NEW THEORETICAL METHODOLOGY FOR ELUCIDATING THE SOLUTION STRUCTURE OFPEPTIDES FROM NMR DATA .2. FREE-ENERGY OF DOMINANT MICROSTATES OF LEU-ENKEPHALIN AND POPULATION-WEIGHTED AVERAGE NUCLEAR OVERHAUSER EFFECTSINTENSITIES

A small linear peptide in solution may populate several stable states (called here microstates) in thermodynamic equilibrium; elucidating it s dynamic three dimensional structure by multidimensional nmr is compl ex since the experimentally measured nuclear Overhauser effect intensi ties (NOEs) represent averages over the individual contributions. We p ropose a new methodology based on statistical mechanical consideration s 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 t he contribution to the partition function Z of the most stable microst ates, i.e., those that pertain to a given energy range above the globa l energy minimum (GEM). This relatively small set of dominant microsta tes provides the main contribution to medium- and long-range NOE inten sities. In this work the individual populations and NOEs of the domina nt microstates are determined, and then weighted averages are calculat ed and compared with experiment. Our methodology is applied to the pen tapeptide Leu-enkephalin H-Tyr-Gly-Gly-Phe-Leu-OH, described by the po tential energy function ECEPP. Twenty one significantly different ener gy minimized structures are first identified within the range of 2 kca l/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 the n become ''seeds'' for Monte Carlo (MC) samples (called MC microstates ) illustrate what we define as intermediate chain flexibility: some di hedral angels remain in the vicinity of their seed value, while others visit the full range of [-180 degrees, 180 degrees]. The free energie s of the MC microstates (which lead to the population) 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 th e average [1/r(3)](2)(i), and an effective interatomic distance r(i)(e ff) is defined as r(i)(eff) = [1/r(3)](-1/3)(i), where r is the distan ce 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 whi ch conformations interconvert within, and among, microstates are faste r and slower, respectively, than the rotational reorientation of the m olecule. I-6, weighted by the populations of the MC microstates. This treatment is justified under the assumption that the rates at which co nformations interconvert within, and among, microstates are faster and slower, respectively, than the rotational reorientation of the molecu le. I-6 leads to the virtual theoretical distances, compared to the co rresponding virtual experiment distances, which were obtained previous ly from a cryoprotective solution of Leu-enkephalin at 280 K. A reason able fit is found between theory and experiment. Future research direc tions are outlined. (C) 1996 John Wiley & Sons, Inc.