ider/Progress in Nuclear Resonance Spectroscopy 32(1998)193-275 of carbon spectra with higher sensitivity, Such polar- Fig. 4 shows a plot of J(a)as a function of the fre ization transfer experiments are extremely important quency w for the three correlation times T of 5, 10 and in heteronuclear NMR experiments and are discussed 20 ns. These correlation times represent the motion of further in Section 4.2.3 small, medium and large globular proteins in In addition, Fig ustrates that low fre 2.1. 4. Relaxation motions are especially effective in NMR rel processes for proteins. Using the concept of spectral Relaxation processes re-establish an equilibrium density functions the different behaviour of longitudi distribution of spin properties after a perturbation After a disturbance, the non-equilibrium state decays nal relaxation and relaxation of transverse magnetize the simplest case exponentially characterized by the tion can be rationalized. When considering onl spin-lattice relaxation time T. Re-establishing relaxation due to fluctuating dipolar interactions thermal equilibrium requires changes in the popu- caused by stochastic motion, the relaxation rate TI lation distribution of the spin states and lowers the is proportional to J(wo)since only stochastic magnetic energy of the spin system. Thus, it involves energy fields in the transverse plane at the resonance fre transfer from the spin system to its surroundings quency w, are able to interact with the transverse which are usually referred to as the lattice. Micro- magnetization components, bringing them back to scopically, relaxation is caused by fluctuating values J( o decrease for the three increasing values the z axis. For frequencies larger than 25 MHz the magnetic fields. Dynamical processes such as atomic of Te represented in Fig 4. The longitudinal relaxation actions and facilitate spin-lattice relaxation. The times, therefore, increase for increasing molecular extent of the overlap between the frequency spectrum very small Te the values J (wo)values get smaller aga of the motional process and the relevant resonance leading to an increase of T, compared to the value for lap is described by th density function J(w). Since J()is the Fourier trans- obtained when woTe=l, e.g. at 600 MHz for a Te of form of the time correlation function describing the 0.26 ns. Transverse relaxation shows a different notion, its functional form depends on the mechanism dependence on the molecular weight of the molecule of motion. An exponential correlation function with T2 relaxation not only depends on Jwo)but also on correlation time Te results in the spectral density func J(O) since the z components of stochastic magnetic tion[16,24,29 fields(zero frequency)reduce the phase coherence of transverse magnetization components which con 1(0)=31+ ( 8) sequently sum up to a smaller macroscopic magneti zation. Since J(o) increases monotonously with J() 0°s]|=20ms 4tc=lOns T. 5n 0.001 001 0102051250[109rads] 63280160320800v[MHz] 4. Plot of the spectral density function /(o)(Eq (8))versus the frequency w on a logarithmic scale, Three correlation times 5, 10 and 20 ns indicated which represent small, medium and large proteins. The frequency scale is given in units of rad s and in MHz