A Coarse-Grained Elastic Network Atom Contact Model and Its Use in the Simulation of Protein Dynamics and the Prediction of the Effect of Mutations

Normal mode analysis (NMA) methods are widely used to study dynamic aspects of protein structures. Two critical components of NMA methods are coarse-graining in the level of simplification used to represent protein structures and the choice of potential energy functional form. There is a trade-off between speed and accuracy in different choices. In one extreme one finds accurate but slow molecular-dynamics based methods with all-atom representations and detailed atom potentials. On the other extreme, fast elastic network model (ENM) methods with C_α−only representations and simplified potentials that based on geometry alone, thus oblivious to protein sequence. Here we present ENCoM, an Elastic Network Contact Model that employs a potential energy function that includes a pairwise atom-type non-bonded interaction term and thus makes it possible to consider the effect of the specific nature of amino-acids on dynamics within the context of NMA. ENCoM is as fast as existing ENM methods and outperforms such methods in the generation of conformational ensembles. Here we introduce a new application for NMA methods with the use of ENCoM in the prediction of the effect of mutations on protein stability. While existing methods are based on machine learning or enthalpic considerations, the use of ENCoM, based on vibrational normal modes, is based on entropic considerations. This represents a novel area of application for NMA methods and a novel approach for the prediction of the effect of mutations. We compare ENCoM to a large number of methods in terms of accuracy and self-consistency. We show that the accuracy of ENCoM is comparable to that of the best existing methods. We show that existing methods are biased towards the prediction of destabilizing mutations and that ENCoM is less biased at predicting stabilizing mutations.     

Meta-analysis of the difference of medians

We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of medians. To include these studies in meta-analysis, several authors have recently proposed methods to estimate the sample mean and standard deviation from the median, sample size, and several commonly reported measures of spread. Researchers frequently apply these methods to estimate the difference of means and its variance for each primary study and pool the difference of means using inverse variance weighting. In this work, we develop several methods to directly meta-analyze the difference of medians. We conduct a simulation study evaluating the performance of the proposed median-based methods and the competing transformation-based methods. The simulation results show that the median-based methods outperform the transformation-based methods when meta-analyzing studies that report the median of the outcome, especially when the outcome is skewed. Moreover, we illustrate the various methods on a real-life data set.     

Inferring the temperature dependence of population parameters: the effects of experimental design and inference algorithm

Understanding and quantifying the temperature dependence of population parameters, such as intrinsic growth rate and carrying capacity, is critical for predicting the ecological responses to environmental change. Many studies provide empirical estimates of such temperature dependencies, but a thorough investigation of the methods used to infer them has not been performed yet. We created artificial population time series using a stochastic logistic model parameterized with the Arrhenius equation, so that activation energy drives the temperature dependence of population parameters. We simulated different experimental designs and used different inference methods, varying the likelihood functions and other aspects of the parameter estimation methods. Finally, we applied the best performing inference methods to real data for the species Paramecium caudatum. The relative error of the estimates of activation energy varied between 5% and 30%. The fraction of habitat sampled played the most important role in determining the relative error; sampling at least 1% of the habitat kept it below 50%. We found that methods that simultaneously use all time series data (direct methods) and methods that estimate population parameters separately for each temperature (indirect methods) are complementary. Indirect methods provide a clearer insight into the shape of the functional form describing the temperature dependence of population parameters; direct methods enable a more accurate estimation of the parameters of such functional forms. Using both methods, we found that growth rate and carrying capacity of Paramecium caudatum scale with temperature according to different activation energies. Our study shows how careful choice of experimental design and inference methods can increase the accuracy of the inferred relationships between temperature and population parameters. The comparison of estimation methods provided here can increase the accuracy of model predictions, with important implications in understanding and predicting the effects of temperature on the dynamics of populations.     

Simple Methods for Testing the Molecular Evolutionary Clock Hypothesis

Simple statistical methods for testing the molecular evolutionary clock hypothesis are developed which can be applied to both nucleotide and amino acid sequences. These methods are based on the chi-square test and are applicable even when the pattern of substitution rates is unknown and/or the substitution rate varies among different sites. Furthermore, some of the methods can be applied even when the outgroup is unknown. Using computer simulations, these methods were compared with the likelihood ratio test and the relative rate test. The results indicate that the powers of the present methods are similar to those of the likelihood ratio test and the relative rate test, in spite of the fact that the latter two tests assume that the pattern of substitution rates follows a certain model and that the substitution rate is the same among different sites, while such assumptions are not necessary to apply the present methods. Therefore, the present methods might be useful.     

