Scaling and self-organized criticality in proteins: Lysozyme c.

Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein functionality is often dominated by long-range hydro(phobic/philic) interactions, which both drive protein compaction and mediate protein-protein interactions. In contrast to previous reductionist short-range hydrophobicity scales, the holistic Moret-Zebende hydrophobicity scale [Phys. Rev. E 75, 011920 (2007)] represents a hydroanalytic tool that bioinformatically quantifies SOC in a way fully compatible with evolution. Hydroprofiling identifies chemical trends in the activities and substrate binding abilities of model enzymes and antibiotic animal lysozymes c , as well as defensins, which have been the subject of tens of thousands of experimental studies. The analysis is simple and easily performed and immediately yields insights not obtainable by traditional methods based on short-range real-space interactions, as described either by classical force fields used in molecular-dynamics simulations, or hydrophobicity scales based on transference energies from water to organic solvents or solvent-accessible areas.