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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Anisotropic Network Model ： ウィキペディア英語版 Anisotropic Network Model The Anisotropic Network Model (ANM) is a simple yet powerful tool made for Normal Mode Analysis of proteins, which has been successfully applied for exploring the relation between function and dynamics for many proteins. It is essentially an Elastic Network Model for the Cα atoms with a step function for the dependence of the force constants on the inter-particle distance. == Theory == The Anisotropic Network Model was introduced in 2000 (Atilgan et al., 2001; Doruker et al., 2000), inspired by the pioneering work of Tirion (1996), succeeded by the development of the Gaussian network model (GNM) (Bahar et al., 1997; Haliloglu et al., 1997), and by the work of Hinsen (1998) who first demonstrated the validity of performing EN NMA at residue level. It represents the biological macromolecule as an elastic mass-and-spring network, to explain the internal motions of a protein subject to a harmonic potential. In the network each node is the Cα atom of the residue and the springs represent the interactions between the nodes. The overall potential is the sum of harmonic potentials between interacting nodes. To describe the internal motions of the spring connecting the two atoms, there is only one degree of freedom. Qualitatively, this corresponds to the compression and expansion of the spring in a direction given by the locations of the two atoms. In other words, ANM is an extension of the Gaussian Network Model to three coordinates per atom, thus accounting for directionality. The network includes all interactions within a cutoff distance, which is the only predetermined parameter in the model. Information about the orientation of each interaction with respect to the global coordinates system is considered within the Force constant matrix (H) and allows prediction of anisotropic motions. Consider a sub-system consisting of nodes i and j, let ri = (xi yi zi) and let rj = (xj yj zj) be the instantaneous positions of atoms i and j. The equilibrium distance between the atoms is represented by sijO and the instantaneous distance is given by sij. For the spring between i and j, the harmonic potential in terms of the unknown spring constant γ, is given by: $V\_\; =\; \}^o)\}^2$ The second derivatives of the potential, Vij with respect to the components of ri are evaluated at the equilibrium position, i.e. sijO = sij, are $^2\}\; =\; ^2\}\; =\; ^2$ $=$ The force constant of the system can be described by the Hessian Matrix – (second partial derivative of potential V): $\backslash Eta\; =\; \backslash begin\; \}\; \backslash \backslash \; \}\; \backslash end$ Each element Hi,j is a 3×3 matrix which holds the anisotropic information regarding the orientation of nodes i,j. Each such sub matrix (or the "super element" of the Hessian) is defined as: Using the definition of the potential, the Hessian can be expanded as, which can then be written as, Here, the force constant matrix, or the hessian matrix H holds information about the orientation of the nodes, but not about the type of the interaction (such is whether the interaction is covalent or non-covalent, hydrophobic or non-hydrophobic, etc.). In addition, the distance between the interacting nodes is not considered directly. To account for the distance between the interactions we can weight each interaction between nodes i, j by the distance, sp. The new off-diagonal elements of the Hessian matrix take the below form, where p is an empirical parameter: The counterpart of the Kirchhoff matrix Γ of the GNM is simply (1/γ) Η in the ANM. Its decomposition yields 3N - 6 non-zero eigenvalues, and 3N - 6 eigenvectors that reflect the respective frequencies and shapes of the individual modes. The inverse of Η, which holds the desired information about fluctuations is composed of N x N super-elements, each of which scales with the 3 x 3 matrix of correlations between the components of pairs of fluctuation vectors. The Hessian, however is not invertible, as its rank is 3N-6 (6 variables responsible to a rigid body motion). To obtain a pseudo inverse, a solution to the eigenvalue problem is obtained: $H\; =\; U\backslash Lambda$ The pseudo-inverse is composed of the 3N-6 eigenvectors and their respective non-zero eigen values. Where λi are the eigenvalues of H sorted by their size from small to large and Ui the corresponding eigenvectors. The eigenvectors (the columns of the matrix U) describe the vibrational direction and the relative amplitude in the different modes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Anisotropic Network Model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.