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PubMed2000

Mathematical modelling of insect neuropeptide potencies. Are quantitatively predictive models possible?

The potencies of natural adipokinetic hormones and synthetic variants have been determined in Locusta migratoria using the lipid mobilisation assay in vivo, and/or the acetate uptake assay in vitro. These data are combinations of previously published and unpublished data (a total of sixty-nine analogues), and form data sets for the construction of mathematical models of the hormone potencies. The sequence variations of amino acids in both natural and artificial adipokinetic hormone analogues were described using continuous descriptor scales z(1)', z(2)', and z(3)', each previously published scale being derived from various properties of the amino acids. By means of these z'-scales and partial least squares regression we attempted to model the potencies in Locusta migratoria of adipokinetic hormones in the two assays. Correlations (r(2) values) between predicted and actual potencies of the different peptides were up to 0.73. We discuss the potential of the partial least squares method for formulating quantitative relationships between different hormone structures and their potencies, and describe how the procedure might be used in structure-activity prediction with the construction of an optimised peptide data set.

Amino Acid Sequence↗
PubMed1987

Quantitative genetic models of sexual selection: a review.

Quantitative genetic models of sexual selection have disproven some of the central tenets of both the handicap mechanism and the 'sexy son' hypothesis. These results suggest that the 'good genes' approach to sexual selection may often lead to erroneous results. Runaway sexual selection seems possible under a wide variety of circumstances. Quantitative genetic models have revealed runaway processes for sexually selected attributes expressed in both sexes and for attributes of parental care. Furthermore, the runaway could occur simultaneously in a series of populations that straddle an environmental gradient. While the models support the feasibility of runaway processes, empirical studies are needed to evaluate whether runaways actually happen. Estimates of critical genetic parameters are particularly needed, as well as measures of natural and sexual selection acting on the same population. The models also show that sexual selection has tremendous potential to produce population differentiation, particularly in epigamic traits. Differentiation is promoted by indeterminancy of evolutionary outcome, transient differences among populations during the final slow approach to equilibrium, sampling drift among equilibrium populations, and the tendency of sexual selection to amplify geographic variation arising from spatial differences in natural selection. Recent work with two- and three-locus models of sexual selection has produced results that parallel the results of the polygenic models (Kirkpatrick, 1982, 1985, 1986; Seger, 1985). Thus the feature of indeterminate equilibria (outcome dependent on initial conditions) is common to both types of model.

Animals↗
PubMed2005

A quantitative genetics model for viability selection.

Viability selection will change gene frequencies of loci controlling fitness. Consequently, the frequencies of marker loci linked to the viability loci will also change. In genetic mapping, the change of marker allelic frequencies is reflected by the departure from Mendelian segregation ratio. The non-Mendelian segregation of markers has been used to map viability loci along the genome. However, current methods have not been able to detect the amount of selection (s) and the degree of dominance (h) simultaneously. We developed a method to detect both s and h using an F2 mating design under the classical fitness model. We also developed a quantitative genetics model for viability selection by proposing a continuous liability controlling the viability of individuals. With the liability model, mapping viability loci has been formulated as mapping quantitative trait loci. As a result, nongenetic systematic environmental effects can be easily incorporated into the model and subsequently separated from the genetic effects of the viability loci. The quantitative genetic model has been verified with a series of Monte Carlo simulation experiments.

Algorithms↗
PubMed1990

Search for faster methods of fitting the regressive models to quantitative traits.

The regressive models describe familial patterns of dependence of quantitative measures by specifying regression relationships among a person's phenotype and genotype and the phenotypes and genotypes of antecedents. When the number of sibs in the pattern of dependence increases, as in the class D regressive model, computation of the likelihood becomes time consuming, since the Elston-Stewart algorithm cannot be used generally. On the other hand, the simpler class A regressive model, which imposes a restriction on the sib-sib correlation, may lead to inference of a spurious major gene, as already observed in some instances. A simulation study is performed to explore the robustness of class A model with respect to false inference of a major gene and to search for faster methods of computing the likelihood under class D model. The class A model is not robust against the presence of a sib-sib correlation exceeding that specified by the model, unless tests on transmission probabilities are performed carefully: false detection of a major gene is reduced from a number of 26-30 to between 0 and 4 data sets out of 30 replicates after testing both the Mendelian transmission and the absence of transmission of a major effect against the general transmission model. Among various approximations of the likelihood formulation of the class D model, approximations 6 and 8 are found to work appropriately in terms of both the estimation of all parameters and hypothesis testing, for each generating model. These approximations lessen the computer time by allowing use of the Elston-Stewart algorithm.

