Gaucher Disease: Task 10 - Normal mode analysis

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lab journal

With normal mode analysis (NMA), you are able to simulate or analyze the natural resonant globular movements of proteins. There are two different web-servers available to do a NMA, WEBnm@ and ElNemo. Both base on elastic network models (ENM). They provide the following information:

WEBnm@

• deformation energy
• atomic fluctuations
• 2D correlation matrix of residue movement
• atomic displacement

ElNemo

• frequency of a mode (normalized relative to the lowest mode frequency)
• collectivity of a mode (what part of the atoms move together)
• normal modes (PDB files) and their animations (in GIF format) of the top five modes
• RMSD with respect to the second reference structure (if given)
• 2D matrices of distance fluctuations between all C-alpha atom pairs (CA-vari)
• visualization of the mean square displacement of all C-alpha atoms associated with a given mode (<R2>)
• distance variation between successive pairs of CA atoms in the two extreme conformations that were computed for this mode (DQMIN/DQMAX) (still an experimental feature CA-strain)

WEBnm@

WEBnm@ uses only alpha carbon atoms in the models for the normal mode analysis. The number of calculated modes depends on the residue number. In case of less than 1200 residues, 200 modes are calculated for the protein. Otherwise, the number of calculated modes corresponds to only 1/6 of the sequence length modes. As the first six modes refer to mode configurations, the best mode with the lowest frequency is mode 7. The deformation energy is calculated for the 14 best modes (mode 7-20). However, all other features provided by webnm@ are only available for the modes 7-12.

Movements

<figtable id="energy">

Mode	Deformation Energy	Visualisation	Movements
7	174.43	Mode 7	This mode is hinge-moving with a little twist in the area of both chains linked to each other. Compared to chain B, chain A is more flexible.
8	251.61	Mode 8	Mode 8 has a stronger hinge movement. The movement directions of both chains are diagonal. According to this directions they hinge together.
9	344.99	Mode 9	Both chains twist around a vertical axis in different directions.
10	759.13	Mode 10	The whole structure is breathing. Chain B seems to be a bit more flexible in its breathing, than the lower one. The breath happens on slightly shifted axis.
11	1099.96	Mode 11	The chains are breathing. But in contrary to mode 10, the breathing is on a vertical axis.

Five best values of the deformation energy for the lowest-frequency non-trivial modes. In the mode visualization the lower chain is chain A.

</figtable>

Domains

<figure id="reso">

Figure 1: Motions of correlated residues of glucocerebrosidase. The squares at the bottom left and at the top right show the correlated motions within a chain. The two other squares represents motions between the chains. Also the domains can be seen very clear, as residues of the same domain have in general a higher movement correlation to each other than to residues of other chains.

</figure> <figure id="struc">

Figure 2: Visualization of the domains.

</figure> <figure id="fluc">

Figure 3: Fluctuations of the residues. Residues of chain B start at position 496. The square of the fluctuation of each C-alpha atom (for all non-trivial modes), normalized so that the sum over all residues is equal to 100. [1]

</figure>

The glucocerebrosidase shows a domain definition according to their chains. Within the chains, which are identical, a very big domain and a small domain can be seen (<xr id="struc"/>). The domains can also be identified by their movements in a correlated motion map (<xr id="reso"/>). In <xr id="reso"/> the big domains are centered in each chain. The smaller one consists of two parts in the sequence, which are located before and after the residues of the big domain. A correlation of motions between residues at the beginning and the end of a chain can be observed. In 3D space those two correlating parts are formed together to a bunch of sheets. In contrary, the big domain consists of a high number of helices and a few sheets. All domain databases agree with each other that the bigger domain has a glycosidic characteristics. However, they differ in their information about the second domain. While Pfam neglects a second domain, CATH classifies it as an alpha-mannosidase II and SCOP identifies it as a beta-glycanases. Between the chains there is only a slight movement correlation observable. Some residues of the big domain in one chain correlate with a few other residues at the beginning and outside the small domain of the other chain. The two chains are connected by those residue contacts.

As chain A and B are identical, the following domain definition concentrates on one chain:

Pfam

• 1 domain
• PF02055: glycoside hydrolase family 30

CATH

• 2 domains
• 3.20.20.10: glycosidases
• 2.60.40.1180: alpha-mannosidase II

SCOP

• 2 domains
• b.71.1.2: composite domain of glycosyl hydrolase families 5, 30, 39 and 51
• c.1.8.3: beta-glycanases

The fluctuation map (<xr id="fluc"/>) represents the sum of the displacements in each mode weighted by the inverse of their corresponding eigenvalues. Displaced regions can be seen by high fluctuation values. In <xr id="fluc"/> we can observe a very high isolated peak between both chains. This peak identifies a local flexibility between the chains which is at the same time the most flexible part of the protein.