Evaluation of the Spiral Plate Maker for the Enumeration of Micro-organisms in Foods

A statistically based comparison of five methods of enumerating bacteria in foods has been undertaken to assess the potential application of the Spiral Plate Maker (Gilchrist et al. 1973) which is claimed to reduce very significantly the costs involved in the quantitative estimation of viable micro-organisms in foods. The performance of the Spiral Plate Maker was compared with that of three conventional methods (pour plate, surface spread plate and drop count) for the examination of four types of food by four different operators. Analysis of variance showed that there were no differences between the methods at the 5% level although some isolated interactions occurred. Regression and correlation coefficients between the various methods were all highly significant and the results obtained by the spiral plate method were within the limits of error for traditional quantitative methods. The spiral plate method, in many cases, can replace advantageously any of the other methods for the quantitative estimation of viable microorganisms in foods. Labour requirements for the enumeration of micro-organisms by the spiral plate method were only 31% of that required for one conventional method. In addition considerable savings in materials were achieved.     

Haplotype frequency estimation in the presence of genotyping errors

Several statistical methods have been proposed to estimate haplotype frequencies, either based on unrelated individuals or based on families. These estimates may yield insights on population genetics as well as associations between candidate regions and disease of interest. One limitation of the existing methods is that all these methods make the implicit assumption that there are no genotyping errors. However, genotyping errors are unavoidable in practice. Numerous methods have been developed to incorporate genotyping errors in genetic studies, but none to date have addressed the issues of haplotype inference in the presence of genotyping errors. In this article, we develop statistical methods for haplotype inference incorporating genotyping errors. We describe how our methods can be applied to analyze unrelated individuals as well as nuclear families. Our simulation results show that the proposed methods perform well in the presence of genotyping errors.     

Complexity of the simplest species tree problem

The multispecies coalescent model provides a natural framework for species tree estimation accounting for gene-tree conflicts. Although a number of species tree methods under the multispecies coalescent have been suggested and evaluated using simulation, their statistical properties remain poorly understood. Here, we use mathematical analysis aided by computer simulation to examine the identifiability, consistency, and efficiency of different species tree methods in the case of three species and three sequences under the molecular clock. We consider four major species-tree methods including concatenation, two-step, independent-sites maximum likelihood, and maximum likelihood. We develop approximations that predict that the probit transform of the species tree estimation error decreases linearly with the square root of the number of loci. Even in this simplest case, major differences exist among the methods. Full-likelihood methods are considerably more efficient than summary methods such as concatenation and two-step. They also provide estimates of important parameters such as species divergence times and ancestral population sizes,whereas these parameters are not identifiable by summary methods. Our results highlight the need to improve the statistical efficiency of summary methods and the computational efficiency of full likelihood methods of species tree estimation.     

Assessing Uncertainty in the Rooting of the SARS-CoV-2 Phylogeny

The rooting of the SARS-CoV-2 phylogeny is important for understanding the origin and early spread of the virus. Previously published phylogenies have used different rootings that do not always provide consistent results. We investigate several different strategies for rooting the SARS-CoV-2 tree and provide measures of statistical uncertainty for all methods. We show that methods based on the molecular clock tend to place the root in the B clade, whereas methods based on outgroup rooting tend to place the root in the A clade. The results from the two approaches are statistically incompatible, possibly as a consequence of deviations from a molecular clock or excess back-mutations. We also show that none of the methods provide strong statistical support for the placement of the root in any particular edge of the tree. These results suggest that phylogenetic evidence alone is unlikely to identify the origin of the SARS-CoV-2 virus and we caution against strong inferences regarding the early spread of the virus based solely on such evidence.     

A survey of the methods for the characterization of microbial consortia and communities

