Evaluation of nitric oxide synthase activity and inhibition kinetics by chemiluminescence.

The binding affinity (K(I)) and inactivation rate (k(inact)) parameters of nitric oxide synthase (NOS) inhibitors are typically estimated by kinetic activity studies. Methods currently used in the estimation of these parameters frequently employ radiolabeled materials and require intensive sample preparation. We have devised a simple, reproducible, and sensitive method for the kinetic analysis of NOS activity and inhibition kinetics using chemiluminescence. We have used this method to characterize enzyme activity for purified murine macrophage nitric oxide synthase (NOS II). Using this method, we have also estimated the inhibitory parameters for a series of competitive antagonists and mechanism-based inactivators of NOS II. The estimated parameters are in agreement with those reported using other methods. We conclude that the chemiluminescence method can be used for kinetic studies of NOS activity and inhibition. This method represents a more efficient means for conducting kinetic studies of NOS inhibition.     

Estimation of deleterious genomic mutation parameters in natural populations by accounting for variable mutation effects across loci

The genomes of all organisms are subject to continuous bombardment of deleterious genomic mutations (DGM). Our ability to accurately estimate various parameters of DGM has profound significance in population and evolutionary genetics. The Deng-Lynch method can estimate the parameters of DGM in natural selfing and outcrossing populations. This method assumes constant fitness effects of DGM and hence is biased under variable fitness effects of DGM. Here, we develop a statistical method to estimate DGM parameters by considering variable mutation effects across loci. Under variable mutation effects, the mean fitness and genetic variance for fitness of parental and progeny generations across selfing/outcrossing in outcrossing/selfing populations and the covariance between mean fitness of parents and that of their progeny are functions of DGM parameters: the genomic mutation rate U, average homozygous effect s, average dominance coefficient h, and covariance of selection and dominance coefficients cov(h, s). The DGM parameters can be estimated by the algorithms we developed herein, which may yield improved estimation of DGM parameters over the Deng-Lynch method as demonstrated by our simulation studies. Importantly, this method is the first one to characterize cov(h, s) for DGM.     

Simple and Reliable Determination of Intravoxel Incoherent Motion Parameters for the Differential Diagnosis of Head and Neck Tumors

Intravoxel incoherent motion (IVIM) imaging can characterize diffusion and perfusion of normal and diseased tissues, and IVIM parameters are authentically determined by using cumbersome least-squares method. We evaluated a simple technique for the determination of IVIM parameters using geometric analysis of the multiexponential signal decay curve as an alternative to the least-squares method for the diagnosis of head and neck tumors. Pure diffusion coefficients (D), microvascular volume fraction (f), perfusion-related incoherent microcirculation (D*), and perfusion parameter that is heavily weighted towards extravascular space (P) were determined geometrically (Geo D, Geo f, and Geo P) or by least-squares method (Fit D, Fit f, and Fit D*) in normal structures and 105 head and neck tumors. The IVIM parameters were compared for their levels and diagnostic abilities between the 2 techniques. The IVIM parameters were not able to determine in 14 tumors with the least-squares method alone and in 4 tumors with the geometric and least-squares methods. The geometric IVIM values were significantly different (p<0.001) from Fit values (+2±4% and −7±24% for D and f values, respectively). Geo D and Fit D differentiated between lymphomas and SCCs with similar efficacy (78% and 80% accuracy, respectively). Stepwise approaches using combinations of Geo D and Geo P, Geo D and Geo f, or Fit D and Fit D* differentiated between pleomorphic adenomas, Warthin tumors, and malignant salivary gland tumors with the same efficacy (91% accuracy = 21/23). However, a stepwise differentiation using Fit D and Fit f was less effective (83% accuracy = 19/23). Considering cumbersome procedures with the least squares method compared with the geometric method, we concluded that the geometric determination of IVIM parameters can be an alternative to least-squares method in the diagnosis of head and neck tumors.     

Optimisation of OPLS–UA force-field parameters for protein systems using protein data bank

We have previously proposed a method for refining force-field parameters of protein systems, which consists of minimising the summation of the square of the force acting on each atom in the proteins with the structures from the protein data bank (PDB). The results showed that the modified force-field parameters for all-atom model gave structures more consistent with the experimental implications than the original force fields. In this work, we applied this method and a new method to the OPLS–UA force field. In the new method, we perform a minimisation of the average of the root-mean-square deviation of various protein structures from the native structure. We selected some torsion-energy parameters for this optimisation, and 100 molecules from the PDB were used. The results imply that the new force-field parameters gave structures of two peptides more consistent with the experimental implications for the secondary structure-forming tendencies than the original OPLS–UA force field.     

