Adam D. Schuyler

Nonuniform Sampling and Maximum Entropy Reconstruction in Multidimensional NMR

NMR spectroscopy is one of the most powerful and versatile analytic tools available to chemists. The discrete Fourier transform (DFT) played a seminal role in the development of modern NMR, including the multidimensional methods that are essential for characterizing complex biomolecules. However, it suffers from well-known limitations: chiefly the difficulty in obtaining high-resolution spectral estimates from short data records. Because the time required to perform an experiment is proportional to the number of data samples, this problem imposes a sampling burden for multidimensional NMR experiments. At high magnetic field, where spectral dispersion is greatest, the problem becomes particularly acute. Consequently multidimensional NMR experiments that rely on the DFT must either sacrifice resolution in order to be completed in reasonable time or use inordinate amounts of time to achieve the potential resolution afforded by high-field magnets. Maximum entropy (MaxEnt) reconstruction is a non-Fourier method of spectrum analysis that can provide high-resolution spectral estimates from short data records. It can also be used with nonuniformly sampled data sets. Since resolution is substantially determined by the largest evolution time sampled, nonuniform sampling enables high resolution while avoiding the need to uniformly sample at large numbers of evolution times. The Nyquist sampling theorem does not apply to nonuniformly sampled data, and artifacts that occur with the use of nonuniform sampling can be viewed as frequency-aliased signals. Strategies for suppressing nonuniform sampling artifacts include the careful design of the sampling scheme and special methods for computing the spectrum. Researchers now routinely report that they can complete an N-dimensional NMR experiment 3(N-1) times faster (a 3D experiment in one ninth of the time). As a result, high-resolution three- and four-dimensional experiments that were prohibitively time consuming are now practical. Conversely, tailored sampling in the indirect dimensions has led to improved sensitivity. Further advances in nonuniform sampling strategies could enable further reductions in sampling requirements for high resolution NMR spectra, and the combination of these strategies with robust non-Fourier methods of spectrum analysis (such as MaxEnt) represent a profound change in the way researchers conduct multidimensional experiments. The potential benefits will enable more advanced applications of multidimensional NMR spectroscopy to study biological macromolecules, metabolomics, natural products, dynamic systems, and other areas where resolution, sensitivity, or experiment time are limiting. Just as the development of multidimensional NMR methods presaged multidimensional methods in other areas of spectroscopy, we anticipate that nonuniform sampling approaches will find applications in other forms of spectroscopy.

Normal mode analysis of proteins: a comparison of rigid cluster modes with Cα coarse graining

Abstract The ability to infer dynamic motions from an equilibrium (static) conformation of a protein can be essential in establishing structure–function relationships. In particular, the low-frequency motions are of functional interest because statistical mechanics predicts these motions will have the largest amplitudes. In this paper, we address the computational cost of normal mode analysis (NMA) applied to a C α -based elastic network model (C α -NMA) and present a new coarse-grained rigid-body-based analysis (cluster-NMA). This new method represents a protein as a collection of rigid bodies interconnected with harmonic potentials. This representation produces reduced degree-of-freedom (DOF) equations of motion (EOMs) which, even in the case of large structures (10 3+ residues), enables the computation of normal modes to be done on a desktop PC. We present the complete theory and analysis of cluster-NMA and also include its application to a variety of structures. The results of the new method are compared with C α -NMA and it is shown that cluster-NMA produces very good approximations to the lowest modes at a fraction of the computational cost.

Sparse sampling methods in multidimensional NMR

Although the discrete Fourier transform played an enabling role in the development of modern NMR spectroscopy, it suffers from a well-known difficulty providing high-resolution spectra from short data records. In multidimensional NMR experiments, so-called indirect time dimensions are sampled parametrically, with each instance of evolution times along the indirect dimensions sampled via separate one-dimensional experiments. The time required to conduct multidimensional experiments is directly proportional to the number of indirect evolution times sampled. Despite remarkable advances in resolution with increasing magnetic field strength, multiple dimensions remain essential for resolving individual resonances in NMR spectra of biological macromolecues. Conventional Fourier-based methods of spectrum analysis limit the resolution that can be practically achieved in the indirect dimensions. Nonuniform or sparse data collection strategies, together with suitable non-Fourier methods of spectrum analysis, enable high-resolution multidimensional spectra to be obtained. Although some of these approaches were first employed in NMR more than two decades ago, it is only relatively recently that they have been widely adopted. Here we describe the current practice of sparse sampling methods and prospects for further development of the approach to improve resolution and sensitivity and shorten experiment time in multidimensional NMR. While sparse sampling is particularly promising for multidimensional NMR, the basic principles could apply to other forms of multidimensional spectroscopy.

Insulin-like growth factor-I for the treatment of amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease that affects both upper and lower motor neurons (MN) resulting in weakness, paralysis and subsequent death. Insulin-like growth factor-I (IGF-I) is a potent neurotrophic factor that has neuroprotective properties in the central and peripheral nervous systems. Due to the efficacy of IGF-I in the treatment of other diseases and its ability to promote neuronal survival, IGF-I is being extensively studied in ALS therapeutic trials. This review covers in vitro and in vivo studies examining the efficacy of IGF-I in ALS model systems and also addresses the mechanisms by which IGF-I asserts its effects in these models, the status of the IGF-I system in ALS patients, results of clinical trials, and the need for the development of better delivery mechanisms to maximize IGF-I efficacy. The knowledge obtained from these studies suggests that IGF-I has the potential to be a safe and efficacious therapy for ALS.

