Evaluation of protein 15N relaxation times by inverse Laplace transformation

Relaxation times (T1, T2, T1rho) are usually evaluated from exponential decay data by least-squares fitting methods. For this procedure, the integrals or amplitudes of signals must be determined, which can be laborious with large data sets. Moreover, the fitting requires a priori knowledge of the number of exponential components responsible for the decay. We have adapted inverse Laplace transformation (ILT) for the analysis of relaxation data. Exponential components are resolved with ILT to reciprocal space on their corresponding relaxation rate values. The ILT approach was applied to 3D linewidth-resolved 15N HSQC experiments to evaluate 15N T1 and T2 relaxation times of ubiquitin. The resulting spectrum is a true 3D spectrum, where the signals are separated by their 1H and 15N chemical shifts (HSQC correlations) and by their relaxation rate values (R1 or R2). From this spectrum, the relaxation times can be obtained directly with a simple peak-picking procedure.     

Modeling of the pseudo-colloids migration for multi-member decay chains with a arbitrary flux boundary condition in a fractured porous medium

A deep geologic disposal is the prime option for the long-term isolation of high-level radioactive waste (HLW) in many countries. For deeply located repositories, a radionuclide released from a failed waste container moves through the engineered and natural barriers before it reaches a biosphere. The pseudo-colloid which a radionuclide is adsorbed on a moving natural humic or fulvic colloid can be generated in a fractured porous medium. The size of a colloid is in general in the order of a hundred nanometer so that its migration velocity in a fracture is higher than that of a radionuclide due to the hydrochromatic effect. A large colloid cannot diffuse easily into a surrounding rock. Also, there are many kinds of actinides and these actinides have decay chains. In this analysis, the canonical form solution is derived for a pseudo-colloid and a solute in a fracture and a surrounding rock with a realistic inlet boundary condition with multi-member decay chains. It is used the Fortran based a computational code which uses a special subroutine for the inversion of Laplace transform. Consequently, the role of the pseudo-colloid in the fractured porous medium is important and also their decay chains aren’t neglected in the performance assessment of the HLW.     

Parallels between multiple population-period transient spectroscopy and multidimensional coherence spectroscopies

We have recently shown that homogeneous and heterogeneous kinetics can be distinguished by experiments that compare the evolution of the population of a state over two time intervals [E. van Veldhoven et al., ChemPhysChem 8, 1761 (2007)]. This paper elaborates on the analogy between these multiple population-period transient spectroscopy (MUPPETS) experiments and more familiar spectroscopies based on the evolution of coherences. Using a modified inverse-Laplace transform, a standard kinetics decay is re-expressed as a "rate spectrum." A nonexponential decay creates a linewidth in this spectrum. Mechanisms for line broadening in rate spectra are compared to those for line broadening in frequency-domain spectra. Homogeneous and heterogeneous kinetics are defined precisely and are shown to be the counterparts of homogeneous and inhomogeneous line broadenings in frequency-domain spectra. Homogeneous line broadening mechanisms are further divided into equilibrium and nonequilibrium mechanisms, with equilibrium mechanisms more prevalent in frequency spectra and nonequilibrium mechanisms more prevalent in rate spectra. Spectral representations of two-dimensional MUPPETS experiments are developed that are equivalent to two-dimensional coherence spectroscopies. In particular, spectra equivalent to hole-burning and to correlation spectra are defined. Frequency-domain spectra are often modeled as an inhomogeneous distribution of identical homogeneous line shapes. A parallel homogeneous-heterogeneous model for kinetics is defined. Within this model, MUPPETS has sufficient information to completely separate the homogeneous and heterogeneous contributions to a nonexponential decay, even when the homogeneous contribution is nonexponential.     

利用迭代软阈值方法抑制恒时演化类核磁共振实验中的采样截断伪峰

采样截断,即信号衰减殆尽之前结束采样,会在核磁共振(NMR)谱图中引入振荡状伪峰,进而影响谱图质量.在多维核磁共振实验中,为减少实验时间并为后续脉冲序列保留自旋相干,采样必然在信号衰减完毕之前结束,因此采样截断在所难免.变迹法(窗函数法)可以抑制采样截断造成的伪峰,但会导致谱峰增宽.线性预测也有助于减小截断伪峰.采样截断最严重的场合,是在恒时演化类实验中.这类实验的间接维演化时间固定,因此间接维采样信号强度没有表观衰减.本研究提出的迭代软阈值方法(Iterative Soft Thresholding,IST)虽然因为调节参数困难而在一般场合中应用受限,但恒时演化类(Constant time,CT)NMR实验的间接维信号缺没有表观衰减,这为IST处理参数设置提供了简化条件.本研究通过数据模拟和实验数据,证明了IST是抑制CT-NMR实验中采样截断伪峰的有效方法,并与其它相关方法进行了对比.     

