The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows.

A structural identifiability analysis is performed on a mathematical model for the coupled transmission of two classes of pathogen. The pathogens, classified as major and minor, are aetiological agents of mastitis in dairy cows that interact directly and via the immunological reaction in their hosts. Parameter estimates are available from experimental data for all but four of the parameters in the model. Data from a longitudinal study of infection are used to estimate these unknown parameters. A novel approach and application of structural identifiability analysis is combined in this paper with the estimation of cross-protection parameters using epidemiological data.     

Direct comparison of turbulence measurements by Langmuir probe technique and by reflectometry

A comparative analysis of the experimental results from two diagnostic methods—reflectometry and Langmuir probe technique—is carried out, and advantages and drawbacks of these methods are considered; in particular, a comparison is made between their spectral characteristics. The problems arising in interpreting the experimental reflectometric results are thoroughly discussed. To resolve these problems, a stochastic turbulence model with statistical, spectral, and correlation turbulent plasma properties close to the measured ones is constructed. The model is used to simulate the propagation of an electromagnetic wave in a model turbulent plasma. A comparison of the numerical results with the experimental data shows a high spatial locality of reflectometric measurements.     

Modeling P-loops domain of sodium channel: homology with potassium channels and interaction with ligands

A large body of experimental data on Na+ channels is available, but the interpretation of these data in structural terms is difficult in the absence of a high-resolution structure. Essentially different electrophysiological and pharmacological properties of Na+ and K+ channels and poor identity of their sequences obstruct homology modeling of Na+ channels. In this work, we built the P-loops model of the Na+ channel, in which the pore helices are arranged exactly as in the MthK bacterial K+ channel. The conformation of the selectivity-filter region, which includes residues in positions -2 through +4 from the DEKA locus, was shaped around rigid molecules of saxitoxin and tetrodotoxin that are known to form multiple contacts with this region. Intensive Monte Carlo minimization that started from the MthK-like conformation produced practically identical saxitoxin- and tetrodotoxin-based models. The latter was tested to explain a wide range of experimental data that were not used at the model building stage. The docking of tetrodotoxin analogs unambiguously predicted their optimal orientation and the interaction energy that correlates with the experimental activity. The docking of mu-conotoxin produced a binding model consistent with experimentally known toxin-channel contacts. Monte Carlo-minimized energy profiles of tetramethylammonium pulled through the selectivity-filter region explain the paradoxical experimental data that this organic cation permeates via the DEAA but not the AAAA mutant of the DEKA locus. The model is also consistent with earlier proposed concepts on the Na+ channel selectivity as well as Ca2+ selectivity of the EEEE mutant of the DEKA locus. Thus, the model integrates available experimental data on the Na+ channel P-loops domain, and suggests that it is more similar to K+ channels than was believed before.     

The epidemiology of BSE in cattle herds in Great Britain. II. Model construction and analysis of transmission dynamics.

Mathematical model that describe the key processes determining the pattern of the bovine spongiform encephalopathy (BSE) epidemic in British cattle are derived that allow for infection from feed as well as maternal and direct horizontal transmission. Heterogeneous susceptibility classes are also incorporated into the analysis. Maximum likelihood methods are used to estimate parameters and to obtain confidence intervals from available experimental and epidemiological data. A comprehensive sensitivity analysis of all model parameters and distributional assumptions is presented. Additional validation is provided by fitting the model to independent data collected in Northern Ireland. Model estimates and predictions based on BSE case data for Great Britain and Northern Ireland, together with their implications, are reviewed, and future research priorities discussed.     

Modeling substrate inhibition of microbial growth

This article presents a general equation for substrate inhibition of microbial growth using a statistical thermodynamic approach. Existing empirical models adapted from enzyme kinetics, for example, the Haldane-Andrews equation, often criticized for not being physically based for microbial growth, are shown to derive from the general equation in this article, and their empirical parameters are shown to be well defined physically. Three sets of experimental data from the literature are used to test the modeling abilities of the general equation to represent experimental data. The results are compared with those obtained by fitting the same data set to a widely used empirical model existing in the literature. The general equation is found to represent all three experimental data sets better than the alternative model tested. In addition, a graphical method existing in enzyme kinetics is successfully adapted and further developed to determine the number of inhibition sites of a basic functional unit of a bacterial cell. (c) 1996 John Wiley & Sons, Inc.     

