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

Collectivity

Low Collectivity of Mode 4:

Visualization of Normal Modes

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 4.

Results

Visualization of Normal Modes

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5