Constraint Techniques for Solving the Protein Structure Prediction Problem

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse. Show more

A three-dimensional lattice model of a protein is used to investigate the properties required for its folding to the native state. The polypeptide chain is represented as a 27 bead heteropolymer whose lowest energy (native) state can be determined by an exhaustive enumeration of all fully compact conformations. A total of 200 sequences with random interactions are generated and subjected to Monte Carlo simulations to determine which chains find the ground state in a short time; i.e. which sequences overcome the folding problem referred to as the Levinthal paradox. Comparison of the folding and non-folding sequences is used to identify the features that are required for fast folding to the global energy minimum. It is shown that successful folding does not require certain attributes that have been previously proposed as necessary for folding; these include a high number of short versus long-range contacts in the native state, a high content of the secondary structure in the native state, a strong correlation between the native contact map and the interaction parameters, and the existence of a high number of low energy states with near-native conformation. Instead, the essential difference between the folding and the non-folding sequences is the nature of the energy spectrum. The necessary and sufficient condition for a sequence to fold rapidly in the present model is that the native state is a pronounced energy minimum. As a consequence, the thermodynamic stability of the native state of a folding sequence has a sigmoidal dependence on temperature. This permits such a sequence to satisfy both the thermodynamic and the kinetic requirements for folding; i.e. the native state predominates thermodynamically at temperatures that are high enough for folding to be kinetically possible. The applicability of the present results to real proteins is discussed. Show more