A statistical mechanical model for beta-sheet formation

There is much current interest in developing peptides that fold into monome ric beta-sheets in aqueous solution in order to measure the forces responsi ble for the formation of this important protein secondary structure. To int erpret 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 beta-sh eet/coil equilibrium. We consider every structurally allowed conformation f or sheets of two, three, or four strands, and calculate the stability of ea ch. The model includes parameters for beta-sheet preference, with or withou t hydrogen bonds, and for beta-turn preference. We treat a beta-sheet as a succession of columns with each column containing noncovalently bonded resi dues in the sheet. Partition functions are efficiently generated using a ma trix that contains an entry for every column pair. All of the information o n the sheet/coil equilibrium is contained within the partition function. We have used this to calculate the probability of forming beta-sheets of two, three, or four strands as a function of beta-turn and beta-sheet residue p reference. We find that beta-hairpins and beta-meanders are favored by mode rate beta-turn and beta-sheet residue preferences, and that very stable she ets have more strands. Analysis of experimental data gives the free energy change for transferring a residue from coil to beta-sheet with hydrogen bon d formation as -0.7kcal . mol(-1) and without hydrogen bond formation as 0. 9 kcal . mol(-1) at 298 K in methanol, comparable values to those in alpha- helices.