A Mathematical Approach to Cross-Linked Structures in Viral Capsids: Predicting the Architecture of Novel Containers for Drug Delivery

Understanding the structure of viruses is an important first step in terms of many applications in virology, including the protein engineering of containers to enable more effective drug delivery. In particular, the viral capsids, i.e. the protective shells on the exterior of viruses containing the important genetic code, play an important role in the context of gene therapy, where small amounts of therapeutic DNA is packaged into a capsid which then penetrates the cell membrane and delivers its payload. Cross-linking structures are particular additional covalent bonds that can occur in addition to the already present hydrophobic interactions and hydrogen bonds between the proteins. Their importance lies in the fact that they render the capsid particularly stable. Here we shall introduce a mathematical method to predict possible locations for these additional bonds of cross-linking. We will give examples of failed cases as well as of cases where cross-linking structures are possible. These results serve as a pointer for experimentalists as to which types of cross-linking structures may possibly be engineered and exploited in the framework of drug delivery.