Compactness of Icosahedral Viruses Reveals High Mass Packing of Protruding Features
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A method of studying viral protein design was developed to describe the distribution of mass throughout viral capsid proteins. Protein compactness was measured using an interparticle distance measurement and a capsid thickness based cutoff was utilized to define scoring regions. Analyzing the compactness scores across several icosahedral viruses showed a subtle inverse relationship between particle density and compactness. Protruding features were indicated as regions of low particle density and high compactness, suggesting that these features are uniquely designed for mechanical and biological purposes. Because protrusions sit on icosahedral great circles and point array gauge points, this could be an additional mechanism that viruses use to adhere to better symmetry. The two protein binding complexes analyzed in this study were both regions of middle compactness, indicating that the mass of these features was averagely distributed when compared to other sites on the capsid. Given that protrusions also serve a biological function, this study does not yield a clear connection between compactness and the way that surface residues are arranged to interact with other biological materials. Additional functional features should be analyzed to determine how protein design affects these interactions. In future experiments, one might look into studying complexes containing accessory proteins. Accessory proteins can stabilize viruses during assembly and often protect the capsid from its environment. Determining the regions where these proteins bind and how they affect the overall compactness score could provide insight into how protein-protein interactions change the structural conformation of viruses. Analysis across several T1 and T3 viruses and a single T7 virus indicated that this method was most robust for studying smaller viruses. Further analysis of T7 and T13 viruses are necessary to determine whether this calculation is capable of analyzing larger structures. Additional modifications for future versions of the compactness measurement may provide more substantial results for larger viruses. One issue in the analysis of HK97 was that its CT , calculated using the 90th percentile most radial point, tried to exceed the upper limit of 20 _A. Having a large and relatively thin capsid, HK97 and other T7 viruses may require a different method to determine a cutoff. Calculating an appropriate cutoff based on a radial distribution function may solve this issue. Additionally, redefining the bounded regions using a point clustering method may be an even better approach that will replace the need to calculate a cutoff, altogether. Since these clusters will most likely separate secondary protein features, one issue with this method is the trade-o_ of biological context. Measuring the atomic packing of proteins based on an interparticle distance measurement is a useful tool to describe the distribution of mass throughout protein structures. To further elucidate on whether this measurement can describe vibrational dynamics, analysis using normal mode flexible fitting (NMFF) of virus capsids can be compared with compactness results. Given that this measurement provides some indication of mechanics it may be utilized as a computationally cheap initial description of protein dynamics. While compactness will not replace intensive computational approaches, it can be used to analyze groups of icosahedral viruses as a robust user-friendly tool.