacement system

One biggest obstacle in molecular programming is that there is still no direct method to compile any existed mathematical model into biochemical reaction in order to solve a computational problem. In this paper, the implementation of DNA Strand Displacement system based on nature-inspired computation is observed. By using the Immune Network Theory and Chemical Reaction Network, the compilation of DNA-based operation is defined and the formulation of its mathematical model is derived. Furthermore, the implementation on this system is compared with the conventional implementation by using silicon-based programming. From the obtained results, we can see a positive correlation between both. One possible application from this DNA-based model is for a decision making scheme of intelligent computer or molecular robot.     

Novel mathematical method for quantitative expression of deviation from the Higuchi model

A simple mathematical method to express the deviation in release profile of a test product following Higuchi's kinetics from an ideal Higuchi release profile was developed. The method is based on calculation of area under the curve (AUC) by using the trapezoidal rule. The precision of prediction depends on the number of data points. The method is exemplified for 2 dosage forms (tablets of diltiazem HCl and microspheres of diclofenac sodium) that are designed to release the drug over a 12-hour period. The method can be adopted for the formulations where drug release is incomplete (<100%) or complete (100%) at last sampling time. To describe the kinetics of drug release from the test formulation, zero-order, first-order, Higuchi's. Hixson-Crowell's, and Weibull's models were used. The criterion for selecting the most appropriate model was based on the goodness-of-fit test. The release kinetics of the tablets and microspheres were explained by the Higuchi model. The release profiles of the test batches were slightly below the ideal Higuchi release profile. For the test products, observed percentage deviation from an ideal Higuchi profile is less than 16% for tablets and less than 11% for microspheres. The proposed method can be extended to the modified release formulations that are designed to release a drug over 6, 18, or 24 hours. If the data points are not evenly separated, the ideal drug release profile and AUC are calculated according to the specific sampling time. The proposed method may be used for comparing formulated products during the research and development stage, for quality control of the products, or for promoting products by comparing performance of the test product with that of the innovator's product.     

Predicting the Timing and Duration of Sleep in an Operational Setting Using Social Factors

In recent years, there has been increasing interest in the use of bio‐mathematical models to predict alertness, performance, and/or fatigue in operational settings. Current models use only biological factors to make their estimations, which can be limited in operational settings where social and geo‐physical factors also dictate when sleep occurs. The interaction between social and biological factors that help determine the timing and duration of sleep during layover periods have been investigated in order to create and initially validate a mathematical model that may better predict sleep in the field. Participants were 32 male transmeridian airline pilots (17 captains, 10 first officers, and 5 second officers) flying the Sydney‐Bangkok‐London‐Singapore‐Sydney (SYD‐LHR) pattern. Participants continued their regular schedule while wearing activity monitors and completing sleep and work diaries. The theoretical sleep timing model underpinning this analysis consists of separate formulations for short (<32 h) and long (>32 h) break periods. Longer break periods are split into three distinct phases—recovery (break start until first local night), personal (first local night until last local night), and preparation phases (last local night until break end)—in order to exploit potential differences specific to each. Furthermore, an iterative procedure combining prediction and retrodiction (i.e., using future duty timing information to predict current sleep timing) was developed to optimize predictive ability. Analysis found an interaction between the social and circadian sleep pressures that changed over the break period. Correlation analysis indicated a strong relationship between the actual sleep and new model's predictions (r=0.7–0.9), a significant improvement when compared to existing models (r=0.1–0.4). Social and circadian pressures play important roles in regulating sleep for international flight crews. An initial model has been developed in order to regulate sleep in these crews. The initial results have shown promise when applied to small sets of data; however, more rigorous validation must be carried out.     

