Time Optimal Control in Spin Systems

In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. Moreover, the general proofs are no more difficult than the specific problems of current interest. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group, what is the minimum time required to steer the system from some initial point to a specified final point? In NMR spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two spin system.Comment: 20 Pages, 3 figure

The Fantastic Four: A plug 'n' play set of optimal control pulses for enhancing nmr spectroscopy

We present highly robust, optimal control-based shaped pulses designed to replace all 90{\deg} and 180{\deg} hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substituted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90{\deg} and 180{\deg} point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1 ms pulses provide uniform performance over resonance offsets of 20 kHz (1H) and 35 kHz (13C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of (+/-)15% (1H) and (+/-)10% (13C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600 MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).Comment: 28 pages, 19 figure

Origin and removal of mixed-phase artifacts in gradient sensitivity enhanced heteronuclear single quantum correlation spectra

Here we describe phasing anomalies observed in gradient sensitivity enhanced 15N-1H HSQC spectra, and analyze their origin. It is shown that, as a result of 15N off-resonance effects, dispersive contributions to the 1H signal become detectable, and lead to 15N-offset dependent phase errors. Strategies that effectively suppress these artifacts are presented

The exchange activities of [Fe] hydrogenase (iron–sulfur-cluster-free hydrogenase) from methanogenic archaea in comparison with the exchange activities of [FeFe] and [NiFe] hydrogenases

[Fe] hydrogenase (iron–sulfur-cluster-free hydrogenase) catalyzes the reversible reduction of methenyltetrahydromethanopterin (methenyl-H4MPT+) with H2 to methylene-H4MPT, a reaction involved in methanogenesis from H2 and CO2 in many methanogenic archaea. The enzyme harbors an iron-containing cofactor, in which a low-spin iron is complexed by a pyridone, two CO and a cysteine sulfur. [Fe] hydrogenase is thus similar to [NiFe] and [FeFe] hydrogenases, in which a low-spin iron carbonyl complex, albeit in a dinuclear metal center, is also involved in H2 activation. Like the [NiFe] and [FeFe] hydrogenases, [Fe] hydrogenase catalyzes an active exchange of H2 with protons of water; however, this activity is dependent on the presence of the hydride-accepting methenyl-H4MPT+. In its absence the exchange activity is only 0.01% of that in its presence. The residual activity has been attributed to the presence of traces of methenyl-H4MPT+ in the enzyme preparations, but it could also reflect a weak binding of H2 to the iron in the absence of methenyl-H4MPT+. To test this we reinvestigated the exchange activity with [Fe] hydrogenase reconstituted from apoprotein heterologously produced in Escherichia coli and highly purified iron-containing cofactor and found that in the absence of added methenyl-H4MPT+ the exchange activity was below the detection limit of the tritium method employed (0.1 nmol min−1 mg−1). The finding reiterates that for H2 activation by [Fe] hydrogenase the presence of the hydride-accepting methenyl-H4MPT+ is essentially required. This differentiates [Fe] hydrogenase from [FeFe] and [NiFe] hydrogenases, which actively catalyze H2/H2O exchange in the absence of exogenous electron acceptors

Asymmetry of 13C labeled 3-pyruvate affords improved site specific labeling of RNA for NMR spectroscopy

