In vivo comprehensive multiphase NMR

Traditionally, due to different hardware requirements, nuclear magnetic resonance (NMR) has developed as two separate fields: one dealing with solids, and one with solutions. Comprehensive multiphase (CMP) NMR combines all electronics and hardware (magic angle spinning [MAS], gradients, high power Radio Frequency (RF) handling, lock, susceptibility matching) into a universal probe that permits a comprehensive study of all phases (i.e., liquid, gel-like, semisolid, and solid), in intact samples. When applied in vivo, it provides unique insight into the wide array of bonds in a living system from the most mobile liquids (blood, fluids) through gels (muscle, tissues) to the most rigid (exoskeleton, shell). In this tutorial, the practical aspects of in vivo CMP NMR are discussed including: handling the organisms, rotor preparation, sample spinning, water suppression, editing experiments, and finishes with a brief look at the potential of other heteronuclei (²H, ¹⁵N, ¹⁹F, ³¹P) for in vivo research. The tutorial is aimed as a general resource for researchers interested in developing and applying MAS-based approaches to living organisms. Although the focus here is CMP NMR, many of the approaches can be adapted (or directly applied) using conventional high-resolution magic angle spinning, and in some cases, even standard solid-state NMR probes.     

An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems

A strategy for optimal nonlinear feedback control of randomlyexcited structural systems is proposed based on the stochastic averagingmethod for quasi-Hamiltonian systems and the stochastic dynamicprogramming principle. A randomly excited structural system isformulated as a quasi-Hamiltonian system and the control forces aredivided into conservative and dissipative parts. The conservative partsare designed to change the integrability and resonance of the associatedHamiltonian system and the energy distribution among the controlledsystem. After the conservative parts are determined, the system responseis reduced to a controlled diffusion process by using the stochasticaveraging method. The dissipative parts of control forces are thenobtained from solving the stochastic dynamic programming equation. Boththe responses of uncontrolled and controlled structural systems can bepredicted analytically. Numerical results for a controlled andstochastically excited Duffing oscillator and a two-degree-of-freedomsystem with linear springs and linear and nonlinear dampings, show thatthe proposed control strategy is very effective and efficient.     

Optimal controller placement in modal control of complex systems

Within the framework of modal control of large systems, a simple approach is advanced for the determination of optimal control configuration under an energy constraint, i.e., optimal locations of a limited number of controllers such that the total energy requirement for control is minimized. It is shown that the resulting design criterion is a simple function of projections of the control matrix onto components of eigenvectors associated with the affected eigenvalues. Furthermore, it is applicable to both single-input and multi-input systems. Systems possessing distinct complex eigenvalues are considered but the approach is equally applicable to other types of systems. Examples show that the minimum-energy control configuration also tends to be the most effective in terms of accomplishing control objectives.     

NMR studies of interionic interactions in N-methylformamide

The NMR chemical shifts of alkali and thallium(I) salts with various monovalent anions have been measured in N-methylformamide solution. Lithium-7 chemical shifts are virtually concentration and counter-ion independent, presumably due to an absence of direct cation-anion interactions. The sodium-23, potassium-39 and cesium-133 chemical shifts of the salts studied depend on the anion and vary linearly with the concentration. The observed behavior can be accounted for by the formation of collisional ion pairs. On the other hand, the thallium-205 chemical shifts of thallium(I) nitrate and perchlorate were anion-dependent and varied non-linearly with the salt concentration. These results are indicative of contact ion pair formation; formation constants were calculated to be 2.6±0.4 M ^–1 for TlNO ₃ and 1.7±0.5 M ^–1 for TlClO ₄ . The cesium-133 NMR spectra of several mixed electrolyte systems also have been measured in N-methylformamide solution. The¹³³Cs chemical shifts also change linearly with the concentrations of the salts added to 0.10 M CsI/NMF solutions. The influence of the anions on the chemical shifts is the same as that observed for cesium salts alone.     

