NOE intensities from multiple conformations in solution analyzed by the complete relaxation matrix approach

In the refinement procedure for macromolecular structure determination by NMR, extraction of interproton distances from experimental NOE intensities is crucial. In particular, major problems could arise when NMR experimental data are the result of a weighted average of multiple conformations in solution (rapid exchange). In this case the usual “static” averaged structure derived from the observed spectroscopic data may even be devoid of physical meaning. It is well known that the complete relaxation matrix analysis approach is valuable for calculating distances from NOESY intensities. This approach works by producing hybrid NOE matrices in which the missing experimental intensities are replaced by theoretical values computed from a model and then converted into distances by back-calculation using a standard matrix technique. To verify the capability of such an approach to discern between time-averaged and static coordinate-averaged NOE data, we investigated a DNA oligomer as a test case. In this work, we used “synthetic” NOE intensities obtained by different mixtures of A-form DNA and B-form DNA. The complete relaxation matrix analysis was performed using the program MARDIGRAS. In particular we focused our attention on the intraresidue base H6/H8-H2′ and H6/H8-H3′ distances that are very sensitive to sugar repuckering. These “synthetic” results are then compared with several real cases.     

Two-Dimensional Transferred Nuclear-Overhauser Effects with Incomplete Averaging of Free- and Bound-Ligand Resonances

Two distinct time scales prevail in the study of conformational exchange in general and specifically in deriving the protein-bound conformations of ligands by two-dimensional transferred-NOE experiments. Fast-exchange compared to the chemical-shift difference leads to a complete averaging of the free and bound resonances of the ligands, while fast exchange compared to the longitudinal relaxation rate 1/T₁ and cross relaxation results in an average of the relaxation matrices in the free and bound states. Slower chemical exchange leads to incomplete averaging of the free and bound resonances, giving rise to a reduction of transferred NOEs compared to fast-exchange conditions, Theoretical analysis and simulation results indicated that, in the absence of information on the chemical-shift time scale, transferred NOEs may be quantitated only to an accuracy with average NOE intensities and transferred NOEs to the free ligands as upper and lower bounds, respectively. Regardless of the exchange conditions, NOE intensities can be approximated by the NOEs transferred to the free ligands when a large excess of the free ligands (α_b < 0.1) is used to amplify the NOE transfers between the bound protons, These results suggest that two-dimensional transferred-NOE experiments (transferred NOESY) can be applied in situations of intermediate and slow exchange as long as the fraction of bound ligands is small and the exchange rates are fast enough to transfer the cross-relaxation pathways in the protein-ligand complex to the easily detected resonances of the free ligands,     

Transient NOE-exchange-relay experiment: application to ligand-protein binding under slow exchange conditions

A new version of one-dimensional (1)H experiment has been developed to probe ligand binding to macromolecular targets. The experiment, called transient NOE-exchange relay, is similar to the 'reverse NOE pumping' technique [A. Chen, M.J. Shapiro, J. Am. Chem. Soc. 122 (2000) 414-415]. The T(2) filter is used to erase protein magnetization, and the saturation then spreads from protein to bound ligand (via NOE) and further to a free ligand (via on-off exchange). The ligand signals, monitored as a function of mixing time, present a familiar 'dip' pattern characteristic of transient NOE or transient exchange experiments. In addition to the T(2) filter, we have also implemented a T(1) filter which makes use of the fact that the selective T(1)(-1) rates in macromolecules are much higher than those in small ligands. To model the experiment, complete relaxation and exchange matrix analysis has been invoked. This formalism was further used as a starting point to develop a simplified treatment where the relaxation and exchange components are represented by 2x2 matrix and, in addition, there is a special term responsible for coupling of ligand magnetization to the protein spin bath. The proposed experimental scheme has been tested on a system of peanut agglutinin complexed with Me-beta-D-galactopyranoside, which is known to be in a slow exchange regime. The results suggest that the NOE-exchange-relay experiment can be used at the advanced stages of the drug development process to confirm high-affinity ligand binding.     

