Completely automated, highly error-tolerant macromolecular structure determination from multidimensional nuclear overhauser enhancement spectra and chemical shift assignments

The major rate-limiting step in high-throughput NMR protein structure determination involves the calculation of a reliable initial fold, the elimination of incorrect nuclear Overhauser enhancement (NOE) assignments, and the resolution of NOE assignment ambiguities. We present a robust approach to automatically calculate structures with a backbone coordinate accuracy of 1.0-1.5 A from datasets in which as much as 80% of the long-range NOE information (i.e., between residues separated by more than five positions in the sequence) is incorrect. The current algorithm differs from previously published methods in that it has been expressly designed to ensure that the results from successive cycles are not biased by the global fold of structures generated in preceding cycles. Consequently, the method is highly error tolerant and is not easily funnelled down an incorrect path in either three-dimensional structure or NOE assignment space. The algorithm incorporates three main features: a linear energy function representation of the NOE restraints to allow maximization of the number of simultaneously satisfied restraints during the course of simulated annealing; a method for handling the presence of multiple possible assignments for each NOE cross-peak which avoids local minima by treating each possible assignment as if it were an independent restraint; and a probabilistic method to permit both inactivation and reactivation of all NOE restraints on the fly during the course of simulated annealing. NOE restraints are never removed permanently, thereby significantly reducing the likelihood of becoming trapped in a false minimum of NOE assignment space. The effectiveness of the algorithm is demonstrated using completely automatically peak-picked experimental NOE data from two proteins: interleukin-4 (136 residues) and cyanovirin-N (101 residues). The limits of the method are explored using simulated data on the 56-residue B1 domain of Streptococcal protein G.     

Practical aspects of (1)H transverse paramagnetic relaxation enhancement measurements on macromolecules

The use of (1)H transverse paramagnetic relaxation enhancement (PRE) has seen a resurgence in recent years as method for providing long-range distance information for structural studies and as a probe of large amplitude motions and lowly populated transient intermediates in macromolecular association. In this paper we discuss various practical aspects pertaining to accurate measurement of PRE (1)H transverse relaxation rates (Gamma(2)). We first show that accurate Gamma(2) rates can be obtained from a two time-point measurement without requiring any fitting procedures or complicated error estimations, and no additional accuracy is achieved from multiple time-point measurements recorded in the same experiment time. Optimal setting of the two time-points that minimize experimental errors is also discussed. Next we show that the simplistic single time-point measurement that has been commonly used in the literature, can substantially underestimate the true value of Gamma(2), unless a relatively long repetition delay is employed. We then examine the field dependence of Gamma(2), and show that Gamma(2) exhibits only a very weak field dependence at high magnetic fields typically employed in macromolecular studies. The theoretical basis for this observation is discussed. Finally, we investigate the impact of contamination of the paramagnetic sample by trace amounts (5%) of the corresponding diamagnetic species on the accuracy of Gamma(2) measurements. Errors in Gamma(2) introduced by such diamagnetic contamination are potentially sizeable, but can be significantly reduced by using a relatively short time interval for the two time-point Gamma(2) measurement.     

Characterizing Methyl‐Bearing Side Chain Contacts and Dynamics Mediating Amyloid β Protofibril Interactions Using 13Cmethyl‐DEST and Lifetime Line Broadening

Many details pertaining to the formation and interactions of protein aggregates associated with neurodegenerative diseases are invisible to conventional biophysical techniques. We recently introduced ¹⁵N dark‐state exchange saturation transfer (DEST) and ¹⁵N lifetime line‐broadening to study solution backbone dynamics and position‐specific binding probabilities for amyloid β (Aβ) monomers in exchange with large (2–80 MDa) protofibrillar Aβ aggregates. Here we use ¹³C_methyl DEST and lifetime line‐broadening to probe the interactions and dynamics of methyl‐bearing side chains in the Aβ‐protofibril‐bound state. We show that all methyl groups of Aβ40 populate direct‐contact bound states with a very fast effective transverse relaxation rate, indicative of side‐chain‐mediated direct binding to the protofibril surface. The data are consistent with position‐specific enhancements of ¹³C_methyl‐${R{{{\rm tethered}\hfill \atop 2\hfill}}}$ values in tethered states, providing further insights into the structural ensemble of the protofibril‐bound state.     

