Fractals and self-organized criticality in proteins

Self-organized criticality, a powerful concept, originated in 1987 as an extension of fractal geometries to thermodynamic systems in the vicinities of instabilities. The value of fractal methods can be greatly enhanced in realistic models that exploit accurate fractal values derived from homogeneous (possibly curated) Big Data. We illustrate this point by discussing the derivation of fractal exponents describing protein-water interactions, and their application to protein roughness, protein binding and potentially protein engineering. The examples studied are evolution of lysozyme c and acylphosphatase, and mutational effects on their aggregation.