Computer Simulation↗
PubMed1999

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model.

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. A number of invariant features of multijoint planar reaching movements have been observed in measured hand trajectories. These features include roughly straight hand paths and bell-shaped speed profiles where the trajectory curvatures between transverse and radial movements have been found to be different. For quantitative and statistical investigations, we obtained a large amount of trajectory data within a wide range of the workspace in the horizontal and sagittal planes (400 trajectories for each subject). A pair of movements within the horizontal and sagittal planes was set to be equivalent in the elbow and shoulder flexion/extension. The trajectory curvatures of the corresponding pair in these planes were almost the same. Moreover, these curvatures can be accurately reproduced with a linear regression from the summation of rotations in the elbow and shoulder joints. This means that trajectory curvatures systematically depend on the movement location and direction represented in the intrinsic body coordinates. We then examined the following four candidates as planning spaces and the four corresponding computational models for trajectory planning. The candidates were as follows: the minimum hand jerk model in an extrinsic-kinematic space, the minimum angle jerk model in an intrinsic-kinematic space, the minimum torque change model in an intrinsic-dynamic-mechanical space, and the minimum commanded torque change model in an intrinsic-dynamic-neural space. The minimum commanded torque change model, which is proposed here as a computable version of the minimum motor command change model, reproduced actual trajectories best for curvature, position, velocity, acceleration, and torque. The model's prediction that the longer the duration of the movement the larger the trajectory curvature was also confirmed. Movements passing through via-points in the horizontal plane were also measured, and they converged to those predicted by the minimum commanded torque change model with training. Our results indicated that the brain may plan, and learn to plan, the optimal trajectory in the intrinsic coordinates considering arm and muscle dynamics and using representations for motor commands controlling muscle tensions.

Adult↗
PubMed1986

Reaction sequences for (Na+ + K+)-dependent ATPase hydrolytic activities: new quantitative kinetic models.

To delineate better the reaction sequence of the (Na+ + K+)-ATPase and illuminate properties of the active site, kinetic data were fitted to specific quantitative models. For the (Na+ + K+)-ATPase reaction, double-reciprocal plots of velocity against ATP (in the millimolar range), with a series of fixed KCl concentrations, are nearly parallel, in accord with the ping pong kinetics of ATP binding at the low-affinity sites only after Pi release. However, contrary to requirements of usual formulations, Pi is not a competitor toward ATP. A new steady-state kinetic model accommodates these data quantitatively, requiring that under usual assay conditions most of the enzyme activity follows a sequence in which ATP adds after Pi release, but also requiring a minor alternative pathway with ATP adding after K+ binds but before Pi release. The fit to the data also reveals that Pi binds nearly as rapidly to E2 X K X ATP as to E2 X K, whereas ATP binds quite slowly to E2 X P X K: the site resembles a cul-de-sac with distal ATP and proximal Pi sites. For the K+-nitrophenyl phosphatase reaction also catalyzed by this enzyme, the apparent affinities for both substrate and Pi (as inhibitor) decrease with higher KCl concentrations, and both Pi and TNP-ATP appear to be competitive inhibitors toward substrate with 10 mM KCl but noncompetitive inhibitors with 1 mM KCl. These data are accommodated quantitatively by a steady-state model allowing cyclic hydrolytic activity without obligatory release of K+, and with exclusive binding of substrate vs. either Pi or TNP-ATP. The greater sensitivity of the phosphatase reaction to both Pi and arsenate is attributable to the weaker binding by the occluded-K+ enzyme form occurring in the (Na+ + K+)-ATPase reaction sequence. The steady-state models are consistent with cyclical interconversion of high- and low-affinity substrate sites accompanying E1/E2 transitions, with distortion to low-affinity sites altering not only affinity and route of access but also separating the adenine- and phosphate-binding regions, the latter serving in the E2 conformation as the active site for the phosphatase reaction.

