Patterns in Protein Flexibility: A Comparison of NMR "Ensembles", MD Trajectories, and Crystallographic B-Factors

Assessment of Four Theoretical Approaches to Predict Protein Flexibility in the Crystal Phase and Solution

In this paper, we evaluated the ability of four coarse-grained methods to predict protein flexible regions with potential biological importance, UNRES-flex, UNRES-DSSP-flex (based on the united residue model of polypeptide chains without and with secondary structure restraints, respectively), CABS-flex (based on the C-α, C-β, and side chain model), and nonlinear rigid block normal mode analysis (NOLB) with a set of 100 protein structures determined by NMR spectroscopy or X-ray crystallography, with all secondary structure types. End regions with high fluctuations were excluded from analysis. The Pearson and Spearman correlation coefficients were used to quantify the conformity between the calculated and experimental fluctuation profiles, the latter determined from NMR ensembles and X-ray B-factors, respectively. For X-ray structures (corresponding to proteins in a crowded environment), NOLB resulted in the best agreement between the predicted and experimental fluctuation profiles, while for NMR structures (corresponding to proteins in solution), the ranking of performance is CABS-flex > UNRES-DSSP-flex > UNRES-flex > NOLB; however, CABS-flex sometimes exaggerated the extent of small fluctuations, as opposed to UNRES-DSSP-flex.

XFEL structure of carbonic anhydrase II: a comparative study of XFEL, NMR, X-ray and neutron structures

The combination of X-ray free-electron lasers (XFELs) with serial femtosecond crystallography represents cutting-edge technology in structural biology, allowing the study of enzyme reactions and dynamics in real time through the generation of `molecular movies'. This technology combines short and precise high-energy X-ray exposure to a stream of protein microcrystals. Here, the XFEL structure of carbonic anhydrase II, a ubiquitous enzyme responsible for the interconversion of CO2 and bicarbonate, is reported, and is compared with previously reported NMR and synchrotron X-ray and neutron single-crystal structures.

Improving IDP theoretical chemical shift accuracy and efficiency through a combined MD/ADMA/DFT and machine learning approach

This work extends the multi-scale computational scheme for the quantum mechanics (QM) calculations of Nuclear Magnetic Resonance (NMR) chemical shifts (CSs) in proteins that lack a well-defined 3D structure. The scheme couples the sampling of an intrinsically disordered protein (IDP) by classical molecular dynamics (MD) with protein fragmentation using the adjustable density matrix assembler (ADMA) and density functional theory (DFT) calculations. In contrast to our early investigation on IDPs (Pavlíková Přecechtělová et al., J. Chem. Theory Comput., 2019, 15, 5642-5658) and the state-of-the art NMR calculations for structured proteins, a partial re-optimization was implemented on the raw MD geometries in vibrational normal mode coordinates to enhance the accuracy of the MD/ADMA/DFT computational scheme. In addition, machine-learning based cluster analysis was performed on the scheme to explore its potential in producing protein structure ensembles (CLUSTER ensembles) that yield accurate CSs at a reduced computational cost. The performance of the cluster-based calculations is validated against results obtained with conventional structural ensembles consisting of MD snapshots extracted from the MD trajectory at regular time intervals (REGULAR ensembles). CS calculations performed with the refined MD/ADMA/DFT framework employed the 6-311++G(d,p) basis set that outperformed IGLO-III calculations with the same density functional approximation (B3LYP) and both explicit and implicit solvation. The partial geometry optimization did not universally improve the agreement of computed CSs with the experiment but substantially decreased errors associated with the ensemble averaging. A CLUSTER ensemble with 50 structures yielded ensemble averages close to those obtained with a REGULAR ensemble consisting of 500 MD frames. The cluster based calculations thus required only a fraction of the computational time.

A B-factor for NOEs?

Nuclear Overhauser effects (NOEs) are influenced by motion. Here, we derive exact, analytical results for a model of isotropic, harmonic fluctuations of atom positions that corresponds to the one underlying crystallographic B-factors. The model includes steric repulsion and yields closed-form expressions for the expected value of general invertible functions of the distance between two atoms, with the special case r^-6 for NOEs. We discuss the implications for the definition of an NOE-based B-factor in solution NMR.

Uses and Abuses of the Atomic Displacement Parameters in Structural Biology

B-factors determined with X-ray crystallographic analyses are commonly used to estimate the flexibility degree of atoms, residues, and molecular moieties in biological macromolecules. In this chapter, the most recent studies and applications of B-factors in protein engineering and structural biology are briefly summarized. Particular emphasis is given to the limitations in using B-factors, in order to prevent inappropriate applications. It is eventually predicted that future applications will involve anisotropically refined B-factors, deep learning, and data produced by cryo-EM.

Special Issue-The Conformational Universe of Proteins and Peptides: Tales of Order and Disorder

Among biological macromolecules, proteins hold prominent roles in a vast array of physiological and pathological processes [...].