Electron Density Redistribution Accounts for Half the Cooperativity of r Helix Formation Alexandre V. Morozov, ² Kiril Tsemekhman, ‡ and David Baker* ,§ Center for Studies in Physics and Biology, The Rockefeller UniVersity, 1230 York AVenue, New York, New York 10021, Department of Chemistry, UniVersity of Washington, Box 351700, Seattle, Washington 98195, and Department of Biochemistry, UniVersity of Washington, Box 357350, Seattle, Washington 98195 ReceiVed: December 8, 2005; In Final Form: January 25, 2006 The energy of R helix formation is well known to be highly cooperative, but the origin and relative importance of the contributions to helical cooperativity have been unclear. Here we separate the energy of helix formation into short range and long range components by using two series of helical dimers of variable length. In one dimer series two monomeric helices interact by forming hydrogen bonds, while in the other they are coupled only through long range, primarily electrostatic interactions. Using Density Functional Theory, we find that approximately half of the cooperativity of helix formation is due to electrostatic interactions between residues, while the other half is due to nonadditive many-body effects brought about by redistribution of electron density with helix length. Alpha helix formation in the gas phase is highly coopera- tive: the energy per residue increases with increasing helix length. 1 Understanding the nature of R helical cooperativity is important from both conceptual and practical points of view: in order to model cooperative energetics with empirical models one needs to know the relative importance of the underlying physical effects. While cooperativity in R helices, 1 multiply stranded  sheets, 2 and clusters of small molecules 3 has been previously documented in the literature, the origin of R helix cooperativity and the relative magnitude of the many-body, nonadditive contribution have not been quantitatively analyzed. The increase in the energy per residue with helix length can be decomposed into two parts: first, the increase in the favorable long-range, primarily dipole-dipole electrostatic interactions (Scheme 1; E LR (n)), as more residues become available to interact with; and second, the increase in the strength of the short-range interactions (Scheme 1; E SR (n)) due to the electron density redistribution with length which acts to enhance intrahelical hydrogen bonds. The relative contributions of these two effects have not been quantitatively decomposed in previous studies. Here we separate the short- and long-range contributions to helix cooperativity by studying the dimerization energy of a short probe helix with another helix of variable length (Figure 1 and Scheme 1). In one series of helical models (P-NC n ) the probe helix (P) is hydrogen bonded to the main helix (NC n ), with both molecules sharing a common helical axis. Stronger short-range interactions brought about by electron density redistribution with length will be manifested in the strengths of the two interhelical hydrogen bonds. In the other series (P- C n ), the residues in the longer helix that hydrogen bond to the probe are removed and hence long-range electrostatic interac- tions become dominant. We compute the dimerization energies for both series of models as the difference between the absolute * Corresponding author. E-mail: dabaker@u.washington.edu. ² The Rockefeller University. ‡ Department of Chemistry, University of Washington. § Department of Biochemistry, University of Washington. SCHEME 1: Schematic Representation of r Helical Dimers and Dimerization Energies a a EP-NCn is the dimerization energy with the hydrogen bonded helix; EP-Cn is the dimerization energy with the helix from which two hydrogen bonded ALA residues are removed. ELR(n) ) EP-Cn is the long range contribution to the total dimerization energy; ESR(n) ) EP-NCn - EP-Cn is the short range contribution to the total dimerization energy. NCn represents a helix with n + 2 residues. Two hydrogen bonds between the probe and the main helix are shown as dashed lines. Figure 1. Structural model of the dimer between the probe helix and the 6-residue main helix, with hydrogen bonds shown in yellow. Carbon atoms are colored green if a residue belongs to P or N, and cyan if a residue belongs to C n. Aliphatic hydrogen atoms are not shown. P, N, and Cn are as defined in Scheme 1. 4503 2006, 110, 4503-4505 Published on Web 02/21/2006 10.1021/jp057161f CCC: $33.50 © 2006 American Chemical Society