Complete relaxation and conformational exchange matrix (CORCEMA) analysis of intermolecular saturation transfer effects in reversibly forming ligand-receptor complexes

A couple of recent applications of intermolecular NOE (INOE) experiments as applied to biomolecular systems involve the (i) saturation transfer difference NMR (STD-NMR) method and (ii) the intermolecular cross-saturation NMR (ICS-NMR) experiment. STD-NMR is a promising tool for rapid screening of a large library of compounds to identify bioactive ligands binding to a target protein. Additionally, it is also useful in mapping the binding epitopes presented by a bioactive ligand to its target protein. In this latter application, the STD-NMR technique is essentially similar to the ICS-NMR experiment, which is used to map protein-protein or protein-nucleic acid contact surfaces in complexes. In this work, we present a complete relaxation and conformational exchange matrix (CORCEMA) theory (H. N. B. Moseley et al., J. Magn. Reson. B 108, 243-261 (1995)) applicable for these two closely related experiments. As in our previous work, we show that when exchange is fast on the relaxation rate scale, a simplified CORCEMA theory can be formulated using a generalized average relaxation rate matrix. Its range of validity is established by comparing its predictions with those of the exact CORCEMA theory which is valid for all exchange rates. Using some ideal model systems we have analyzed the factors that influence the ligand proton intensity changes when the resonances from some protons on the receptor protein are saturated. The results show that the intensity changes in the ligand signals in an intermolecular NOE experiment are very much dependent upon: (1) the saturation time, (2) the location of the saturated receptor protons with respect to the ligand protons, (3) the conformation of the ligand-receptor interface, (4) the rotational correlation times for the molecular species, (5) the kinetics of the reversibly forming complex, and (6) the ligand/receptor ratio. As an example of a typical application of the STD-NMR experiment we have also simulated the STD effects for a hypothetical trisaccharide bound to a protein. The CORCEMA theory for INOE and the associated algorithm are useful in a quantitative interpretation of the intensity changes in the ligand in both the STD-NMR and ICS-NMR, provided the identity of the receptor protons experiencing direct RF saturation is known. The formalism presented here is likely to be useful in the design of bioactive ligands to a specific target protein and in the quantitative mapping of binding epitopes and interfaces between molecules in complexes.     

射频场照射下扩展的Solomon方程及射频场的照射对异核体系弛豫速率与NOE的影响

根据WBR理论,采用“改进的矩阵计算方法”,推导出了射频场照射下扩展的Solomon方程,并据此研究了射频场的照射对异核体系各种弛豫速率与NOE的影响,得出了如下结论:1)给出的方程比Boulat和Bodenhausen的方程更准确、更具普遍性,能够具体描述射频场对各种弛豫速率与NOE的影响.2)射频场的照射对纵向与横向弛豫速率的影响甚微,可以忽略,而交叉弛豫速率在射频场的照射下则有一定程度的降低.3)射频场的照射将使NOE变弱,且射频场越强,NOE越弱. 关键词： 核磁共振 Solomon方程 弛豫 射频场     

利用CαH系统的零量子-双量子混合相干的弛豫测量研究蛋白质动力学(英文)

越来越多的证据说明,"传统"的弛豫测量(T1, T2, NOE)不足以完整描述蛋白质的复杂动态,如化学交换、构型交换或相互作用导致的动态改变.涉及到多量子相干弛豫机制可以提供额外的动态信息.该文测量2个蛋白质的CαH系统的混合零量子和双量子弛豫速率随CPMG序列中脉冲间隔及温度的变化来探讨蛋白质中的动态及温度的影响.发现2种蛋白之质中均存在可观的交换效应,且与残基位置有关.进一步的分析表明,两位点交换模型不足以解释蛋白质的复杂动态.     

Correction of spin diffusion during iterative automated NOE assignment

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus beta-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.     

Dissipative evolution of quantum statistical ensembles and nonlinear response to a time-periodic perturbation

We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and the bathed system. The statistical states of the ensemble are described in terms of density matrices. Supposing the bath to be held at some - not necessarily thermal - statistical equilibrium and tracing over the bath degrees of freedom, we obtain reduced density matrices defining the statistical states of the bathed system. The master equations describing the evolution of these reduced density matrices are derived under the most general conditions. On time scales that are large with respect to the bath correlation time and with respect to the reciprocal transition frequencies of the bathed system, the resulting evolution of the reduced density matrix of the bathed system is of Markovian type. The detailed balance relations valid for a thermal equilibrium of the bath are derived and the conditions for the validity of the fluctuation-dissipation theorem are given. Based on the general approach, we investigate the non-linear response of the bathed subsystem to a time-periodic perturbation. Summing the perturbation series we obtain the coherences and the populations for arbitrary strengths of the perturbation.Received: 26 November 2003, Published online: 30 January 2004PACS: 05.30.-d Quantum statistical mechanics - 33.35. + r Electron resonance and relaxation - 33.25. + k Nuclear resonance and relaxation     