Data Sampling in Multidimensional NMR: Fundamentals and Strategies

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (free induction decay) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform, the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records were already well understood, and despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. In this chapter we review the fundamentals of uniform and nonuniform sampling methods in one- and multidimensional NMR.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure–function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster‐NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of β1,4‐galactosyltransferase‐T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed. Proteins 2009.

Literature-based discovery of diabetes- and ROS-related targets

BackgroundReactive oxygen species (ROS) are known mediators of cellular damage in multiple diseases including diabetic complications. Despite its importance, no comprehensive database is currently available for the genes associated with ROS.MethodsWe present ROS- and diabetes-related targets (genes/proteins) collected from the biomedical literature through a text mining technology. A web-based literature mining tool, SciMiner, was applied to 1,154 biomedical papers indexed with diabetes and ROS by PubMed to identify relevant targets. Over-represented targets in the ROS-diabetes literature were obtained through comparisons against randomly selected literature. The expression levels of nine genes, selected from the top ranked ROS-diabetes set, were measured in the dorsal root ganglia (DRG) of diabetic and non-diabetic DBA/2J mice in order to evaluate the biological relevance of literature-derived targets in the pathogenesis of diabetic neuropathy.ResultsSciMiner identified 1,026 ROS- and diabetes-related targets from the 1,154 biomedical papers (http://jdrf.neurology.med.umich.edu/ROSDiabetes/). Fifty-three targets were significantly over-represented in the ROS-diabetes literature compared to randomly selected literature. These over-represented targets included well-known members of the oxidative stress response including catalase, the NADPH oxidase family, and the superoxide dismutase family of proteins. Eight of the nine selected genes exhibited significant differential expression between diabetic and non-diabetic mice. For six genes, the direction of expression change in diabetes paralleled enhanced oxidative stress in the DRG.ConclusionsLiterature mining compiled ROS-diabetes related targets from the biomedical literature and led us to evaluate the biological relevance of selected targets in the pathogenesis of diabetic neuropathy.

Strategic approaches to developing drug treatments for ALS

Significant progress in understanding the cellular mechanisms of motor neuron degeneration in amyotrophic lateral sclerosis (ALS) has not been matched with the development of therapeutic strategies to prevent disease progression. The multiple potential causes and relative rarity of the disease are two significant factors that make drug development and assessment in clinical trials extremely difficult. We review recent progress in promoting therapeutics into clinical trials and highlight the value of moderate throughput screening for the acceleration and improvement of drug design.

Knowledge-based nonuniform sampling in multidimensional NMR

The full resolution afforded by high-field magnets is rarely realized in the indirect dimensions of multidimensional NMR experiments because of the time cost of uniformly sampling to long evolution times. Emerging methods utilizing nonuniform sampling (NUS) enable high resolution along indirect dimensions by sampling long evolution times without sampling at every multiple of the Nyquist sampling interval. While the earliest NUS approaches matched the decay of sampling density to the decay of the signal envelope, recent approaches based on coupled evolution times attempt to optimize sampling by choosing projection angles that increase the likelihood of resolving closely-spaced resonances. These approaches employ knowledge about chemical shifts to predict optimal projection angles, whereas prior applications of tailored sampling employed only knowledge of the decay rate. In this work we adapt the matched filter approach as a general strategy for knowledge-based nonuniform sampling that can exploit prior knowledge about chemical shifts and is not restricted to sampling projections. Based on several measures of performance, we find that exponentially weighted random sampling (envelope matched sampling) performs better than shift-based sampling (beat matched sampling). While shift-based sampling can yield small advantages in sensitivity, the gains are generally outweighed by diminished robustness. Our observation that more robust sampling schemes are only slightly less sensitive than schemes highly optimized using prior knowledge about chemical shifts has broad implications for any multidimensional NMR study employing NUS. The results derived from simulated data are demonstrated with a sample application to PfPMT, the phosphoethanolamine methyltransferase of the human malaria parasite Plasmodium falciparum.

Random phase detection in multidimensional NMR

Despite advances in resolution accompanying the development of high-field superconducting magnets, biomolecular applications of NMR require multiple dimensions in order to resolve individual resonances, and the achievable resolution is typically limited by practical constraints on measuring time. In addition to the need for measuring long evolution times to obtain high resolution, the need to distinguish the sign of the frequency constrains the ability to shorten measuring times. Sign discrimination is typically accomplished by sampling the signal with two different receiver phases or by selecting a reference frequency outside the range of frequencies spanned by the signal and then sampling at a higher rate. In the parametrically sampled (indirect) time dimensions of multidimensional NMR experiments, either method imposes an additional factor of 2 sampling burden for each dimension. We demonstrate that by using a single detector phase at each time sample point, but randomly altering the phase for different points, the sign ambiguity that attends fixed single-phase detection is resolved. Random phase detection enables a reduction in experiment time by a factor of 2 for each indirect dimension, amounting to a factor of 8 for a four-dimensional experiment, albeit at the cost of introducing sampling artifacts. Alternatively, for fixed measuring time, random phase detection can be used to double resolution in each indirect dimension. Random phase detection is complementary to nonuniform sampling methods, and their combination offers the potential for additional benefits. In addition to applications in biomolecular NMR, random phase detection could be useful in magnetic resonance imaging and other signal processing contexts.