An analysis of biphasic time courses: the inactivation of (Na+ + K+)-ATPase and Ca2+-ATPase by ATP-analogs

The inactivation of (NA+ + K+)-ATPase and Ca2+-ATPase brought about by the substitution of ATP by covalently binding analogs is studied. Most of the analogs cause biphasic courses of inactivation. The families of time courses obtained for different concentrations of the analog exhibit a characteristic feature that is common to both ATPases. The times of transition from one branch to the other of the biphasic curves are practically independent of the concentration of the analog. An analysis of the eigenvalues from different reaction models shows that for these time evolutions the enzyme exists necessarily in two states, only one of which is active for the analog. As a preliminary attempt, the models have been fitted to the experimental data of three different sets of families of curves. It is demonstrated that a two-sites model of inactivation of (Na+ + K+)-ATPase postulated in the literature cannot be valid.     

Analysis of progress curves. Rate law of pyruvate kinase type I from Escherichia coli.

Progress curves of the reaction catalysed by pyruvate kinase from Escherichia coli K12, designed to cover the four-dimensional concentration space of phosphoenolpyruvate, ADP, Mg2+ and ATP in the regulatory region, were recorded with the pH-stat method (pH 7.0 and 25 degrees C). Additional initial-rate measurement were performed to assess specific points. Two methods for the evaluation of progress curves were used: fitting the rate law to the rates obtained from the tangents of the progress curves and fitting the integrated rate law directly to the curves. Two models, both extensions of the concerted model given by Monod, Wyman & Changeux [(1965) J. Mol. Biol. 12, 88--118] with four protomers, could be fitted to the data within the experimental error. Model discrimination in favour of one of these models was possible by proper experimental design. In the selected model one conformational state of the enzyme forms the active complex. The active site of a second conformational state forms abortive complexes with Mg2+, causing strong inhibition at high Mg2+ concentrations. In the absence of ligands, most of the enzyme is in a third state that binds ATP at an allosteric site.     

Small-angle X-ray-scattering investigation and structural-model study of the fatty-acid synthetase from pig liver (author's transl)

The structure of the fatty acid synthetase from pig liver was studied on models based upon structural and functional properties selected from pertinent results available from numerous investigations carried out with fatty acid synthetases from this and other sources. When comparing small-angle X-ray-scattering curves calculated with these models and curves obtained from small-angle X-ray-scattering experiments carried out with the pig-liver enzyme, we tried to select a model which would lead to an acceptable correlation between the calculated and the experimental curves and at the same time fulfil the known structural and functional requirements. The comparison of the curves was started with a model of low complexity. The observed discrepancy, together with arguments from the structural and the functional properties, helped decide which is the next most reasonable model to be considered. This procedure was repeated for five models of increasing complexity. In the model which led to the best fit the multienzyme complex is composed of two halves in an assymetric conformation including hollow spaces. This highly anisotropic model would imply that the two halves change their conformation each time a synthetic cycle is completed and that the growing fatty acid is handed over from one half to the other.     

Exploration of the structural features defining the conduction properties of a synthetic ion channel.

The finite-difference Poisson-Boltzmann methodology was applied to a series of parallel, alpha-helical bundle models of the designed ion channel peptide Ac-(LSSLLSL)3-CONH2. This method is able to fully describe the current-voltage curves for this channel and quantitatively explains their cation selectivity and rectification. We examined a series of energy-minimized models representing different aggregation states, side-chain rotamers, and helical rotations, as well as an ensemble of structures from a molecular dynamics trajectory. Potential energies were computed for single, permeating K+ and Cl- ions at a series of positions along a central pathway through the models. A variable-electric-field Nernst-Planck electrodiffusion model was used, with two adjustable parameters representing the diffusion coefficients of K+ and Cl- to scale the individual ion current magnitudes. The ability of a given DelPhi potential profile to fit the experimental data depended strongly on the magnitude of the desolvation of the permeating ion. Below a pore radius of 3.8 A, the predicted profiles showed large energy barriers, and the experimental data could be fit only with unrealistically high values for the K+ and Cl- diffusion coefficients. For pore radii above 3.8 A, the desolvation energies were 2kT or less. The electrostatic calculations were sensitive to positioning of the Ser side chains, with the best fits associated with maximum exposure of the Ser side-chain hydroxyls to the pore. The backbone component was shown to be the major source of asymmetry in the DelPhi potential profiles. Only two of the energy-minimized structures were able to explain the experimental data, whereas an average of the dynamics structures gave excellent agreement with experimental results. Thus this method provides a promising approach to prediction of current-voltage curves from three-dimensional structures of ion channel proteins.     

