Structure of proteins: Packing of a-helices and pleated sheets

Simple models are presented that describe the rules for almost all the packing that occurs between and among cu-helices and pleated sheets. These packing rules, together with the primary and secondary s tructures , are the major determinants of the three-dimensional s tructure of prote ins . Twenty-six years ago, Pauling and his colleagues (1, 2) presented the a-helix and the parallel and antiparallel pleated sheets as models for the local folding (secondary structure) of the polypeptide chain in proteins. Since then, various physical techniques (principally x-ray crystal structure analysis) have clearly shown that these secondary structures are almost universally present in protein molecules. We present here models that describe the rules that govern how cu-helices and pleated sheets pack together to form the three-dimensional (tertiary) structure of proteins, The rules were developed empirically: a priori models were checked and refined by a detailed analysis of the residue-to-residue contacts that occur between and among the cu-helices and pleated sheets in 17 proteins. To do this analysis we made extensive use of a computer graphics system for proteins developed by P. J. Pauling and his colleagues (to be published) d f an o numerical calculations. The models describe almost all of the secondary structure packings we have so far observed. In a later publication they will be used to present a detailed analysis of known structures. The determining principles Two principles have a dominating influence on the way in which secondary structures associate. 1. Residues that become buried in the interior of a protein close-pack: they occupy a volume similar to that which they occupy in crystals of their amino acid (3,4). 2, Associated secondary structures retain a conformation close to the minimum free energy conformation of the isolated secondary structures. This second principle is illustrated by the observation that almost all the protein main-chain torsion angles, cpand rl/, lie in regions of torsion angle space that are free from steric strainthat is, in the normally allowed regions of the Ramachandran map (5). Le Master and Richards, as reported by Richards (6), found that this is also true for the side-chain angle ~1. In a detailed analysis of the conformational potentials of the residue side chains in bovine pancreatic trypsin inhibitor, Gelin and Karplus (7) showed that their conformations were close to those of the free amino acid. The static close-packed image of proteins that is implicit in these two principles is, of course, only true of the time-averaged structure. Individual molecules are subject to large transient thermodynamic (and therefore conformational) fluctuations 0 . The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked ‘~adv~~~~se~@~~” in accordance with I8 U. S. C. $1734 solely to indicate this fact. The two principles imply that the secondary structures found in protein molecules interact in a manner that gives the maximum van der Waals energy and induces no appreciable steric strain. The rules described below for secondary structure associations arise from these two principles and from the intrinsic geometrical properties of cu-helices and pleated sheets,