New method for field studies on the parapatric distribution of sibling species

Spatial segregation (parapatry) often occurs between closely related species. The distributions of the two species are sometimes defined with a small overlapping zone (called a `sympatric area') which generally shifts. Exclusion is necessary to explain the persistence and shift of such a spatial pattern. Field studies are carried out to identify the type of interaction that leads to the required exclusion. This is usually achieved by estimating competition and predation parameters to define the type of interaction strong enough to imply exclusion. But interaction parameters are estimated by quantitative methods which require prolonged observation (5–10 years). These estimations are thus difficult to obtain and are open to criticism because of the spatial and temporal variations in the biotic context. Now the study of these variations requires estimation of several other interaction parameters (for different times and sites); therefore, we are unable to discuss these criticisms from a study of realistic duration. We have, therefore, developed a faster study method using the spatial properties of the sympatric area (width and velocity). We used a between-species competition and a predation model, spatially extended with coupled map lattice formalism (CML), to generate substitution waves corresponding to the `moving sympatric area' and to study their spatial properties (asymptotic width and velocity). The relationships between the asymptotic width and the interaction level had different shapes with competition and predation parameters. We used this difference to define a rapid study method that does not use quantitative estimations of the interaction parameters. This method is more reliable than the usual method with respect to the above criticisms. These findings may have considerable consequences for field studies of parapatry.     

Generalized linear mixture models for handling nonignorable dropouts in longitudinal studies

This paper presents a method for analysing longitudinal data when there are dropouts. In particular, we develop a simple method based on generalized linear mixture models for handling nonignorable dropouts for a variety of discrete and continuous outcomes. Statistical inference for the model parameters is based on a generalized estimating equations (GEE) approach (Liang and Zeger, 1986). The proposed method yields estimates of the model parameters that are valid when nonresponse is nonignorable under a variety of assumptions concerning the dropout process. Furthermore, the proposed method can be implemented using widely available statistical software. Finally, an example using data from a clinical trial of contracepting women is used to illustrate the methodology.     

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers''-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers''-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Statistical method for prediction of gait kinematics with Gaussian process regression

We propose a novel methodology for predicting human gait pattern kinematics based on a statistical and stochastic approach using a method called Gaussian process regression (GPR). We selected 14 body parameters that significantly affect the gait pattern and 14 joint motions that represent gait kinematics. The body parameter and gait kinematics data were recorded from 113 subjects by anthropometric measurements and a motion capture system. We generated a regression model with GPR for gait pattern prediction and built a stochastic function mapping from body parameters to gait kinematics based on the database and GPR, and validated the model with a cross validation method. The function can not only produce trajectories for the joint motions associated with gait kinematics, but can also estimate the associated uncertainties. Our approach results in a novel, low-cost and subject-specific method for predicting gait kinematics with only the subject's body parameters as the necessary input, and also enables a comprehensive understanding of the correlation and uncertainty between body parameters and gait kinematics.     

Equations for segregation frequencies determined by Weinberg's generalized method in a model of a single autosomal 2-allelic locus with incomplete penetrance

Equations are proposed for segregation frequencies determined by generalized Weinberg's method (SFw). The equations give an expression for SFw in terms of basic parameters of a single autosomal two-allele locus model with incomplete penetrance (SAL-2 model), namely, in terms of the frequency of one of the alleles and the penetrances of three genotypes (p, II2, II1, II0). The equations proposed are intended to be included into the system of equations to find the basic parameters of the SAL-2 model.     

Development of a variational scheme for model inversion of multi-area model of brain. Part II: VBEM method

In Part I and Part II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN). In this paper, we develop the VBEM method to estimate posterior distributions of parameters of MEN. We choose suitable prior distributions for the model parameters in order to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms. The proposed VBEM algorithm starts with initialization and consists of repeated iterations of a variational Bayesian expectation step (VB E-step) and a variational Bayesian maximization step (VB M-step). Posterior distributions of the model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step. We develop a variational extended Kalman smoother (VEKS) to infer the distribution of the hidden state in the VB E-step and derive the forward and backward passes of VEKS, analogous to the Kalman smoother. In Part I, we evaluate and validate the VBEM method using simulation studies.     

The use of the logarithmic transformation in the calculation of the transport parameters of a system that obeys Michaelis–Menten kinetics

1. A logarithmic method is described for the calculation of the transport parameters, K(m) and V(max.)' of a biological system obeying Michaelis-Menten kinetics. 2. This logarithmic method leads to a way of estimating the transport parameters that has not apparently been used previously. It allows the separation of variance due to V(max.) from other variance, and so reduces the fiducial limits that can be placed on an estimation of K(m). 3. The results of studies on the transport of l-histidine and l-monoiodohistidine by rat intestinal sacs in vitro have been used to illustrate the application of the new method. Estimates of the transport parameters have also been made by two alternative procedures. The relative merits of the three methods are discussed.     

A tetrapeptide-based method for polyproline II-type secondary structure prediction

We describe a new method for polyproline II-type (PPII) secondary structure prediction based on tetrapeptide conformation properties using data obtained from all globular proteins in the Protein Data Bank (PDB). This is the first method for PPII prediction with a relatively high level of accuracy (approximately 60%). Our method uses only frequencies of different conformations among oligopeptides without any additional parameters. We also attempted to predict alpha-helices and beta-strands using the same approach. We find that the application of our method reveals interrelation between sequence and structure even for very short oligopeptides (tetrapeptides).     