A survey of the available literature on methods most frequently used for the identification and characterization of microbial strains, communities, or consortia is presented. The advantages and disadvantages of the various methodologies were examined from several perspectives including technical, economic (time and cost), and regulatory. The methods fall into 3 broad categories: molecular biological, biochemical, and microbiological. Molecular biological methods comprise a broad range of techniques that are based on the analysis and differentiation of microbial DNA. This class of methods possesses several distinct advantages. Unlike most other commonly used methods, which require the production of secondary materials via the manipulation of microbial growth, molecular biological methods recover and test their source materials (DNA) directly from the microbial cells themselves, without the requirement for culturing. This eliminates both the time required for growth and the biases associated with cultured growth, which is unavoidably and artificially selective. The recovered nucleic acid can be cloned and sequenced directly or subpopulations can be specifically amplified using polymerase chain reaction (PCR), and subsequently cloned and sequenced. PCR technology, used extensively in forensic science, provides researchers with the unique ability to detect nucleic acids (DNA and RNA) in minute amounts, by amplifying a single target molecule by more than a million-fold. Molecular methods are highly sensitive and allow for a high degree of specificity, which, coupled with the ability to separate similar but distinct DNA molecules, means that a great deal of information can be gleaned from even very complex microbial communities. Biochemical methods are composed of a more varied set of methodologies. These techniques share a reliance on gas chromatography and mass spectrometry to separate and precisely identify a range of biomolecules, or else investigate biochemical properties of key cellular biomolecules. Like the molecular biological methods, some biochemical methods such as lipid analyses are also independent of cultured growth. However, many of these techniques are only capable of producing a profile that is characteristic of the microbial community as a whole, providing no information about individual members of the community. A subset of these methodologies are used to derive taxonomic information from a community sample; these rely on the identification of key subspecies of biomolecules that differ slightly but characteristically between species, genera, and higher biological groupings. However, when the consortium is already growing in chemically defined media (as is often the case with commercial products), the rapidity and relatively low costs of these procedures can mitigate concerns related to culturing biases. Microbiological methods are the most varied and the least useful for characterizing microbial consortia. These methods rely on traditional tools (cell counting, selective growth, and microscopic examination) to provide more general characteristics of the community as a whole, or else to narrow down and identify only a small subset of the members of that community. As with many of the biochemical methods, some of the microbiological methods can fairly rapidly and inexpensively create a community profile, which can be used to compare 2 or more entire consortia. However, for taxonomic identification of individual members, microbiological methods are useful only to screen for the presence of a few key predetermined species, whose preferred growth conditions and morphological characteristics are well defined and reproducible.     

Cladistic and phylogenetic biogeography: the art and the science of discovery

All methods used in historical biogeographical analysis aim to obtain resolved area cladograms that represent historical relationships among areas in which monophyletic groups of taxa are distributed. When neither widespread nor sympatric taxa are present in the distribution of a monophyletic group, all methods obtain the same resolved area cladogram that conforms to a simple vicariance scenario. In most cases, however, the distribution of monophyletic groups of taxa is not that simple. A priori and a posteriori methods of historical biogeography differ in the way in which they deal with widespread and sympatric taxa. A posteriori methods are empirically superior to a priori methods, as they provide a more parsimonious accounting of the input data, do not eliminate or modify input data, and do not suffer from internal inconsistencies in implementation. When factual errors are corrected, the exemplar presented by M.C. Ebach & C.J. Humphries (Journal of Biogeography, 2002, 29 , 427) purporting to show inconsistencies in implementation by a posteriori methods actually corroborates the opposite. The rationale for preferring a priori methods thus corresponds to ontological rather than to epistemological considerations. We herein identify two different research programmes, cladistic biogeography (associated with a priori methods) and phylogenetic biogeography (associated with a posteriori methods). The aim of cladistic biogeography is to fit all elements of all taxon–area cladograms to a single set of area relationships, maintaining historical singularity of areas. The aim of phylogenetic biogeography is to document, most parsimoniously, the geographical context of speciation events. The recent contribution by M.C. Ebach & C.J. Humphries (Journal of Biogeography, 2002, 29 , 427) makes it clear that cladistic biogeography using a priori methods is an inductivist/verificationist research programme, whereas phylogenetic biogeography is hypothetico‐deductivist/falsificationist. Cladistic biogeography can become hypothetic‐deductive by using a posteriori methods of analysis.     

On the meaning of the distance-to-target weighting method and normalisation in Life Cycle Impact assessment

Distance-to-target weighting methods are widely used in life cycle impact assessment. The methods rank impacts as being more important the further away society’s activities are from achieving the desired targets for the pollutants. However, we feel that the scientific bases of the distance-to-target methods still need more clarification. This article illustrates how multiattribute value theory (MAVT) can be applied to interpret the impact category weights as well as the aggregation rule and normalisation used in the distant-to-target methods. Our comparison revealed that under certain conditions two of the three commonly used impact assessment methods (Ecoindicator 95, ET-method) applying distance-to-target weighting are consistent with the impact assessment framework derived from MAVT. This consistency holds for non-zero targets with equal importance and linear damage functions passing through the origin. We show that the MAVT framework offers a foundation for the methodological development in life cycle impact assessment.     

On the methods of calculation of the electrostatic potential in a protein channel

The profiles of the electrostatic potential along the axis of a gramicidin channel were calculated using two quantum chemistry methods (EHT and CNDO/2) and three methods of force fields (AMBER, CHARMM, and OPLS). The calculations were performed without taking into account the contribution of water. A comparative analysis of the calculated profiles indicated that the electrostatic field of point charges of the CHARMM force field is close to that obtained by the quantum chemistry methods. It was concluded that there is no need to calculate the electric field using laborious quantum-mechanical methods since the less laborious method of the CHARMM force field gives approximately the same results.     

