Normal mode analysis of proteins: a comparison of rigid cluster modes with C(alpha) coarse graining

The ability to infer dynamic motions from an equilibrium (static) conformation of a protein can be essential in establishing structure-function relationships. In particular, the low-frequency motions are of functional interest because statistical mechanics predicts these motions will have the largest amplitudes. In this paper, we address the computational cost of normal mode analysis (NMA) applied to a C(alpha)-based elastic network model (C(alpha)-NMA) and present a new coarse-grained rigid-body-based analysis (cluster-NMA). This new method represents a protein as a collection of rigid bodies interconnected with harmonic potentials. This representation produces reduced degree-of-freedom (DOF) equations of motion (EOMs) which, even in the case of large structures (10(3+) residues), enables the computation of normal modes to be done on a desktop PC. We present the complete theory and analysis of cluster-NMA and also include its application to a variety of structures. The results of the new method are compared with C(alpha)-NMA and it is shown that cluster-NMA produces very good approximations to the lowest modes at a fraction of the computational cost.     

A general-purpose coarse-grained molecular dynamics program

In this article, we describe a general-purpose coarse-grained molecular dynamics program COGNAC (COarse Grained molecular dynamics program by NAgoya Cooperation). COGNAC has been developed for general molecular dynamics simulation, especially for coarse-grained polymer chain models. COGNAC can deal with general molecular models, in which each molecule consists of coarse-grained atomic units connected by chemical bonds. The chemical bonds are specified by bonding potentials for the stretching, bending and twisting of the bonds, each of which are the functions of the position coordinates of the two, three and four atomic units. COGNAC can deal with both isotropic and anisotropic interactions between the non-bonded atomic units. As an example, the Gay-Berne potential is implemented. New potential functions can be added to the list of existing potential functions by users. COGNAC can do simulations for various situations such as under constant temperature, under constant pressure, under shear and elongational deformation, etc. Some new methods are implemented in COGNAC for modeling multiphase structures of polymer blends and block copolymers. A density biased Monte Carlo method and a density biased potential method can generate equilibrium chain configurations from the results of the self-consistent field calculations. Staggered reflective boundary conditions can generate interfacial structures with smaller system size compared with those of periodic boundary conditions.     

On the model granularity to simulate protein dynamics: A biological physics view on biomolecular computing

What granularity is needed to carry out computer simulations of biomolecular reactions/motions? This is one of the central issues of the in silico biomolecular computing. In this paper, we addressed this issue by studying model granularity dependence of the native structure dynamics of protein molecules. We conducted molecular dynamics simulations employing three different protein models: the model with full atomic details and two coarse-grained models in which only C_α atoms interacting with each other through simple potentials are considered. In addition to the observed agreement among the three models in terms of isotropic thermal fluctuation, principal component analysis showed that the coarse-grained models can also reproduce the anisotropy (or directionality) of the fluctuation, particularly of collective modes having relevance to molecular function. This indicates that the dependence of the essential dynamics of a protein molecule on the model granularity is weak, although it was also shown that incorporation of the Lennard–Jones-type potential into the harmonic-potential-based coarse-grained model improves the reproducibility to some degree, and that a plastic nature of structural dynamics observed in the full atomic model transforms into an elastic one in the coarse-grained models. The coarse-grained model can be applied to a molecular motor system, which may lead to a new view of biomolecular computing in the context of biological physics.     

蛋白质的分组重量编码及在结构型预测的应用

从氨基酸的物化特性出发,利用物理学中“粗粒化”思想,提出了一种蛋白质序列的分组重量编码方法(Encoding Basedon Grouped Weight,简记为EBGW),并结合组分耦联算法进行结构型预测的研究。对标准集T359中359个蛋白质的Resubstitution检验和Jack-knife检验预测准确性分别达到99.72%和91.09%,其中Jack-knife检验总体预测精度比相同条件下采用氨基酸组成编码的方法提高了约7%,特别是α+β类的预测精度提高了15%。实验结果表明蛋白质序列的EBGW编码方法能够有效地提取字母序列中蕴含的结构信息。     

Efficient prediction of protein conformational pathways based on the hybrid elastic network model

