The maximum penalty criterion for ridge regression: application to the calibration of the force constant in elastic network models. Issue 7 (30th May 2017)

• Record Type: Journal Article
• Authors: Dehouck, Yves; Bastolla, Ugo
• Is Part Of: Integrative biology. Volume 9:Issue 7(2017:Jul.)
• Page Start: 627
• Page End: 641
• Publication Date: 2017-05-30
• Subjects: Biology -- Periodicals; Technology -- Periodicals; Biological systems -- Periodicals; 570.5
• DOI: 10.1039/c7ib00079k
• Languages: English
• ISSNs: 1757-9694

Abstract

Abstract : Using ridge regression with new criteria derived from an analogy with statistical mechanics, we evaluate the relative contributions of rigid-body and internal fluctuations in X-ray B-factors and improve the calibration of computational models of protein dynamics. Abstract : Tikhonov regularization, or ridge regression, is a popular technique to deal with collinearity in multivariate regression. We unveil a formal analogy between ridge regression and statistical mechanics, where the objective function is comparable to a free energy, and the ridge parameter plays the role of temperature. This analogy suggests two novel criteria for selecting a suitable ridge parameter: specific-heat ( C v ) and maximum penalty (MP). We apply these fits to evaluate the relative contributions of rigid-body and internal fluctuations, which are typically highly collinear, to crystallographic B-factors. This issue is particularly important for computational models of protein dynamics, such as the elastic network model (ENM), since the amplitude of the predicted internal motion is commonly calibrated using B-factor data. After validation on simulated datasets, our results indicate that rigid-body motions account on average for more than 80% of the amplitude of B-factors. Furthermore, we evaluate the ability of different fits to reproduce the amplitudes of internal fluctuations in X-ray ensembles from the B-factors in the corresponding single X-ray structures. The new ridge criteria are shown to be markedly superior to the commonly used two-parameter fit that neglects rigid-body rotations and to the full fits regularized under generalized cross-validation. In conclusion, the proposed fits ensure a more robust calibration of the ENM force constant and should prove valuable in other applications.