Mathematics of protein pathological misfolding

"Protein folding is defined as a process by which a polypeptide chain performs a search in conformational space with the objective of achieving the so-called native conformation to global free-energy minimum under a given set of physiochemical conditions of the medium." Misfolding then, is the process by which this objective is not achieved. Protein Folding Quality Assessment (PFQA), is characterized by a three-parameter distribution function Phi(T) referred to as the PFQA function. It uses results of protein folding processes to assess the output quality of protein folding. Protein misfolding is implicated in the initial cause of many conformational diseases. Folding of cytosolic protein can be regarded as the performance of the protein after it is produced or manufactured by the synthesis processes. Protein folding through different mechanisms and pathways has been extensively covered in [J.D. Bryngelson, P.G. Wolynes, Spin glass and statistical mechanics of protein folding, Proc. Natl. Acad. Sci. USA 84 (1987) 7524; J. Wang, Statistics, pathways and dynamics of single molecule folding, J. Chem. Phys. 118 (2) (2003) 953; N.D. Socci, J.N. Onuchic, P.G. Wolynes, Diffusive dynamics of the reaction coordinates for protein folding funnels, J. Chem. Phys. 104 (14) (1996); D. Thirumalai, From minimal models to real proteins, time scales for protein folding kinetics, J. Phys. I France 5 (1995) 1457]. The model is based on growth models of Ratkowsky, Richards, etc. [D.A. Ratkowski, T.J. Reeds, Choosing near-linear parameters logistic model for radio-ligand and related assays, Biometrics 42 (1986) 575] for a three-parameters model to handle the quality assessment of the folding process. Thus a complete distribution can be found, thanks to the scale, location and shape parameters.