A quantitative test of the size efficiency hypothesis by means of a physiologically structured model

According to the size‐efficiency hypothesis (SEH) larger bodied cladocerans are better competitors for food than small bodied species. In environments with fish, however, the higher losses of the large bodied species due to size‐selective predation may shift the balance in favor of the small bodied species. Here we present a theoretical framework for the analysis of the competitive abilities of zooplankton species that takes both competition and predation into account in one coherent analysis. By applying the conceptually well‐understood framework of physiologically structured population models we were able to predict the relative difference in predation rates necessary to cause a shift in dominance of the large‐bodied species (Daphnia pulicaria) to the small‐bodied species (D. galeata). These predictions depend only on seven easily interpretable parameters per species: size at birth, size at maturity and maximum size, age at maturity, maximal clutch size, egg development time and finally the half‐saturation constant for food. The critical equilibrium mortality of D. pulicaria was 0.16 d^?1 at food concentrations close to the critical food concentration of D. galeata, i.e. D. pulicaria will win the competition as long as its mortality rate is below 0.16 d^?1. At higher food concentrations the differential mortality curve (plotting equilibrium mortalities of both species against each other) approached a linear function with a slope of one and an intercept equal to the difference in maximal population birth rates. The prediction of critical predation rates was independent of the ingestion rate of the cladocerans and the algal carrying capacity and food regeneration rate of the environment although the mechanism works through competition for a shared algal food resource. We interpret these findings in terms of the relative predation risk large and small‐bodied cladocerans will face in various freshwater ecosystems.     

Sleep deprivation impairs calcium signaling in mouse splenocytes and leads to a decreased immune response

Background

Sleep is a physiological event that directly influences health by affecting the immune system, in which calcium (Ca^2 +) plays a critical signaling role. We performed live cell measurements of cytosolic Ca^2 + mobilization to understand the changes in Ca^2 + signaling that occur in splenic immune cells after various periods of sleep deprivation (SD).

Methods

Adult male mice were subjected to sleep deprivation by platform technique for different periods (from 12 to 72 h) and Ca^2 + intracellular fluctuations were evaluated in splenocytes by confocal microscopy. We also performed spleen cell evaluation by flow cytometry and analyzed intracellular Ca^2 + mobilization in endoplasmic reticulum and mitochondria. Additionally, Ca^2 + channel gene expression was evaluated

Results

Splenocytes showed a progressive loss of intracellular Ca^2 + maintenance from endoplasmic reticulum (ER) stores. Transient Ca^2 + buffering by the mitochondria was further compromised. These findings were confirmed by changes in mitochondrial integrity and in the performance of the store operated calcium entry (SOCE) and stromal interaction molecule 1 (STIM1) Ca^2 + channels.

Conclusions and general significance

These novel data suggest that SD impairs Ca^2 + signaling, most likely as a result of ER stress, leading to an insufficient Ca^2 + supply for signaling events. Our results support the previously described immunosuppressive effects of sleep loss and provide additional information on the cellular and molecular mechanisms involved in sleep function.     

Mapping site indices for five Pacific Northwest conifers using a physiologically based model

Questions: How well can we predict tree growth potential (site index) of five, locally dominant tree species in reference to estimates made with a detailed vegetation classification? Location: The forested region of the Pacific Northwest, USA and Canada. Methods: We employed a physiologically based process model (3‐PG, Physiological Processes to Predict Growth) to generate estimates of site index under averaged climatic conditions (1971–2000) generated from hundreds of weather stations and extrapolated, with adjustments for topography, across the region at 1‐km resolution. The model was parameterized from published information, but we had to assume fixed values of soil water storage capacity at 200 mm and soil fertility at 70% of maximum across the region. Field estimates of site index for the five dominant species were derived from published correlations with detailed mapping of vegetation provided by The British Columbia Ministry of Forests and Range. Results: The site indices projected with the 3‐PG model for the five species combined, when compared with those produced by the Ministry of Forests and Range, produced an r² averaging ～0.5 with a standard error of 2.8 m at 50 yr, equivalent to 10% of the mean. Some of the variation may be attributed to inadequate information on soil properties. Importantly, the relationship between the two estimates was not significantly different from a 1:1 line, with an intercept of zero. Conclusions: The 3‐PG modelling approach offers a means of predicting spatial variation in site indices across the Pacific Northwest and provides a basis for predicting future site indices under a changing climate.     