Comparative analysis of the theoretical models of a hot dense plasma and the density functional theory

A general set of self-consistent field equations that describes the state of the whole ensemble of atoms and ions in a hot dense plasma is derived using the density functional theory. The set of equations is used to obtain equations of the Thomas-Fermi model, the Hartree-Fock-Slater model, the detail configuration account method, and the ion model. This approach makes it possible to identify the physical approximations underlying the theoretical models and to analyze their applicability ranges. Some of the results obtained from the Hartree-Fock-Slater model, the detail configuration account method, and the ion model are compared with the experimental data.     

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

Perturbation analysis analyzed—mathematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.     

Conceptual, methodological and computational issues concerning the compartmental modeling of a complex biological system: Postprandial inter-organ metabolism of dietary nitrogen in humans

A multi-compartmental model has been developed to describe dietary nitrogen (N) postprandial distribution and metabolism in humans. This paper details the entire process of model development, including the successive steps of its construction, parameter estimation and validation. The model was built using experimental data on dietary N kinetics in certain accessible pools of the intestine, blood and urine in healthy adults fed a [15N]-labeled protein meal. A 13-compartment, 21-parameter model was selected from candidate models of increasing order as being the minimum structure able to properly fit experimental data for all sampled compartments. Problems of theoretical identifiability and numerical identification of the model both constituted mathematical challenges that were difficult to solve because of the large number of unknown parameters and the few experimental data available. For this reason, new robust and reliable methods were applied, which enabled (i) a check that all model parameters could theoretically uniquely be determined and (ii) an estimation of their numerical values with satisfactory precision from the experimental data. Finally, model validation was completed by first verifying its a posteriori identifiability and then carrying out external validation.     

Correlation between the osmotic second virial coefficient and the solubility of proteins

A correlation between the osmotic second virial coefficient and the solubility of proteins is derived from classical thermodynamics to support an empirical relation previously found by Wilson and co-workers (1). The model is based on the equality of fugacities of the protein in the equilibrium phases, with the details of the model depending on the standard state used. The parameters in this model have been fitted to data for several systems, mainly with lysozyme as the protein. The model is found to describe experimental data, with variations in protein concentration, salt type and concentration, temperature, and pH, both qualitatively and quantitatively. Agreement between the model and the experimental data is very good for protein solubilities up to 30 mg/mL. Above this value the model underpredicts the experimental data, probably as a result of multibody interactions that are not included in the model here. Variations of the model parameters with protein type, temperature, pH, and salt type are discussed.     

A model of xylitol production by the yeast Candida mogii

Production of xylitol from xylose in batch fermentations of Candida mogii ATCC 18364 is discussed in the presence of glucose as the cosubstrate. Various initial ratios of glucose and xylose concentrations are assessed for their impact on yield and rate of production of xylitol. Supplementation with glucose at the beginning of the fermentation increased the specific growth rate, biomass yield and volumetric productivity of xylitol compared with fermentation that used xylose as the sole carbon source. A mathematical model is developed for eventual use in predicting the product formation rate and yield. The model parameters were estimated from experimental observations, using a genetic algorithm. Batch fermentations, which were carried out with xylose alone and a mixture of xylose and glucose, were used to validate the model. The model fitted well with the experimental data of cell growth, substrate consumption and xylitol production.     

A Stochastic Model for the Predatory Behaviour of Naive Spiderlings (Araneas: Salticidae)

A stochastic model is proposed for the hunting behaviour of jumping spiders when they are newly emerged from the egg-sac. The model takes into account the fact that the spiders are often unsuccessful when they attempt to catch prey for the first time and also the fact that their rate of response to prey slows down with time if they are unsuccessful. It is shown that the spiderlings ability to catch perceived prey improves with the number of prey captured. The model has been fitted to experimental data using the method of maximum likelihood and a good fit has been obtained. The model could be used as part of a model for the whole predation system.     

The roles of ecological and evolutionary influences in providing structure to parasite species assemblages.