Various computational models have gained immense attention by analyzing the dynamic characteristics of proteins. Several models have achieved recognition by fulfilling either theoretical or experimental predictions. Nonetheless, each method possesses limitations, mostly in computational outlay and physical reality. These limitations remind us that a new model or paradigm should advance theoretical principles to elucidate more precisely the biological functions of a protein and should increase computational efficiency. With these critical caveats, we have developed a new computational tool that satisfies both physical reality and computational efficiency. In the proposed hybrid elastic network model (HENM), a protein structure is represented as a mixture of rigid clusters and point masses that are connected with linear springs. Harmonic analyses based on the HENM have been performed to generate normal modes and conformational pathways. The results of the hybrid normal mode analyses give new physical insight to the 70S ribosome. The feasibility of the conformational pathways of hybrid elastic network interpolation (HENI) was quantitatively evaluated by comparing three different overlap values proposed in this paper. A remarkable observation is that the obtained mode shapes and conformational pathways are consistent with each other. Our timing results show that HENM has some advantage in computational efficiency over a coarse-grained model, especially for large proteins, even though it takes longer to construct the HENM. Consequently, the proposed HENM will be one of the best alternatives to the conventional coarse-grained ENMs and all-atom based methods (such as molecular dynamics) without loss of physical reality.     

Elastic models of conformational transitions in macromolecules

We develop a computationally efficient and physically realistic method to simulate the transition of a macromolecule between two conformations. Our method is based on a coarse-grained elastic network model in which contact interactions between spatially proximal parts of the macromolecule are modelled with Gaussian/harmonic potentials. To delimit the interactions in such models, we introduce a cutoff to the permitted number of nearest neighbors. This generates stiffness (Hessian) matrices that are both sparse and quite uniform, hence, allowing for efficient computations. Several toy models are tested using our method to mimic simple classes of macromolecular motions such as stretching, hinge bending, shear, compression, ligand binding and nucleic acid structural transitions. Simulation results demonstrate that the method developed here reliably generates sequences of feasible intermediate conformations of macromolecules, since our method observes steric constraints and produces monotonic changes to virtual bond angles and torsion angles. A final application is made to the opening process of the protein lactoferrin.     

基于Alpha Fold数据库分析蛋白质进化中的统计规律

由DeepMind开发的AlphaFold在蛋白质结构预测领域取得了前所未有的巨大突破,对生命科学的研究产生了革命性的影响。基于大规模的结构预测,AlphaFold结构预测数据库得以建立,它包含2亿多种蛋白,并覆盖了数十种物种的完整蛋白质组。该综述介绍了在“后AlphaFold时代”利用统计物理方法研究蛋白质进化问题的一些最新进展。传统的蛋白质进化研究往往关注同一个家族的蛋白质序列或者结构(微观视角),而随着AlphaFold预测的海量蛋白质结构的出现,研究者可以把视角扩展到大量蛋白质的集合,甚至是直接对比不同物种体内的全部蛋白质,从中挖掘统计趋势(宏观视角)。基于AlphaFold数据库,通过对比40多种模式生物体内相似链长的蛋白质,研究者发现了蛋白质分子进化中的统计规律。随着物种复杂性的提高,蛋白质结构将趋向于更高的柔性和模块化程度,蛋白质序列将趋向于出现更显著的亲疏水片段分隔,蛋白质的功能专一性也不断提高。这些基于AlphaFold的统计研究在分子进化和物种进化之间建立了联系,有助于理解生物复杂性的演化。     

Image Denoising Using Generalized Anisotropic Diffusion

Motivated by some recent works in fractional-order anisotropic diffusions, we introduce a class of generalized anisotropic diffusion equations for image denoising. We first define a new type of derivative (called G-derivative), which contains the fractional derivative as a special case, using the Fourier transform, then the generalized anisotropic diffusion equations are Euler–Lagrange equations of a cost functional which is an increasing function of the absolute value of the G-derivative of the image intensity function. All the G-derivative operators constitute a ring, and the semigroup property of the G-derivative consists with the semigroup property of the fractional derivative, so the resulting generalized anisotropic diffusions can be seen as generalizations of the fractional-order anisotropic diffusions. We also discuss the generalized Sobolev space described by the G-derivative and some variants of generalized anisotropic diffusions. The discretization of the G-derivative is computed in the frequency domain, and the stability analysis of the difference scheme is given. We list some generalized anisotropic diffusions and apply them to image denoising. Numerical results show that new models have great potentials in image denoising.     

