Sweat loss prediction using a multi-model approach

A new multi-model approach (MMA) for sweat loss prediction is proposed to improve prediction accuracy. MMA was computed as the average of sweat loss predicted by two existing thermoregulation models: i.e., the rational model SCENARIO and the empirical model Heat Strain Decision Aid (HSDA). Three independent physiological datasets, a total of 44 trials, were used to compare predictions by MMA, SCENARIO, and HSDA. The observed sweat losses were collected under different combinations of uniform ensembles, environmental conditions (15–40°C, RH 25–75%), and exercise intensities (250–600 W). Root mean square deviation (RMSD), residual plots, and paired t tests were used to compare predictions with observations. Overall, MMA reduced RMSD by 30–39% in comparison with either SCENARIO or HSDA, and increased the prediction accuracy to 66% from 34% or 55%. Of the MMA predictions, 70% fell within the range of mean observed value ± SD, while only 43% of SCENARIO and 50% of HSDA predictions fell within the same range. Paired t tests showed that differences between observations and MMA predictions were not significant, but differences between observations and SCENARIO or HSDA predictions were significantly different for two datasets. Thus, MMA predicted sweat loss more accurately than either of the two single models for the three datasets used. Future work will be to evaluate MMA using additional physiological data to expand the scope of populations and conditions.     

Climate change,species distribution models,and physiological performance metrics: predicting when biogeographic models are likely to fail

Modeling the biogeographic consequences of climate change requires confidence in model predictions under novel conditions. However, models often fail when extended to new locales, and such instances have been used as evidence of a change in physiological tolerance, that is, a fundamental niche shift. We explore an alternative explanation and propose a method for predicting the likelihood of failure based on physiological performance curves and environmental variance in the original and new environments. We define the transient event margin (TEM) as the gap between energetic performance failure, defined as CT_max, and the upper lethal limit, defined as LT_max. If TEM is large relative to environmental fluctuations, models will likely fail in new locales. If TEM is small relative to environmental fluctuations, models are likely to be robust for new locales, even when mechanism is unknown. Using temperature, we predict when biogeographic models are likely to fail and illustrate this with a case study. We suggest that failure is predictable from an understanding of how climate drives nonlethal physiological responses, but for many species such data have not been collected. Successful biogeographic forecasting thus depends on understanding when the mechanisms limiting distribution of a species will differ among geographic regions, or at different times, resulting in realized niche shifts. TEM allows prediction of the likelihood of such model failure.     

New mathematical model to estimate tissue blood perfusion, thermal contact resistance and core temperature

Analytical solutions were developed based on the Green's function method to describe heat transfer in tissue including the effects of blood perfusion. These one-dimensional transient solutions were used with a simple parameter estimation technique and experimental measurements of temperature and heat flux at the surface of simulated tissue. It was demonstrated how such surface measurements can be used during step changes in the surface thermal conditions to estimate the value of three important parameters: blood perfusion (w(b)), thermal contact resistance (R"), and core temperature of the tissue (T(core)). The new models were tested against finite-difference solutions of thermal events on the surface to show the validity of the analytical solution. Simulated data was used to demonstrate the response of the model in predicting optimal parameters from noisy temperature and heat flux measurements. Finally, the analytical model and simple parameter estimation routine were used with actual experimental data from perfusion in phantom tissue. The model was shown to provide a very good match with the data curves. This demonstrated the first time that all three of these important parameters (w(b), R", and T(core)) have simultaneously been estimated from a single set of thermal measurements at the surface of tissue.     

USING PHYLOGENETIC TREES TO STUDY SPECIATION AND EXTINCTION

One tool in the study of the forces that determine species diversity is the null, or simple, model. The fit of predictions to observations, good or bad, leads to a useful paradigm or to knowledge of forces not accounted for, respectively. It is shown how simple models of speciation and extinction lead directly to predictions of the structure of phylogenetic trees. These predictions include both essential attributes of phylogenetic trees: lengths, in the form of internode distances; and topology, in the form of internode links. These models also lead directly to statistical tests which can be used to compare predictions with phylogenetic trees that are estimated from data. Two different models and eight data sets are considered. A model without species extinction consistently yielded predictions closer to observations than did a model that included extinction. It is proposed that it may be useful to think of the diversification of recently formed monophyletic groups as a random speciation process without extinction.     