肝细胞癌患者自噬相关基因的预后作用

构建由自噬相关基因组成的预后模型,预测肝细胞癌(HCC)患者的生存预后情况,为其个性化诊疗和临床研究提供依据.利用TCGA数据库中HCC的测序信息与人类自噬数据库联合,筛选差异表达的自噬相关基因,对其进行GO富集与KEGG通路分析;通过单因素与多因素Cox分析筛选与患者生存预后明显相关的风险基因,构建预后风险评分模型;...     

Modelling the effect of high pressure on the inactivation kinetics of a pressure-resistant strain of Pediococcus damnosus in phosphate buffer and gilt-head seabream (Sparus aurata)

AIMS: The aim of this research was to: (i) determine the inactivation pattern of a pressure-resistant strain of Pediococcus damnosus by high hydrostatic pressure in phosphate buffer (pH 6.7) and gilt-head seabream using the linear, biphasic and Weibull models; and (ii) validate the applicability of the Weibull model to predict survival curves at other experimental pressure levels. METHODS AND RESULTS: A pressure-resistant strain of P. damnosus was exposed to a range of pressures (500, 550, 600 and 650 MPa) in phosphate buffer (pH 6.7) and gilt-head seabream for up to 8 min at ambient temperature (23 degrees C). Inactivation kinetics were described by the linear, biphasic and Weibull models. Increasing the magnitude of the pressure applied resulted in increasing levels of inactivation. Pronounced tailing effect was observed at pressures over 600 MPa. The Weibull and biphasic models consistently produced better fit than the linear model as inferred by the values of the root mean squared error, coefficient of determination (R2) and accuracy factor (A(f)). The scale factor (b) of the Weibull model was linearly correlated with pressure (P) treatment in the whole pressure range. Substituting the b parameter in the initial Weibull function and calculating the shape factor (n) by linear interpolation, high pressure (P) was directly incorporated into the model providing reasonable predictions of the survival curves at 570 and 630 MPa. Comparison between the survival curves in phosphate buffer and gilt-head seabream showed a clear protective effect of the food matrix on the resistance of the micro-organism, especially at 500 and 550 MPa. CONCLUSIONS: The Weibull and biphasic models were more flexible to describe the survival curves of P. damnosus in the experimental pressure range, taking also into account the tailing effect that could not be included in the linear model. The Weibull model could also give reasonable predictions of the survival curves at other experimental pressures in both pressure menstrua. As the food matrix has a protective effect in microbial inactivation, the development of accurate mathematical models should be done directly on real food to avoid under- or over-processing times. SIGNIFICANCE AND IMPACT OF THE STUDY: The development of accurate models to describe the survival curves of micro-organisms under high hydrostatic pressure treatment would be very important to the food industry for process optimisation, food safety and extension of the applicability of high pressure processing.     

Shapes and functions of species–area curves (II): a review of new models and parameterizations

This paper has extended and updated my earlier list and analysis of candidate models used in theoretical modelling and empirical examination of species–area relationships (SARs). I have also reviewed trivariate models that can be applied to include a second independent variable (in addition to area) and discussed extensively the justifications for fitting curves to SARs and the choice of model. There is also a summary of the characteristics of several new candidate models, especially extended power models, logarithmic models and parameterizations of the negative-exponential family and the logistic family. I have, moreover, examined the characteristics and shapes of trivariate linear, logarithmic and power models, including combination variables and interaction terms. The choice of models according to best fit may conflict with problems of non-normality or heteroscedasticity. The need to compare parameter estimates between data sets should also affect model choice. With few data points and large scatter, models with few parameters are often preferable. With narrow-scale windows, even inflexible models such as the power model and the logarithmic model may produce good fits, whereas with wider-scale windows where inflexible models do not fit well, more flexible models such as the second persistence (P2) model and the cumulative Weibull distribution may be preferable. When extrapolations and expected shapes are important, one should consider models with expected shapes, e.g. the power model for sample area curves and the P2 model for isolate curves. The choice of trivariate models poses special challenges, which one can more effectively evaluate by inspecting graphical plots.     

