Using methods of molecular dynamics and specialized sampling techniques for free energy calculations, studies of helix capping mechanism and thermodynamics, helix propagation, and cooperatively in helix formation will he studied. The focus in helix capping calculations during this grant period will be studies of N-terminal capping by Asn, Asp,Gln and Glu and of the ability of Gly to form a capping interaction at the C-terminus. Alanine will also be examined as a reference for a neutral capping group. Our work on helix propagation will explore the length dependence of propagation at the N- and C-termini of alanine based helices. The primary objective of this work is to understand and reconcile experiments on length dependent helix equilibria. New umbrella sampling methods are proposed for development to aid our investigations of cooperatively in helix folding. These umbrella sampling methods operatively separate local, non-cooperative, behavior from cooperative behavior and permit the cooperative aspects of helix formation to be examined directly. Applications of this new approach will focus on the mechanistic nature of helix formation and where cooperatively affects itself. Specific applications will begin in alanine oligomers to make connection with other recent theoretical calculations and then move to systems currently under study experimentally. Also proposed for development in the ensuing grant period are new methods for chemical free energy simulations. These methods will combine the techniques of extended Hamiltonian dynamics, where the chemical progress variables, the lambdas, in free energy simulations become dynamic variables of the system, with umbrella sampling to provide a more efficient and controllable means of performing chemical free energy simulations. The object of this development is to permit reliable calculations which explore the role of packing and conformation in the stability of helical bundles, either as assemblies of isolated helices such as in the helical assemblies formed from sequences based upon the GcN4 leucine zipper sequence or in folded protein structures such as myoglobin to be performed. Application of the new methods of lambda- dynamics/umbrella sampling will also be made for N-terminal capping, providing a consistency check between methods of chemical and conformational free energy simulations.