General Expressions for Carr–Purcell–Meiboom–Gill Relaxation Dispersion for <i>N</i>‑Site Chemical Exchange

The Carr–Purcell–Meiboom–Gill (CPMG) nuclear magnetic resonance experiment is widely used to characterize chemical exchange phenomena in biological macromolecules. Theoretical expressions for the nuclear spin relaxation rate constant for two-site chemical exchange during CPMG pulse trains valid for all time scales are well-known as are descriptions of <i>N</i>-site exchange in the fast limit. We have obtained theoretical expressions for <i>N</i>-site exchange outside of the fast limit by using approximations to an average Liouvillian describing the decay of magnetization during a CPMG pulse train. We obtain general expressions for CPMG experiments for any <i>N</i>-site scheme and all experimentally accessible time scales. For sufficiently slow chemical exchange, we obtain closed-form expressions for the relaxation rate constant and a general characteristic polynomial for arbitrary kinetic schemes. Furthermore, we highlight features that qualitatively characterize CPMG curves obtained for various <i>N</i>-site kinetic topologies, quantitatively characterize CPMG curves obtained from systems in various <i>N</i>-site exchange situations, and test distinguishability of kinetic models

Interpreting Protein Structural Dynamics from NMR Chemical Shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged ¹H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail

Thermostability of Enzymes from Molecular Dynamics Simulations

Thermodynamic stability is a central requirement for protein function, and one goal of protein engineering is improvement of stability, particularly for applications in biotechnology. Herein, molecular dynamics simulations are used to predict <i>in vitro</i> thermostability of members of the bacterial ribonuclease HI (RNase H) family of endonucleases. The temperature dependence of the generalized order parameter, <i>S</i>, for four RNase H homologues, from psychrotrophic, mesophilic, and thermophilic organisms, is highly correlated with experimentally determined melting temperatures and with calculated free energies of folding at the midpoint temperature of the simulations. This study provides an approach for <i>in silico</i> mutational screens to improve thermostability of biologically and industrially relevant enzymes

Conformational Dynamics of the Partially Disordered Yeast Transcription Factor GCN4

Molecular dynamics (MD) simulations have been employed to study the conformational dynamics of the partially disordered DNA binding basic leucine zipper domain of the yeast transcription factor GCN4. We demonstrate that back-calculated NMR chemical shifts and spin-relaxation data provide complementary probes of the structure and dynamics of disordered protein states and enable comparisons of the accuracy of multiple MD trajectories. In particular, back-calculated chemical shifts provide a sensitive probe of the populations of residual secondary structure elements and helix capping interactions, while spin-relaxation calculations are sensitive to a combination of dynamic and structural factors. Back-calculated chemical shift and spin-relaxation data can be used to evaluate the populations of specific interactions in disordered states and identify regions of the phase space that are inconsistent with experimental measurements. The structural interactions that favor and disfavor helical conformations in the disordered basic region of the GCN4 bZip domain were analyzed in order to assess the implications of the structure and dynamics of the apo form for the DNA binding mechanism. The structural couplings observed in these experimentally validated simulations are consistent with a mechanism where the binding of a preformed helical interface would induce folding in the remainder of the protein, supporting a hybrid conformational selection/induced folding binding mechanism

Side Chain Dynamics of Carboxyl and Carbonyl Groups in the Catalytic Function of <i>Escherichia coli</i> Ribonuclease H

Many proteins use Asx and Glx (x = n, p, or u) side chains as key functional groups in enzymatic catalysis and molecular recognition. In this study, NMR spin relaxation experiments and molecular dynamics simulations are used to measure the dynamics of the side chain amide and carboxyl groups, ¹³C^γ/δ, in <i>Escherichia coli</i> ribonuclease HI (RNase H). Model-free analysis shows that the catalytic residues in RNase H are preorganized on ps–ns time scales via a network of electrostatic interactions. However, chemical exchange line broadening shows that these residues display significant conformational dynamics on μs–ms time scales upon binding of Mg²⁺ ions. Two groups of catalytic residues exhibit differential line broadening, implicating distinct reorganizational processes upon binding of metal ions. These results support the “mobile metal ion” hypothesis, which was inferred from structural studies of RNase H