Efficiencies of maximum likelihood methods of phylogenetic inferences when different substitution models are used

Choice of a substitution model is a crucial step in the maximum likelihood (ML) method of phylogenetic inference, and investigators tend to prefer complex mathematical models to simple ones. However, when complex models with many parameters are used, the extent of noise in statistical inferences increases, and thus complex models may not produce the true topology with a higher probability than simple ones. This problem was studied using computer simulation. When the number of nucleotides used was relatively large (1000 bp), the HKY+Gamma model showed smaller d(T) topological distance between the inferred and the true trees) than the JC and Kimura models. In the cases of shorter sequences (300 bp) simpler model and search algorithm such as JC model and SA+NNI search were found to be as efficient as more complicated searches and models in terms of topological distances, although the topologies obtained under HKY+Gamma model had the highest likelihood values. The performance of relatively simple search algorithm SA+NNI was found to be essentially the same as that of more extensive SA+TBR search under all models studied. Similarly to the conclusions reached by Takahashi and Nei [Mol. Biol. Evol. 17 (2000) 1251], our results indicate that simple models can be as efficient as complex models, and that use of complex models does not necessarily give more reliable trees compared with simple models.     

Numerical modelling of label-structured cell population growth using CFSE distribution data

Background

Drug-drug interactions resulting from the inhibition of an enzymatic process can have serious implications for clinical drug therapy. Quantification of the drugs internal exposure increase upon administration with an inhibitor requires understanding to avoid the drug reaching toxic thresholds. In this study, we aim to predict the effect of the CYP3A4 inhibitors, itraconazole (ITZ) and its primary metabolite, hydroxyitraconazole (OH-ITZ) on the pharmacokinetics of the anesthetic, midazolam (MDZ) and its metabolites, 1' hydroxymidazolam (1OH-MDZ) and 1' hydroxymidazolam glucuronide (1OH-MDZ-Glu) using mechanistic whole body physiologically-based pharmacokinetic simulation models. The model is build on MDZ, 1OH-MDZ and 1OH-MDZ-Glu plasma concentration time data experimentally determined in 19 CYP3A5 genotyped adult male individuals, who received MDZ intravenously in a basal state. The model is then used to predict MDZ, 1OH-MDZ and 1OH-MDZ-Glu concentrations in an CYP3A-inhibited state following ITZ administration.

Results

For the basal state model, three linked WB-PBPK models (MDZ, 1OH-MDZ, 1OH-MDZ-Glu) for each individual were elimination optimized that resulted in MDZ and metabolite plasma concentration time curves that matched individual observed clinical data. In vivo K_m and V_max optimized values for MDZ hydroxylation were similar to literature based in vitro measures. With the addition of the ITZ/OH-ITZ model to each individual coupled MDZ + metabolite model, the plasma concentration time curves were predicted to greatly increase the exposure of MDZ as well as to both increase exposure and significantly alter the plasma concentration time curves of the MDZ metabolites in comparison to the basal state curves. As compared to the observed clinical data, the inhibited state curves were generally well described although the simulated concentrations tended to exceed the experimental data between approximately 6 to 12 hours following MDZ administration. This deviations appeared to be greater in the CYP3A5 *1/*1 and CYP3A5 *1/*3 group than in the CYP3A5 *3/*3 group and was potentially the result of assuming that ITZ/OH-ITZ inhibits both CYP3A4 and CYP3A5, whereas in vitro inhibition is due to CYP3A4.

Conclusion

This study represents the first attempt to dynamically simulate metabolic enzymatic drug-drug interactions via coupled WB-PBPK models. The workflow described herein, basal state optimization followed by inhibition prediction, is novel and will provide a basis for the development of other inhibitor models that can be used to guide, interpret, and potentially replace clinical drug-drug interaction trials.     

