Information from Relaxation Dispersion Measurements

Relaxation dispersion measurements are applied to systems that are undergoing an exchange process on the microsecond to millisecond timescale. Measurement of the f 2 relaxation rate in a series of experiments where the pulsing frequency is varied results in additional intensity for resonances of nuclei involved in the exchange process [18,19]. The resulting dispersion curve, showing as a function of 1/tqp can be fitted to functions such as [19,20] 

The parameters derived from these fits give information on the relative population of the two states pa and pe, on the rate of exchange fcex(= ab + kba ) between the two states, and on the structure of the excited state, which is given by the chemical shift difference Aw. 

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The information content of nuclear longitudinal relaxation measurements in both paramagnetic and diamagnetic systems can be greatly increased by performing such measurements as a function of the magnetic field. For paramagnetic species, the reason is apparent from the functional form of the equations discussed in Chapter 3 and from the relevant experimental data, reported in Chapter 5. The field dependence of a relaxation rate is called relaxation dispersion, and is abbreviated as NMRD. In principle, NMRD would be helpful for any chemical system, but practical limitations, as will be shown, restrict its use, with a few exceptions, to water protons. 

Initial information about the protein hydration layer came from relaxation studies. Dielectric relaxation (DR) and NMR studies were the first to reveal the existence of water molecules in the restricted environments. Dielectric relaxation measurements show the existence of an additional dispersion in protein solutions with time constants in the 40-50 ps time range (to be contrasted with 8 ps for bulk water), while NMR estimates have varied from system to system, with claims ranging from slow (with lifetimes in excess of 300 ps) to fast (with lifetimes 2-5 ps). The general consensus now appears to be consistent with the DR data. 

T2 dispersion curves contains information about relaxation and chemical exchange or, alternatively, about relaxation and diffusion in internal gradients. The authors presented a eomprehensive set of diffusion and T2 dispersion measurements on casein gels for whieh the protein/water ratio ranges from 0.25 to 0.5. The combination of these methods, taken in conjunetion with coneen-tration dependence, allows a good estimate of the parameters required to fit the data with Luz/Meiboom and Carver/Richards models for relaxation and ehemical exchange. 

The chemical shift dispersion (Table 1) and the temperature dependence of the resonance hne shape provides a qualitative measure of whether the structure is well ordered [2]. However, NMR spectroscopy also provides information relevant to the problem of protein folding in the study of the molten globule states. NMR spectroscopic investigations of molten globules may be more demanding than those of ordered proteins due to spectral overlap arising from poor shift dispersion and to short relaxation times that are due to conformational exchange at intermediate rates on the NMR time scale. 

In contrast to the relatively limited number of experimental approaches utilized to determine electron collisional information for C02 laser species, many different types of experiments have been employed in the determination of heavy particle rates as a function of temperature, for temperatures slightly below room temperature up to several thousand degrees. At room temperature, measurements have been obtained using sound absorption and/or dispersion as well as impact-tube and spectrophone techniques. High temperature rate data have been obtained primarily from shock tube experiments in which electron beam, infrared emission, schlieren, and interferometric diagnostic techniques are employed. For example, as many as 36 separate experiments have been conducted to determine the relaxation rate of the C02 bending mode in pure C02 [59]. The reader is referred to the review by Taylor and Bitterman [59] of heavy-particle processes of importance to laser applications for a detailed description and interpretation of available experimental and theoretical data. 

In addition, luminescence intensity and lifetime data obtained not only from the labelled polymer but also.from emission of dispersed naphthalene, acenaphthene and 1,1-dinaphthyl-l,3-propane (DNP) are briefly discussed. These measurements have provided information not only of relevance to the relaxation behaviour of the polymer matrix but also to the photophysies which occur therein and intramolecularly within the DNP. 

Let us first discuss estimates fi om DR measurements that provide several important pieces of information. These experiments measure the frequency-dependent dielectric constant and provide a measure of a liquid s polarization response at different frequencies. In bulk water, we have two dominant regions. The low-frequency dispersion gives us the well-known Debye relaxation time, Tq, which is equal to 8.3 ps. There is a second prominent dispersion in the high-frequency side with relaxation time constant less than Ips which contains combined contributions from low-frequency intermolecular vibrations and libra-tion. Aqueous protein solutions exhibit at least two more dispersions, (i) A new dispersion at intermediate frequencies, called, d dispersion, which appears at a timescale of about 50 ps in the dielectric spectrum, seems to be present in most protein solutions. This additional dispersion is attributed to water in the hydration layer, (ii) Another dispersion is present at very low frequencies and is attributed to the rotation of the protein. 

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