A comparison of HSQC and HMQC pulse schemes for recording (1)H[bond](13)C correlation maps of protonated methyl groups in highly deuterated proteins is presented. It is shown that HMQC correlation maps can be as much as a factor of 3 more sensitive than their HSQC counterparts and that the sensitivity gains result from a TROSY effect that involves cancellation of intra-methyl dipolar relaxation interactions. (1)H[bond](13)C correlation spectra are recorded on U-[(15)N,(2)H], Ile delta 1-[(13)C,(1)H] samples of (i) malate synthase G, a 723 residue protein, at 37 and 5 degrees C, and of (ii) the protease ClpP, comprising 14 identical subunits, each with 193 residues (305 kDa), at 5 degrees C. The high quality of HMQC spectra obtained in short measuring times strongly suggests that methyl groups will be useful probes of structure and dynamics in supramolecular complexes.

New NMR experiments for the measurement of side-chain dynamics in high molecular weight ( approximately 100 kDa) proteins are presented. The experiments quantify (2)H spin relaxation rates in (13)CH(2)D or (13)CHD(2) methyl isotopomers and, for applications to large systems, offer significant gains both in sensitivity (2-3-fold) and resolution over previously published HSQC schemes. The methodology has been applied to investigate Ile dynamics in the 723-residue, single polypeptide chain enzyme, malate synthase G. Methyl-axis order parameters, S(axis), characterizing the amplitudes of motion of the methyl groups, have been derived from both (13)CH(2)D and (13)CHD(2) probes and are in excellent agreement. The distribution of order parameters is trimodal, reflecting the range of dynamics that are available to Ile residues. A reasonable correlation is noted between and inverse temperature factors from X-ray studies of the enzyme. The proposed methodology significantly extends the range of protein systems for which side-chain dynamics can be studied.

In TROSY experiments, relaxation interference effects are exploited to produce spectra with improved resolution and signal-to-noise. Such experiments cannot be explained using the standard product operator formalism, but must instead be analyzed at the level of individual density matrix elements. Herein we illustrate this point using an example from our recent work on a TROSY 1 H-13 C correlation experiment for methyl groups in large proteins. Methyl groups are useful spectroscopic probes of protein structure and dynamics because they are found throughout the critical core region of a folded protein and their resonances are intense and well dispersed. Additionally, it is relatively easy to produce highly deuterated protein samples that are 1 H, 13 C labeled at selected methyl positions, facilitating studies of high molecular weight systems. Methyl groups are relaxed by a network of 1 H-1 H and 1 H-13 C dipolar interactions, and in the macromolecular limit the destructive interference of these interactions leads to unusually slow relaxation for certain density matrix elements. It is this slow relaxation that forms the basis for TROSY experiments. We present a detailed analysis of evolution and relaxation during HSQC and HMQC pulse schemes for the case of a 13 C 1 H 3 spin system attached to a macromolecule. We show that the HMQC sequence is already optimal with respect to the TROSY effect, offering a significant sensitivity enhancement over HSQC at any spectrometer field strength. The gain in sensitivity is established experimentally using samples of two large proteins, malate synthase G (81.4 kDa) and ClpP protease (305 kDa), both highly deuterated and selectively 1 H, 13 C-labeled at isoleucine d methyl positions.

We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes an algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.PACS numbers: 03.67. Lx, 03.67.Pp, A computer that uses the laws of quantum mechanics to store and manipulate information could in theory perform certain tasks such as searching [1] and factoring [2] with incredible efficiency. The most critical problem that must be solved to make quantum computing possible on a useful scale is decoherence, the inevitable process of entanglement between a quantum computer and its environment. Decoherence causes the superposition states that carry information within the computer to decay rapidly. Several solutions to the decoherence problem have been proposed (for a review, see [3]). One technique, quantum error avoidance, calls for information within the computer to be carried exclusively by quantum states that are not adversely affected by decoherence [4,5,6,7] (for a review, see [8]). Here we present the first experimental proof that a nontrivial quantum computation can be protected against decoherence [9]. Using quantum error avoidance, we have constructed a nuclear magnetic resonance quantum computer [10,11,12] which is unaffected by certain types of decoherence. Our computer successfully executes Grover's quantum search algorithm [1] in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.Decoherence is typically characterized by the decay of off-diagonal elements in a system's density matrix ρ. Formally, decoherence takes the system from state ρ i to a statewhere the Kraus operators E d describe transformations that may result from the system-environment coupling (theyWhen the coupling between a quantum system and its environment possesses an element of symmetry, some of the system's states will be immune to decoherence [4,5,6,7,8]. These states span a decoherence-free subspace (DFS). The quantum computer we have constructed comprises two decoherence-free logical quantum bits (qubits [3]), encoded in the DFSs of four noisy physical qubits. The code protects against multiple-qubit errors [7]: To satisfy the symmetry condition for the existence of DFSs, we assume the system-environment coupling affects certain pairs of qubits rather than affecting each qubit independently. Note that this error model is different from the popular "collective decoherence" model [4,5,6].The multiple qubit errors model is relevant to a number of physical systems recently used as quantum computers [7]. For example, t...

A comparison of three labeling strategies for studies involving side chain methyl groups in high molecular weight proteins, using 13CH3, 13CH2D, and 13CHD2 methyl isotopomers, is presented. For each labeling scheme, 1H-13C pulse sequences that give optimal resolution and sensitivity are identified. Three highly deuterated samples of a 723 residue enzyme, malate synthase G, with 13CH3, 13CH2D, and 13CHD2 labeling in Ile delta1 positions, are used to test the pulse sequences experimentally, and a rationalization of each sequence's performance based on a product operator formalism that focuses on individual transitions is presented. The HMQC pulse sequence has previously been identified as a transverse relaxation optimized experiment for 13CH3-labeled methyl groups attached to macromolecules, and a zero-quantum correlation pulse scheme (13CH3 HZQC) has been developed to further improve resolution in the indirectly detected dimension. We present a modified version of the 13CH3 HZQC sequence that provides improved sensitivity by using the steady-state magnetization of both 13C and 1H spins. The HSQC and HMQC spectra of 13CH2D-labeled methyl groups in malate synthase G are very poorly resolved, but we present a new pulse sequence, 13CH2D TROSY, that exploits cross-correlation effects to record 1H-13C correlation maps with dramatically reduced linewidths in both dimensions. Well-resolved spectra of 13CHD2-labeled methyl groups can be recorded with HSQC or HMQC; a new 13CHD2 HZQC sequence is described that provides improved resolution with no loss in sensitivity in the applications considered here. When spectra recorded on samples prepared with the three isotopomers are compared, it is clear that the 13CH3 labeling strategy is the most beneficial from the perspective of sensitivity (gains > or =2.4 relative to either 13CH2D or 13CHD2 labeling), although excellent resolution can be obtained with any of the isotopomers using the pulse sequences presented here.