ElNemo

ElNemo uses also only the C-alpha atoms of the structure for normal mode analysis, therefore it takes only the ATOM record from the PDB file, ignoring the HETATM record of a ligand. We ran ElNemo with our reference structure 1OGS without changing anything, so that the ligand could be ignored for the normal mode calculation.

For the normal mode analysis we specified a cutoff of 10 Å between the C-alpha atoms. A hundred modes were calculated, sorted with rising frequency and numbered from 7 to 106, because the fist 6 lowest frequency modes are trivial ()have low complexity) and omitted (<R2>, frequency and collectivity information of all found modes), however, <R2> (see the feature list at the beginning of the page) were computed only for the first 50 modes. For the best non-trivial five modes (7-11), i.e. with lowest frequency, more information is provided, including PDB files and animations in GIF format. B-factor analysis of ElNemo server yielded correlation of 0.662 for 1006 C-alpha atoms (main result page). The best five modes are presented in <xr id="elnemo_modes"/>.

<figtable id="elnemo_modes">

Mode	Frequency	Collectivity	Animations			Description
			a	b	c
7	1.00	0.7546				Hinge motion of the two identical chains.
8	1.22	0.7472				Twist motion of the both chains in opposite directions to the axis which connects the chains combined with a slight bending movement between the two domains (described in the WEBnm@ section) in each chain.
9	1.74	0.7765				Twist motion of the both chains in opposite directions to the axis which connects the chains, similar to that in mode 8 (but no bending between the domains).
10	3.36	0.7970				Breathing of the chains and a slight bending movement between the two domains in each chain.
11	4.30	0.8301				Movement of the chains towards each other and back in the perpendicular direction to the axis connecting them, combined with a slight twist, similar to that in modes 8 and 9. A slight breathing and a hinge movement between the two domains in each chain, similar to that in mode 10, is detectable.

Five lowest-frequency modes for the structure 1OGS created by ElNemo (cutoff used to identify elastic interactions=10).

</figtable>

As we can see from the animations of the best five modes, the most flexible regions are where the two chains connect to each other (make a twist, a hinge and a movement towards each other and back on perpendicular from the chain connecting axis) and inside the chains the regions between the two domains (SCOP and CATH) are most flexible (produce a sort of a hinge movement). Other regions inside the domains seem to be stable.

Discussion

As mentioned, both servers calculate the normal modes from the C-alpha atoms of a structure only. In principle, 3N-6 normal modes could be calculated, where N is the number of atoms in the protein molecule. This number the be explained very simply. Each atom has three coordinates in the space and thus 3N degrees of freedom. However, to account for rotation symmetry and translation, two times 3 degrees of freedom must be subtracted. As the GBA protein has 536 residues and thus 536 C-alpha atoms, 1602 normal modes can be computed. However, it is very calculation intensive to find all of them. In normal mode analysis we are interested only in slow, "big range" movements on the chain and domain levels, therefore only few low frequency normal modes are of interest.

As we do not have a structure completely without a ligand, but only structures with different, not native ligands. The reason for is that the complex with the native ligand, glucosylceramide, is too unstable and the enzyme processes the glucosylceramide instantly into the substrates, ceramide and glucose. Therefore, unfortunately we do not have structures with different conformations for glucocerebrosidase. For this reason, we could not do the option of calculation of normal modes with two different structures. Simply deleting of a ligand from the PDB structure would not result in a change of the main chain coordinates and thus have no effect on the normal modes.

ElNemo does not compute a deformation energy, like WEBnm@. Moreover, WEBnm@ gives more information on residue flexibility. Altogether, the modes computed by the both servers describe very similar motions.

Unlike molecular dynamics (MD), NMA can only compute slow, globular and harmonic motions of a protein. Nevertheless, NMA can help to understand protein motions on the domain and inter-chain level with a comparatively low computational cost. This is a great advantage over the much more time consuming MD. However, NMA only takes the C-alpha atoms into account, thus only main chain movements can influence normal modes, whereas MD accounts for the movements of all atoms in a molecule. Thus, MD can simulate the movements of side chains and thus account for an influence of each SNP, whereas NMA can only notice the effect of an SNP, if it changes the location of the C-alpha atom.

Sources

WEBnm@:

1. WEBnm@ server
   
2. Siv Midtun Hollup, Gisle Salensminde & Nathalie Reuter. (2005) WEBnm@: a web application for normal mode analyses of proteins. BMC Bioinformatics 6: 52.

ElNemo:

1. ElNemo server
   
2. K. Suhre & Y.H. Sanejouand, ElNemo: a normal mode web-server for protein movement analysis and the generation of templates for molecular replacement. Nucleic Acids Research, 32, W610-W614, 2004.
   
3. K. Suhre & Y.H. Sanejouand, On the potential of normal mode analysis for solving difficult molecular replacement problems. Acta Cryst. D vol.60, p796-799, 2004 © International Union of Crystallography.