Effects of thermal denaturation on the longitudinal relaxation time (T1) of water protons in protein solutions: study of the factors determining the T1 of water protons

The factors determining the longitudinal relaxation time (T1) of water protons in protein solutions were investigated by analyzing the effects of thermal denaturation on the T1 of the water protons. We treated the water protons and the protein protons "on a protein surface" as a dipole-dipole coupled two-spin system where relative translational diffusion is the dominant mechanism, and measured the change in the time development of the nuclear Overhauser effect (NOE) factors of the water protons. The T1 of the water protons was shortened markedly when the proteins were thermally denatured. Our analysis indicates that this relaxation enhancement is due to an increase in the value of the translational correlation time as well as the fraction of hydration water molecules, though the influence of "proton exchange" between the water protons and the labile protein protons cannot be completely neglected.     

Spin excitations in granular structures with ferromagnetic nanoparticles

Spin excitations and relaxation in a granular structure which contains metallic ferromagnetic nanoparticles in an insulating amorphous matrix are studied in the framework of the s-d exchange model. As the d system, we consider the granule spins, and the s system is represented by localized electrons in the amorphous matrix. In the one-loop approximation with respect to the s-d exchange interaction for a diagram expansion of the spin Green’s function, the spin excitation spectrum is found, which consists of spin-wave excitations in the granules and of polarized spin excitations. In polarized spin excitations, a change in the granule spin direction is accompanied by an electron transition with a spin flip between two sublevels of a split localized state in the matrix. We considered polarized spin relaxation (relaxation of the granule spins occurring by means of polarized spin excitations) determined by localized deep energy states in the matrix and the thermally activated electronic cloud of the granule. It is found that polarized spin relaxation is efficient over a wide frequency range. Estimates made for structures with cobalt granules showed that this relaxation could be observed in centimetric, millimetric, and submillimetric wavelength ranges.     

Inverse vibration problem for un-damped 3-dimensional multi-story shear building models

Various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional (2-D) shear building structural models for a given set of vibratory frequencies. The suggested methods are based on the specific characteristics of the Jacobi matrices, i.e., symmetric, tri-diagonal and semi-positive definite matrices. However, in case of three dimensional (3-D) structural models, those methods are no longer applicable, since their stiffness matrices are not tri-diagonal. In this paper the inverse problem for a special class of vibratory structural systems, i.e., 3-D shear building models, is investigated. A practical algorithm is proposed for solving the inverse eigenvalue problem for un-damped, 3-D shear buildings. The problem is addressed in two steps. First, using the target frequencies, a so-called normalized eigenvector matrix, which is a banded matrix containing the information related to the frequencies and mode shapes of the target structural system, is determined. In this regard, similar to the solution of inverse problem for 2-D shear building structural models in which an auxiliary structure is constructed by adding constraints (or springs) to the original system, three auxiliary structures are proposed to solve the problem for 3-D cases. In the second step, the normalized eigenvector matrix is utilized to obtain the normalized stiffness matrix; in turn, this matrix is decomposed into the stiffness and mass matrices of the system. Finally, a numerical example is presented to demonstrate the efficiency of the proposed algorithm in determining the mass and stiffness matrices of a 3-D structural model for a given set of target vibrational frequencies.     

Spin relaxation and chemical exchange in NMR simulations

Theory for describing the density matrix of a spin system experiencing chemical exchange and relaxation during the steps of an NMR experiment is presented in a form suitable for computation. Features in the theory that arise from exchange are discussed in detail, and comparisons to the exchange-free situation are made. A general computer program to carry out simulations of NMR experiments is described, and several examples of its performance are presented.     

