Critical Mutations of the SARS-CoV-2 Virus

SARS-CoV-2 presents an opportunity to understand better the role of viral mutations. The Alpha and Delta variants of SARS-CoV-2 provide particular insight. We argue that looking at the mutations through a physical chemistry lens provides a deeper understanding of viral evolutionary trends. We advocate here the use of quantitative (mathematical) methods, based on physical chemistry foundations, to analyze viruses. The behavior of viral proteins depends both on structural properties (how the protein sidechains are configured in three dimensional space) and epistructural properties (how the protein interacts with the enveloping solvent, e.g., water). In both cases, physical chemistry (and ultimately quantum mechanics) plays a dominant role. There are many barriers to entry for quantitative scientists (e.g., mathematicians) to study viruses. At the simplest level, there are multiple ways to describe a virus, by its genomic sequence (RNA or DNA) or its protein sequence. Many papers assume that the context is clear when the word ‘sequence’ is used, but the novice would be forgiven for confusion. But there are much more complicated issues of terminology and interpretation that can make it very hard to understand what is going on. The book [1] was written in part to clarify this. We use the SARS-CoV-2 virus mutations here as the basis for a primer on the tools in [1] and to exhibit the kinds of observations they can yield. We attempt here both to lower the barrier of entry to the subject and to raise the level of rigor in the discussion by showing how a much more quantitative view can be beneficial. We do this by explaining concepts in simple, quantitative terms. In many cases, this involves measuring distances between atoms in PDB files. Thus we quantify what it means to be a hydrogen bond, a salt bridge, to be underwrapped, all of which have rigorous definitions [1]. Our goal here is to look at virus mutation from a mathematical perspective, with a particular focus on the SARS-CoV-2 virus [2]. This is for two reasons. First of all, it has become one of the greatest threats to humanity of all time. But the second is more positive: SARS-CoV-2 is very widely studied, and this allows new opportunities for understanding viruses in general. Any advances could have a very wide impact. We can compare and contrast two closely related viruses by considering mutations of a single virus. This allows us to focus on particular features and their impact on disease. Certain mutations of the SARS-CoV-2 virus have been the focus of attention, especially those in the spike protein [3]. We will limit our attention here to this protein for simplicity. While pure genomic sequence analysis [4] is extremely valuable, and certainly mathematically rigorous, we will stress here a different approach. Instead we focus on the amino acid sequence with a physical chemistry perspective. This brings in new mathematical tools that have yet to be fully utilized [1]. Typical sequence analysis sees all sidechains as the same, whereas physical chemistry allows us to differentiate them, to study their interactions, and to quantify epistructural behavior as well. Using standard sequence analysis helps us understanding what mutations are important, but adding a physical chemistry perspective informs us why they are important. Thus we can see that all mutations are not created equal, but some can be viewed as a “smoking gun” in certain contexts. We examine three mutations in detail, explaining why they play a significant role in enhancing the effectiveness of SARS-CoV-2 mutants. Each one has a different physical chemistry signature, and taken together they provide a blueprint for analysing viruses, and proteins, in general.