The Second Law, Gibbs Free Energy, Geometry, and Protein Folding

The fundamental physical law of protein folding is the second law of thermodynamics. The key to solve protein folding problem is to derive an analytic formula of the Gibbs free energy. It has been overdue for too long. Let  be a monomeric globular protein whose  atoms  are classified into hydrophobicity classes , . For each conformation  of , we apply quantum statistics to the corresponding single molecule thermodynamic system  to obtain Gibbs free energy  of protein folding in physiological environment En, where  is the volume of , a region enclosed by the molecular surface ,  the diameter of a water molecule,  and ’s chemical potentials per unit volume and area, and  and  the areas of  and . The  and its gradient  not only reduce the protein structure prediction to a pure mathematical problem of finding minimizers of an analytic function , but also supply new insights in understanding the kinetics of the protein folding process.