Machine Learning: How Much Does It Tell about Protein Folding Rates?

Abstract

The prediction of protein folding rates is a necessary step towards understanding the principles of protein folding. Due to the increasing amount of experimental data, numerous protein folding models and predictors of protein folding rates have been developed in the last decade. The problem has also attracted the attention of scientists from computational fields, which led to the publication of several machine learning-based models to predict the rate of protein folding. Some of them claim to predict the logarithm of protein folding rate with an accuracy greater than 90%. However, there are reasons to believe that such claims are exaggerated due to large fluctuations and overfitting of the estimates. When we confronted three selected published models with new data, we found a much lower predictive power than reported in the original publications. Overly optimistic predictive powers appear from violations of the basic principles of machine-learning. We highlight common misconceptions in the studies claiming excessive predictive power and propose to use learning curves as a safeguard against those mistakes. As an example, we show that the current amount of experimental data is insufficient to build a linear predictor of logarithms of folding rates based on protein amino acid composition.

Solution of Levinthal’s Paradox and a Physical Theory of Protein Folding Times

“…To summarize, the theoretical and semi-empirical methods (that use such meaningful parameters as the chain length [51,69,70], protein globule cross-section [71], α-helical content [72], locality of contacts [73], contact order [74,75], etc., but do not use or use a very small number of adjustable parameters) show better predictive power and correlation with experiment than the current machine learning techniques that use too many adjustable parameters (provided that correlations are obtained on testing and not training sets) [99]. Given the still relatively low number of experimental points, the purely statistical and machine learning techniques can be currently useful only for fine-tuning small second-order corrections to the existing rough but physically or biologically meaningful estimates, or for finding relatively small corrections for parameters already known to play a physically or biologically meaningful role in folding [83].…”

“…To study this phenomenon, which, in principle, can lead to drastically worse results obtained for the testing sets than those reported for the training sets, Corrales et al checked three machine learning methods by applying them to new data, data not used when building the models [99]. It turned out that for all three considered machine learning methods the obtained correlations were significantly worse than those declared in the original publications.…”

“…To illustrate the problem of the low amount of available data, Corrales et al built the model having 19 adjustable parameters based on the amino acid occurrences in proteins having different folding times [99]:…”

“…The same for the above described (see Equation (2) and Figures 2 and 3) model, where t = τ × exp[L 2/3 ], that has no adjustable parameters (right). Adapted from [99] with minor modifications.…”

Folding with a protein's native shortcut network

“…2ABD and 1ST7 are respectively, the bovine and yeast structures of the extensively studied four helix bundle ACBP (acyl-coenzyme A-binding protein), whose folding pathway could challenge our infeasible SSU restriction (section 2.5). ACBP is also interesting because, depending on experimental conditions, it can be classified as a multi-state folder [15,33]. 1QYS is a de novo protein with < 100 residues but exhibits non-cooperative behavior, and has a very stable intermediate structure [38].…”