基于服务关系统计的多粒度服务组合方法

传统工作流方法进行服务组合存在两个问题,服务组合无法自动生成和复杂服务无法重用,基于服务关系统计的多粒度服务组合方法（MSWC）有效解决了这两个问题。MSWC包括服务关系统计学习、服务粗分和服务细分三个部分, 分别用于进行服务关系统计计算、服务分组和服务映射。通过服务关系统计学习计算了有逻辑和无逻辑的服务关联度;服务粗分将服务需求分解为无逻辑关系的组;而服务细分通过逻辑概率将服务分组映射成系统中已有的复杂服务,将这些复杂服务串接起来,即完成服务组合。因为三个步骤均是自动执行,因此MSWC是自动组合方法,而服务分组最终映射为系统已有的复杂服务,因此是一个多粒度服务组合方法。最后通过实验结果分析表明,该算法能够很好地适应网络上Web Service快速增长的情况,并且具备较好的服务组合性能。     

Using data compression for multidimensional distribution analysis [molecular biology]

A new method for multi-dimensional distribution analysis using a data compression technique applied to the knowledge-based mean-force potentials between residues for the analysis of protein sequence-structure compatibility performs much better than that of conventional 1D distance-based potentials derived from binned distributions.     

Sampling properties of the spectrum and coherency of sequences of action potentials

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This article begins with a review of these quantities, their interpretation, and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented that builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low-variance gaussian process. It is found that in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus. Although the material discussed is of general applicability to point processes, attention will be confined to sequences of neuronal action potentials (spike trains), the motivation for this work.     

A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information

A sparser but more efficient connection rule (called a bond-cutoff method) for a simplified alpha-carbon coarse-grained elastic network model is presented. One of conventional connection rules for elastic network models is the distance-cutoff method, where virtual springs connect an alpha-carbon with all neighbor alpha-carbons within predefined distance-cutoff value. However, though the maximum interaction distance between alpha-carbons is reported as 7 angstroms, this cutoff value can make the elastic network unstable in many cases of protein structures. Thus, a larger cutoff value (>11 angstroms) is often used to establish a stable elastic network model in previous researches. To overcome this problem, a connection rule for backbone model is proposed, which satisfies the minimum condition to stabilize an elastic network. Based on the backbone connections, each type of chemical interactions is considered and added to the elastic network model: disulfide bonds, hydrogen bonds, and salt-bridges. In addition, the van der Waals forces between alpha-carbons are modeled by using the distance-cutoff method. With the proposed connection rule, one can make an elastic network model with less than 7 angstroms distance cutoff, which can reveal protein flexibility more sharply. Moreover, the normal modes from the new elastic network model can reflect conformational changes of a given protein better than ones by the distance-cutoff method. This method can save the computational cost when calculating normal modes of a given protein structure, because it can reduce the total number of connections. As a validation, six example proteins are tested. Computational times and the overlap values between the conformational change and infinitesimal motion calculated by normal mode analysis are presented. Those animations are also available at UMass Morph Server (http://biomechanics.ecs.umass.edu/umms.html).     

基于局部方差改进的超声图像各向异性扩散去噪算法

针对各向异性扩散算法不能有效区分强噪声和弱边缘的缺点,提出了一种基于图像局部统计特征改进的算法。该算法在对图像进行各向异性扩散去噪的过程中,使用梯度阈值找到图像中灰度变化较大的点,再通过计算局部方差和局部去心方差的差值判断该点是否为噪声点,若是噪声点则使用均值滤波处理。对仿真图像和临床超声图像的实验结果表明:与传统的各向异性扩散算法相比,改进的算法在图像去噪和特征保留的能力上得到了良好的提升。     

On the approximate solution of the delay integral equation of the statistical theory of radiation damage

In the statistical theory of radiation damage, the mean number of atoms displaced in the atomic cascade is given by a delay integral equation with specified initial conditions. Numerical procedures the use spline functions in conjuction with appropriate quadrature rules are presented for the construction of continuous approximations to the mean number of displaced atoms, represented by the delay integral. The methods presented are shown to be stable and to be of order (m + 1) for spline functions of degree m. Finally, the method for quadratic splines is used to compute the mean number of displaced atoms for atomic collisions with Firsov potentials, and with truncated Coulomb potentials.     

