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.

Computational investigation of the effect of thermal perturbation on the mechanical unfolding of titin I27

“…However, it should be noted that these parameters were developed based on individual amino acids and small peptides, and benchmarked over a test set of proteins [38]. It was recently shown that even small errors in the potential energy functions tend to accumulate for large protein structures, and may result in not very accurate descriptions of the global minima [39]. This may be a crucial factor when using the potential energy functions in ab initio predictions of folded states.…”

On the Assessment of Structural Protein Models with ROSETTA-Design and HMMer: Value, Potential and Limitations

“…However, even if the number of protein structural folds is smaller that the sequence space, the folding problem is still unsolved, because exploring the total number of conformations available to a protein or its energy landscape are NP-hard problems (Hart & Istrail 1997), and because the available methods to calculate the energy of a protein conformation imply a large systematic error (Faver et al, 2011).…”

“…But only a few simplified solutions, implying low-precision, can tackle an electronic macromolecular system, and even these demand a large amount of computational resources (He & Merz, 2010). The common simplifications, based on molecular mechanics, do carry a systematic error that precludes the accurate finding of the true native energy minimum (Faver et al, 2011).…”

“…None of them achieves 100% success, and even the most successful can fail where other, usually less reliable, may succeed (Kryshtafovych et al, 2009;Melo & Feytmans, 1998 This last kind are usually designated as unrefined models. c. Unrefined models can be recognized with various energy scoring strategies (Luthy et al, 1992;Shi et al, 2009;Hu & Jiang, 2010;Melo & Feytmans, 1998); and can be corrected through the use of molecular mechanics software (Rosales-León et al, 2012;Fiser & Sali 2003), though this approach has limitations, as mentioned before (Faver et al, 2011;Hu & Jiang, 2010;Melo & Feytmans, 19985). d. Wrong models instead may frequently be deceitful, because, due to their systematic error [5], a molecular mechanics force-field may report a low energy value, as long as the chemical and geometrical details are well refined.…”

Prediction of trypsin/molecular fragment binding affinities by free energy decomposition and empirical scores

“…In this spirit, we introduce a novel procedure for the estimation and correction of energy function errors into our results. Our lab has been investigating the effects of energy function errors and means of correcting for these errors in different applications [7][8][9]. In this work we applied our error estimation methods to the rescoring of docked ligands, to test whether it would improve our ability to rank ligands by affinity.…”