Multisensory integration in the superior colliculus: a neural network model

Neurons in the superior colliculus (SC) are known to integrate stimuli of different modalities (e.g., visual and auditory) following specific properties. In this work, we present a mathematical model of the integrative response of SC neurons, in order to suggest a possible physiological mechanism underlying multisensory integration in SC. The model includes three distinct neural areas: two unimodal areas (auditory and visual) are devoted to a topological representation of external stimuli, and communicate via synaptic connections with a third downstream area (in the SC) responsible for multisensory integration. The present simulations show that the model, with a single set of parameters, can mimic various responses to different combinations of external stimuli including the inverse effectiveness, both in terms of multisensory enhancement and contrast, the existence of within- and cross-modality suppression between spatially disparate stimuli, a reduction of network settling time in response to cross-modal stimuli compared with individual stimuli. The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain several aspects of multisensory integration.     

Stability of a model of human granulopoiesis using continuous maturation

A class of mathematical models involving a convection-reaction partial differential equation (PDE) is introduced with reference to recovering human granulopoiesis after high dose chemotherapy with stem cell support. The stability properties of the model are addressed by means of numerical investigations and analysis. A simplified model with proliferation rate and mobilization rate independent of maturity shows that the model is stable as the maturation rate grows without bounds, but may go through stable and non-stable regimens as the maturation rate varies. It is also shown that the system is stable when parameters are chosen to approximate a real physiological situation. System characteristics do not change profoundly by introduction of a maturity-dependent proliferation and mobilization rate, as is necessary to make the model operate more in accordance with hematological observations. However, by changing the system mitotic responsiveness with respect to changes in cytokine level, the system is still stable but may show persistent oscillations much resembling clinical observations of cyclic neutropenia. Furthermore, in these cases, changes in the model feedback signal caused by, for instance, an impaired effective cytokine elimination by cell receptors may enforce these oscillations markedly.     

Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development

The thymus provides a stable microenvironment for post-natal thymocyte development that is finely regulated by a complicated network of cytokines, chemokines, cell-cell contacts, etc., the dysregulations of which contribute to many immunologic diseases including malignant lymphomas. A physiologically structured model in the form of first order partial differential equation (PDE) was developed to simulate the whole process. The combined effects of the thymic microenvironment were conceptualized into two (proliferation and differentiation) fields to serve as kernels of the PDE. In this paper, a novel method is developed to estimate the maturity-time structures of the two fields based solely on cell population data that are experimentally viable. Numerical examples demonstrate the effectiveness of the present method in revealing the two-dimensional (maturity and time) landscapes of the thymic microenvironment.      

The effect of Hamming distances in a computational model of selection by consequences

McDowell (2004) instantiated the Darwinian principles of selection, recombination, and mutation in a computational model of selection by consequences. The model has been tested under a variety of conditions and the outcome is quantitatively indistinguishable from that displayed by live organisms. The computational model animates a virtual organism with a repertoire of 100 behaviors, selected from the integers from 0 to 1023, where the corresponding binary representations constitute the behavior's genotypes. Using strings of binary digits raises the specific problem of Hamming distances: the number of bits that must be changed from 1 to 0 or from 0 to 1 in order to obtain another string of equal length. McDowell hypothesized that the Hamming distance may be computationally equivalent to the changeover delay used in experiments with live organisms. The results of the present experiments confirmed this hypothesis and revealed a robust rule about the effects of Hamming distances within the model, namely, in order to obtain good matching, the difference between the Hamming distance that separates the target classes and the largest Hamming distance comprised within a class must be equal to or larger than three.     

数学判别模型在预测害虫种群动态上的应用

根据两个总体的Fisher判别准则,建立了预测害虫种群动态的数学判别模型,对山东省惠民县1967～1977年共11年二代棉铃虫发生程度的两类资料进行了数量分析,建立了数学模型：y＝0．0127x1－0．023X2,对历史资料的回代验证与独立样本的预测,符合率在90％以上。