弱耦合自旋1/2二核系统二维动态NMR谱

二维动态NMR谱通常可由三脉冲实验得到。但如果核系统有标量耦合,就有可能混淆实验所得的信息。本文在Liouvelle空间中求出二核弱耦合系统的二维理论动态谱,给出AX(I=1/2)系统中的密度矩阵的解析解。文中指出:(1)在梯度脉冲作用之后,密度矩阵将留下z分量、零量子相干和双量子相干。(2)标量耦合与交换作用、弛豫作用的影响不同。前者只对零量子相干及双量子相干有贡献。如果实验得当,有希望消除标量耦合对动态谱的干扰。 关键词：     

Analysis of Spin Diffusion and Cross Correlation on the Net Nuclear Overhauser Effect in NMR

The effect of dipole–dipole cross correlations on the net nuclear Overhauser effect (NOE) has been analyzed here for realistic systems by extending the three-spin calculations to four and five spins in order to account for additional cross correlations and spin diffusion. These have been compared with the addition of leakage terms to the three-spin system. The additional spins enhance cross-correlation effects on one hand but on the other act as supplementary relaxation pathways for the magnetization to diffuse. This analysis shows that for a linear array of spins in the long-correlation limit, dipole–dipole cross correlations increase net NOE, while spin diffusion decreases it, and that the cumulative effect is a reduced effect of cross correlations. In other geometries and correlation limits, the effect of cross correlations on net NOE is generally small.     

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.     

Nuclear relaxation and anisotropic molecular reorientation of o-dichlorobenzene

Proton recovery curves are reported for nonselective 180°-τ-90°-FT spin-lattice relaxation of a dilute solution of o-dichlorobenzene in carbon disulfide. An exact density matrix analysis, combined with measured¹³C relaxation rates, is used to obtain the principal reorientational correlation times. Differences between these values and those found previously for 1,2,3-trichlorobenzene in the same solvent can be rationalized in terms of molecular shape. Exact density matrix calculations of proton relaxation are compared with an approximate treatment in which dipolar cross correlation and nonlinear mixing effects of strong pulses are ignored. It is shown that simple formulae arising from the approximate treatment successfully account for the average relaxation rate of a given multiplet, but fail to account for differential relaxation of lines within a multiplet.     

Surface exchange reactions and diffusion in composite materials: A finite element approach

A two-dimensional square grain model has been applied to model oxygen exchange processes between a gas phase and a ceramic composite consisting of two randomly distributed phases of equal grain size (side length of squares). Both average diffusion profiles for thin films and the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated numerically by means of the finite element method. The boundary conditions refer to an instantaneous change of the oxygen partial pressure in the surrounding gas phase, which gives rise to surface exchange reactions as well as to diffusion in the composite. Both local equilibrium at the interface between different phases (host phase and inclusions) and blocking heterophase boundaries have been taken into account. The numerical results are compared with the analytical solution for diffusion in a homogeneous medium introducing effective diffusion and surface exchange coefficients. When the relaxation time for effective medium diffusion is considerably shorter than that for the transport process from the host phase into the inclusions, relaxation curves with two separate time constants are predicted. Based on analytical approximations, relaxation times for various limiting cases are given.     

Quantum information transmission between two qubits through an intermediary photon gas

The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.     

Choosing a Spin-Lock Transmitter Position Which Minimizes HOHAHA Distortions of ROESY Spectra. Observation of a Correlation-Time Dependence of Frequency Offset

A technique for reliably selecting a transmitter position for rotating-frame NOE experiments which minimize scalar coupling artifacts is described. The technique makes use of the COSY spectrum of the molecule in question. The method is illustrated by application to thiostrepton, an antibiotic of molecular weight 1665. For an individual compound, the range of transmitter settings over which HOHAHA distortions are observed is found to depend on the molecular correlation time of the compound under study. The origin of this effect is discussed in terms of rotating-frame relaxation during the spin-lock period.     

Observation of long-range small-molecule NOEs using a neoteric sensitivity enhancement scheme.

A new method to increase the sensitivity of the 1D transient NOE experiment for molecules in the positive NOE regime is presented. This method, the reverse NOE, simply replaces the conventional relaxation delay between scans. Transient positive NOE enhancements from all other spins are used to accelerate the recovery of the target resonance toward its equilibrium intensity. In favorable cases, the intensity of the target peak at the start of an experiment can actually be increased beyond its equilibrium value. There is also a sensitivity enhancement in the rapid pulsing regime, where recovery is always incomplete. This sensitivity enhancement is illustrated with the one-dimensional double pulsed field gradient spin echo NOE experiment to observe a "fourth-order" NOE. Sensitivity gains of 30% are demonstrated.