Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high‐throughput analysis of rigid body modeling and simulation results. We also introduce a constant‐time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano‐d.inrialpes.fr/software/RigidRMSD . © 2014 Wiley Periodicals, Inc.     

Using quaternions to calculate RMSD

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well-known formula due to Kabsch. We analyze the various cases that may arise, and give a complete enumeration of the special cases in terms of the arrangement of the eigenvalues of a traceless, 4 x 4 symmetric matrix. A key result here is an expression for the gradient of the RMSD as a function of model parameters. This can be useful, for example, in finding the minimum energy path of a reaction using the elastic band methods or in optimizing model parameters to best fit a target structure.     

KCl effect on the solubility of five different amino acids in water

Using the analytical gravimetric method the solubility of glycine and dl-alanine in aqueous systems of KCl at 323.15 K, and of l-isoleucine, l-threonine and l-serine in the same system, at 298.15 and 323.15 K, were measured for salt concentrations ranging up to 2.0 molal.     

Is the rigid-body assumption reasonable?: Insights into the effects of dynamics on the electrostatic analysis of barnase-barstar

Electrostatically-driven association of proteins is important to many biological functions, and understanding which amino acid residues contribute to these interactions is crucial to protein design. Theoretical calculations that are used to elucidate the role of electrostatics in association are typically based on a single experimentally determined protein structure, while an underlying rigid-body assumption is adopted. The goal of this study was to investigate the role of conformational fluctuations on electrostatic interaction energies, as applied to the electrostatic analysis of barnase-barstar. For our calculations, we apply theoretical alanine-scan mutagenesis to introduce charge perturbations by replacing every ionizable residue with alanine, one at a time. Electrostatic clustering and free energy calculations based on the Poisson-Boltzmann method are used to evaluate the effects of each perturbation. Molecular dynamics simulations are performed for the barnase-barstar parent complex and seven experimental alanine mutations from the literature, in order to introduce relaxation before and after mutation. We discuss the effects of dynamics, in the form of pre- and post-mutation relaxation, on electrostatic clustering and free energies of association in light of experimental data. We also examine the utility of nine electrostatic similarity methods for clustering of barnase alanine-scan mutants. Our calculations suggest that the rigid-body assumption is reasonable for electrostatic calculations of barnase-barstar.     

Explicit treatment of force contribution from alignment tensor using overdetermined linear equations and its application in NMR structure determination

Residual dipolar coupling (RDC) provides valuable information about the orientation of each internuclear vector in a macromolecule with respect to the static magnetic field. However, structure determination utilizing RDC still remains challenging without additional restraints such as NOE. In this context, a novel approach has been developed to efficiently extract structural information from RDC by successive application of singular value decomposition (SVD) method in the course of NMR structure determination. Force contribution from the alignment tensor is rigorously formulated in the context of SVD, and assessments have been made to verify its numerical accuracy. The efficacy of this approach is illustrated by showing that RDC restraints alone can restore a distorted beta-hairpin to native-like structure using the replica-exchange molecular dynamics simulations.     

Finding the needle in a haystack: educing native folds from ambiguous ab initio protein structure predictions

Current ab initio structure‐prediction methods are sometimes able to generate families of folds, one of which is native, but are unable to single out the native one due to imperfections in the folding potentials and an inability to conduct thorough explorations of the conformational space. To address this issue, here we describe a method for the detection of statistically significant folds from a pool of predicted structures. Our approach consists of clustering and averaging the structures into representative fold families. Using a metric derived from the root‐mean‐square distance (RMSD) that is less sensitive to protein size, we determine whether the simulated structures are clustered in relation to a group of random structures. The clustering method searches for cluster centers and iteratively calculates the clusters and their respective centroids. The centroid interresidue distances are adjusted by minimizing a potential constructed from the corresponding average distances of the cluster structures. Application of this method to selected proteins shows that it can detect the best fold family that is closest to native, along with several other misfolded families. We also describe a method to obtain substructures. This is useful when the folding simulation fails to give a total topology prediction but produces common subelements among the structures. We have created a web server that clusters user submitted structures, which can be found at http://bioinformatics.danforthcenter.org/services/scar. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 339–353, 2001     

蛋白质折叠类型的分类建模与识别

蛋白质的氨基酸序列如何决定空间结构是当今生命科学研究中的核心问题之一. 折叠类型反映了蛋白质核心结构的拓扑模式, 折叠识别是蛋白质序列-结构研究的重要内容. 我们以占Astral 1.65序列数据库中α, β和α/β三类蛋白质总量41.8%的36个无法独立建模的折叠类型为研究对象, 选取其中序列一致性小于25%的样本作为训练集, 以均方根偏差(RMSD)为指标分别进行系统聚类, 生成若干折叠子类, 并对各子类建立基于多结构比对算法(MUSTANG)结构比对的概形隐马尔科夫模型(profile-HMM). 将Astral 1.65中序列一致性小于95%的9505个样本作为检验集, 36个折叠类型的平均识别敏感性为90%, 特异性为99%, 马修斯相关系数(MCC)为0.95. 结果表明: 对于成员较多, 无法建立统一模型的折叠类型, 基于RMSD的系统分类建模均可实现较高准确率的识别, 为蛋白质折叠识别拓展了新的方法和思路, 为进一步研究奠定了基础.     

Abnormal characteristics of binary molecular clusters in DMSO–ethanol mixtures under external electric fields

For the nonlinearly phenomena on the dielectric properties of dimethyl sulfoxide (DMSO)–ethanol mixtures under a low intensity microwave field, we propose a conjecture that there exist some abnormal molecular clusters. To interpret the mechanism of abnormal phenomena and confirm our conjecture about the existence of abnormal molecular clusters, an in-depth investigation about the structure evolutions of (DMSO)_m(C₂H₅OH)_n (m = 0–4; n = 0–4; m + n ≤ 4) molecular clusters induced by external electric fields has been given by using density functional theory. The results show that there exist some binary molecular clusters with large cluster radii in mixtures, and some of them are unstable under exposure of electric fields. It implies that the existence of certain abnormal molecular clusters in DMSO-ethanol mixtures results in their abnormality of dielectric properties.     

Implicit and explicit solvent models for modeling a bifunctional arene ruthenium hydrogen‐storage catalyst: A classical and ab initio molecular simulation study

Classical and ab initio, density functional theory‐ and semiempirical‐based molecular simulation, including molecular dynamics, have been carried out to compare and contrast the effect of explicit and implicit solvation representation of tetrahydrofuran (THF) solvent on the structural, energetic, and dynamical properties of a novel bifunctional arene ruthenium catalyst embedded therein. Particular scrutiny was afforded to hydrogen‐bonding and energetic interactions with the THF liquid. It was found that the presence of explicit THF solvent molecules is required to capture an accurate picture of the catalyst's structural properties, particularly in view of the importance of hydrogen bonding with the surrounding THF molecules. This has implications for accurate modeling of the reactivity of the catalyst. © 2014 Wiley Periodicals, Inc.