Task 9: Normal Mode Analysis

There are several forces acting within a protein. Most of these forces have one or more equilibrium states. In reality the protein is flexible. That means, that the atoms of the system swing around these equilibrium states. These swinging around the equilibrium states can be approximated by the harmonic approximation. The forces can then be replaced by a less complex system of springs. With this model it is possible to calculate large motions of the protein by Normal Mode Analysis.

In opposite to Molecular Dynamics this is very fast and it is not a simulation it is a calculation of possible simple and large motions.

In this task we want to try several servers, which calculate normal mode analysis. A detailed description of the task can be found here. For most runs we used the structure 1J8U for our protein PAH. In the case of the all-atom NMA we used a smaller protein to test the server and this kind of approach.

Webnma

The server WEBnm@ uses only the C-alpha atoms to calculate the normal modes. The calculations are performed using the Molecular Modelling Toolkit with the C-alpha force field.

The used input format is very easy (see below).

Results

The server offers different statistics and visualizations to the performed NMA calculation.

• An atomic displacement analysis plots the displacement of each C-alpha atom, therefore one can inspect the parts of the protein, which are the most displaced for each mode. These plots are shown for PAH below.
• Mode visualization and vector field analysis. The vector field representation of the modes shows the directions and (relative) amplitude of the displacements undergone by different parts of the protein as vectors. The visualization and the vector field analysis can be downloaded as vmd-files. But these files seem to be broken. The mode visualizations of PAH are shown below.

Plots of atomic displacement

Mode 7

Mode 8

Mode 9

Mode 10

Mode 11

Visualization of Normal Modes

Mode 7

Mode 8

Mode 9

Mode 10

Mode 11

ElNemo

ElNemo is a webserver using the Elastic Network Model to calculate the normal modes of proteins (Tirion, 1996; Tama et al., 2000; Delarue and Sanejouand, 2002). The Elastic Network is a network model of a protein. Usually the nodes in this network are the C-alpha atoms and the edges are the interactions within the protein simulated as springs. This approach sufficient to calculate the low-frequency normal modes of a protein.

The input form of elNemo seems to be not that simple at the first glance. The form is splitted in several subsections.

In the basic section you just have to define the protein structure by file or by copy-and-paste of the atom-section. Additionally one should define a job-title and specify an e-mail address. The e-mail address is useful, because the jobs need usually some time.

In the supplementary section you can define how many slow modes you want to see. Additionally you can define the number of structures calculated for each mode by defining the maximum and minimum amplitude and the step of amplitude.

The comparing section can be used to define a second conformation of the protein. elNemo calculates then the contribution of each normal mode to the second structure.

The last section is for experts. Here you can define the granularity of the elastic network model. That means you can define the size of the substructures used for nodes and the threshold for interactions used as edges.

Compared to the default settings we just changed the cutoff for interactions to 15 Angstrom in the expert section.

Results

ElNemo calculates several statistics and visualizations for the calculated Normal Modes:

• In an Overall normal mode analysis ElNemo calculates statistics concerning collectivity and overlap. Collectivity means in this case a measure for the collective protein motion in each calculated normal mode. The overlap is calculated if a second initial structure was used in the comparing section of the input form. The overlap measures how much a normal mode contributes to the second observed conformation.
• B-factors. The B-factor is a measure for flexibility in a protein. Using the first 100 normal modes elNemo can calculate the expected B-factor of each residue and can compare it to the B-factors of the initial structure.
• Individual normal mode statistics. For each mode elNemo calculates several statistics. If the option was used animated images are generated showing the movement according to the normal mode. C-alpha maximum distance fluctuations between all pairs of C-alpha atoms are calculated for each mode. The normalized mean square displacement of all C-alpha atoms in the protein is calculated. A graph displaying the distance variation between successive pairs of CA atoms in the two extreme conformations that were computed for this mode (maximum/minimum amplitude) is calculated.
• Additionally one can calculate more fine grained models for each normal mode.
• Additionally one can calculate superpositions of two normal modes.

Collectivity

Low Collectivity of Mode 4:

B-Factor

The following plot was created by R and the raw numbers calculated by elNemo. ElNemo itself has a very nice webpage representation of the data, but it is not that nice for the wiki.

Visualization of Normal Modes

Mode 7

Mode 8

Mode 9

Mode 10

Mode 11

CA-fluctuations

Mode 7

Mode 8

Mode 9

Mode 10

Mode 11

Anisotropic Network Model web server

The Anisotropic Network Model web server is a web server for the calculation of the normal modes of proteins. This web server uses the Anisotropic network model (ANM) for the calculation of the normal modes (Bahar et al., 2000; Bahar et al., 2001). The ANM is a kind of Elastic Network. In this concrete case each node is the Cα atom of a residue and the edges are interactions between interacting nodes. Two nodes are interacting if their distance is below a certain threshold. The interactions are calculated by harmonic potentials. In contrast to the Gaussian Network Model the orientation of each interaction is considered in the calculation of the normal modes.

The input form of the server is very simple. Besides the definition of the used initial protein structure, one just has to/can define the cutoff distance for interactions and a distance weight. The distance weight adjusts the correlation between calculated and experimental B-factors.

In our case we just adjusted the weight factor to 3.

Results

The server calculates several statistics and visualizations to the performed normal mode analysis:

• On the result web page it is possible to play around with several values in the visualization. For example one can choose the normal mode to be displayed and for this mode one can choose the frequency and amplitude of motion. One can add vectors to the visualization, which describe the movement of different parts of the protein. One can also adjust the coloring, the visualization of bonds and atoms and adding labels to chosen amino acids. It is also possible to have a look at the elastic network model for different distance thresholds. It is also possible to focus on the interactions between chains. This visualization on the web site is very powerful.
• The server offers the option to calculate a pdb file for one normal mode. The user can choose the resolution of the different conformations listed in this file.
• The user can obtain pymol scripts for the different normal modes.
• It is possible to calculate the anisotropic temperature factors.
• The user can calculate the B-factors on the basis of the calculated normal modes.
• It is possible to calculate the distance fluctuations and deformation energy between residues within the protein for a normal mode. Here the user can choose two different approaches: scalar or vectorial. In the vectorial view differences of orientation are also considered.
• It is possible to create a plot for the calculated B-factors of different normal modes and the experimental B-factors. However the average calculated B-factors do not work properly and do not appear in the plot. Additionally the B-factors of the normal modes seem to be unnormalized.
• It is possible to have a look at the different calculated eigenvalues, which represent the frequency of the normal mode in the normal mode analysis.
• The server offers a feature, where one can calculate the covariance of different normal modes. But at least for us this feature did not work.

The listing above shows the sever is powerful and offers a lot of additional statistics. But some of them did not work properly at least for our analysis.

Visualization of Normal Modes

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

B-factors

The experimental B-factors

The calculated B-factors for the different Normal Modes

Residue displacement analysis

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

oGNM – Gaussian network model

Introduction to the method

oGNM is a online web-service for the computation of structural dynamics in proteins by using a Gaussian network model. This means that this method is able to compute isotropic and Gaussian fluctuations of nodes (which are our C-alpha atoms). This web-service originated from the iGNM database which computed the dynamic of 20 058 structures accessible in the PDB database. The main advantages of oGNM is :

• that it is not limited to relatively small proteins or to a single domain of a protein.
• it is very fast. results for the different modes are returned within seconds.
• it allows the computation of not only proteins but also of RNA/DNA alone and proteins with RNA/DNA complexes.

Execution

Submission of job was done via the webinterface (see figure below). We choose the structure 1J8U for our PAH protein and selected a 15 Angstrom cutoff.

1J8U