Cytochemical methods for the detection of apoptosis.

Detection of apoptotic cell death in cells and tissues has become of paramount importance in many fields of modern biology, including studies of embryonic development, degenerative disease, and cancer biology. In addition to methods that employ biochemical analysis of large populations of cells, cytochemical methods have recently been extensively used both in individual cells and in tissues. Most of these methods exploit properties of dying cells that are more or less specific for the apoptotic process. However, considerable confusion exists over the interpretation of some of these methods and their usefulness in all settings. This review attempts to summarize the more recent advances in cytochemical detection of apoptosis and emphasizes some of the pitfalls that confuse the interpretation of results of these methods.     

Inferences on the common mean of several normal populations based on the generalized variable method

This article presents procedures for hypothesis testing and interval estimation of the common mean of several normal populations. The methods are based on the concepts of generalized p-value and generalized confidence limit. The merits of the proposed methods are evaluated numerically and compared with those of the existing methods. Numerical studies show that the new procedures are accurate and perform better than the existing methods when the sample sizes are moderate and the number of populations is four or less. If the number of populations is five or more, then the generalized variable method performs much better than the existing methods regardless of the sample sizes. The generalized variable method and other existing methods are illustrated using two examples.     

理性设计提高蛋白质热稳定性的研究进展

通过理性设计提高蛋白质的热稳定性一直是当今计算生物学及蛋白质工程领域中的一个研究热点。与传统的定向进化的方法相比,该方法具有目的性强、效率高的优点,对扩大蛋白质的应用范围与探究蛋白质结构和功能的关系均具有重要意义。本文详细介绍了影响蛋白质热稳定性的因素,以及一些常用的通过理性设计来提高蛋白质的热稳定性的策略。由于影响蛋白质热稳定性的因素众多,并且众多因素之间还具有千丝万缕的联系,到目前为止研究人员还没有提出一个公认的适合于所有蛋白质的理性设计的策略,这也是现代计算生物学家及蛋白质工程学家们努力研究的一个重要方向。     

Different versions of the Dayhoff rate matrix

Many phylogenetic inference methods are based on Markov models of sequence evolution. These are usually expressed in terms of a matrix (Q) of instantaneous rates of change but some models of amino acid replacement, most notably the PAM model of Dayhoff and colleagues, were originally published only in terms of time-dependent probability matrices (P(t)). Previously published methods for deriving Q have used eigen-decomposition of an approximation to P(t). We show that the commonly used value of t is too large to ensure convergence of the estimates of elements of Q. We describe two simpler alternative methods for deriving Q from information such as that published by Dayhoff and colleagues. Neither of these methods requires approximation or eigen-decomposition. We identify the methods used to derive various different versions of the Dayhoff model in current software, perform a comparison of existing and new implementations, and, to facilitate agreement among scientists using supposedly identical models, recommend that one of the new methods be used as a standard.     

Analysis of the origin of the Vietnam dairy cow breed using the results of marker character study]

The phylogenesis analysis of Vietnam milk cows breed was performed using eleven different mathematical methods. 14 to 144 markers were used in this analysis, whose synthesis is controlled by eleven genetical systems of blood groups and six polymorphic systems of proteins. It has been demonstrated that the accuracy of the phylogenesis analysis depends on the quality of the markers applied and on the methods used. It was established that the way of breed formation was reflected in the dendrogram composed by the matrix based on the formula of Eisner and Meshcheryakova (1978). The properties of other methods in use are discussed.     

Confidence intervals for the difference in the success rates of two treatments in the analysis of correlated binary responses

In clinical studies, we often compare the success rates of two treatment groups where post‐treatment responses of subjects within clusters are usually correlated. To estimate the difference between the success rates, interval estimation procedures that do not account for this intraclass correlation are likely inappropriate. To address this issue, we propose three interval procedures by direct extensions of recently proposed methods for independent binary data based on the concepts of design effect and effective sample size used in sample surveys. Each of them is then evaluated with four competing variance estimates. We also extend three existing methods recommended for complex survey data using different weighting schemes required for those three existing methods. An extensive simulation study is conducted for the purposes of evaluating and comparing the performance of the proposed methods in terms of coverage and expected width. The interval estimation procedures are illustrated using three examples in clinical and social science studies. Our analytic arguments and numerical studies suggest that the methods proposed in this work may be useful in clustered data analyses.