Some applications of nonlinear convergence accelerators

A number of established nonlinear convergence acceleration methods are presented. It is discussed how these methods, and also some new algorithms, can be applied successfully to Fourier series. Some of the new accelerators are tailored for these-series. Others are also useful for other types of series and sequences, and not only for convergence acceleration, but also for extrapolation or summation problems. Applications to the numerical inversion of the Laplace transform and to a Fourier series arising in the Matsubara formalism are presented. © 1993 John Wiley & Sons, Inc.     

Competition between excitation and electronic decay of short-lived molecular states

The nuclear dynamics accompanying the excitation to and the subsequent decay of an electronic state is discussed. Particular attention is paid to cases, in which the whole process cannot be divided into two steps (excitation and decay) since the excitation and the decay times are of the same order of magnitude. The recently introduced time-dependent formulation of the theory describing the wave packets’ dynamics is extended to include the excitation process. The wave packets can be related to the intensity of the emitted particles. Most of the resulting integrals can actually be performed by employing eigenstates of the Hamiltonians corresponding to the involved potential energy surfaces. This leads to the so called “timeindependent” formulation of the theory. Computational details of the implementation of the corresponding “timedependent” and “time-independent” methods are presented. Illustrative applications are given to illuminate both the influence of the excitation process and the lifetime of the decaying state. It emerges that the intuitive interpretation of the spectra (within the above two step model) may fail. Insight into the process is gained by studying the evolution of the spectra as a function of time. The appearance of “atomic lines” due to dissociative decaying and final states is investigated in some detail.     

Quantitative analysis of the dynamic behaviour of photochromic systems

The good understanding of a photochromic reaction mechanism requires the establishment of the list of all the transient species and the definition of their connecting processes. The purpose of kinetic studies is the determination of the main photochromic parameters, such as the quantum yields of photoisomerization, rate constants of thermal relaxation and spectra of transient species. These data allow the establishment of structure properties relationships in order to select the best substituents to improve photochromic performances within a given series. In this review, we describe the dynamic behaviour of various photochromic systems during thermal relaxation after irradiation, from the simplest mono-exponential decay to the more complicated multi-exponential dynamics. Then, we analyse the evolution of the long-lived isomers under continuous irradiation. Several pedagogical examples and tricks to perform easy kinetic analysis are given in the appendices.     

EXtended ACquisition Time (EXACT) NMR—A Case for ′Burst′ Non‐Uniform Sampling

A strong case exists for the introduction of burst non‐uniform sampling (NUS) in the direct dimension of NMR spectroscopy experiments. The resulting gaps in the NMR free induction decay can reduce the power demands of long experiments (by switching off broadband decoupling for example) and/or be used to introduce additional pulses (to refocus homonuclear coupling, for example). The final EXtended ACquisition Time (EXACT) spectra are accessed by algorithmic reconstruction of the missing data points and can provide higher resolution in the direct dimension than is achievable with existing non‐NUS methods.     

Time-resolved relaxation dynamics of Hgn- (11 <or = n <or = 16,n = 18) clusters following intraband excitation at 1.5 eV

Electron-nuclear relaxation dynamics are studied in Hg(n) (-) (11 相似文献   

Simultaneous quantification and identification of individual chemicals in metabolite mixtures by two-dimensional extrapolated time-zero (1)H-(13)C HSQC (HSQC(0))

Quantitative one-dimensional (1D) (1)H NMR spectroscopy is a useful tool for determining metabolite concentrations because of the direct proportionality of signal intensity to the quantity of analyte. However, severe signal overlap in 1D (1)H NMR spectra of complex metabolite mixtures hinders accurate quantification. Extension of 1D (1)H to 2D (1)H-(13)C HSQC leads to the dispersion of peaks along the (13)C dimension and greatly alleviates peak overlapping. Although peaks are better resolved in 2D (1)H-(13)C HSQC than in 1D (1)H NMR spectra, the simple proportionality of cross peaks to the quantity of individual metabolites is lost by resonance-specific signal attenuation during the coherence transfer periods. As a result, peaks for individual metabolites usually are quantified by reference to calibration data collected from samples of known concentration. We show here that data from a series of HSQC spectra acquired with incremented repetition times (the time between the end of the first (1)H excitation pulse to the beginning of data acquisition) can be extrapolated back to zero time to yield a time-zero 2D (1)H-(13)C HSQC spectrum (HSQC(0)) in which signal intensities are proportional to concentrations of individual metabolites. Relative concentrations determined from cross peak intensities can be converted to absolute concentrations by reference to an internal standard of known concentration. Clustering of the HSQC(0) cross peaks by their normalized intensities identifies those corresponding to metabolites present at a given concentration, and this information can assist in assigning these peaks to specific compounds. The concentration measurement for an individual metabolite can be improved by averaging the intensities of multiple, nonoverlapping cross peaks assigned to that metabolite.     