Selective isotopic labeling provides an unparalleled window within which to study the structure and dynamics of RNAs by high resolution NMR spectroscopy. Unlike commonly used carbon sources, the asymmetry of 13C-labeled pyruvate provides selective labeling in both the ribose and base moieties of nucleotides using E. coli variants, that until now were not feasible. Here we show that an E. coli mutant strain that lacks succinate and malate dehydrogenases (DL323) and grown on [3-13C]-pyruvate affords ribonucleotides with site specific labeling at C5′ (~95%) and C1′ (~42%) and minimal enrichment elsewhere in the ribose ring. Enrichment is also achieved at purine C2 and C8 (~95%) and pyrimidine C5 (~100%) positions with minimal labeling at pyrimidine C6 and purine C5 positions. These labeling patterns contrast with those obtained with DL323 E. coli grown on [1, 3-13C]-glycerol for which the ribose ring is labeled in all but the C4′ carbon position, leading to multiplet splitting of the C1′, C2′ and C3′ carbon atoms. The usefulness of these labeling patterns is demonstrated with a 27-nt RNA fragment derived from the 30S ribosomal subunit. Removal of the strong magnetic coupling within the ribose and base leads to increased sensitivity, substantial simplification of NMR spectra, and more precise and accurate dynamic parameters derived from NMR relaxation measurements. Thus these new labels offer valuable probes for characterizing the structure and dynamics of RNA that were previously limited by the constraint of uniformly labeled nucleotides

Selective 13C labeling of nucleotides for large RNA NMR spectroscopy using an E. coli strain disabled in the TCA cycle

Escherichia coli (E. coli) is an ideal organism to tailor-make labeled nucleotides for biophysical studies of RNA. Recently, we showed that adding labeled formate enhanced the isotopic enrichment at protonated carbon sites in nucleotides. In this paper, we show that growth of a mutant E. coli strain DL323 (lacking succinate and malate dehydrogenases) on 13C-2-glycerol and 13C-1,3-glycerol enables selective labeling at many useful sites for RNA NMR spectroscopy. For DL323 E. coli grown in 13C-2-glycerol without labeled formate, all the ribose carbon atoms are labeled except the C3′ and C5′ carbon positions. Consequently the C1′, C2′ and C4′ positions remain singlet. In addition, only the pyrimidine base C6 atoms are substantially labeled to ~96% whereas the C2 and C8 atoms of purine are labeled to ~5%. Supplementing the growth media with 13C-formate increases the labeling at C8 to ~88%, but not C2. Not unexpectedly, addition of exogenous formate is unnecessary for attaining the high enrichment levels of ~88% for the C2 and C8 purine positions in a 13C-1,3-glycerol based growth. Furthermore, the ribose ring is labeled in all but the C4′ carbon position, such that the C2′ and C3′ positions suffer from multiplet splitting but the C5′ position remains singlet and the C1′ position shows a small amount of residual C1′–C2′ coupling. As expected, all the protonated base atoms, except C6, are labeled to ~90%. In addition, labeling with 13C-1,3-glycerol affords an isolated methylene ribose with high enrichment at the C5′ position (~90%) that makes it particularly attractive for NMR applications involving CH2-TROSY modules without the need for decoupling the C4′ carbon. To simulate the tumbling of large RNA molecules, perdeuterated glycerol was added to a mixture of the four nucleotides, and the methylene TROSY experiment recorded at various temperatures. Even under conditions of slow tumbling, all the expected carbon correlations were observed, which indicates this approach of using nucleotides obtained from DL323 E. coli will be applicable to high molecular weight RNA systems

Signal enhancement in protein NMR using the spin-noise tuning optimum

We have assessed the potential of an alternative probe tuning strategy based on the spin-noise response for application in common high-resolution multi-dimensional biomolecular NMR experiments with water signal suppression on aqueous and salty samples. The method requires the adjustment of the optimal tuning condition, which may be offset by several 100 kHz from the conventional tuning settings using the noise response of the water protons as an indicator. Although the radio frequency-pulse durations are typically longer under such conditions, signal-to-noise gains of up to 22% were achieved. At salt concentrations up to 100 mM a substantial sensitivity gain was observed

Altered Metabolism of Growth Hormone Receptor Mutant Mice: A Combined NMR Metabonomics and Microarray Study

Growth hormone is an important regulator of post-natal growth and metabolism. We have investigated the metabolic consequences of altered growth hormone signaling in mutant mice that have truncations at position 569 and 391 of the intracellular domain of the growth hormone receptor, and thus exhibit either low (around 30% maximum) or no growth hormone-dependent STATS signaling respectively. These mutants result in altered liver metabolism, obesity and insulin resistance