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 Precechtelová 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.

Convergent views on disordered protein dynamics from NMR and computational approaches.

Intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs) is a class of biologically important proteins exhibiting specific biophysical characteristics. They lack a hydrophobic core, and their conformational behavior is strongly influenced by electrostatic interactions. IDPs and IDRs are highly dynamic, and a characterization of the motions of IDPs and IDRs is essential for their physically correct description. NMR together with molecular dynamics simulations are the methods best suited to such a task because they provide information about dynamics of proteins with atomistic resolution. Here, we present a study of motions of a disordered C-terminal domain of the delta subunit of RNA polymerase from Bacillus subtilis. Positively and negatively charged residues in the studied domain form transient electrostatic contacts critical for the biological function. Our study is focused on investigation of ps-ns dynamics of backbone of the delta subunit based on analysis of amide 15N NMR relaxation data and molecular dynamics simulations. In order to extend an informational content of NMR data to lower frequencies, which are more sensitive to slower motions, we combined standard (high-field) NMR relaxation experiments with high-resolution relaxometry. Altogether, we collected data reporting the relaxation at 12 different magnetic fields, resulting in an unprecedented data set. Our results document that the analysis of such data provides a consistent description of dynamics and confirms the validity of so far used protocols of the analysis of dynamics of IDPs also for a partially folded protein. In addition, the potential to access detailed description of motions at the timescale of tens of ns with the help of relaxometry data is discussed. Interestingly, in our case, it appears to be mostly relevant for a region involved in the formation of temporary contacts within the disordered region, which was previously proven to be biologically important.

Choice of Force Field for Proteins Containing Structured and Intrinsically Disordered Regions.

Biomolecular force fields optimized for globular proteins fail to properly reproduce properties of intrinsically disordered proteins. In particular, parameters of the water model need to be modified to improve applicability of the force fields to both ordered and disordered proteins. Here, we compared performance of force fields recommended for intrinsically disordered proteins in molecular dynamics simulations of three proteins differing in the content of ordered and disordered regions (two proteins consisting of a well-structured domain and of a disordered region with and without a transient helical motif and one disordered protein containing a region of increased helical propensity). The obtained molecular dynamics trajectories were used to predict measurable parameters, including radii of gyration of the proteins and chemical shifts, residual dipolar couplings, paramagnetic relaxation enhancement, and NMR relaxation data of their individual residues. The predicted quantities were compared with experimental data obtained within this study or published previously. The results showed that the NMR relaxation parameters, rarely used for benchmarking, are particularly sensitive to the choice of force-field parameters, especially those defining the water model. Interestingly, the TIP3P water model, leading to an artificial structural collapse, also resulted in unrealistic relaxation properties. The TIP4P-D water model, combined with three biomolecular force-field parameters for the protein part, significantly improved reliability of the simulations. Additional analysis revealed only one particular force field capable of retaining the transient helical motif observed in NMR experiments. The benchmarking protocol used in our study, being more sensitive to imperfections than the commonly used tests, is well suited to evaluate the performance of newly developed force fields.

Boosting the resolution of low-field [Formula: see text] relaxation experiments on intrinsically disordered proteins with triple-resonance NMR.

Improving our understanding of nanosecond motions in disordered proteins requires the enhanced sampling of the spectral density function obtained from relaxation at low magnetic fields. High-resolution relaxometry and two-field NMR measurements of relaxation have, so far, only been based on the recording of one- or two-dimensional spectra, which provide insufficient resolution for challenging disordered proteins. Here, we introduce a 3D-HNCO-based two-field NMR experiment for measurements of protein backbone [Formula: see text] amide longitudinal relaxation rates. The experiment provides accurate longitudinal relaxation rates at low field (0.33 T in our case) preserving the resolution and sensitivity typical for high-field NMR spectroscopy. Radiofrequency pulses applied on six different radiofrequency channels are used to manipulate the spin system at both fields. The experiment was demonstrated on the C-terminal domain of [Formula: see text] subunit of RNA polymerase from Bacillus subtilis, a protein with highly repetitive amino-acid sequence and very low dispersion of backbone chemical shifts.

Quantum Chemical Calculations of NMR Chemical Shifts in Phosphorylated Intrinsically Disordered Proteins.

Quantum mechanics (QM) calculations are applied to examine 1H, 13C, 15N, and 31P chemical shifts of two phosphorylation sites in an intrinsically disordered protein region. The QM calculations employ a combination of (1) structural ensembles generated by molecular dynamics, (2) a fragmentation technique based on the adjustable density matrix assembler, and (3) density functional methods. The combined computational approach is used to obtain chemical shifts (i) in the S19 and S40 residues of the nonphosphorylated and (ii) in the pS19 and pS40 residues of the doubly phosphorylated human tyrosine hydroxylase 1 as the system of interest. We study the effects of conformational averaging and explicit solvent sampling as well as the effects of phosphorylation on the computed chemical shifts. Good to great quantitative agreement with the experiment is achieved for all nuclei, provided that the systematic error cancellation is optimized by the choice of a suitable NMR standard. The effect of the standard reference on the computed 15N and 31P chemical shifts is demonstrated by employing three different referencing methods. Error bars associated with the statistical averaging of the computed 31P chemical shifts are larger than the difference between the 31P chemical shift of pS19 and pS40. The sequence trend of 31P shifts therefore could not be reliably reproduced. On the contrary, the calculations correctly predict the change of the 13C chemical shift for CB induced by the phosphorylation of the serine residues. The present work demonstrates that QM calculations coupled with molecular dynamics simulations and fragmentation techniques can be used as an alternative to empirical prediction tools in the structure characterization of intrinsically disordered proteins.

