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Cytoskeletons are self-organized networks based on polymerized proteins:actin, tubulin, and driven by motor proteins, such as myosin, kinesin anddynein. Their positive Darwinian evolution enables them to approach optimizedfunctionality (self-organized criticality). Our theoretical analysis useshydropathic waves to identify and contrast the functional differences betweenthe polymerizing $\alpha$ and $\beta$ tubulin monomers, which are similar inlength and secondary structures, as well as having indistinguishablephylogenetic trees. We show how evolution has improved water-driven flexibilityespecially for $\alpha$ tubulin, and thus facilitated heterodimer microtubuleassembly, in agreement with recent atomistic simulations and topologicalmodels. We conclude that the failure of phylogenetic analysis to identifyfunctionally specific positive Darwinian evolution has been caused by 20thcentury technical limitations. These are overcome using 21st centuryquantitative mathematical methods based on thermodynamic scaling andhydropathic modular averaging. Our most surprising result is the identificationof large level sets, especially in hydrophobic extrema, with boththermodynamically first- and second-order scaled water waves. Our calculationsinclude explicitly long-range water-protein interactions described by fractals.We also suggest a much-needed corrective for large protein drug developmentcosts.

Self-Organized Networks with Long-Range Interactions: Tandem Darwinian Evolution of $\alpha$ and $\beta$ Tubulin