Hemochromatosis Normal modes

Lab journal

Introduction

<figure id="timescale">

Figure 1: Timescale of protein motions <ref name="timescale_motions"> Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins Ivet Bahar, Timothy R. Lezon, Ahmet Bakan, and Indira H. Shrivastava Chemical Reviews 2010 110 (3), 1463-1497</ref>

</figure>

Normal mode analysis(NMA) is used to study the globular motions of a protein. It is useful, because other computational techniques like molecular dynamics are only reasonably applicable for time scales of up to 1 ms. But globular protein motions are slow and often take longer (see <xr id="timescale"/>).

WebNMA and elNemo are two different web servers for normal mode analysis that are based on elastic network models(ENM). Both provide the same information but in different representations:

• WebNMA
  • normal modes and corresponding animations
  • average residue fluctuations
  • 2D correlated residue movement map

• elNemo
  • normal modes and corresponding animations
  • average residue fluctuations
  • pairwise correlated residue movement as a list

The modes are only calculated from the C-alpha atoms of the proteins residues. In principal, 3N-6 normal modes could be computed, where N is the number of atoms in the molecule. The reasoning behind this number is, that each atom in a molecule has three coordinates and the molecule thus has 3N degrees of freedom. However, three degrees of freedom have to be omitted to account for translation and another three have to be omitted to account for rotational symmetry. For the HFE protein with 272 residues, 810 normal modes can be calculated, but only the low frequency normal modes are of interest, because they resemble slow motions.

elNemo

<figure id="elnemo">

Figure 2: Visualisation of the five most interesting and distinct normal modes of the HFE protein computed with elNemo. The immunoglobulin (Ig) domain is colored in yellow-red and the MHC-like domain in blue-green.

Mode 7	Mode 8	Mode 11	Mode 12	Mode 13
This mode shows a hinge motion about the connection between the two domains. The immunoglobulin domain and the MHC-like domain move towards each other.	This mode also shows a hinge motion about the domain connection, but in this case, the Ig domain twists away from the upward moving MHC-like domain.	A hinge motion of the Ig domain and a breathing motion of the MHC-like domain can be observed in mode 11.	Mode 12 and 13 both show a slight hinge motion of the Ig domain and a strong breathing motion of the MHC-like domain. This observation can be expected, because the MHC domain is part of the binding interface to the ferritin receptor, thus this interface needs to be flexible.

</figure>

<xr id="elnemo"/> shows the five most most interesting and distinct normal modes of the HFE protein. The first six are omitted because they are of low complexity.

WebNM@

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<figtable id="energy">

Table 1: Deformation energy of the six first normal modes computed with webNMA.

Mode	Deformation Energy
7	325.91
8	817.13
9	849.13
10	1452.95
11	1876.97
12	2972.27

</figtable>

Apart from elNemo, we also used webNMA to compute the normal modes of the HFE protein. The deformation energy of the six first normal modes is given in <xr id="energy"/>. These values, while having no real physical correspondence, give the difference between the energy of the ENM in the input conformation and the energy at full extension of a normal mode movement. They can give a hint on the amount of energy, relative to the other normal modes, that is required to perform a motion.

<figtable id="webnma_modes7to12">

Table 2: Visualization of the normal modes 7 to 12 for 1A6Z chain A computed with WebNMA. The original protein structure is shown in green and the movement of the C alpha atoms is shown as a red ribbon.

Mode 7	Mode 8	Mode 9	Mode 10	Mode 11	Mode 12
In this mode, a downward motion of the MHC domain is combined with a flapping motion of the Ig domain, that in conjunction can be viewed as a slightly tilted hinge motion.	Mode 8 shows a twisting motion where the Ig domain twists to the left and the MHC domain twists into the backwards direction of the viewplane.	Another twisting motion is shown, but this time, the Ig domain twists upwards and the MHC domain moves, like a rocking chair, into the viewplane.	This mode shows a hinge motion about the connection between the two domains that move towards each other.	Mode 11 shows a backward tilting motion of the Ig domain together with a backward twisting motion of the MHC domain.	In this mode, the two domains exhibit a slight hinge motion while shifting themselves towards each other.

</figtable>

The movements of the normal modes 7 to 12 are visualised in <xr id="webnma_modes7to12"/>.

Although the individual corresponding modes differ slightly, there is no difference between the motion spectrum of the normal modes computed with elNemo and webNMA. Both web servers found the same types of motions. The main difference between the servers is their speed and how they present the results. WebNMA is faster and yielded results for the tested protein in under 5 minutes, while elNemo took several hours. Also WebNMA computes analyses only when requested, thus avoiding unnecessary computation time.

Domain definition

<figure id="corr_motions">

Figure 3: Correlated residue motions for the HFE protein

</figure>

<xr id="corr_motions"/> shows two distinct zones with correlated movement. The first zone starts at the beginning of the sequence and ends at residue 175. The second zone starts at residue 176 and extends until the end of the sequence. Based on this observation, two domains can be assigned to the two zones. SCOP, CATH and Pfam all assign the same two domains to the HFE protein. <xr id="1a6z_domains" /> shows a 3D visualisation of the HFE protein and the MHC I domain (green) and the immunoglobulin domain (blue). This is in complete accordance with the domain assignment based on the correlated motion matrix.

References:

CATH MHC domain CATH Ig domain

SCOP MHC domain SCOP Ig domain

Pfam domains

<figure id="1a6z_domains">

Figure 4: Pymol visualisation of the two domains of the HFE protein from different perspectives. The MHC I domain is colored in green and the immunoglobulin domain in blue.

Side view

Front view

Top view

</figure>

Flexibility

<figure id="fluctuations" >

Figure 5: Visualisation of 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. The fluctuations are the sum of the atomic displacements in each mode weighted by the inverse of their corresponding eigenvalues.

</figure>

The HFE protein contains regions that are more flexible than others. <xr id="fluctuations"/> contains a plot from webNMA that shows for each residue on the x-axis the normalized squared fluctuations. High peaks correspond to highly flexible regions, which are connected by rigid stretches.

<figure id="3d_fluc">

Figure 6: The flexibility of the C-alpha atoms of the HFE protein is shown color coded, where red indicates no flexibility, white indicates medium flexibility and blue indicates high flexibility.

Side view

Front view

</figure>

Another way to look at the C-alpha fluctuation data is shown in figure <xr id="3d_fluc"/>. The 3D visualisation of the HFE protein is color coded. More flexible regions (blue) are almost exclusively located at the ends of the protein. On the contrary, the most stable regions (red) are the hinge of the protein, i.e. the stretch, that connects the two domains, and the cores of the two domains.

Comparison of Molecular Dynamics and Normal Mode Analysis

In comparison to molecular dynamics (MD), normal mode analysis can grasp the slow and globular motions of a protein. Although it can only grasp the harmonic part of these motions, it gives a good insight into them at comparably low computational cost. MD takes the influence of the side chains into account by modeling them explicitly, whereas NMA only takes them into account implicitly through the position of the C-alpha atoms. Thus, MD can model the effect of side chain movements and SNPs on the proteins dynamics, whereas NMA cannot do this.

References

<references />