Structure and Functions of Microtubule Associated Proteins Tau and MAP2c: Similarities and Differences.

The stability and dynamics of cytoskeleton in brain nerve cells are regulated by microtubule associated proteins (MAPs), tau and MAP2. Both proteins are intrinsically disordered and involved in multiple molecular interactions important for normal physiology and pathology of chronic neurodegenerative diseases. Nuclear magnetic resonance and cryo-electron microscopy recently revealed propensities of MAPs to form transient local structures and long-range contacts in the free state, and conformations adopted in complexes with microtubules and filamentous actin, as well as in pathological aggregates. In this paper, we compare the longest, 441-residue brain isoform of tau (tau40), and a 467-residue isoform of MAP2, known as MAP2c. For both molecules, we present transient structural motifs revealed by conformational analysis of experimental data obtained for free soluble forms of the proteins. We show that many of the short sequence motifs that exhibit transient structural features are linked to functional properties, manifested by specific interactions. The transient structural motifs can be therefore classified as molecular recognition elements of tau40 and MAP2c. Their interactions are further regulated by post-translational modifications, in particular phosphorylation. The structure-function analysis also explains differences between biological activities of tau40 and MAP2c.

Functionally specific binding regions of microtubule-associated protein 2c exhibit distinct conformations and dynamics.

Microtubule-associated protein 2c (MAP2c) is a 49-kDa intrinsically disordered protein regulating the dynamics of microtubules in developing neurons. MAP2c differs from its sequence homologue Tau in the pattern and kinetics of phosphorylation by cAMP-dependent protein kinase (PKA). Moreover, the mechanisms through which MAP2c interacts with its binding partners and the conformational changes and dynamics associated with these interactions remain unclear. Here, we used NMR relaxation and paramagnetic relaxation enhancement techniques to determine the dynamics and long-range interactions within MAP2c. The relaxation rates revealed large differences in flexibility of individual regions of MAP2c, with the lowest flexibility observed in the known and proposed binding sites. Quantitative conformational analyses of chemical shifts, small-angle X-ray scattering (SAXS), and paramagnetic relaxation enhancement measurements disclosed that MAP2c regions interacting with important protein partners, including Fyn tyrosine kinase, plectin, and PKA, adopt specific conformations. High populations of polyproline II and α-helices were found in Fyn- and plectin-binding sites of MAP2c, respectively. The region binding the regulatory subunit of PKA consists of two helical motifs bridged by a more extended conformation. Of note, although MAP2c and Tau did not differ substantially in their conformations in regions of high sequence identity, we found that they differ significantly in long-range interactions, dynamics, and local conformation motifs in their N-terminal domains. These results highlight that the N-terminal regions of MAP2c provide important specificity to its regulatory roles and indicate a close relationship between MAP2c's biological functions and conformational behavior.

Spectral density mapping at multiple magnetic fields suitable for (13)C NMR relaxation studies.

Standard spectral density mapping protocols, well suited for the analysis of (15)N relaxation rates, introduce significant systematic errors when applied to (13)C relaxation data, especially if the dynamics is dominated by motions with short correlation times (small molecules, dynamic residues of macromolecules). A possibility to improve the accuracy by employing cross-correlated relaxation rates and on measurements taken at several magnetic fields has been examined. A suite of protocols for analyzing such data has been developed and their performance tested. Applicability of the proposed protocols is documented in two case studies, spectral density mapping of a uniformly labeled RNA hairpin and of a selectively labeled disaccharide exhibiting highly anisotropic tumbling. Combination of auto- and cross-correlated relaxation data acquired at three magnetic fields was applied in the former case in order to separate effects of fast motions and conformational or chemical exchange. An approach using auto-correlated relaxation rates acquired at five magnetic fields, applicable to anisotropically moving molecules, was used in the latter case. The results were compared with a more advanced analysis of data obtained by interpolation of auto-correlated relaxation rates measured at seven magnetic fields, and with the spectral density mapping of cross-correlated relaxation rates. The results showed that sufficiently accurate values of auto- and cross-correlated spectral density functions at zero and (13)C frequencies can be obtained from data acquired at three magnetic fields for uniformly (13)C-labeled molecules with a moderate anisotropy of the rotational diffusion tensor. Analysis of auto-correlated relaxation rates at five magnetic fields represents an alternative for molecules undergoing highly anisotropic motions.

Spectral density mapping protocols for analysis of molecular motions in disordered proteins.

Spectral density mapping represents the method of choice for investigations of molecular motions of intrinsically disordered proteins (IDPs). However, the current methodology has been developed for well-folded proteins. In order to find conditions for a reliable analysis of relaxation of IDPs, accuracy of the current reduced spectral density mapping protocols applied to IDPs was examined and new spectral density mapping methods employing cross-correlated relaxation rates have been designed. Various sources of possible systematic errors were analyzed theoretically and the presented approaches were tested on a partially disordered protein, delta subunit of bacterial RNA polymerase. Results showed that the proposed protocols provide unbiased description of molecular motions of IDPs and allow to separate slow exchange from fast dynamics.