Three-body interactions improve the prediction of rate and mechanism in protein folding models

Abstract

Here we study the effects of many-body interactions on rate and mechanism in protein folding by using the results of molecular dynamics simulations on numerous coarse-grained C ␣ -model single-domain proteins. After adding three-body interactions explicitly as a perturbation to a Go -like Hamiltonian with native pairwise interactions only, we have found (i) a significantly increased correlation with experimental values and folding rates, (ii) a stronger correlation of folding rate with contact order, matching the experimental range in rates when the fraction of three-body energy in the native state is Ϸ20%, and (iii) a considerably larger amount of three-body energy present in chymotripsin inhibitor than in the other proteins studied.U nderstanding the nature of the interactions that stabilize protein structures and govern protein folding mechanisms is a fundamental problem in molecular biology (1-6) that has applies to structure and function prediction (7-10) as well as rational enzyme design (11). Regarding folding mechanisms, protein folding has long been known to be a cooperative process, at least for smaller single-domain proteins (12). Experimental scenarios that lack a first-order-like folding barrier are rare (13), often in contrast to simulation results. There are other discrepancies between simulation and experiment. For example, although the experimental folding rates for a typical set of 18 two-state, single-domain proteins (given in Materials and Methods) span about six orders of magnitude, simulations of coarsegrained models of the same proteins have rates that vary by about a factor of 100, a discrepancy of four orders of magnitude.How does one then quantify the sources of the barrier that controls the folding rate? The folding barrier is the residual of an incomplete cancellation of large and opposing energetic and entropic contributions, with the relative smallness of the barrier allowing folding to occur on biological time scales (14,15). Among the important energetic contributions that drive folding are solventmediated hydrophobic forces (16), which are known to be weaker on short-length scales, or low concentrations of apolar side-chains (17), a scenario likely to be present when the protein is unfolded. Hence, the solvent-averaged potential governing folding almost certainly contains a nonadditive, many-body component, and several models have been proposed to capture this effect (18-27). The folding free-energy barrier increases as the nonadditivity of interactions is increased (20,21,23,25) because of the decreased energetic correlation between the native conformation and conformations that may be geometrically similar to it.Experimental values give a measure of the strength of native interactions involving a particular amino acid (residue) in the transition state (28), thus quantifying a residue's importance in folding. However the values obtained from simulations of coarsegrained protein models generally do not correlate well with the experimentally determined values. Model proteins are c...

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