Field data confirm the ability of a biophysical model to predict wild primate body temperature

In the face of climate change there is an urgent need to understand how animal performance is affected by environmental conditions. Biophysical models that use principles of heat and mass transfer can be used to explore how an animal's morphology, physiology, and behavior interact with its environment in terms of energy, mass and water balances to affect fitness and performance. We used Niche Mapper™ (NM) to build a vervet monkey (Chlorocebus pygerythrus) biophysical model and tested the model's ability to predict core body temperature (T_b) variation and thermal stress against T_b and behavioral data collected from wild vervets in South Africa. The mean observed T_b in both males and females was within 0.5 °C of NM's predicted T_bs for 91% of hours over the five-year study period. This is the first time that NM's T_b predictions have been validated against field data from a wild endotherm. Overall, these results provide confidence that NM can accurately predict thermal stress and can be used to provide insight into the thermoregulatory consequences of morphological (e.g., body size, shape, fur depth), physiological (e.g. T_b plasticity) and behavioral (e.g., huddling, resting, shade seeking) adaptations. Such an approach allows users to test hypotheses about how animals adapt to thermoregulatory challenges and make informed predictions about potential responses to environmental change such as climate change or habitat conversion. Importantly, NM's animal submodel is a general model that can be adapted to other species, requiring only basic information on an animal's morphology, physiology and behavior.     

Modeling DNA sequence-based cis-regulatory gene networks

Gene network analysis requires computationally based models which represent the functional architecture of regulatory interactions, and which provide directly testable predictions. The type of model that is useful is constrained by the particular features of developmentally active cis-regulatory systems. These systems function by processing diverse regulatory inputs, generating novel regulatory outputs. A computational model which explicitly accommodates this basic concept was developed earlier for the cis-regulatory system of the endo16 gene of the sea urchin. This model represents the genetically mandated logic functions that the system executes, but also shows how time-varying kinetic inputs are processed in different circumstances into particular kinetic outputs. The same basic design features can be utilized to construct models that connect the large number of cis-regulatory elements constituting developmental gene networks. The ultimate aim of the network models discussed here is to represent the regulatory relationships among the genomic control systems of the genes in the network, and to state their functional meaning. The target site sequences of the cis-regulatory elements of these genes constitute the physical basis of the network architecture. Useful models for developmental regulatory networks must represent the genetic logic by which the system operates, but must also be capable of explaining the real time dynamics of cis-regulatory response as kinetic input and output data become available. Most importantly, however, such models must display in a direct and transparent manner fundamental network design features such as intra- and intercellular feedback circuitry; the sources of parallel inputs into each cis-regulatory element; gene battery organization; and use of repressive spatial inputs in specification and boundary formation. Successful network models lead to direct tests of key architectural features by targeted cis-regulatory analysis.     

Genome-scale microbial in silico models: the constraints-based approach

Genome sequencing and annotation has enabled the reconstruction of genome-scale metabolic networks. The phenotypic functions that these networks allow for can be defined and studied using constraints-based models and in silico simulation. Several useful predictions have been obtained from such in silico models, including substrate preference, consequences of gene deletions, optimal growth patterns, outcomes of adaptive evolution and shifts in expression profiles. The success rate of these predictions is typically in the order of 70-90% depending on the organism studied and the type of prediction being made. These results are useful as a basis for iterative model building and for several practical applications.     

A simple model for predicting the effect of hygrothermal conditions on populations of house dust mite Dermatophagoides pteronyssinus (Acari: Pyroglyphidae)

A simple mite population index (MPI) model is presented which predicts the effect on house dust mite populations of any combination of temperature and relative humidity (RH). For each combination, the output is an index, or multiplication factor, such that 1.1 indicates 10% population growth and 0.9 indicates 10% population decline. To provide data for the model, laboratory experiments have been carried out using lab cultures of Dermatophagoides pteronyssinus. The population change was observed for mites held in steady-state conditions at different combinations of temperature and RH over 21 days. From the results, a best-fit equation has been derived which forms the basis of the MPI model. The results also enable a new term to be defined: the Population Equilibrium Humidity, PEH, the RH for a given temperature at which house dust mite populations neither grow nor decline. It is similar to Critical Equilibrium Humidity, the RH below which house dust mites are unable to maintain water balance, but relates to a population of mites (rather than a physiological phenomenon) and is more able to take account of the observed effects of extremes of temperature and RH. Compared with previous population models, the MPI model is potentially more accurate and comprehensive. It can be combined with other simple models (described in previous papers), such as BED, which simulates the average hygrothermal conditions in a bed, given room␣conditions, and Condensation Targeter II, which simulates room conditions given a range of easily obtainable inputs for climate, house type and occupant characteristics. In this way it is now possible, for any individual dwelling, to assess the most effective means of controlling mite populations by environmental means, such as by improving standards of ventilation and insulation, or by modifying the occupant behaviour that affects the hygrothermal environment within a dwelling. Although the MPI model requires further development and validation, it has already proved useful for understanding more clearly how the different hygrothermal conditions found in beds and bedrooms can affect mite populations. It has also demonstrated that there is considerable scope for controlling mites by environmental means in cold winter climates such as the UK.     

