Rigidity analysis of protein biological assemblies and periodic crystal structures

Abstract

Background: We initiate in silico rigidity-theoretical studies of biological assemblies and small crystals for protein structures. The goal is to determine if, and how, the interactions among neighboring cells and subchains affect the flexibility of a molecule in its crystallized state. We use experimental X-ray crystallography data from the Protein Data Bank (PDB). The analysis relies on an effcient graph-based algorithm. Computational experiments were performed using new protein rigidity analysis tools available in the new release of our KINARI-Web server http:// kinari.cs.umass.edu. Results: We provide two types of results: on biological assemblies and on crystals. We found that when only isolated subchains are considered, structural and functional information may be missed. Indeed, the rigidity of biological assemblies is sometimes dependent on the count and placement of hydrogen bonds and other interactions among the individual subchains of the biological unit. Similarly, the rigidity of small crystals may be affected by the interactions between atoms belonging to different unit cells. We have analyzed a dataset of approximately 300 proteins, from which we generated 982 crystals (some of which are biological assemblies). We identified two types of behaviors. (a) Some crystals and/or biological assemblies will aggregate into rigid bodies that span multiple unit cells/asymmetric units. Some of them create substantially larger rigid cluster in the crystal/biological assembly form, while in other cases, the aggregation has a smaller effect just at the interface between the units. (b) In other cases, the rigidity properties of the asymmetric units are retained, because the rigid bodies did not combine. We also identified two interesting cases where rigidity analysis may be correlated with the functional behavior of the protein. This type of information, identified here for the first time, depends critically on the ability to create crystals and biological assemblies, and would not have been observed only from the asymmetric unit. For the Ribonuclease A protein (PDB file 5RSA), which is functionally active in the crystallized form, we found that the individual protein and its crystal form retain the flexibility parameters between the two states. In contrast, a derivative of Ribonuclease A (PDB file 9RSA), has no functional activity, and the protein in both the asymmetric and crystalline forms, is very rigid. For the vaccinia virus D13 scaffolding protein (PDB file 3SAQ), which has two biological assemblies, we observed a striking asymmetry in the rigidity cluster decomposition of one of them, which seems implausible, given its symmetry. Upon careful investigation, we tracked the cause to a placement decision by the Reduce software concerning the hydrogen atoms, thus affecting the distribution of certain hydrogen bonds. The surprising result is that the presence or lack of a very few, but critical, hydrogen bonds, can drastically affect the rigid cluster decomposition of the biological assembly.

Geometric analysis characterizes molecular rigidity in generic and non-generic protein configurations

“…While singularities form a non-dense subset of configuration space [18], biomolecules could exploit specific characteristics of non-genericity such as increased instantaneous mobility [42], a change of motion pattern [38] or large motions along emerging hinge axes to control accessibility of substates. Many biomolecules possess structural symmetries that allow geometrically concerted motions [30, 23]. …”

Graphs of Hydrogen-Bond Networks to Dissect Protein Conformational Dynamics

“…For the soluble protein SecA, an H-bond network at the nucleotide-binding site was qualitatively similar when computed from 4 static structures solved at resolutions of 2.5–3.2 Å, or from MD simulations started from one of those structureshowever, additional H-bonds were sampled transiently at room temperature during MD . In rigidity analyses of biological assemblies, it was found that certain H-bonds can profoundly alter the rigidity of a protein complex . These considerations suggest that both the resolution and the number of internal waters need to be accounted for when selecting data sets of static protein structures for H-bond network analyses.…”

The accuracy of NMR protein structures in the Protein Data Bank

“…About 13% of NMR structures in the PDB comprise more than one polymer chain, ie are oligomers or have bound peptides. It has been previously shown using Xray crystal structures that interactions between subchains can significantly affect the rigidity of biological assemblies as a whole 26 . Here we analyse ANSURR scores computed for 550 biological assemblies that were calculated using NMR).…”