New theoretical methodology for elucidating the solution structure of peptides from NMR Data. II. Free energy of dominant microstates of leu-enkephalin and population-weighted average nuclear overhauser effects intensities

A small linear peptide in solution may populate several stable states (called here microstates) in thermodynamic equilibrium; elucidating its dynamic three dimensional structure by multidimensional nmr is complex since the experimentally measured nuclear Overhauser effect intensities (NOEs) represent averages over the individual contributions. We propose a new methodology based on statistical mechanical considerations for analyzing nmr data of such peptides. In a previous paper [called paper I, H. Meirovitch et al. (1995) Journal of Physical Chemistry, 99, 4847-4854] we have developed theoretical methods for determining the contribution to the partition function Z of the most stable microstates, i.e., those that pertain to a given energy range above the global energy minimum (GEM). This relatively small set of dominant microstates provides the main contribution to medium- and long-range NOE intensities. In this work the individual populations and NOEs of the dominant microstates are determined, and then weighted averages are calculated and compared with experiment. Our methodology is applied to the pentapeptide Leu-enkephalin H-Tyr-Gly-Gly-Phe-Leu-OH, described by the potential energy function ECEPP. Twenty one significantly different energy minimized structures are first identified within the range of 2 kcal/mol above the GEM by an extensive conformational search; this range has been found in paper I to contribute 0.6 of Z. These structures then become "seeds" for Monte Carlo (MC) simulations designed to keep the molecule relatively close to its seed Indeed, the MC samples (called MC microstates) illustrate what we define as intermediate chain flexibility: some dihedral angles remain in the vicinity of their seed value, while others visit the full range of [-180°, 180°]. The free energies of the MC microstates (which lead to the populations) are calculated by the local states method, which (unlike other techniques) can handle any chain flexibility. The NOE of MC microstate i is calculated as the average 〈1/r³〉_i², and an effective interatomic distance r_i^eff is defined as r_i^eff = 〈1/r³〉_i^-1/3, where r is the distance between two protons. Under the "initial rate approximation," and neglecting angular modulations, the overall intensity I is the average over r_i^eff-6, weighted by the populations of the MC microstates. This treatment is justified under the assumption that the rates at which conformations interconvert within, and among, microstates are faster and slower, respectively, than the rotational reorientation of the molecule. I^-6 leads to the virtual theoretical distances, compared to the corresponding virtual experimental distances, which were obtained previously from a cryoprotective solution of Leu-enkephalin at 280 K. A reasonable fit is found between theory and experiment. Future research directions are outlined.