Assessing biodiversity with species accumulation curves; inventories of small reptiles by pit‐trapping in Western Australia

Abstract We examined 11 non‐linear regression models to determine which of them best fitted curvilinear species accumulation curves based on pit‐trapping data for reptiles in a range of heterogeneous and homogenous sites in mesic, semi‐arid and arid regions of Western Australia. A well‐defined plateau in a species accumulation curve is required for any of the models accurately to estimate species richness. Two different measures of effort (pit‐trapping days and number of individuals caught) were used to determine if the measure of effort influenced the choice of the best model(s). We used species accumulation curves to predict species richness, determined the trapping effort required to catch a nominated percentage (e.g. 95%) of the predicted number of species in an area, and examined the relationship between species accumulation curves with diversity and rarity. Species richness, diversity and the proportion of rare species in a community influenced the shape of species accumulation curves. The Beta‐P model provided the best overall fit (highest r²) for heterogeneous and homogeneous sites. For heterogeneous sites, Hill, Rational, Clench, Exponential and Weibull models were the next best. For homogeneous habitats, Hill, Weibull and Chapman–Richards were the next best models. There was very little difference between Beta‐P and Hill models in fitting the data to accumulation curves, although the Hill model generally over‐estimated species richness. Most models worked equally well for both measures of trapping effort. Because the number of individuals caught was influenced by both pit‐trapping effort and the abundance of individuals, both measures of effort must be considered if species accumulation curves are to be used as a planning tool. Trapping effort to catch a nominated percentage of the total predicted species in homogeneous and heterogeneous habitats varied among sites, but even for only 75% of the predicted number of species it was generally much higher than the typical effort currently being used for terrestrial vertebrate fauna surveys in Australia. It was not possible to provide a general indication of the effort required to predict species richness for a site, or to capture a nominated proportion of species at a site, because species accumulation curves are heavily influenced by the characteristics of particular sites.     

不同性别河北柴鸡早期生长规律及其生长曲线拟合

本研究运用Logistic、Gompertz和Bertalanffy三种非线性模型对不同性别河北柴鸡早期生长规律和生长曲线进行分析及拟合比较.结果表明,3种曲线模型拟合度均达到0.99以上,但Gompertz曲线模型在拟合度和预测极限生长量、拐点周龄和最大周增重等方面相对较好.进一步分析表明,河北柴鸡公鸡的极限体重和拐点体重均高于母鸡,拐点周龄性别间差异不大,公鸡最大周增重与实际观测值接近.本文有助于了解不同性别河北柴鸡各自的生长模式及其对营养、环境的需求,为开展规模化饲养提供参考.     

A comparison of two Hill-type skeletal muscle models on the construction of medial gastrocnemius length-tension curves in humans in vivo

Human length-tension curves are traditionally constructed using a model that assumes passive tension does not change during contraction (model A) even though the animal literature suggests that passive tension can decrease (model B). The study's aims were threefold: 1) measure differences in human medial gastrocnemius length-tension curves using model A vs. model B, 2) test the reliability of ultrasound constructed length-tension curves, and 3) test the robustness of fascicle length-generated length-tension curves to variations between the angle and fascicle length relationship. An isokinetic dynamometer manipulated and measured ankle angle while ultrasound was used to measure medial gastrocnemius fascicle length. Supramaximal tibial nerve stimulation was used to evoke resting muscle twitches. Length-tension curves were constructed using model A {angle-torque [A-T((A))], length-torque [L-T((A))]} or model B {length-torque [L-T((B))]} in three conditions: baseline, heel-lift (where the muscle was shortened at each angle), and baseline repeated 2 h later (+2 h). Length-tension curves constructed from model B differed from those produced via model A, indicated by a significant increase in maximum torque (≈23%) when using L-T((B)) vs. L-T((A)). No parameter measured was different between baseline and +2 h for any method, indicating good reliability when using ultrasound. Length-tension curves were unaffected by the heel-lift condition when using L-T((A)) or L-T((B)) but were affected when using A-T((A)). Since the muscle model used significantly alters human length-tension curves, and given animal data indicate model B to be more accurate when passive tension is present, we recommend that model B should be used when constructing medial gastrocnemius length-tension curves in humans in vivo.     