Animals↗
PubMed1992

Genetic Tobit factor analysis: quantitative genetic modeling with censored data.

Parameters of quantitative genetic models have traditionally been estimated by either algebraic manipulation of familial correlations (or familial mean squares), biometric model fitting, or multiple-group covariance structure analysis. With few exceptions, researchers who have used these methods for the analysis of twin data have assumed that their data were multinormal and, consequently, have used normal-theory estimation methods. It is shown that normal-theory methods produce biased genetic and environmental parameter estimates when data are censored. Specifically, with censored data, (1) normal-theory estimates of narrow-sense heritability are either positively or negatively biased, whereas (2) estimates of shared-familial environmental variance are always biased downward. An alternative method for estimating genetic and environmental parameters from censored twin data is proposed. The method is called genetic Tobit factor analysis (GTFA) and is an extension of the Tobit factor analysis model developed by Muthén (Br. J. Math. Stat. Psychol. 42, 241-250, 1989). Using a Monte Carlo design, the performance of GTFA is compared to traditional quantitative genetic methods in both large and small data sets. The results of this study suggest that GTFA is the preferred method for the genetic modeling of censored data obtained from twins.

Genetics, Behavioral↗
PubMedDate not supplied

Rational selection of training and test sets for the development of validated QSAR models.

Quantitative Structure-Activity Relationship (QSAR) models are used increasingly to screen chemical databases and/or virtual chemical libraries for potentially bioactive molecules. These developments emphasize the importance of rigorous model validation to ensure that the models have acceptable predictive power. Using k nearest neighbors (kNN) variable selection QSAR method for the analysis of several datasets, we have demonstrated recently that the widely accepted leave-one-out (LOO) cross-validated R2 (q2) is an inadequate characteristic to assess the predictive ability of the models [Golbraikh, A., Tropsha, A. Beware of q2! J. Mol. Graphics Mod. 20, 269-276, (2002)]. Herein, we provide additional evidence that there exists no correlation between the values of q2 for the training set and accuracy of prediction (R2) for the test set and argue that this observation is a general property of any QSAR model developed with LOO cross-validation. We suggest that external validation using rationally selected training and test sets provides a means to establish a reliable QSAR model. We propose several approaches to the division of experimental datasets into training and test sets and apply them in QSAR studies of 48 functionalized amino acid anticonvulsants and a series of 157 epipodophyllotoxin derivatives with antitumor activity. We formulate a set of general criteria for the evaluation of predictive power of QSAR models.

Algorithms↗
PubMed1976

Inhibition of T cell activity in vivo: a test model for quantitative evaluation.

A test model is presented which, in comparison with the conventional models of skin transplantation or graft-versus-host (GvH) reaction in mice, permits a more sensitive quantitative evaluation of T cell inhibition in vivo. Prospective donors (type AA) are immunized with prospective recipient material (type AB); the resulting T cell reaction of A versus B is inhibited by consecutive treatment. Extent of inhibition can be evaluated after transfer of the pretreated AA material onto AB recipients by calculation of remaining GvH reactivity, if compared to adequate control tranfers. In this model the target animal for T cell reactivity (the AB recipient) remains untouched from immunosuppressive regimen.

Animals↗
PubMed1982

Quantitative autoradiographic measurements of blood-brain barrier permeability in the rat glioma model.

Quantitative autoradiographic technique was applied in measuring blood-brain barrier (BBB) permeability of autochthonous gliomas in rats. In small tumors (less than 2 mm in diameter), no increase in BBB permeability was noted. As the tumor grew and neovascularization occurred, BBB permeability increased in the center of the tumor, and it was suggested that the BBB was partly disrupted in the neovascularized vessels. In the fully grown tumors, BBB permeability was markedly increased in the viable part of the tumor to levels similar to the choroid plexus. Yet, the BBB was partly preserved at the periphery of the tumor and in the brain adjacent to the tumor. The heterogeneity of the BBB phenomenon according to the stage of tumor growth may be a major obstacle for uptake of chemotherapeutic drugs that do not cross the BBB easily.