A base-pairing model of duplex formation. I. Watson-Crick pairing geometries

We present a base-pairing model of oligonucleotide duplex formation and show in detail its equivalence to the nearest-neighbor dimer methods from fits to free energy of duplex formation data for short DNA-DNA and DNA-RNA hybrids containing only Watson-Crick pairs. For completeness, the corresponding RNA-RNA parameters are included. In this approach, the connection between rank-deficient polymer and rank-determinant oligonucleotide parameter sets for DNA duplexes is transparent. The method is generalized to include RNA-DNA hybrids where the rank-deficient model with 11 dimer parameters in fact provides slightly improved predictions relative to the standard method with 16 independent dimer parameters (DeltaG mean errors of 4.5 and 5.4%, respectively).     

The parameters of the stochastic leaky integrate-and-fire neuronal model

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data. Action Editor: Nicolas Brunel     

Dynamic modeling of genetic networks using genetic algorithm and S-system

MOTIVATION: The modeling of system dynamics of genetic networks, metabolic networks or signal transduction cascades from time-course data is formulated as a reverse-problem. Previous studies focused on the estimation of only network structures, and they were ineffective in inferring a network structure with feedback loops. We previously proposed a method to predict not only the network structure but also its dynamics using a Genetic Algorithm (GA) and an S-system formalism. However, it could predict only a small number of parameters and could rarely obtain essential structures. In this work, we propose a unified extension of the basic method. Notable improvements are as follows: (1) an additional term in its evaluation function that aims at eliminating futile parameters; (2) a crossover method called Simplex Crossover (SPX) to improve its optimization ability; and (3) a gradual optimization strategy to increase the number of predictable parameters. RESULTS: The proposed method is implemented as a C program called PEACE1 (Predictor by Evolutionary Algorithms and Canonical Equations 1). Its performance was compared with the basic method. The comparison showed that: (1) the convergence rate increased about 5-fold; (2) the optimization speed was raised about 1.5-fold; and (3) the number of predictable parameters was increased about 5-fold. Moreover, we successfully inferred the dynamics of a small genetic network constructed with 60 parameters for 5 network variables and feedback loops using only time-course data of gene expression.     

利用半球图像法提取植被冠层结构特征参数

植被冠层结构深刻地影响着植物群落与环境的相互作用,对植被冠层结构的研究是深入理解植被生态系统格局、过程及其运作机制的重要基础。冠层结构特征参数的快速测量方法是植被冠层结构研究的前提,目前测量方法主要是基于实际测量的地面法,地面法一般费时费力,受人为因素影响较大,因此本文探索利用半球图像法获取植被冠层结构特征参数。通过对半球图像进行几何纠正并建立参数图层,与分类后的植被冠层图层进行运算提取植被冠层结构特征参数。将该方法应用于祁连山旺腰沟流域青海云杉冠层结构特征参数的提取,包括植被冠幅、冠层面积、冠层周长等,结果显示：半球图像法能够较好的提取植被冠层结构特征参数,该方法具有简单、客观、可重复等优点,也可作为植被冠层结构变化的监测方法。     

Comparison of two optimization methods to derive energy parameters for protein folding: perceptron and Z score

Two methods were proposed recently to derive energy parameters from known native protein conformations and corresponding sets of decoys. One is based on finding, by means of a perceptron learning scheme, energy parameters such that the native conformations have lower energies than the decoys. The second method maximizes the difference between the native energy and the average energy of the decoys, measured in terms of the width of the decoys' energy distribution (Z-score). Whereas the perceptron method is sensitive mainly to "outlier" (i.e., extremal) decoys, the Z-score optimization is governed by the high density regions in decoy-space. We compare the two methods by deriving contact energies for two very different sets of decoys: the first obtained for model lattice proteins and the second by threading. We find that the potentials derived by the two methods are of similar quality and fairly closely related. This finding indicates that standard, naturally occurring sets of decoys are distributed in a way that yields robust energy parameters (that are quite insensitive to the particular method used to derive them). The main practical implication of this finding is that it is not necessary to fine-tune the potential search method to the particular set of decoys used.     

Approximate interval estimation of the difference in binomial parameters: correction for skewness and extension to multiple tables

Recently, Beal (1987, Biometrics 43, 941-950) found Mee's modification of Anbar's approximate interval estimation for the difference in binomial parameters to be a good choice in small sample sizes. As this method can be derived from the score theory of Bartlett, it is easily corrected for skewness. Exact numerical evaluation shows that this correction is not as important for this case as for the ratio of binomial parameters (Gart and Nam, 1988, Biometrics 44, 323-338). The score theory is also used to extend this method to the stratified or multiple-table case. Thus, good approximate interval estimates for differences, ratios, and odds ratios of binomial parameters can all be derived from the same general theory.