The aluminum ordering in aluminosilicates: a dipolar 27Al NMR spectroscopy study

The spatial ordering of aluminum atoms in CsAl(SiO3)2 and 3Al2O3.2SiO2 was probed by 27Al dipolar solid-state NMR spectroscopy. The 27Al response to a Hahn spin-echo pulse sequence in a series of aluminum-containing model crystalline compounds demonstrates that quantitative 27Al homonuclear dipolar second moments can be obtained to within +/-20% of the theoretical values, if evaluation of the spin-echo response curve is limited to short evolution periods (2t1 < or = 0.10 ms). Additionally, selective excitation of the central transition m = 1/2 --> -1/2 is necessary in order to ensure quantitative results. Restriction of spin exchange affecting the dephasing of the magnetization may decelerate the spin-echo decay at longer evolution periods. Considering these restraints, the method was used to probe the spatial distribution of aluminum atoms among the tetrahedral sites in two aluminosilicate materials. Experimental 27Al spin-echo response data for the aluminosilicates CsAl(SiO3)2 (synthetic pollucite) and 3Al2O3.2SiO2 (mullite) are compared with theoretical data based on (I) various degrees of aluminum-oxygen-aluminum bond formation among tetrahedrally coordinated aluminum atoms (Al(T(d) )-O-Al(T(d) )) and (II) the maximum avoidance of Al(T(d) )-O-Al(T(d) ) bonding. Analysis of the second moment values and resulting echo decay responses suggests that partial suppression of spin exchange among aluminum atoms in crystallographically distinct sites may contribute to the 27Al spin echo decay in 3Al2O3.2SiO2, thus complicating quantitative analysis of the data. Silicon-29 and aluminum-27 magic angle spinning (MAS) NMR spectra of 3Al2O3.2SiO2 are consistent with those previously reported. The experimental 27Al spin-echo response behavior of CsAl(SiO3)2 differs from the theoretical response behavior based on the maximum avoidance of Al-O-Al bonding between tetrahedral aluminum sites in CsAl(SiO3)2. A single unresolved resonance is observed in both the silicon-29 and aluminum-27 MAS spectra of CsAl(SiO3)2.     

Global Analysis of Correlation Functions: Dynamic Light Scattering from Polymers and Block Copolymers

Dynamic light scattering has become a standard technique for investigating colloidal suspensions, polymer solutions, melts, blends, gels and other more complex systems. The experimental field autocorrelation function ĝ_l(t) can often be well modeled by a Laplace transform relating ĝ_l(t) to a distribution of decay times A(tau). In simple systems, A(τ) can usually be directly related to a distribution of molecular weights, particle sizes, diffusion coefficients, relaxation times or other physically relevant quantities. With constrained regularization methods, the parameter‐free estimation of A(τ) has become straightforward. In complex systems, the resulting A(τ) may contain several components the identification of which is not always obvious. The problem often originates in a superposition of components that have different variations of the decay time with the scattering vector. We present the method based on a simultaneous fit of several autocorrelation fuctions (ACF) measured at several different scattering angles, which, using simple and reasonable assumptions, yields a robust analysis of the spectra of decay times. The application of the method is illustrated on simulated autocorrelation functions as well as on real experimental data obtained on a variety of polymer systems.     