Using Complex Integration to Compute Multivariate Normal Probabilities

Abstract

The execution of most multiple comparison methods involves, at least in part, the computation of the probability that a multivariate normal or multivarite t random vector is in a hyper-rectangle. In multiple comparison with a control as well as multiple comparison with the best (of normal populations or multinomial cell probabilities), the correlation matrix R of the random vector is nonsingular and of the form , where D is a diagonal matrix and is a known vector. It is well known that, in this case, the multivariate normal rectangular probability can be expressed as a one-dimensional integral and successfully computed using Gaussian quadrature techniques. However, in multiple comparison with the mean (sometimes called analysis of means) of normal distributions, all-pairwise comparisons of three normal distributions, as well as simultaneous inference on multinomial cell probabilities themselves, the correlation matrix is singular and of the form . It is not well known that, in this latter case, the multivariate normal rectangular probability can still be expressed as a single integral, albeit one with complex variables in its integrand. Previously published proofs of the validity of this expression either contained a gap or relied on a numerical demonstration, and this article will provide an analytic proof. Furthermore, we explain how this complex integral can be computed accurately, using Romberg integration of complex variables when the dimension is low, and using ?idák's inequality as an approximation when the dimension is at least moderate.     

Improvements in lipid suppression for 1H NMR-based metabolomics: Applications to solution-state and HR-MAS NMR in natural and in vivo samples

Proton nuclear magnetic resonance (NMR) spectra of intact biological samples often show strong contributions from lipids, which overlap with signals of interest from small metabolites. Pioneering work by Diserens et al. demonstrated that the relative differences in diffusivity and relaxation of lipids versus small metabolites could be exploited to suppress lipid signals, in high-resolution magic angle spinning (HR-MAS) NMR spectroscopy. In solution-state NMR, suspended samples can exhibit very broad water signals, which are challenging to suppress. Here, improved water suppression is incorporated into the sequence, and the Carr-Purcell-Meiboom-Gill sequence (CPMG) train is replaced with a low-power adiabatic spinlock that reduces heating and spectral artefacts seen with longer CPMG filters. The result is a robust sequence that works well in both HR-MAS as well as static solution-state samples. Applications are also extended to include in vivo organisms. For solution-state NMR, samples containing significant amount of fats such as milk and hemp hearts seeds are used to demonstrate the technique. For HR-MAS, living earthworms (Eisenia fetida) and freshwater shrimp (Hyalella azteca) are used for in vivo applications. Lipid suppression techniques are essential for non-invasive NMR-based analysis of biological samples with a high-lipid content and adds to the suite of experiments advantageous for in vivo environmental metabolomics.     

Effective boundary slip and wetting characteristics of water on substrates with effects of surface morphology

ABSTRACT

In the present study, molecular dynamics (MD) simulation was used to investigate the relationship between wetting behaviour and slip length on patterned substrates. We adopted two solid surfaces of Si(100) and graphite due to similarities in their intrinsic contact angle. Contact angle and apparent slip length were obtained using discrete simulations with the same thermodynamic states. In the present study, a number of questions regarding surface roughness and the problem of contact angle (θ) and slip length (L_s) are discussed. These questions include the relationship between θ and surface roughness, the characteristics used to describe the difference between static and dynamic fluid fields and the reason for a lack of multilayer sticking observed in the current cases. Our results indicate that the quasi-universal θ ? L_s equation proposed by Hung et al. (2008) is applicable to cases involving a Cassie-like nanoscale roughened surface. In contrast, in cases with a Wenzel-like nanostructure, the no-slip boundary conditions are independent of variations in the contact angle. The adoption of a Wenzel–Cassie hybrid model helped to verify that the fluid density inside the cavity is a critical indicator of wettability of the wall–fluid interface. Our results also demonstrate that ρ_{f, cav} is a critical property in the measurement of hydrodynamic effects and thus its importance as an indicator of the validity of the equation θ ? L_s. The average time that water molecules are trapped and the number of averaged hydrogen bonds within cavities in a dynamic fluid field were also investigated.