The energy computation paradox and ab initio protein folding

Abstract

The routine prediction of three-dimensional protein structure from sequence remains a challenge in computational biochemistry. It has been intuited that calculated energies from physics-based scoring functions are able to distinguish native from nonnative folds based on previous performance with small proteins and that conformational sampling is the fundamental bottleneck to successful folding. We demonstrate that as protein size increases, errors in the computed energies become a significant problem. We show, by using error probability density functions, that physics-based scores contain significant systematic and random errors relative to accurate reference energies. These errors propagate throughout an entire protein and distort its energy landscape to such an extent that modern scoring functions should have little chance of success in finding the free energy minima of large proteins. Nonetheless, by understanding errors in physics-based score functions, they can be reduced in a post-hoc manner, improving accuracy in energy computation and fold discrimination.

Figure 1. Example model systems used to build-up interactions in proteins.

Accurate interaction energies for the model systems are assumed to yield accurate global interaction energies for a folded protein.

Figure 2. Distortions in computed energy landscapes due to error propagation.

If each microstate of a protein under study contains a significant amount of error in its calculated energy (shown here as error bars), computed folding surfaces become distorted with respect to the actual folding surface. This effect introduces difficulty in distinguishing between local minima on the folding surface and in finding the native folds of proteins. This effect is magnified for especially large proteins with many intramolecular contacts contributing to their stable protein folds.

Figure 3. Histogram and probability density functions describing errors in B97-D/TZVP absolute electronic interaction energies of molecular fragments built from the native fold of ubiquitin.

Figure 4. Dependence of random error estimates on chain length.

Larger protein folds have more intramolecular interactions and thus larger propagated random errors in evaluated total energies. This effect is expected to lead to difficulty in predicting the native folds of large proteins since it leads to unpredictable distortions in the overall energy surface.