Thermodynamic scaling theory, previously applied mainly to small proteins, here analyzes quantitative evolution of the titled functional network giant hub enzymes.The broad domain structure identified homologically is confirmed hydropathically using amino acid sequences only. The most surprising results concern the evolution of the tyrosine kinase globular surface roughness from avian to mammals, which is first order, compared to the evolution within mammals from rodents to humans, which is second order. The mystery of the unique amide terminal region of proto oncogene tyrosine protein kinase is resolved by the discovery there of a septad targeting cluster, which is paralleled by an octad catalytic cluster in tyrosine kinase in humans and a few other species. These results, which go far towards explaining why these proteins are among the largest giant hubs in protein interaction networks, use no adjustable parameters.Because of the complexity of globular proteins, their evolution is a challenging problem, with only a few quantitative successes so far, notably for small proteins, Hen Egg White (lysozyme c, ~ 140 amino acids, aa) [1] and neuroglobin (~150 aa), using thermodynamic scaling theory [2].Here we discuss much larger nonreceptor (no transmembrane domain) tyrosine kinase Syk (635 aa) and proto-oncogene tyrosine protein kinase Src (539 aa), which are giant hub signaling enzymes that can transfer a phosphate group from ATP to a protein in a cell [3,4]. These proteins are well described on their human Web-based Uniprot homepages. Syk is a giant hub in human protein interaction networks, with 7 molecular functions and 57 biological processes (Uniprot), while a more recent search [5] listed Syk in its Table 2 as the most connected protein localized in both the cytoplasm and cell membrane (CMP) with 105 interactions. The 2 corresponding numbers for Src, a mitochondrion CMP, are 114 interactions on the Uniprot list, and 208 interactions by the keyword methods of [5]. Standard methods based on aa sequence conservation and structural similarities [6,7] enable division of these large protein into three domains and two transition regions, but the changes in their domain structures with evolution are small and not easily quantified.Progress in analyzing protein evolution now relies on thermodynamic scales, which are of several types. Here we use both classical and modern hydropathicity scales Ψ(aa), which describe the in/out globular folding of protein chains by hydrophobic (in) and hydrophilic (out) aa interactions. The aa-specific classical scales, especially the standard KD scale based on enthalpic changes of short (< 7aa) synthetic peptides from water to air, are well suited to describing protein functions that are primarily first-order (a few large interactions) [8]. The modern ultraprecise MZ scale, based on critical points and fractals, corresponds to sequence segments of order a membrane thickness (~ 20 aa) or longer [9], and describes protein functions and changes that are primarily second-order (many small in...