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Recently, we proposed a new method, based on protein profiles derived from physicochemical dynamic time warping (PCDTW), to functionally/structurally classify coronavirus spike protein receptor binding domains (RBD). Our method, as used herein, uses waveforms derived from two physicochemical properties of amino acids (molecular weight and hydrophobicity (MWHP)) and is designed to reach into the twilight zone of homology, and therefore, has the potential to reveal structural/functional relationships and potentially homologous relationships over greater evolutionary time spans than standard primary sequence alignment-based techniques. One potential application of our method is inferring deep evolutionary relationships such as those between the RBD of the spike protein of betacoronaviruses and functionally similar proteins found in other families of viruses, a task that is extremely difficult, if not impossible, using standard multiple alignment-based techniques. Here, we applied PCDTW to compare members of four divergent families of viruses to betacoronaviruses in terms of MWHP physicochemical similarity of their RBDs. We hypothesized that some members of the families Arteriviridae, Astroviridae, Reoviridae (both from the genera rotavirus and orthoreovirus considered separately), and Toroviridae would show greater physicochemical similarity to betacoronaviruses in protein regions similar to the RBD of the betacoronavirus spike protein than they do to other members of their respective taxonomic groups. This was confirmed to varying degrees in each of our analyses. Three arteriviruses (the glycoprotein-2 sequences) clustered more closely with ACE2-binding betacoronaviruses than to other arteriviruses, and a clade of 33 toroviruses was found embedded within a clade of non-ACE2-binding betacoronaviruses, indicating potentially shared structure/function of RBDs between betacoronaviruses and members of other virus clades. [ABSTRACT FROM AUTHOR]