A new algorithm for analysis of the homology in protein primary structure

A new algorithm for analysis of the homology and genetic semihomology in protein sequence is described. It assumes the close relation between the compared amino acids and their codons in related proteins. The algorithm is based on the network of the genetic relationship between amino acids and, thus differs from the commonly used statistical matrices. The results obtained by using this method are more comprehensive than used at present, and reflect the actual mechanism of protein differentiation and evolution. They concern: (1) location of homologous and semihomologous sites in compared proteins; (2) precise estimation of insertion/deletion gaps in non-homologous fragments; (3) analysis of internal homology and semihomology; (4) precise location of domains in multidomain proteins; (5) estimation of genetic code of non-homologous fragments; (6) construction of genetic probes; (7) studies on differentiation processes among related proteins; (8) estimation of the degree of relationship among related proteins; (9) studies on the evolution mechanism within homologous protein families and (10) confirmation of actual relationship of sequences showing low degree of homology.     

Using Generalized Estimating Equation to Learn Decision Tree with Multivariate Responses

Previous decision tree algorithms have used Mahalanobis distance for multiple continuous longitudinal response or generalized entropy index for multiple binary responses. However, these methods are limited to either continuous or binary responses. In this paper, we suggest a new tree-based method that can analyze any type of multiple responses by using a statistical approach, called GEE (generalized estimating equations). The value of this new technique is demonstrated with reference to an application using web-usage survey. This work was supported by grant No. R05-2003-000-11281-0 from the Basic Research Program of the Korea Science & Engineering Foundation.     

一种基于布尔运算的无线传感器网络TOA定位算法

提出一种基于布尔运算的无线传感器网络TOA定位新算法.算法针对室外定位,通过实验测得TOA测距误差的先验统计规律.在进行TOA定位时,算法首先根据测距值和先验统计参数建立同维布尔矩阵,然后利用矩阵运算和平方差判别式确定未知节点的估计位置.仿真和实验表明,与最小二乘(LSE)定位算法和优选残差加权(ORwgh)定位算法相比较,本文算法具有更好的定位精度,且在信标节点数大于6时具有更小的定位耗时.     

Continuous case-based reasoning

Case-based reasoning systems have traditionally been used to perform high-level reasoning in problem domains that can be adequately described using discrete, symbolic representations. However, many real-world problem domains, such as autonomous robotic navigation, are better characterized using continuous representations. Such problem domains also require continuous performance, such as on-line sensorimotor interaction with the environment, and continuous adaptation and learning during the performance task. This article introduces a new method for continuous case-based reasoning, and discusses its application to the dynamic selection, modification, and acquisition of robot behaviors in an autonomous navigation system, SINS (self-improving navigation system). The computer program and the underlying method are systematically evaluated through statistical analysis of results from several empirical studies. The article concludes with a general discussion of case-based reasoning issues addressed by this research.     

A hybrid multi-loop genetic-algorithm/simplex/spatial-grid method for locating the optimum orientation of an adsorbed protein on a solid surface

Atomistic simulation of protein adsorption on a solid surface in aqueous environment is computationally demanding, therefore the determination of preferred protein orientations on the solid surface usually serves as an initial step in simulation studies. We have developed a hybrid multi-loop genetic-algorithm/simplex/spatial-grid method to search for low adsorption-energy orientations of a protein molecule on a solid surface. In this method, the surface and the protein molecule are treated as rigid bodies, whereas the bulk fluid is represented by spatial grids. For each grid point, an effective interaction region in the surface is defined by a cutoff distance, and the possible interaction energy between an atom at the grid point and the surface is calculated and recorded in a database. In searching for the optimum position and orientation, the protein molecule is translated and rotated as a rigid body with the configuration obtained from a previous Molecular Dynamic simulation. The orientation-dependent protein-surface interaction energy is obtained using the generated database of grid energies. The hybrid search procedure consists of two interlinked loops. In the first loop A, a genetic algorithm (GA) is applied to identify promising regions for the global energy minimum and a local optimizer with the derivative-free Nelder-Mead simplex method is used to search for the lowest-energy orientation within the identified regions. In the second loop B, a new population for GA is generated and competitive solution from loop A is improved. Switching between the two loops is adaptively controlled by the use of similarity analysis. We test the method for lysozyme adsorption on a hydrophobic hydrogen-terminated silicon (110) surface in implicit water (i.e., a continuum distance-dependent dielectric constant). The results show that the hybrid search method has faster convergence and better solution accuracy compared with the conventional genetic algorithm.