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| 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.
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| == Theory ==
| | If you reverse breathe it means that you are trying to fill up something that is deflating. 3 width are versatile, and can be used on low mountain trails and the alpencross. Every person is different and you should looking for a bike that fit's you best. “Whereas past research emphasized whether or not a relationship existed between bicycle riding on a saddle and erectile dysfunction, Schrader now says that the next step of contemporary research on the subject should focus on intervention. It will be business as normal, very successful business as normal. <br><br>The "derailleur" attached to the gear shifter moves the chain from one ring to another. * Numbness - Impingement of small nerve branches between the second and third or third and fourth toes can cause swelling that results in numbness, tingling, or burning, or sharp shooting pains into the toes. The blogs and news feeds can also be shared among the friends and family free of cost via the social media networks. Just like a rectangle you have 2 long sides and 2 short sides. These are stable forks whose weights are directly in proportion to their durability. <br><br>The price will naturally be higher during prime riding seasons in spring and summer. Bikes are a great way to get around - they're fun, they're cheap to fuel (they burn only calories) and they're a great way to get fit. Mountain biking is all about stretching your limits, enjoying the ambience, feel the mood swings of mountains weather and then reaching to the final destination. I'd been slowly coming to that conclusion over the course of about a year or so and that mutant nose hair pretty much confirmed it. In addition, being positioned over the rear tire makes for an extremely light front end, which is hard to hold down on inclines. <br><br>In the recent article section, you can find the list of biking related articles with a detailed description present on the official website. There is anything from shocks to gears, special wheels, exclusive take care of bars that can be immediately switched to match the terrain you're riding on and so substantially much more. Trying out various sizes is the first step in choosing the correct folding bike. Sign up to get a mountain bike expedition and relive people childhood biking wonder and thrills with a whole new tier. Which leads me to my favourite materials for hardtails. |
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| 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. <br /> It represents the biological macromolecule as an elastic mass-and-spring network (Figure.1.), 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.
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| <gallery> | |
| File:elastic network model.png|Figure 1: Elastic Network Model
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| </gallery> | |
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| 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 r<sub>i</sub> = (x<sub>i</sub> y<sub>i</sub> z<sub>i</sub>) and let r<sub>j</sub> = (x<sub>j</sub> y<sub>j</sub> z<sub>j</sub>) be the instantaneous positions of atoms i and j. The equilibrium distance between the atoms is represented by s<sub>ij</sub><sup>O</sup> and the instantaneous distance is given by s<sub>ij</sub>. For the spring between i and j, the harmonic potential in terms of the unknown spring constant γ, is given by:<br /> | |
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| <math>V_{ij} = {\gamma\over 2}{( s_{ij} - {s_{ij}}^o)}^2</math>
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| The second derivatives of the potential, Vij with respect to the components of ri are evaluated at the equilibrium position, i.e. s<sub>ij</sub><sup>O</sup> = s<sub>ij</sub>, are
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| <math>{\partial^2 V_{ij}\over\partial{x_i}^2} = {\gamma\over {s_{ij}}^2} {(x_j - x_i)}^2 </math>
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| <math>{\partial^2 V_{ij}\over\partial x_i\partial y_j} = {-\gamma\over {s_{ij}}^2} {(x_j - x_i)}{(y_j-y_i)} </math> <br />
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| The force constant of the system can be described by the [[Hessian Matrix]] – (second partial derivative of potential V): | |
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| <math>\Eta = \begin{bmatrix} {H_{ii}} & {H_{ij}} \\ {H_{ji}} & {H_{jj}} \end{bmatrix} </math> <br />
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| 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:
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| <math>H_{ij} = \begin{bmatrix} {\partial^2 V_{ij}\over\partial x_i\partial x_j} & {\partial^2 V_{ij}\over\partial x_i\partial y_j} & {\partial^2 V_{ij}\over\partial x_i\partial z_j} \\ {\partial^2 V_{ij}\over\partial y_i\partial x_j} & {\partial^2 V_{ij}\over\partial y_i\partial y_j} & {\partial^2 V_{ij}\over\partial y_i\partial z_j} \\ {\partial^2 V_{ij}\over\partial z_i\partial x_j} & {\partial^2 V_{ij}\over\partial z_i\partial y_j} & {\partial^2 V_{ij}\over\partial z_i\partial z_j}\end{bmatrix} </math> <br / >
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| Using the definition of the potential, the Hessian can be expanded as,
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| <math>H_{ij} = {-\gamma\over {s_{ij}}^2} \begin{bmatrix} {(x_j - x_i)(x_j - x_i)} & {(x_j - x_i)(y_j - y_i)} & {(x_j - x_i)(z_j - z_i)} \\ {(y_j - y_i)(x_j - x_i)} & {(y_j - y_i)(y_j - y_i)} & {(y_j - y_i)(z_j - z_i)} \\{(z_j - z_i)(x_j - x_i)} & {(z_j - z_i)(y_j - y_i)} & {(z_j - z_i)(z_j - z_i)} \end{bmatrix}</math>
