The finite number of global motion patterns available to symmetric protein complexes

The functional motions and related key residues behind the uncoating of coxsackievirus A16

The coxsackievirus A16 (CVA16) is a highly contagious virus that causes the hand, foot, and mouth disease, which seriously threatens the health of children. At present, there are still no available antiviral drugs or effective treatments against the infection of CVA16, and thus it is of great significance to develop anti-CVA16 vaccines. However, the intrinsic uncoating property of the capsid may destroy the neutralizing epitopes and influence its immunogenicity, which hinders the vaccine developments. In the present work, the functional-quantity-based elastic network model analysis method developed by our group was extended to combine with group theory to investigate the uncoating motions of the CVA16 capsid, and then the functionally key residues controlling the uncoating motions were identified by our functional-quantity-based perturbation method. Several motion modes encoded in the topological structure of the capsid were revealed to be responsible for the uncoating of CVA16 particle. These modes predominantly contribute to the fluctuation of the gyration radius of the capsid. Then, by using the perturbation method, four clusters of key sites involved in the uncoating motions were identified, whose perturbations induce significant changes in the fluctuation of the gyration radius. These key residues are mainly located at the 2-fold channels, the quasi 3-fold channels, the bottom of the canyons, and the inter-subunit interfaces around the 3-fold axes. Our studies are helpful for better understanding the uncoating mechanism of the CVA16 capsid and provide potential target sites to prevent the uncoating motions, which is valuable for the vaccine design against CVA16.

The near-symmetry of protein oligomers: NMR-derived structures

The majority of oligomeric proteins form clusters which have rotational or dihedral symmetry. Despite the many advantages of symmetric packing, protein oligomers are only nearly symmetric, and the origin of this phenomenon is still in need to be fully explored. Here we apply near-symmetry analyses by the Continuous Symmetry Measures methodology of protein homomers to their natural state, namely their structures in solution. NMR-derived structural data serves us for that purpose. We find that symmetry deviations of proteins are by far higher in solution, compared to the crystalline state; that much of the symmetry distortion is due to amino acids along the interface between the subunits; that the distortions are mainly due to hydrophilic amino acids; and that distortive oligomerization processes such as the swap-domain mechanism can be identified by the symmetry analysis. Most of the analyses were carried out on distorted C2-symmetry dimers, but C3 and D2 cases were analyzed as well. Our NMR analysis supports the idea that the crystallographic B-factor represents non-classical crystals, in which different conformers pack in the crystal, perhaps from the conformers which the NMR analysis provides.

A time and memory efficient recipe for fast normal mode computations of complexes with icosahedral symmetry

With the recent breakthroughs in experimental technologies, structure determination of extremely large assemblies, many with icosahedral symmetry, has been rapidly accelerating. Computational studies of their dynamics are important to deciphering their functions as well as to structural refinement but are challenged by their extremely large size, which ranges from hundreds of thousands to even millions of atoms. Group theory can be used to significantly speed up the normal mode computations of these symmetric complexes, but the derivation is often obscured by the complexity of group theory and consequently is not widely accessible. To address this problem, this work presents an easy recipe for normal mode computations of complexes with icosahedral symmetry. The recipe details how the Hessian matrix in symmetry coordinates can be constructed in a few easy steps of matrix multiplications, without going through the complexity of group theory. All the "ingredient" matrices required in the recipe are fully provided in the Supplemental Information for easy reproduction. The work is timely considering the expected large in-flux of many more icosahedral assemblies in the near future. The recipe uses a minimum amount of memory and solves the normal modes in a significantly reduced amount of time, making it feasible to perform normal mode computations of these assemblies on most computer systems.

Fast Normal Mode Computations of Capsid Dynamics Inspired by Resonance

Increasingly more and larger structural complexes are being determined experimentally. The sizes of these systems pose a formidable computational challenge to the study of their vibrational dynamics by normal mode analysis. To overcome this challenge, this work presents a novel resonance-inspired approach. Tests on large shell structures of protein capsids demonstrate there is a strong resonance between the vibrations of a whole capsid and those of individual capsomeres. We then show how this resonance can be taken advantage of to significantly speed up normal mode computations.