The quality of molecular mechanics force fields is vital for the accurate in silico characterization of proteins. However, the development of better force fields has been a formidable challenge. Important improvements in force fields have been made recently; for example, CHARMM22/CMAP [1] and Ambers ff99SB [2] have been validated for several proteins by comparison of experimental NMR data, including spin relaxation data [1][2][3] and dipolar couplings, [4] with those predicted by molecular dynamics (MD) simulations. Another type of NMR observable is the chemical shift whose relationship to three-dimensional (3D) protein structures is increasingly well understood.[5] A recent comparison of calculated and experimental protein 13 C chemical shifts suggests that there is considerable room for additional improvements of the force field. [6] In spite of their capacity to rigorously cross-validate MD trajectories, NMR parameters of proteins have not been used to actively guide the improvement of protein potentials. For each new combination of force-field parameters, weeks of computing time are required to generate new MD trajectories of whole proteins, thereby rendering a systematic exploration of force-field parameters prohibitively expensive. Therefore, past force-field developments have mostly relied upon quantum chemical calculations and spectroscopic data of small molecules and protein fragments.Herein, we introduce a new approach for the optimization of force fields that is applicable to fully intact proteins for which NMR chemical shifts (or other NMR parameters) are available. To overcome the computational cost barrier, we reweight a parent trajectory performed with the original force field (V old ) for a new test force field (V new ) by using Boltzmanns relationship [Eq. (1) where p old (j) and p new (j) are the relative weights and V old (j) and V new (j) are the potential energies of a snapshot j for the old and new force field, respectively; k is Boltzmanns constant and T is the simulation temperature. Although reweighting is a common tool for enhancing conformational sampling, [7] it has not been used for force-field optimization directly applied to intact proteins.Our approach starts with the calculation of chemical shifts of all carbon nuclei Ca, Cb, and C' for each snapshot of the parent MD trajectory, which are then stored for subsequent analysis. Time-averaged chemical shifts are calculated with equal weights, p old (j) = 1/N, for all N snapshots and compared with the experimental chemical shifts by means of the rootmean-square deviation (RMSD) in ppm. The force field is then iteratively revised using the downhill simplex minimization algorithm, which in turn changes the weight of each snapshot according to Equation (1) and thereby allows a systematic improvement of the agreement between the experimental chemical shifts and the back-calculated average shifts from the new weights p new (j). In this way, a vast number of trial potentials can be screened for entire proteins through the reuse of the parent...

Despite their importance in macromolecular interactions and functions, the dynamics of lysine side-chain amino groups in proteins are not well understood. In this study, we have developed the methodology for the investigations of the dynamics of lysine NH3(+) groups by NMR spectroscopy and computation. By using 1H−15N heteronuclear correlation experiments optimized for 15NH3(+) moieties, we have analyzed the dynamic behavior of individual lysine NH3(+) groups in human ubiquitin at 2 °C and pH 5. We modified the theoretical framework developed previously for CH3 groups and used it to analyze 15N relaxation data for the NH3(+) groups. For six lysine NH3(+) groups out of seven in ubiquitin, we have determined model-free order parameters, correlation times for bond rotation, and reorientation of the symmetry axis occurring on a pico- to nanosecond time scale. From CPMG relaxation dispersion experiment for lysine NH3(+) groups, slower dynamics occurring on a millisecond time scale have also been detected for Lys27. The NH3(+) groups of Lys48, which plays a key role as the linkage site in ubiquitination for proteasomal degradation, was found to be highly mobile with the lowest order parameter among the six NH3(+) groups analyzed by NMR. We compared the experimental order parameters for the lysine NH3(+) groups with those from a 1 μs molecular dynamics simulation in explicit solvent and found good agreement between the two. Furthermore, both the computer simulation and the experimental correlation times for the bond rotations of NH3(+) groups suggest that their hydrogen bonding is highly dynamic with a subnanosecond lifetime. This study demonstrates the utility of combining NMR experiment and simulation for an in-depth characterization of the dynamics of these functionally most important side-chains of ubiquitin.

Small oligomers formed early in the process of amyloid fibril formation may be the major toxic species in Alzheimer's disease. We investigate the early stages of amyloid aggregation for the tau fragment AcPHF6 (Ac-VQIVYK-NH2) using an implicit solvent all-atom model and extensive Monte Carlo simulations of 12, 24, and 36 chains. A variety of small metastable aggregates form and dissolve until an aggregate of a critical size and conformation arises. However, the stable oligomers, which are β-sheet-rich and feature many hydrophobic contacts, are not always growth-ready. The simulations indicate instead that these supercritical oligomers spend a lengthy period in equilibrium in which considerable reorganization takes place accompanied by exchange of chains with the solution. Growth competence of the stable oligomers correlates with the alignment of the strands in the β-sheets. The larger aggregates seen in our simulations are all composed of two twisted β-sheets, packed against each other with hydrophobic side chains at the sheet–sheet interface. These β-sandwiches show similarities with the proposed steric zipper structure for PHF6 fibrils but have a mixed parallel/antiparallel β-strand organization as opposed to the parallel organization found in experiments on fibrils. Interestingly, we find that the fraction of parallel β-sheet structure increases with aggregate size. We speculate that the reorganization of the β-sheets into parallel ones is an important rate-limiting step in the formation of PHF6 fibrils.