Animals↗
PubMed1986

Quantitative whole-body autoradiography of radiolabeled antibody distribution in a xenografted human cancer model.

Quantitative whole-body autoradiography (WBAR) was used to study the biodistribution of goat anti-carcinoembryonic antigen and normal goat IgG, each labeled with 125I, in hamsters bearing the carcinoembryonic antigen-producing GW-39 human colonic carcinoma xenograft. Comparisons between computer-assisted videodensitometric profiles of WBARs and tissue radioactivity counts were made at 1, 3, and 7 days following administration of the radiolabeled IgGs. The results indicated that maximal tumor accretion of the radiolabeled antibody and normal IgG occurred within 1-3 days, with a marked selective accretion of antibody in the tumor being evidenced at 3-7 days because of clearance of normal IgG. Radioactivity derived from antibody IgG showed 6.5 to 118.7 times that found in other tissues, as measured by videodensitometry, whereas organ radioactivity counting revealed ratios of only 6.7 to 29.6. Specificity of tumor-cell accretion of the radiolabeled antibody was confirmed by microscopic autoradiography, showing intense labeling of the proliferating perimeters of GW-39 tumors. WBAR was found to have a resolution of 0.10 to 0.25 mm in 100-g hamsters, which appears to be greater than the resolving power of external body imaging by gamma camera scintigraphy. These studies suggest the use of WBAR and microautoradiography to complement external imaging methods for the analysis of antibody distribution and localization in cancer radioimmunodetection models.

Animals↗
PubMedDate not supplied

Prediction of mammalian toxicity of organophosphorus pesticides from QSTR modeling.

Quantitative structure-toxicity relationship (QSTR) models were derived for estimating the acute oral toxicity of organophosphorus pesticides to male and female rats. The 51 chemicals of the training set and the nine compounds of the external testing set were described by means of autocorrelation vectors encoding lipophilicity, molar refractivity, H-bonding acceptor ability (HBA) and H-bonding donor ability (HBD) of the molecules. A feature selection was employed for selecting the most relevant autocorrelation descriptors. A PLS regression analysis and an artificial neural network (ANN) were used for deriving models accounting for the sex of the organisms in the estimation of the toxicity of pesticides. The best results were obtained with an 8/4/1 ANN model trained with theback-propagation and conjugate gradient descent algorithms. The root mean square residual (RMSR) values for the training set and the external testing set equaled 0.29 and 0.26, respectively.

Animals↗
PubMed2002

Modeling for quantitative non-destructive evaluation.

A quantitative approach to non-destructive evaluation (NDE) must be based on models of the measurement processes. A model's purpose is to predict, from first principles, the measurement system's response to material properties and anomalies in a material or structure. For the ultrasonic case a measurement model should include modeling of the generation, propagation and reception of ultrasonic signals, and the ultrasonic interactions that generate the system's response function. A measurement model has many benefits, which are discussed in the paper. Three examples of the productive use of quantitative modeling in conjunction with measured data are presented: the detection and sizing of fatigue cracks which emanate from weep holes in the risers of wing panels in the interior of an aircraft wing by the use of ultrasound generated on the exterior surface of the wing, the determination of the elastic constants of anisotropic thin films deposited on a substrate, and the detection and sizing of surface-breaking cracks by the use of the laser-source scanning technique for laser generated and detected ultrasound.

Journal Article↗
PubMed2001

The validation of biodynamic models.

