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Debye-Waller factor, a measure of X-ray attenuation, can be experimentallyobserved in protein X-ray crystallography. Previous theoretical models havemade strong inroads in the analysis of B-factors by linearly fitting proteinB-factors from experimental data. However, the blind prediction of B-factorsfor unknown proteins is an unsolved problem. This work integrates machinelearning and advanced graph theory, namely, multiscale weighted colored graphs(MWCGs), to blindly predict B-factors of unknown proteins. MWCGs are localfeatures that measure the intrinsic flexibility due to a protein structure.Global features that connect the B-factors of different proteins, e.g., theresolution of X-ray crystallography, are introduced to enable the cross-proteinB-factor predictions. Several machine learning approaches, including ensemblemethods and deep learning, are considered in the present work. The proposedmethod is validated with hundreds of thousands of experimental B-factors.Extensive numerical results indicate that the blind B-factor predictionsobtained from the present method are more accurate than the least squaresfittings using traditional methods.

Blind prediction of protein B-factor and flexibility