Extrapolation of thermodilution curves obtained during a pause in artificial ventilation

The feasibility of three mathematical models to extrapolate the tail of thermodilution curves, when flectures are present in the descending limb, was tested in anesthetized pigs. The models were a local random walk model (LDRW), a log-normal distribution, and a two-compartment model. First, the accuracy of the extrapolation of the tail by each model was tested on two undisturbed curves by taking the truncation at five different points on the descending limb. The extrapolated curve area obtained from each model was compared with total area of the undisturbed curve. Next, dilution curves obtained during inspiratory hold maneuvers and characterized by deflection points were analyzed, taking the truncation just before deflection. The estimates of cardiac output by the models were compared with electromagnetically measured flow in the pulmonary artery. The area of the dilution curve was estimated more accurately when more information on the descending limb was available. The LDRW model and the log-normal distribution were superior to the two-compartment model regarding accuracy of cardiac output estimation and root-mean-square errors of the fit. Both models estimated curve area with an error less than 5% when truncation of the descending limb occurred below 60% of the peak value. In circumstances of mechanical ventilation, where only short periods of constant flow will be present, analyses of dilution curves based on the LDRW model or the log-normal distribution are recommended.     

Cluster-based upper body marker models for three-dimensional kinematic analysis: Comparison with an anatomical model and reliability analysis

Quantifying angular joint kinematics of the upper body is a useful method for assessing upper limb function. Joint angles are commonly obtained via motion capture, tracking markers placed on anatomical landmarks. This method is associated with limitations including administrative burden, soft tissue artifacts, and intra- and inter-tester variability. An alternative method involves the tracking of rigid marker clusters affixed to body segments, calibrated relative to anatomical landmarks or known joint angles. The accuracy and reliability of applying this cluster method to the upper body has, however, not been comprehensively explored. Our objective was to compare three different upper body cluster models with an anatomical model, with respect to joint angles and reliability. Non-disabled participants performed two standardized functional upper limb tasks with anatomical and cluster markers applied concurrently. Joint angle curves obtained via the marker clusters with three different calibration methods were compared to those from an anatomical model, and between-session reliability was assessed for all models. The cluster models produced joint angle curves which were comparable to and highly correlated with those from the anatomical model, but exhibited notable offsets and differences in sensitivity for some degrees of freedom. Between-session reliability was comparable between all models, and good for most degrees of freedom. Overall, the cluster models produced reliable joint angles that, however, cannot be used interchangeably with anatomical model outputs to calculate kinematic metrics. Cluster models appear to be an adequate, and possibly advantageous alternative to anatomical models when the objective is to assess trends in movement behavior.     

Sodium + potassium-activated ATPase of mammalian brain. Regulation of phosphatase activity.

1. The K+-nitrophenylphosphatase activity associated with mammalian brain (Na+ + K+)-ATPase displays K+ activation curves that have intermediary plateaus and maxima in the presence of less than saturating concentrations of Na+. Zero Na+ and saturating Na+ produce sigmoid K+-activation curves with low and high K+ affinities respectively. 2. ATP inhibits K+-activated nitrophenylphosphatase through both competitive and non-competitive mechanisms. ATP is synergistic with Na+ in the mechanism which converts the enzyme from low to high K+ affinity. 3. The Na+ and K+ interactions can be accounted for by equations which describe a model with separate regulatory sites for Na+ and K+ and with K+- requiring catalytic site which is only accessible in one of the two principal conformational stages of the enzyme. 4. The effects of ATP can be accounted for by the same model through interactions at a single nucleotide binding site. Inhibition which is competitive with K+ and non-competitive with substrate arises from stabilization of the inactive enzyme conformation. Inhibition which is non-competitive with K+ and competitive with substrate results from interactions with the active enzyme conformation. The synergism between Na+ and ATP appears to arise as a consequence of the formation of phosphoryl enzyme. 5. A model for (Na+ + K+)-ATPase is discussed which involves in-phase coupling of subunit interactions as suggested by these studies.     