A steady state model for analyzing the cellular binding, internalization and degradation of polypeptide ligands

We demonstrate that the interaction of polypeptide ligands with cells under physiological conditions can be described by a set of steady state equations. These equations include four new rate constants: V_r, the rate of insertion of receptors into the cell membrane; K_e, the endocytotic rate constant of occupied receptors; K_t, the turnover rate constant of unoccupied receptors; and K_h, the rate constant of hydrolysis of internalized ligand. Several simple procedures are described for determining these constants. In experiments in which epidermal growth factor and human fibroblasts were used, the cell-ligand interactions followed the predictions of the steady state model. The utility of the steady state equations is demonstrated by establishing the kinetic basis of the commonly observed “down regulation” phenomenon and by quantitating the effect of methylamine on the endocytotic and degradation rates of epidermal growth factor. We also show that the slope of a “Scatchard plot” of steady state binding data is a complex constant including terms for the endocytotic rate of both occupied and unoccupied receptors. The X-intercept of such a plot is a function of the insertion rate of new receptors, the internalization rate of occupied receptors and the degradation rate of the internalized ligand. The steady state equations allow one to predict changes in cellular ligand binding resulting from alterations in the four rate constants. They also provide a foundation for computer simulations of ligand-cell interactions, which closely correspond to experimental data. These approaches should facilitate studies on the control of cellular activities by these polypeptide ligands.     

Comparison of amplitude recovery dynamics of two limit cycle oscillator models of the human circadian pacemaker

At an organism level, the mammalian circadian pacemaker is a two-dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures--including plasma cortisol, plasma melatonin, and core body temperature (CBT)--all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A = 1), but are markedly different in the prediction of recovery rates when A < 0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaike's Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.     

Modelling the dynamic physical protection of soil organic carbon: Insights into carbon predictions and explanation of the priming effect

The role and significance of physically protected soil organic carbon (SOC) in regulating SOC dynamics remains unclear. Here, we developed a simple theoretical model (DP model) considering dynamic physical protection to simulate the dynamics of protected (C_p) and unprotected SOC (C_u), and compared the modelling results with a conventional two‐pool (fast vs. slow) model considering chemical recalcitrance. The two models were first constrained using extensive SOC data collected from soils with and without fresh carbon (C) inputs under incubation conditions, and then applied to project SOC dynamics and explore mechanisms underpinning the priming effect (PE). Overall, both models explained more than 99% of the variances in observed SOC dynamics. The DP model predicted that C_p accounted for the majority of total SOC. As decomposition proceeds, the proportion of C_p reached >90% and kept relatively constant. Although the similar performance of the two models in simulating observed total SOC dynamics, their predictions of future SOC dynamics were divergent, challenging the predictions of widely used pool‐based models. The DP model also suggested alternative mechanisms underpinning the priming of SOC decomposition by fresh C inputs. The two‐pool model suggested that the PE was caused by the stimulated decomposition rates, especially for the slow recalcitrant pool, while the DP model suggested that the PE might be the combined consequence of stimulated C_u decomposition, the liberation of C_p to decomposition and the inhibition of the protection of unprotected SOC. The model‐data integration provided a new explanation for the PE, highlighting the importance of liberation of initially physically protected SOC to decomposition by new C inputs. Our model‐data integration demonstrated the importance of simulating physical protection processes for reliable SOC predictions, and provided new insights into mechanistic understanding of the priming effect.     

Predictive ADMET studies, the challenges and the opportunities

Predictive ADMET is the new 'hip' area in drug discovery. The aim is to use large databases of ADMET data associated with structures to build computational models that link structural changes with changes in response, from which compounds with improved properties can be designed and predicted. These databases also provide the means to enable predictions of human ADMET properties to be made from human in vitro and animal in vivo ADMET measurements. Both methods are limited by the amount of data available to build such predictive models, the limitations of modelling methods and our understanding of the systems we wish to model. The current failures, successes and opportunities are reviewed.     