Parasite species assemblages currently are thought to range from isolationist to interactive, their dynamic properties being related to the number of species and types of hosts involved. The literature contains few experimental tests of this concept, however, and many of the host/parasite systems studied to date are not amenable to experimental manipulation. In this review, the presence of a parasite species, in a sample of host individuals, is considered to be an evolutionary phenomenon, but the parasite's population structure is considered to be an ecological one. Studies that allow evaluation of these 2 influences are comparative in nature and include data from a series of homogeneous samples of host populations. A lottery model is presented, in which hosts acquire their assemblages of parasites by Monte Carlo type sampling from multiple kind arrays; the major structuring influence is the relative probability of becoming infected by various parasite species. Claims of parasite species interaction need to be supported by studies showing departures from the predictions of this model. The species density and infraassemblage diversity index distributions are recommended as quantitative tools useful in such work.     

An Integrated Model of Eicosanoid Metabolism and Signaling Based on Lipidomics Flux Analysis

There is increasing evidence for a major and critical involvement of lipids in signal transduction and cellular trafficking, and this has motivated large-scale studies on lipid pathways. The Lipid Metabolites and Pathways Strategy consortium is actively investigating lipid metabolism in mammalian cells and has made available time-course data on various lipids in response to treatment with KDO₂-lipid A (a lipopolysaccharide analog) of macrophage RAW 264.7 cells. The lipids known as eicosanoids play an important role in inflammation. We have reconstructed an integrated network of eicosanoid metabolism and signaling based on the KEGG pathway database and the literature and have developed a kinetic model. A matrix-based approach was used to estimate the rate constants from experimental data and these were further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data well for all species, and simulated enzyme activities were similar to their literature values. The quantitative model for eicosanoid metabolism that we have developed can be used to design experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways.     

The brownian ratchet and power stroke models for posttranslational protein translocation into the endoplasmic reticulum

A quantitative analysis of experimental data for posttranslational translocation into the endoplasmic reticulum is performed. This analysis reveals that translocation involves a single rate-limiting step, which is postulated to be the release of the signal sequence from the translocation channel. Next, the Brownian ratchet and power stroke models of translocation are compared against the data. The data sets are simultaneously fit using a least-squares criterion, and both models are found to accurately reproduce the experimental results. A likelihood-ratio test reveals that the optimal fit of the Brownian ratchet model, which contains one fewer free parameter, does not differ significantly from that of the power stroke model. Therefore, the data considered here cannot be used to reject this import mechanism. The models are further analyzed using the estimated parameters to make experimentally testable predictions.     

Modulation of gramicidin A open channel lifetime by ion occupancy.

The hypothesis that the gramicidin A channel stability depends on the level of ion occupancy of the channel was used to derive a mathematical model relating channel lifetime to channel occupancy. Eyring barrier permeation models were examined for their ability to fit the zero-voltage conductance, current-voltage, as well as lifetime data. The simplest permeation model required to explain the major features of the experimental data consists of three barriers and four sites (3B4S) with a maximum of two ions occupying the channel. The average lifetime of the channel was calculated from the barrier model by assuming the closing rate constant to be proportional to the probability of the internal channel sites being empty. The link between permeation and lifetime has as its single parameter the experimentally determined averaged lifetime of gramicidin A channels in the limit of infinitely dilute solutions and has therefore no adjustable parameters. This simple assumption that one or more ions inside the channel completely stabilize the dimer conformation is successful in explaining the experimental data considering the fact that this model for stabilization is independent of ion species and configurational occupancy. The model is used to examine, by comparison with experimental data, the asymmetrical voltage dependence of the lifetime in asymmetrical solutions, the effects of blockers, and the effects of elevated osmotic pressure.     

A MATHEMATICAL MODEL OF THROMBOPOIESIS IN RATS

A mathematical model of thrombopoiesis in rats is presented. This has four compartments; stem cells, megakaryocytes, thrombocytes and thrombopoietin. A high thrombopoietin concentration influences bone marrow proliferation in three ways. Firstly the stem cells are stimulated and a slow increase in megakaryocyte number follows. Secondly there are additional endomitoses in the (early) megakaryocytes resulting in an increase in megakaryocyte volume. Thirdly the megakaryocyte maturation time is shortened. The parameters of the model are determined from experimental values for the normal, maximum and minimum proliferation rates, maturation times and destruction rates. The model is tested by comparing simulated results for acute and chronic thrombocytopenia and thrombocytosis with experimental curves from the literature. The model and data agree within the limits of experimental error. Not all of the thrombopoietic regulatory system is known yet, so some important alternative hypotheses are investigated and compared with the model. Several hypotheses have been excluded in this way.