Using conjoined rigid body/torsion angle simulated annealing to determine the relative orientation of covalently linked protein domains from dipolar couplings

A simple and robust method for determining the relative orientations of covalently linked protein domains using conjoined rigid body/torsion angle dynamics simulated annealing on the basis of residual dipolar couplings is presented. In this approach each domain is treated as a rigid body and the relevant degrees of conformational freedom are restricted to the backbone torsion angles (phi, psi) of the linker between the domains. By this means translational information afforded by the presence of an intact linker is preserved. We illustrate this approach using the domain-swapped dimer of the HIV-inactivating protein cyanovirin-N as an example.     

Sources of and solutions to problems in the refinement of protein NMR structures against torsion angle potentials of mean force

It is often the case that a substantial number of torsion angles (both backbone and sidechain) in structures of proteins and nucleic acids determined by NMR are found in physically unlikely and energetically unfavorable conformations. We have previously proposed a database-derived potential of mean force comprising one-, two-, three-, and four-dimensional potential surfaces which describe the likelihood of various torsion angle combinations to bias conformational sampling during simulated annealing refinement toward those regions that are populated in very high resolution (< or =1.75 A) crystal structures. We now note a shortcoming of our original implementation of this approach: namely, the forces it places on atoms are very rough. When the density of experimental restraints is low, this roughness can both hinder convergence to commonly populated regions of torsion angle space and reduce overall conformational sampling. In this paper we describe a modification that completely eliminates these problems by replacing the original potential surfaces by a sum of multidimensional Gaussian functions. Structures refined with the new Gaussian implementation now simultaneously enjoy excellent global sampling and excellent local choices of torsion angles.     

Numerical solution of the Hodgkin-Huxley equations in a moving coordinate system. Simulation of nerve impulse transmission over long distances

The theory required for the solution of the Hodgkin-Huxley equations for the transmission of the nerve impulse in a moving coordinate system are presented. Using this theory, simulations of the transmission of the nerve impulse over large distances (e.g., 1 m) may be carried out rapidly and accurately. The above theory may be applied to other diffusion problems by appropriate modification to the problem concerned.     

Spin-state selective carbon-detected HNCO with TROSY optimization in all dimensions and double echo-antiecho sensitivity enhancement in both indirect dimensions

A carbon-detected TROSY-optimized experiment correlating 1HN, 15N, and 13C' resonances, referred to as c-TROSY-HNCO is presented, in which the 1HN and 15N TROSY effects are maintained in both indirect dimensions, while the directly detected 13C' is doubly TROSY-optimized with respect to 1HN and 15N. A new strategy for sensitivity enhancement, the so-called double echo-antiecho (dEA), is described and implemented in the c-TROSY-HNCO experiment. dEA offers sensitivity enhancement of square root of 2 in both indirect dimensions and is generally applicable to many multidimensional experiments. A carbon-detected HNCO experiment, c-HNCO, without TROSY optimization and sensitivity enhancement is also designed for comparison purposes. Relaxation simulations show that for a protein with a rotational correlation time of 10 ns or larger, the c-TROSY-HNCO experiment displays comparable or higher signal-to-noise (S/N) ratios than the c-HNCO experiment, although the former selects only 1/4 of the initial magnetization relative to the later. The high resolution afforded in the directly detected carbon dimension allows direct measurement of the doublet splitting to extract 1JCalphaC' scalar and 1DCalphaC' residual dipolar couplings. Simulations indicate that the c-TROSY-HNCO experiment offers higher precision (lower uncertainty) compared to the c-HNCO experiment for larger proteins. The experiments are applied to 15N/13C/2H/[Leu,Val]-methyl-protonated IIBMannose, a protein of molecular mass 18.6 kDa with a correlation time of approximately 10 ns at 30 degrees C. The experimental pairwise root-mean-square deviation for the measured 1JCalphaC' couplings obtained from duplicate experiments is 0.77 Hz. By directly measuring the doublet splitting, the experiments described here are expected to be much more tolerant to nonuniform values of 1JCalphaC' (or 1JCalphaC' + 1DCalphaC' for aligned samples) and pulse imperfections due to the smaller number of applied pulses in the "out-and-stay" coherence transfer in the c-HNCO-TROSY experiment relative to conventional 1H-detected "out-and-back" quantitative J correlation experiments. A carbon-detected TROSY-optimized experiment correlating 1HN, 15N, and 13C' resonances, referred to as c-TROSY-HNCO is presented, in which the 1HN and 15N TROSY effects are maintained in both indirect dimensions, while the directly detected 13C' is doubly TROSY-optimized with respect to 1HN and 15N. A new strategy for sensitivity enhancement, the so-called double echo-antiecho (dEA), is described and implemented in the c-TROSY-HNCO experiment. dEA offers sensitivity enhancement of in both indirect dimensions and is generally applicable to many multidimensional experiments.