Exploration of Peptide Free Energy Surfaces

The Conformational Free Energy Thermodynamic Integration (CFTI) method, a new multidimensional approach for conformational free energy simulations, is presented. The method is applied to two problems of biochemical interest: exploration of the free energy surfaces of helical alanine (Ala) and α-methylalanine (Aib) homopeptides in vacuum and the cost of pre-organization of the opioid peptide Tyr-D-Pen-Gly-Phe-D-Pen (DPDPE) peptide for disulfide bond formation. In the CFTI approach a single molecular dynamics simulation with all ø and ψ dihedrals kept fixed yields the complete conformational free energy gradient for the studied peptides. For regular structures of model peptides (Ala)_n and (Aib)_n where n=6,8,10 and Aib is a-methylalanine in vacuum, free energy maps in the helical region of ø- ψ space are calculated, and used to roughly locate stable states. The locations of the free energy minima are further refined by the novel procedure of free energy optimization by steepest descent down the gradient, leading to structures in excellent agreement with experimental data. The stability of the minima with respect to deformations is studied by analysis of second derivatives of the free energy surface. Analysis of free energy components and molecular structures uncovers the molecular mechanism for the propensity of Aib peptides for the 3₁₀-helix structure in the interplay between the quality and quantity of hydrogen bonds. For the linear form of the DPDPE peptide in solution, free energy differences are calculated between four conformers: Cyc, representing the structure adopted by the linear peptide prior to disulfide bond formation, β _c and β _E, two slightly different β-turns previously identified as representative, stable structures of the peptide, and Ext, an extended structure. The simulations indicate that β _E is the most stable of the studied conformers of linear DPDPE in aqueous solution, with β _c , Cyc and Ext having free energies higher by 2.3, 6.3, and 28.2 kcal/mol, respectively. The free energy differences of 4.0 kcal/mol between β _c and Cyc, and 6.3 kcal/mol between β _E and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S-S bond formation to proceed.