vGNM: a better model for understanding the dynamics of proteins in crystals - PubMed (original) (raw)
vGNM: a better model for understanding the dynamics of proteins in crystals
Guang Song et al. J Mol Biol. 2007.
Abstract
The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new GNM, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified and others to become less important. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.
Figures
Figure 1
Example of two different myoglobin crystal structures showing different temperature factors. The two structures, 1ABS.pdb (space group: P6) and 1AJG.pdb (space group: P21), of the same protein (sperm whale myoglobin), display rather different B-factors. The correlation between the two is only 0.61.
Figure 2
Comparison of the correlations between experimental and calculated B-factors for 113 proteins from GNM and vGNM. The improvement is shown in dot dash line. vGNM produces significantly better correlations with a mean value of 0.81 (over all the proteins) as compared to 0.59 from normal GNM.
Figure 3
(a) The B-factors calculated from vGNM and GNM for calmodulin (1osa.pdb). vGNM is able to reproduce extremely well the experimental B-factors. (b) the internal modes selected by vGNM, showing that the lowest frequency mode is not activated at all and the third lowest frequency mode makes the largest contribution.
Figure 4
The percentage contributions of rigid body translation and rotation to the total fluctuations for all proteins. The mean rigid body contribution is about 59%, with 44% from translational and 15% from rotational motions.
Figure 5
The translation contribution to B-factors (wtrans inEq. 7) varies as the number of low frequency modes that are included in the least squares fit increases, for six example proteins of varies sizes.The contribution usually becomes stabilized after a small number of modes are included. The vertical dashed line marks where the number of modes is 20.
Figure 6
The magnitude of the rotation contribution to B-factors (wrotate in Eq. 7) varies as the number of low frequency modes that are included in the least squares fit increases, for six example proteins of varies sizes. The contribution becomes stabilized after a small number of modes are included. The vertical dashed line marks where the number of modes is 20.
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