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| which can then be written as,
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| <math>H_{ij} = {-\gamma\over {s_{ij}}^2} \begin{bmatrix} x_j - x_i\\y_j - y_i\\z_j-z_i \end{bmatrix} \begin{bmatrix} x_j - x_i & y_j - y_i & z_j-z_i \end{bmatrix}</math>
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| 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:<br />
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| <math>H_{ij} = {- 1 \over {s_{ij}}^{p+2}} \begin{bmatrix} {(X_j - X_i)(X_j - X_i)} & {(X_j - X_i)(Y_j - Y_i)} & {(X_j - X_i)(Z_j - Z_i)}\\{(Y_j - Y_i)(X_j - X_i)} & {(Y_j - Y_i)(Y_j - Y_i)} & {(Y_j - Y_i)(Z_j - Z_i)}\\{(Z_j - Z_i)(X_j - X_i)} & {(Z_j - Z_i)(Y_j - Y_i)} & {(Z_j - Z_i)(Z_j - Z_i)} \end{bmatrix}</math> | |
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| 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: | |
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| <math>H = U\Lambda{U^T}</math>
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| 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.
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| == Comparing ANM and GNM ==
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| ANM and GNM are both based on an elastic network model. The GNM has proven itself to accurately describe the vibrational dynamics of proteins and their complexes in numerous studies. Whereas the GNM is limited to the evaluation of the [[mean squared displacement]]s and cross-correlations between fluctuations, the motion being projected to a mode space of N dimensions, the ANM approach permits us to evaluate directional preferences and thus provides 3-D descriptions of the 3N - 6 internal modes.
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| It has been observed that GNM fluctuation predictions agree better with experiments than those computed with ANM. The higher performance of GNM can been attributed to its underlying potential, which takes account of orientational deformations, in addition to distance changes.
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| == Evaluation of the Model ==
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| ANM has been evaluated on a large set of proteins to establish the optimal model parameters that achieve the highest correlation with experimental data and its limits of accuracy and applicability. The ANM is evaluated by comparing the fluctuations predicted from theory and those experimentally observed (B-factors deposited in the PDB). During evaluation, the following observations have been made about the models behavior.
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| - ANM shows insensitivity to the choice of cutoff distance within a certain range, like GNM.<br />
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| - Weighting the interactions by distance improves the correlation.<br />
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| - Residue fluctuations in globular proteins are shown to be more accurately predicted, than those in non-globular proteins.<br />
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| - Significant improvement in agreement with experiments is observed with increase in the resolution of the examined structure.<br />
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| - While understanding how the accuracy of the predicted fluctuations is related to solvent accessibilities, the predictions for buried residues are shown to be in significantly better agreement with the experimental data as compared to the solvent-exposed ones.<br />
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| - Polar/charged residues are more accurately predicted than hydrophobic ones, a possible consequence of the involvement of surface hydrophobic residues in crystal contacts.
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| == Applications of ANM ==
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| Recent notable applications of ANM where it has proved to be a promising tool for describing the collective dynamics of the bio-molecular system, include the studies of: <br />
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| - [[Hemoglobin]], by Chunyan et al., 2003.<br />
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| - [[Influenza virus]] Hemagglutinin A, by Isin et al., 2002.<br />
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| - [[Tubulin]], by Keskin et al., 2002.<br />
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| - HIV-1 [[reverse transcriptase]] complexed with different inhibitors, by Temiz and Bahar, 2002.<br />
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| - [[HIV-1 protease]], by Micheletti et al., 2004; Vincenzo et al., 2006.<br />
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| - DNA-polymerase, by Delarue and Sanejouand, 2002.<br />
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| - [[Motor proteins]], by Zheng and Brooks, 2005; Zheng and Brooks, 2005; Zheng and Doniach, 2003.<br />
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| - [[Membrane proteins]] including potassium channels, by Shrivastava and Bahar, 2006.<br />
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| - [[Rhodopsin]], by Rader et al., 2004.<br />
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| - [[Nicotinic acetylcholine receptor]], by Hung et al., 2005; Taly et al., 2005 and a few more.
