Solvophobically driven folding of nonbiological oligomers.

In solution, biopolymers commonly fold into well-defined three-dimensional structures, but only recently has analogous behavior been explored in synthetic chain molecules. An aromatic hydrocarbon backbone is described that spontaneously acquires a stable helical conformation having a large cavity. The chain does not form intramolecular hydrogen bonds, and solvophobic interactions drive the folding transition, which is sensitive to chain length, solvent quality, and temperature.

Statistical theory for protein combinatorial libraries. Packing interactions, backbone flexibility, and the sequence variability of a main-chain structure.

Combinatorial experiments provide new ways to probe the determinants of protein folding and to identify novel folding amino acid sequences. These types of experiments, however, are complicated both by enormous conformational complexity and by large numbers of possible sequences. Therefore, a quantitative computational theory would be helpful in designing and interpreting these types of experiment. Here, we present and apply a statistically based, computational approach for identifying the properties of sequences compatible with a given main-chain structure. Protein side-chain conformations are included in an atom-based fashion. Calculations are performed for a variety of similar backbone structures to identify sequence properties that are robust with respect to minor changes in main-chain structure. Rather than specific sequences, the method yields the likelihood of each of the amino acids at preselected positions in a given protein structure. The theory may be used to quantify the characteristics of sequence space for a chosen structure without explicitly tabulating sequences. To account for hydrophobic effects, we introduce an environmental energy that it is consistent with other simple hydrophobicity scales and show that it is effective for side-chain modeling. We apply the method to calculate the identity probabilities of selected positions of the immunoglobulin light chain-binding domain of protein L, for which many variant folding sequences are available. The calculations compare favorably with the experimentally observed identity probabilities.

Statistical theory of combinatorial libraries of folding proteins: energetic discrimination of a target structure.

A self-consistent theory is presented that can be used to estimate the number and composition of sequences satisfying a predetermined set of constraints. The theory is formulated so as to examine the features of sequences having a particular value of Delta=E(f)-(u), where E(f) is the energy of sequences when in a target structure and (u) is an average energy of non-target structures. The theory yields the probabilities w(i)(alpha) that each position i in the sequence is occupied by a particular monomer type alpha. The theory is applied to a simple lattice model of proteins. Excellent agreement is observed between the theory and the results of exact enumerations. The theory provides a quantitative framework for the design and interpretation of combinatorial experiments involving proteins, where a library of amino acid sequences is searched for sequences that fold to a desired structure.

Local conformational signals and the statistical thermodynamics of collapsed helical proteins.

We investigate the role that local conformational tendencies can have in guiding the folding of helical proteins, using simple statistical mechanical models. The theory provides a synthesis of classical models of the helix-coil transition in polymers with an approximate treatment of the effects of excluded volume, confinement, and packing alignment of the helices based on a free energy function. The theory studies the consequences of signals encoded locally in the sequence as stabilization energies associated with three types of local structure: native helical conformations, native non-helical conformations, and native helix caps or start-stop signals. The role of randomness in the energies of conformations due to tertiary interactions is also studied vis-à-vis the difficulty of conformational search. The thermal behavior of the model is presented for realistic values of the conformational signal energies, which can be estimated from experimental studies on peptide fragments. Estimates are made for the relative contribution of local signals and specific tertiary interactions to the folding stability gap.