vGNM: a better model for understanding the dynamics of proteins in crystals.

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.

[1]  Tirion,et al.  Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis. , 1996, Physical review letters.

[2]  G. Phillips,et al.  Dynamics of proteins in crystals: comparison of experiment with simple models. , 2002, Biophysical journal.

[3]  J Kuriyan,et al.  Rigid protein motion as a model for crystallographic temperature factors. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[4]  David Baker,et al.  Improvement of comparative model accuracy by free-energy optimization along principal components of natural structural variation. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[5]  M. DePristo,et al.  Is one solution good enough? , 2006, Nature Structural &Molecular Biology.

[6]  G. Phillips,et al.  Comparison of the dynamics of myoglobin in different crystal forms. , 1990, Biophysical journal.

[7]  Full-matrix refinement of the protein crambin at 0.83 A and 130 K. , 1995, Acta crystallographica. Section D, Biological crystallography.

[8]  G. Phillips,et al.  Cross-validation tests of time-averaged molecular dynamics refinements for determination of protein structures by X-ray crystallography. , 1994, Acta crystallographica. Section D, Biological crystallography.

[9]  A. Atilgan,et al.  Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. , 1997, Folding & design.

[10]  N Go,et al.  Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data. , 1992, Journal of molecular biology.

[11]  P Gros,et al.  Inclusion of thermal motion in crystallographic structures by restrained molecular dynamics. , 1990, Science.

[12]  G N Murshudov,et al.  Use of TLS parameters to model anisotropic displacements in macromolecular refinement. , 2001, Acta crystallographica. Section D, Biological crystallography.

[13]  D. Cruickshank,et al.  The analysis of the anisotropic thermal motion of molecules in crystals , 1956 .

[14]  N Go,et al.  Refinement of protein dynamic structure: normal mode refinement. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[15]  K. N. Trueblood,et al.  On the rigid-body motion of molecules in crystals , 1968 .

[16]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[17]  R Diamond,et al.  On the use of normal modes in thermal parameter refinement: theory and application to the bovine pancreatic trypsin inhibitor. , 1990, Acta crystallographica. Section A, Foundations of crystallography.

[18]  R. Jernigan,et al.  Global ribosome motions revealed with elastic network model. , 2004, Journal of structural biology.

[19]  Guang Song,et al.  An enhanced elastic network model to represent the motions of domain‐swapped proteins , 2006, Proteins.

[20]  K. Hinsen,et al.  Analysis of domain motions in large proteins , 1999, Proteins.