Heterogeneous communities with lognormal species abundance distribution: Species-area curves and sustainability

Heterogeneous species abundance models are models in which the dynamics differ between species, described by variation among parameters defining the dynamics. Using a dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution it is first shown that different degrees of heterogeneity may result in equivalent species abundance distributions. An alternative to Preston's canonical lognormal model is defined by assuming that reduction in resources, for example reduction in available area, increases the density regulation of each species. This leads to species-individual curves and species-area curves that are approximately linear in a double logarithmic plot. Preston's canonical parameter gamma varies little along these curves and takes values in the neighborhood of one. Quite remarkably, the curves, which define the sensitivity of the community to area reductions, are independent of the heterogeneity among species for this model. As a consequence, the curves can be estimated from a single sample from the community using the Poisson lognormal distribution. It is shown how to perform sensitivity analysis with respect to over-dispersion in sampling relative to the Poisson distribution as well as sampling intensity, that is, the fraction of the community sampled. The method is exemplified by analyzing three simulated data sets.     

北京东灵山地区植物群落多样性研究一种-面积曲线的拟合与评价

 本文选择了10条曲线作为种—面积曲线的拟合模型,它们分别是 S=b+aA (1) S= b+alnA (2) S=(b+alnA)c (3) S=aln(A+1) (4) S=aln(bA+1) (5) S= aAb (6) S=aA/(1+bA) (7) S=c/(1+ae-bA) (8) S=c-ae-bA (9) S=a(1-e-bA) (10) 对其中的7个非线性模型给出了参数初值的计算方法,并用Gauss—Newton或Marquardt方法计算非线性最优解。又选择了剩余标准差(RSE)、相关指数(CRI)、偏差绝对值的平均值(AAD)和相对偏差绝对值的平均值(AARD)作为模型拟合优劣的4个评价指标。研究结果表明：1)7个非线性模型中参数初值的计算方法是可行的。从4个评价指标来看,它们的非线性最小二乘解都明显优于线性最小二乘解;2)10个模型的拟合效果都相当好,对5个样地及其各层拟合的共200个CRI中有71.5％大于0.9,89％大于0.8,其中曲线(3)和(9)最好,其次是(5)、(6)、(2),(1)和(10)最差;3)秩相关分析表明,3个评价指标RSE、AAD和AARD相互之间存在极强的正秩相关,因此在本研究中,它们的评价结果具很强的一致性。     

Sodium inactivation in nerve fibers

A number of models proposed to account for the sodium conductance changes are shown to fall into two classes. The Hodgkin-Huxley (HH) model falls into a class (I) in which the conductance depends on two or more independent variables controlled by independent processes. The Mullins, Hoyt, and Goldman models fall into class II in which conductance depends directly on one variable only, a variable which is controlled by two or more coupled processes. The HH and Hoyt models are used as specific examples of the two classes. It is shown that, contrary to a recently published report, the results from double experiments can be equally well accounted for by both models. It is also shown that steady-state conditioning, or “inactivation,” curves, obtained at more than one test potential, can be used to distinguish the two models. The HH equations predict that such curves should be shifted, by very small amounts, in the hyperpolarizing direction when more depolarizing test potentials are used, while the Hoyt model predicts that they should be shifted in the depolarizing direction, by quite appreciable amounts. Several pieces of published experimental information are used as tests of these predictions, and give tentative support to the class II model. Further experiments are necessary before a definite conclusion can be reached.     

Description of two-metal biosorption equilibria by Langmuir-type models

A biosorbent prepared from Ascophyllum nodosum seaweed biomass, FCAN2, was examined for its sorption capacity. Equilibrium batch sorption studies were performed using two-matal systems containing either (Cu + Zn), (Cu + Cd), or (Zn + Cd). In the evaluation of the two-metal sorption system performance, simple isotherm curves had to be replaced by three-dimensional sorption isotherm surfaces. In order to describe the isotherm surfaces mathematically, three Langmuir-type models were evaluated. The apparent one-parameter Langmuir constant (b) was used to quantify FCAN2 "affinity" for one metal in the presence of another one. The uptake of Zn decreased drastically when Cu or Cd were present. The uptake of Cd wasmuch more sensitive to the presence of Cu than to that of Zn. The presence of Cd and Zn alter the "affinity" of FCAN2 for Cu the least at high Cu equilibrium concentrations. The mathematical model of the two-metal sorption system enabled quantitative estimation of one-metal (bio)sorption inhibition due to the influence of a second metal. (c) 1995 John Wiley & Sons Inc.