How Frequently Should Mechanomers Exercising Desired Functions Occur in Well-Conformed Random Mechanomer Stocks?

Proteins vary widely in the numbers and orders of the amino acids of which they are composed, but three hundred amino acids is a typical natural protein length and size, and if all proteins with all possible amino acid orders of that length were synthesized, the total mass of protein synthesized would be several hundred powers of ten times the mass of our galaxy. Plainly, if each and every protein function could be performed by only one specific protein with one specific amino acid order, no biological process or artificial procedure could ever develop such. But the evolution of proteins and other mechanomers, and the development and function of antibodies in the body, and vaccination and the development and use of antisera and monoclonal antibodies, all prove not only that mechanomers with different monomer orders can share a given function but that there must be a fantastically high degree of coincidence of function among them. Hundreds out of the millions of different antibodies in the body typically complex with a given antigen, which incidence of one in ten thousand is taken here to be that of such simplest function among well-conformed random mechanomers (taking the restriction of antibody complexing to its antigen binding site alone to cancel out multiple antibody complexing of different parts of antigen). And the greater the number of functions performed by a mechanomer, and the greater their complexities, the lower will be such incidence of such mechanomer, the incidence with two sites performing such functions taken here to be about one in ten thousand squared or one in one hundred million, and the incidence with three one in ten thousand cubed or one in one trillion.