A Statistical Mechanical Model for β-Sheet Formation

There is much current interest in developing peptides that fold into monomeric β-sheets in aqueous solution in order to measure the forces responsible for the formation of this important protein secondary structure. To interpret results on secondary structure in peptides it is essential to use a statistical mechanical model than considers the stability of every possible conformation of the peptide. Here we develop a novel model for the β-sheet/coil equilibrium. We consider every structurally allowed conformation for sheets of two, three, or four strands, and calculate the stability of each. The model includes parameters for β-sheet preference, with or without hydrogen bonds, and for β-turn preference. We treat a β-sheet as a succession of columns with each column containing noncovalently bonded residues in the sheet. Partition functions are efficiently generated using a matrix that contains an entry for every column pair. All of the information on the sheet/coil equilibrium is contained within the partition function. We have used this to calculate the probability of forming β-sheets of two, three, or four strands as a function of β-turn and β-sheet residue preference. We find that β-hairpins and β-meanders are favored by moderate β-turn and β-sheet residue preferences, and that very stable sheets have more strands. Analysis of experimental data gives the free energy change for transferring a residue from coil to β-sheet with hydrogen bond formation as −0.7 kcal•mol -1 and without hydrogen bond formation as 0.9 kcal•mol -1 at 298 K in methanol, comparable values to those in α-helices.