A Cubic Equation of State for Amyloid Plaque Formation

Protein function depends on both protein structure and amino acid (aa) sequence. Here we show that modular features of both structure and function can be quantified from the aa sequence alone for the amyloid 770 aa precursor protein A4. Both the new second order hydropathicity scale, based on evolutionary optimization (self-organized criticality), and the standard first order scale, based on complete protein (water-air) unfolding, yield thermodynamically significant features of amyloid function related to spinodal decomposition into modules. Spinodal crossings are marked by breaks in slope of algebraic functions of aa sequences. The new scale is associated with a lower effective temperature than the standard scale. In his 1943 Dublin lectures “What is Life?”, Erwin Schrodinger described an “aperiodic crystal” which could carry genetic information, a description credited by Francis Crick and James D. Watson with having inspired their discovery of DNA [1,2]. Schrodinger arrived at this picture from thermodynamic theories concerning protein stability and information content. Thus one can say that Schrodinger may have been the first theorist to conjecture that protein functionality could be usefully described thermodynamically. Here we take Schrodinger’s reasoning one step further, by analyzing the aa sequence of the amyloid precursor, and showing that it contains strong thermodynamic features. For a homologous group of proteins with a common fold, one can pass directly from (aa sequence) to functional relations, without attempting to elucidate all the intermediate structural stages, such as oligomer formation. A powerful tool in this analysis is an accurate hydropathic