Applications of real-time thermoregulatory models to occupational heat stress: validation with military and civilian field studies

A real-time thermoregulatory model using noninvasive measurements as inputs was developed for predicting physiological responses of individuals working long hours. The purpose of the model is to reduce heat-related injuries and illness by predicting the physiological effects of thermal stress on individuals while working. The model was originally validated mainly by using data from controlled laboratory studies. This study expands the validation of the model with field data from 26 test volunteers, including US Marines, Australian soldiers, and US wildland fire fighters (WLFF). These data encompass a range of environmental conditions (air temperature: 19-30° C; relative humidity: 25-63%) and clothing (i.e., battle dress uniform, chemical-biological protective garment, WLFF protective gear), while performing diverse activities (e.g., marksmanship, marching, extinguishing fires, and digging). The predicted core temperatures (Tc), calculated using environmental, anthropometric, clothing, and heart rate measures collected in the field as model inputs, were compared with subjects' Tc collected with ingested telemetry temperature pills. Root mean standard deviation (RMSD) values, used for goodness of fit comparisons, indicated that overall, the model predictions were in close agreement with the measured values (grand mean of RMSD: 0.15-0.38° C). Although the field data showed more individual variability in the physiological data relative to more controlled laboratory studies, this study showed that the performance of the model was adequate.     

Comparison of Amplitude Recovery Dynamics of Two Limit Cycle Oscillator Models of the Human Circadian Pacemaker

At an organism level, the mammalian circadian pacemaker is a two‐dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures—including plasma cortisol, plasma melatonin, and core body temperature (CBT)—all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A=1), but are markedly different in the prediction of recovery rates when A<0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaike's Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.     

Effects of directional environmental change on extinction dynamics in experimental microbial communities are predicted by a simple model

Global temperatures are expected to rise between 1.1 and 6.4°C over the next 100 years, although the exact rate will depend on future greenhouse emissions, and will vary spatially. Temperature can alter an individual's metabolic rate, and consequently birth and death rates. In declining populations, these alterations may manifest as changes in the rate of that population's decline, and subsequently the timing of extinction events. Predicting such events could therefore be of considerable use. We use a small‐scale experimental system to investigate how the rate of temperature change can alter a population's time to extinction, and whether it is possible to predict this event using a simple phenomenological model that incorporates information about population dynamics at a constant temperature, published scaling of metabolic rates, and temperature. In addition, we examine 1) the relative importance of the direct effects of temperature on metabolic rate, and the indirect effects (via temperature driven changes in body size), on predictive accuracy (defined as the proximity of the predicted date of extinction to the mean observed date of extinction), 2) the combinations of model parameters that maximise accuracy of predictions, and 3) whether substituting temperature change through time with mean temperature produces accurate predictions. We find that extinction occurs earlier in environments that warm faster, and this can be accurately predicted (R² > 0.84). Increasing the number of parameters that were temperature‐dependent increased the model's accuracy, as did scaling these temperature‐dependent parameters with either the direct effects of temperature alone, or with the direct and indirect effects. Using mean temperature through time instead of actual temperature produces less accurate predictions of extinction. These results suggest that simple phenomenological models, incorporating metabolic theory, may be useful in understanding how environmental change can alter a population's rate of extinction. Synthesis Understanding how populations will respond to future climatic change is a key goal in ecology, however the exact rate of future warming will vary both spatially and temporally. Consequently, mathematical models must be used to understand the potential range of future population dynamics under various warming scenarios. We use a combination of experimentation and modelling to show that the effects of varying rates of environmental change on population dynamics can be predicted by a simple model. However, the accuracy of these predictions depends upon, amongst other things, a detailed knowledge of how temperature will change over time, rather than approximating this change to mean temperature.     

Spatial scale,topography and thermoregulatory behaviour interact when modelling species’ thermal niches

The spatial scale at which climate and species’ occupancy data are gathered, and the resolution at which ecological models are run, can strongly influence predictions of species performance and distributions. Running model simulations at coarse rather than fine spatial resolutions, for example, can determine if a model accurately predicts the distribution of a species. The impacts of spatial scale on a model's accuracy are particularly pronounced across mountainous terrain. Understanding how these discrepancies arise requires a modelling approach in which the underlying processes that determine a species’ distribution are explicitly described. Here we use a process‐based model to explore how spatial resolution, topography and behaviour alter predictions of a species thermal niche, which in turn constrains its survival and geographic distribution. The model incorporates biophysical equations to predict the operative temperature (T_e), thermal‐dependent performance and survival of a typical insect, with a complex life‐cycle, in its microclimate. We run this model with geographic data from a mountainous terrain in South Africa using climate data at three spatial resolutions. We also explore how behavioural thermoregulation affects predictions of a species performance and survival by allowing the animal to select the optimum thermal location within each coarse‐grid cell. At the regional level, coarse‐resolution models predicted lower T_e at low elevations and higher T_e at high elevations than models run at fine‐resolutions. These differences were more prominent on steep, north‐facing slopes. The discrepancies in T_e in turn affected estimates of the species thermal niche. The modelling framework revealed how spatial resolution and topography influence predictions of species distribution models, including the potential impacts of climate change. These systematic biases must be accounted for when interpreting the outputs of future modelling studies, particularly when species distributions are predicted to shift from uniform to topographically heterogeneous landscapes.     