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| == ANM Web Servers ==
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| The ANM web server developed by Eyal E, Yang LW, Bahar I. in 2006, presents a web-based interface for performing ANM calculations, the main strengths of which are the rapid computing ability and the user-friendly graphical capabilities for analyzing and interpreting the outputs.<br />
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| - Anisotropic Network Model web server. [http://ignmtest.ccbb.pitt.edu/cgi-bin/anm/anm1.cgi]<br />
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| - ANM server. [http://gor.bb.iastate.edu/anm/anm.htm]
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| == References ==
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| 1. Anisotropy of fluctuation dynamics of proteins with an elastic network model, A.R. Atilgan et al., Biophys. J. 80, 505 (2001).<br />
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| 2. Anisotropic network model: systematic evaluation and a new web interface, Eyal E, Yang LW, Bahar I. Bioinformatics. 22, 2619–2627, (2006)<br />
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| 3. Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: application to alpha-amylase inhibitor, Doruker, P, Atilgan, AR & Bahar, I, Proteins, 15, 512-524, ( 2000).<br />
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| 4. Hinsen, K. (1998) Analysis of domain motions by approximate normal mode calculations, Proteins, 33, 417-429. PMID 11159421<br />
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| 5. Bahar,I. et al. (1997) Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Fold Des, 2, 173-181<br />
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| 6. Chennubhotla,C. et al. (2005) Elastic network models for understanding biomolecular machinary: from enzymes to supramolecular assemblies. Phys Biol, 2, S173-S180.<br />
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| 7. Cui,Q. and Bahar,I. (2006) Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems. Chapman & Hall/CRC, Boca Raton, FL.
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| == See also ==
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| - Gaussian Network Model [[Gaussian network model]]
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| [[Category:Molecular modelling]]
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With the backdrop of the Superstition Mountains, you have a scenic mountain bike trail network that can embody every quality of off-road riding in the Southwest. Should you cherished this post as well as you would want to be given more details about Women mountain bike sizing. kindly stop by our own website. You'll ask yourself this question in conjunction with "how much will you pay. For maximum safety, it is important to have a bike-repair multi-tool, a patch kit for flat tires, and tire levers. The remarkable thing though was an electric bike could cover 25 miles on one charge with a bet of pedal power or up to 15 miles on battery power lone. As the area has grown, affordable housing needs have to.
If you reverse breathe it means that you are trying to fill up something that is deflating. 3 width are versatile, and can be used on low mountain trails and the alpencross. Every person is different and you should looking for a bike that fit's you best. “Whereas past research emphasized whether or not a relationship existed between bicycle riding on a saddle and erectile dysfunction, Schrader now says that the next step of contemporary research on the subject should focus on intervention. It will be business as normal, very successful business as normal.
The "derailleur" attached to the gear shifter moves the chain from one ring to another. * Numbness - Impingement of small nerve branches between the second and third or third and fourth toes can cause swelling that results in numbness, tingling, or burning, or sharp shooting pains into the toes. The blogs and news feeds can also be shared among the friends and family free of cost via the social media networks. Just like a rectangle you have 2 long sides and 2 short sides. These are stable forks whose weights are directly in proportion to their durability.
The price will naturally be higher during prime riding seasons in spring and summer. Bikes are a great way to get around - they're fun, they're cheap to fuel (they burn only calories) and they're a great way to get fit. Mountain biking is all about stretching your limits, enjoying the ambience, feel the mood swings of mountains weather and then reaching to the final destination. I'd been slowly coming to that conclusion over the course of about a year or so and that mutant nose hair pretty much confirmed it. In addition, being positioned over the rear tire makes for an extremely light front end, which is hard to hold down on inclines.
In the recent article section, you can find the list of biking related articles with a detailed description present on the official website. There is anything from shocks to gears, special wheels, exclusive take care of bars that can be immediately switched to match the terrain you're riding on and so substantially much more. Trying out various sizes is the first step in choosing the correct folding bike. Sign up to get a mountain bike expedition and relive people childhood biking wonder and thrills with a whole new tier. Which leads me to my favourite materials for hardtails.