Kinetics of protein folding: a lattice model study of the requirements for folding to the native state

A three-dimensional lattice model of a protein is used to investigate the properties required for it 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.