  Cytoskeletons are self-organized networks based on polymerized proteins:
actin, tubulin, and driven by motor proteins, such as myosin, kinesin and
dynein. Their positive Darwinian evolution enables them to approach optimized
functionality (self-organized criticality). Our theoretical analysis uses
hydropathic waves to identify and contrast the functional differences between
the polymerizing $\alpha$ and $\beta$ tubulin monomers, which are similar in
length and secondary structures, as well as having indistinguishable
phylogenetic trees. We show how evolution has improved water-driven flexibility
especially for $\alpha$ tubulin, and thus facilitated heterodimer microtubule
assembly, in agreement with recent atomistic simulations and topological
models. We conclude that the failure of phylogenetic analysis to identify
functionally specific positive Darwinian evolution has been caused by 20th
century technical limitations. These are overcome using 21st century
quantitative mathematical methods based on thermodynamic scaling and
hydropathic modular averaging. Our most surprising result is the identification
of large level sets, especially in hydrophobic extrema, with both
thermodynamically first- and second-order scaled water waves. Our calculations
include explicitly long-range water-protein interactions described by fractals.
We also suggest a much-needed corrective for large protein drug development
costs.
