Self-Organized Criticality: A Prophetic Path to Curing Cancer

While the concepts involved in Self-Organized Criticality have stimulated thousands of theoretical models, only recently have these models addressed problems of biological and clinical importance. Here we outline how SOC can be used to engineer hybrid viral proteins whose properties, extrapolated from those of known strains, may be sufficiently effective to cure cancer. Self-Organized Criticality (SOC) is a concept that has enormous intuitive appeal, which explains why it has been widely discussed, especially in biological contexts [1-3]. To extend these discussions to clinically relevant contexts, one should develop methods for engineering proteins that involve suitable general concepts. Perhaps most fundamental is the globularly compacted character of protein folds, driven by hydropathic forces. All protein chains are folded into globules by water pressure, as proteins have evolved as chains with alternating hydrophilic and hydrophobic segments. There are hundreds of thousands of strains of common viruses, whose full amino acid sequences are known. Here I analyze these sequences quantitatively, and show that their hydropathic evolution has easily recognized Darwinian (punctuated) features. These features are global in nature, and are easily identified mathematically using global methods based on thermodynamic criticality and modern mathematics (post-Euclidean 2 differential geometry). While the common influenza virus discussed here has been rendered almost harmless by decades of vaccination programs, the hierarchical sequential decoding lessons learned here are applicable to other viruses that are emerging as powerful weapons for controlling and even curing common organ cancers. Our first step is to realize that the protein folding problem, which has been the subject of > 10 papers, is of little or no concern here, because it has been largely solved experimentally through structural models obtained by diffraction from protein crystals. These models have revealed many details of static protein structures, which are often sufficient to explain qualitative aspects of protein functionality, yet they have left unexplained many features of protein behavior, such as substantial changes in effectiveness with 1% or fewer mutations of their amino acid (aa) side groups, or the fact that as much as 50% such mutations can occur and yet leave the fold represented by the protein’s peptide chain virtually unchanged to the accessible resolution limit of 0.5A [4,5]. Backbone stability can be turned to advantage by assuming that few % mutations of wild protein strains often leave the fold unchanged, so that such strains belong to a common homology group. For flu glycoproteins this group is remarkably robust, as often > 10 aa deletions from the key transmembrane segment are required to alter fusogenic activity qualitatively [6]. For a homological group of proteins one can now take the next step, and pass directly to (amino acid sequence) – functional relations, without attempting to elucidate all the multiple functional details, such as oligomer formation. This large jump could succeed if we had access to a very accurate hydropathic scale that quantifies the large chain curvatures associated with hydrophobic aa, reflecting their tendencies to be in the globular interior, and the much smaller curvatures associated with hydrophilic aa, reflecting their tendencies to be on the globular 3 surface. It is just here that SOC comes to our aid, in the form of a remarkable discovery [7,8] that has gone almost unnoticed. One uses Voronoi partitioning to construct polyhedra centered on each aa in turn, and from these calculates the solvent accessible (for a 2 A spherical water molecule) surface area  for each aa, averaged over a very large number of structures in the