Abstract
Semi-covariance has attracted significant attention in recent years and is increasingly employed to elucidate statistical phenomena exhibiting fluctuations, such as the similarity or difference in charge patterns of spike proteins among coronaviruses. In this study, by examining values above and below the average/mean based on the positive and negative charge patterns of amino acid residues in the spike proteins of SARS-CoV-2 and its current circulating variants, the proposed methods offer profound insights into the nonlinear evolving trends in those viral spike proteins. Our study indicates that the charge span value can predict the infectivity of the virus and the charge density can estimate the virulence of the virus, and both predicated infectivity and virulence appear to be associated with the capability of viral immune escape. This semi-covariance coefficient analysis may be used not only to predict the infectivity, virulence and capability of immune escape for coronaviruses but also to analyze the functionality of other viral proteins. This study improves our understanding of the trend of viral evolution in terms of viral infectivity, virulence or the capability of immune escape, which remains further validated by more future studies and statistical data.