Calculation of the Free Energy and Cooperativity of Protein Folding

Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design

Molecular modeling and design of regioselectively addressable functionalized templates with rigidified three-dimensional structures

Extensive conformational analysis of a series of beta-alkyl substituted cyclopeptides-cyclo(Pro(1)-Xaa(2)-Nle(3)-Ala(4)-Nle(5)-Pro(6) Xaa(7)-Nle(8)-Ala(9)-Nle(10)) and cyclo[Pro(1)-Xaa(2)-Nle(3)-(Cys(4)-Nle(5)-Pro(6)-Xaa(7)-Nle(8)-Cys(9))-N le(10)] as well as their corresponding unsubstituted core structures cyclo(Pro(1)-Xaa(2)-Ala(3)-Cys(4)-Ala(5)-Pro(6)-Xaa(7)-Ala(8)-Ala(9)-Ala (10)) and cyclo(Pro(1)-Xaa(2)-Ala(3)-Cys(4)-Ala(5)-Pro(6)-Xaa(7)-Ala(8)-Cys(9)-Ala (10)) has been performed employing both the ECEPP/2 and the MAB force fields (Xaa = Gly, L-Ala, D-Ala, Aib, and D-Pro). Results show that (a) possible three-dimensional structures of the cyclo(Pro(1)-Gly(2)-Lys(3)-Ala(4)-Lys(5)-Pro(6)-Gly(7)-Lys(8)-Ala(9)-Lys (10)) molecule are nor limited to a single extended "rectangular" conformation with all Lys side chains oriented at the same side of the molecule; (b) conformational equilibrium in monocyclic analogues obtained by replacements of conformationally flexible Gly residues for L-Ala, D-Ala, Aib, or D-Pro is not significantly shifted towards the target "rectangular" conformational type; and (c) introduction of disulfide bridges between positions 4 and 9 is a very powerful way to stabilize the target conformations in the resulting bicyclic molecules. These findings form the basis for further design of rigidified regioselectively addressable functionalized templates with many application areas ranging from biostructural to diagnostic purposes. (C) 1999 John Wiley & Sons, Inc