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Here we review the development of protein scaling theory, starting frombackgrounds in mathematics and statistical mechanics, and leading to biomedicalapplications. Evolution has organized each protein family in different ways,but scaling theory is both simple and effective in providing readilytransferable dynamical insights complementary for many proteins represented inthe 90 thousand static structures contained in the online Protein Data Base(PDB). Scaling theory is a simplifying magic wand that enables one to searchthe hundreds of millions of protein articles in the Web of Science, andidentify those proteins that present new cost-effective methods for earlydetection and/or treatment of disease through individual protein sequences(personalized medicine). Critical point theory is general, and recently it hasproved to be the most effective way of describing protein networks that haveevolved towards nearly perfect functionality in given environments(self-organized criticality). Evolutionary patterns are governed by commonscaling principles, which can be quantified using scales that have beendeveloped bioinformatically by studying thousands of PDB structures. The mosteffective scales involve either hydropathic globular sculpting interactionsaveraged over length scales centered on membrane dimensions, or exposed betastrand propensities associated with aggregative (strong) protein-proteininteractions.

Quantitative Molecular Scaling Theory of Protein Amino Acid Sequences, Structure, and Functionality