Key role of local regulation in chemosensing revealed by a new molecular interaction-based modeling method

The signaling network underlying eukaryotic chemosensing is a complex combination of receptor-mediated transmembrane signals, lipid modifications, protein translocations, and differential activation/deactivation of membrane-bound and cytosolic components. As such, it provides particularly interesting challenges for a combined computational and experimental analysis. We developed a novel detailed molecular signaling model that, when used to simulate the response to the attractant cyclic adenosine monophosphate (cAMP), made nontrivial predictions about Dictyostelium chemosensing. These predictions, including the unexpected existence of spatially asymmetrical, multiphasic, cyclic adenosine monophosphate–induced PTEN translocation and phosphatidylinositol-(3,4,5)P₃ generation, were experimentally verified by quantitative single-cell microscopy leading us to propose significant modifications to the current standard model for chemoattractant-induced biochemical polarization in this organism. Key to this successful modeling effort was the use of “Simmune,” a new software package that supports the facile development and testing of detailed computational representations of cellular behavior. An intuitive interface allows user definition of complex signaling networks based on the definition of specific molecular binding site interactions and the subcellular localization of molecules. It automatically translates such inputs into spatially resolved simulations and dynamic graphical representations of the resulting signaling network that can be explored in a manner that closely parallels wet lab experimental procedures. These features of Simmune were critical to the model development and analysis presented here and are likely to be useful in the computational investigation of many aspects of cell biology.     

Toward improved model structures for analyzing priming: potential pitfalls of using bulk turnover time

Many studies have shown that elevated atmospheric CO₂ concentrations result in increased plant carbon inputs to soil that can accelerate the decomposition of native soil organic matter, an effect known as priming. Consequently, it is important to understand and quantify the priming effect for future predictions of carbon–climate feedbacks. There are potential pitfalls, however, when representing this complex system with a simple, first‐order model. Here, we show that a multi‐pool soil carbon model can match the change in bulk turnover time calculated from overall respiration and carbon stocks (a one‐pool approach) at elevated CO₂, without a change in decomposition rate constants of individual pools (i.e., without priming). Therefore, the priming effect cannot be quantified using a one‐pool model alone, and even a two‐pool model may be inadequate, depending on the effect size as well as the distribution of soil organic carbon and turnover times. In addition to standard measurements of carbon stocks and CO₂ fluxes, we argue that quantifying the fate of new plant inputs requires isotopic tracers and microbial measurements. Our results offer insights into modeling and interpreting priming from observations.     

Task-induced neural covariability as a signature of approximate Bayesian learning and inference

Perception is often characterized computationally as an inference process in which uncertain or ambiguous sensory inputs are combined with prior expectations. Although behavioral studies have shown that observers can change their prior expectations in the context of a task, robust neural signatures of task-specific priors have been elusive. Here, we analytically derive such signatures under the general assumption that the responses of sensory neurons encode posterior beliefs that combine sensory inputs with task-specific expectations. Specifically, we derive predictions for the task-dependence of correlated neural variability and decision-related signals in sensory neurons. The qualitative aspects of our results are parameter-free and specific to the statistics of each task. The predictions for correlated variability also differ from predictions of classic feedforward models of sensory processing and are therefore a strong test of theories of hierarchical Bayesian inference in the brain. Importantly, we find that Bayesian learning predicts an increase in so-called “differential correlations” as the observer’s internal model learns the stimulus distribution, and the observer’s behavioral performance improves. This stands in contrast to classic feedforward encoding/decoding models of sensory processing, since such correlations are fundamentally information-limiting. We find support for our predictions in data from existing neurophysiological studies across a variety of tasks and brain areas. Finally, we show in simulation how measurements of sensory neural responses can reveal information about a subject’s internal beliefs about the task. Taken together, our results reinterpret task-dependent sources of neural covariability as signatures of Bayesian inference and provide new insights into their cause and their function.