UNLABELLED: Biodynamic models may: (i) represent understanding of how the body moves (i.e., 'mechanistic models'), (ii) summarise biodynamic measurements (i.e., 'quantitative models'), and (iii) provide predictions of the effects of motion on human health, comfort or performance (i.e., 'effects models'). Model validation may involve consideration of evidence used to derive a model, comparison of the model with alternatives, and a comparison between model predictions and independent observations of the predicted qualities or quantities. Models should be associated with a specified range of independent and dependent variables and indicate how intra-subject variability and inter-subject variability are accommodated. Models of the mechanisms of body movement may be validated by demonstrations that the mechanisms are well represented. Models giving numerical predictions ('quantitative models' and 'effects models') should specify the expected accuracy of predictions. 'Effects models' advocated for predicting health, comfort or performance require that: (i) vibration or shock is a proven cause of the specified effect, (ii) within all reasonable ranges of model inputs, there must be reason to expect a positive correlation and acceptable error between the model predictions and the effect, (iii) other variables having a large influence on the effect must be taken into consideration. It is more useful to report the accuracy of 'quantitative models' and 'effects models' models than to state that they are 'validated' or 'un-validated'. Checklists for assessing the quality of a biodynamic model are proposed, taking into account the type of model and the model assertions, the evidence, the assumptions, the accuracy, and the appropriateness of the model. RELEVANCE: Biodynamic models can be used to predict risks of injury or disease. Models can be used to optimise designs in order to minimise predicted risks. However, models can be promulgated and used without knowledge of their accuracy or usefulness.

Animals↗
PubMed1992

On models of quantitative genetic variability: a stabilizing selection-balance model.

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.

Alleles↗
PubMed2005

Derivation of a quantitative minimal model from a detailed elementary-step mechanism supported by mathematical coupling analysis.

Accurate experimental data increasingly allow the development of detailed elementary-step mechanisms for complex chemical and biochemical reaction systems. Model reduction techniques are widely applied to obtain representations in lower-dimensional phase space which are more suitable for mathematical analysis, efficient numerical simulation, and model-based control tasks. Here, we exploit a recently implemented numerical algorithm for error-controlled computation of the minimum dimension required for a still accurate reduced mechanism based on automatic time scale decomposition and relaxation of fast modes. We determine species contributions to the active (slow) dynamical modes of the reaction system and exploit this information in combination with quasi-steady-state and partial-equilibrium approximations for explicit model reduction of a novel detailed chemical mechanism for the Ru-catalyzed light-sensitive Belousov-Zhabotinsky reaction. The existence of a minimum dimension of seven is demonstrated to be mandatory for the reduced model to show good quantitative consistency with the full model in numerical simulations. We derive such a maximally reduced seven-variable model from the detailed elementary-step mechanism and demonstrate that it reproduces quantitatively accurately the dynamical features of the full model within a given accuracy tolerance.

Journal Article↗
PubMed1998

Effects of stimulus integrality on visual attention in older and younger adults: a quantitative model-based analysis.

Twenty-one older and 21 younger adults were administered a series of visual attention tasks. A series of quantitative models was applied to each observer's data to determine whether he or she performed optimally or suboptimally or showed a deficit-in-attentional processing. The results suggested that (a) older and younger observers were affected equally by the integrality-separability manipulation, (b) there are no age-related differences in selective attention performance for either integral or separable-dimension stimuli, (c) there are no age-related differences in dimensional integration performance with separable-dimension stimuli, and (d) older observers were more likely to be suboptimal when asked to integrate information from integral-dimension stimuli. Implications for current theories of attentional processing in normal aging are discussed.

Adult↗
PubMed1997

Quantitative assessment of clinical disease status in primary Sjögren's syndrome. A cross-sectional study using a new classification model.

Quantitative and qualitative assessment of the clinical disease manifestations in 41 primary Sjögren's syndrome (pSS) patients was performed according to a new classification model. Frequencies of subgrouped disease manifestations were as follows: 1) surface exocrine disease: 100%, 2) internal organ exocrine disease: 63%, 3) monoclonal B lymphocyte disease: 5%, 4) inflammatory vascular disease: 71%, 5) non-inflammatory vascular disease: 59%, 6) mediator induced disease: 98%. Summary scores for severity of surface exocrine disease correlated to the summary scores of all other disease manifestations (p = 0.02), to the summary scores of internal organ exocrine disease (p = 0.003), and to the summary scores of mediator induced disease (p = 0.03). Blood leucocyte counts showed significant negative correlations to levels of plasma IgG, serum IgA-RF, IgM-RF, anti-SSA/SSB antibodies, IL-6, and IL-1Ra. We conclude that the model made detailed analysis of the clinical presentation of pSS possible, and thus may assist in elucidating important pathobiological aspect of the disease.

Adult↗