Controlling surface roughness in vapor-deposited poly(amic acid) films by solvent-vapor exposure

A series of vapor-deposited poly(amic acid) (PAA) films were exposed to dimethyl sulfoxide (DMSO) vapors to investigate sorption kinetics and surface smoothing phenomena. Gravimetric sorption and secondary-ion mass spectrometry (SIMS) results are both consistent with frontal (case II) diffusion. These experiments suggest that the solvent front is defined by a sharp interface that delineates the swollen material from the unswollen material. Solvent-vapor smoothing was studied by first depositing PAA onto rough aluminum surfaces, and then, during solvent-vapor exposure, the surface topology was continuously monitored using a light interference microscope. The resulting time-dependent power spectra indicate that high-frequency defects smooth faster than low-frequency defects. This frequency dependence was further investigated by depositing PAA onto a series of sinusoidal surfaces and exposing them to solvent vapor inside a flow channel. The sinusoidal amplitudes decay exponentially with time, with decay constants that are proportional to the surface frequency. To explain the physics of surface smoothing, a two-parameter model is presented and agrees qualitatively with experimental data.     

Determining the resolution of Laplace inversion spectrum

In experiments involving decaying signals, it is often desirable to analyze the data as a sum of exponential decays using the Laplace inversion method. However, Laplace inversion is an ill-conditioned problem, and it is difficult to ascertain the stability of the reconstruction method and resolution of the resulting spectrum. This paper provides an easily computed approximate bound of the resolution and offers guidelines on how to design experiments to improve the spectral resolution.     

SPEED: single‐point evaluation of the evolution dimension

Two‐dimensional NMR spectroscopy can be speeded up by orders of magnitude by severely restricting the number of sampling operations in the evolution dimension–we demonstrate that just a single measurement may suffice. The frequencies evolving in the indirect dimension (t₁) are deduced from the amplitudes of the signals acquired in the direct dimension (t₂). Prior measurements of the one‐dimensional spectra are required. Results are presented for the two‐dimensional ¹³C‐HSQC spectrum of 2‐ethylindanone recorded at a single fixed setting of the evolution time, demonstrating a speed advantage of 120. The method can be extended to multidimensional spectra, with correspondingly greater gains in speed. Copyright © 2007 John Wiley & Sons, Ltd.     

Theory for a wavelet analysis of electrochemical noise in the laplace space with use of two operational frequencies

The image of a random process in the Laplace space may be viewed as resulting from use of a oneway continuous wavelet transform with an exponential as the basic function, i.e. as resulting from the application of the Laplace wavelet. If the Laplace-wavelet variance of an electrochemical noise allows one to determine the Laplace transform of a time-correlation function, i.e. a factual operational spectral density of the noise, then the covariance of two Laplace waveletes of an electrochemical noise, each of which corresponds to its own operational frequency, allows one to verify a local consistency of the initial experimental noise data. The Laplace waveletes are applied rather widely. In fact, any stationary random process and stationary random time sequence can be described with operational noise spectra. Dedicated to the ninetieth anniversary of Ya.M. Kolotyrkin’s birth.     

Theory of Laplace Analysis of Non-Gaussian Noise

An algorithm for directly calculating third-order noise operation spectra, which includes no evaluation of the third-order correlation function as a preliminary stage, is found. For the Ershler–Randles circuit, an expression is found, which links bispectra of the equilibrium electrode potential fluctuation determined in the imaginary and real axes of the Laplace plane. Advantages of using the Laplace space in studies of the fine non-Gaussian structure of random time series are discussed.     

Numerical solution of hydraulic models based on the axially-dispersed plug flow model by Laplace transforms

The problem of solving hydraulic models based on the axially-dispersed plug flow model which are applicable for the mathematical modelling of different flow-through systems both in chemical analysis (e.g., chromatography, flow injection analysis) and chemical industry (e.g., different tubular reactors) is discussed. Methods for numerical inversion of the model solution in the Laplace domain by expanding it into series of orthogonal functions are compared. Best results with respect to precision and consumption of computation time are given by the methods employing Chebyshov polynomials of the first kind and Fourier sine series. These methods were found to be better in these respects than some other frequently used numerical inversion methods.     

Selecting variables for k-means cluster analysis by using a genetic algorithm that optimises the silhouettes

The goal of present work is to analyse the effect of having non-informative variables (NIV) in a data set when applying cluster analysis and to propose a method computationally capable of detecting and removing these variables. The method proposed is based on the use of a genetic algorithm to select those variables important to make the presence of groups in data clear. The procedure has been implemented to be used with k-means and using the cluster silhouettes as fitness function for the genetic algorithm.The main problem that can appear when applying the method to real data is the fact that, in general, we do not know a priori what the real cluster structure is (number and composition of the groups).The work explores the evolution of the silhouette values computed from the clusters built by using k-means when non-informative variables are added to the original data set in both a literature data set as well as some simulated data in higher dimension. The procedure has also been applied to real data sets.