Dynamic information from relaxation

Quadrupolar Interactions. - Quadrupolar coupling constants are sensitive probes of hydrogen bonding. Their accurate knowledge is a major prerequisite when trying to extract dynamical information from relaxation data of quadrupo-... 

One of the most widely used tools to assess protein dynamics are different heteronuclear relaxation parameters. These are in intimate connection with internal dynamics on time scales ranging from picoseconds to milliseconds and there are many approaches to extract dynamical information from a wide range of relaxation data (for a thorough review see Ref. 1). Most commonly 15N relaxation is studied, but 13C and 2H relaxation are the prominent tools to characterize side-chain dynamics.70 Earliest applications utilized 15N Ti, T2 relaxation as well as heteronuclear H- N) NOE experiments to characterize N-H bond motions in the protein backbone.71 The vast majority of studies applied the so-called model-free approach to translate relaxation parameters into overall and internal mobility. Its name contrasts earlier methods where explicit motional models of the N-H vector were used, for example diffusion-in-a-cone or two- or three-site jump, etc. Unfortunately, we cannot obtain information about the actual type of motion of the bond. As reconciliation, the model-free approach yields motional parameters that can be interpreted in each of these motional models. There is a well-established protocol to determine the exact combination of parameters to invoke for each bond, starting from the simplest set to the most complex one until the one yielding satisfactory description is reached. The scheme, a manifestation of the principle of Occam s razor is shown in Table l.72... 

The underlying strategy for extracting dynamical information from NMR relaxation data is based on the equations for either longitudinal (Tfl) or transverse (T2 ) relaxation rates. If relaxation is dominated by the magnetic dipole-dipole interaction between like-spin nuclei, then... 

Apart from rotational dynamics information, NMR relaxation has also been used to understand microviscosity and pH in confined media. In a [C4C4im][Tf2N]/H20/TX-100 microemulsion system, the Ti relaxation time of water molecules has been used as an indicator of microviscosity. Also since the T2 relaxation time of water molecules varies with pH, this experimental result has been exploited to determine the pH of the aqueous micelle core [75]. 

Molecular dynamics information from spin resonance spectroscopies is obtained by the measurement of the spin-lattice relaxation contribution. Spin-lattice relaxation information can be extracted from longitudinal field xSR experiments while the transverse field experiments provide information on spin-spin relaxation. 

Of course, knowledge of the entire spectrum does provide more information. If the shape of the wings of G (co) is established correctly, then not only the value of tj but also angular momentum correlation function Kj(t) may be determined. Thus, in order to obtain full information from the optical spectra of liquids, it is necessary to use their periphery as well as the central Lorentzian part of the spectrum. In terms of correlation functions this means that the initial non-exponential relaxation, which characterizes the system s behaviour during free rotation, is of no less importance than its long-time exponential behaviour. Therefore, we pay special attention to how dynamic effects may be taken into account in the theory of orientational relaxation. 

Spin relaxation in NMR is known to provide information about the dynamics of molecular entities and possibly about molecular geometry or electron distribution. Generally, dynamical information is obtained if the tensor of the relevant relaxation mechanism is known from independent determinations. Conversely, if parameters describing the dynamics of the considered molecule have been deduced beforehand, geometrical parameters may be derived. Only in particular situations, one can hope to access both types of parameters (dynamical and geometrical). For... 

The above theory is usually called the generalized linear response theory because the linear optical absorption initiates from the nonstationary states prepared by the pumping process [85-87]. This method is valid when pumping pulse and probing pulse do not overlap. When they overlap, third-order or X 3 (co) should be used. In other words, Eq. (6.4) should be solved perturbatively to the third-order approximation. From Eqs. (6.19)-(6.22) we can see that in the time-resolved spectra described by x"( ), the dynamics information of the system is contained in p(Af), which can be obtained by solving the reduced Liouville equations. Application of Eq. (6.19) to stimulated emission monitoring vibrational relaxation is given in Appendix III. 

This approach yields spectral densities. Although it does not require assumptions about the correlation function and therefore is not subjected to the limitations intrinsic to the model-free approach, obtaining information about protein dynamics by this method is no more straightforward, because it involves a similar problem of the physical (protein-relevant) interpretation of the information encoded in the form of SD, and is complicated by the lack of separation of overall and local motions. To characterize protein dynamics in terms of more palpable parameters, the spectral densities will then have to be analyzed in terms of model-free parameters or specific motional models derived e.g. from molecular dynamics simulations. The SD method can be extremely helpful in situations when no assumption about correlation function of the overall motion can be made (e.g. protein interaction and association, anisotropic overall motion, etc. see e.g. Ref. [39] or, for the determination of the 15N CSA tensor from relaxation data, Ref. [27]). 

The discussion of the mechanisms and models of the relaxation process given in Section 2.5 shows that the application of time-resolved methods produces substantial advantages in accessing dynamical information, but it does not allow the complete pattern of the dynamic process to be obtained. The analysis of the experimental results requires that a particular dynamic model be assumed. Information on the dynamics is obtained from studies of the dependence of emission intensity on two parameters the frequency (or the wavelength) of emission and on time. The function 7(vem, t) may be investigated by two types of potentially equivalent experiments ... 

A chemical relaxation technique that measures the magnitude and time dependence of fluctuations in the concentrations of reactants. If a system is at thermodynamic equilibrium, individual reactant and product molecules within a volume element will undergo excursions from the homogeneous concentration behavior expected on the basis of exactly matching forward and reverse reaction rates. The magnitudes of such excursions, their frequency of occurrence, and the rates of their dissipation are rich sources of dynamic information on the underlying chemical and physical processes. The experimental techniques and theory used in concentration correlation analysis provide rate constants, molecular transport coefficients, and equilibrium constants. Magde" has provided a particularly lucid description of concentration correlation analysis. See Correlation Function... 

In addition to structural information, dynamic information can also be obtained through NMR. Time scales of both fast (picoseconds) and slow (seconds and longer) processes can be followed. Slow processes such as chemical reactivity are probed by following a change in an NMR property such as chemical shift or transfer of magnetization from one spectral site to another. Detailed kinetic information can be extracted in well-established experiments. Faster processes influence the NMR spin relaxation properties, such as Tt or T2, with kinetic information linked to the specific structure being examined. Model-independent ways... 

From the examples described in this article, it can be seen that NMR has played an important role in the structural and dynamic characterisation of a wide range of peptide toxins. Most of the focus has been on 3D structural characterisation, but NMR can also provide dynamic information, a feature that distinguishes it from X-ray crystallography. Although there have been relatively few NMR relaxation studies of toxins, we expect that there will be an increasing emphasis... 

What is the mechanism of spins dropping down from the state to the a state and fanning out around the two cones, and what determines the rates (R = HT and/ 2 = 1/72) of NMR relaxation These processes are intimately tied to the motion of molecules as they tumble ( reorient ) in solution in their rapid Brownian motion, and measurement of the NMR relaxation parameters T and T2 can even give us detailed information about molecular dynamics (motion) from the point of view of each spin in the molecule. A simplified model... 

In Chapter 2 we found that a perturbed nuclear spin system relaxes to its equilibrium state or steady state by first-order processes characterized by two relaxation times Ti, the spin-lattice, or longitudinal, relaxation time and T2, the spin-spin, or transverse, relaxation time. Thus far in our treatment of NMR we have not made explicit use of relaxation phenomena, but an understanding of the limitations of many NMR methods requires some knowledge of the processes by which nuclei relax. In addition, as we shall see, there is a great deal of information of chemical value, both structural and dynamic, that can be obtained from relaxation phenomena. 

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