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B. BERSCH et al.
relaxation rate constant). Three mechanisms contribute to the measurable
parameter: the dipolar interaction, the chemical shift anisotropy (see above) and
the chemical exchange. Relaxation measurements on proteins have generally
focused on nearly ideal systems such as lSN_1H on labeled proteins and 13C u _ 1 H at
natural abundance, in which cases the relaxation of the nucleus of interest is governed by only one other spin. In order to interpret the relaxation data in terms of
the motion of the vector connecting the two spins, a few assumptions on the CSA
are made which we will not discuss here. It also is important to keep in mind that
relaxation data do not contain information about internal motion much slower
than rotational diffusion. An exception to this rule are chemical or conformational exchange processes. These effects, which only contribute to transverse
relaxation, provide information on [!s-ms range motions, but unfortunately, it is
rather difficult to assess if the chemical shift for each conformation is not known
(see below).
As far as the data analysis is concerned, there are basically two approaches:
1. the modellree formalism (proposed by Lipari and Szabo 1982) supposes a separation between overall rotational diffusion and internal motion. There are
few cases, such as a protein made of a string of modules, where its validity has
been questioned. For each vector, an internal correlation time ('tj, typically in
the picosecond time range) and an order parameter (S2, varying between 1.0
for completely restricted and 0.0 for completely unrestricted motion) are
derived: in regular a-helices or ~-sheets, typical S2 are usually found between
0.8 and 0.9 corresponding to the restricted mobility in the secondary structure
elements.
2. the spectral density mapping method (Peng and Wagner 1992) analyzes the
frequency spectrum of the motions at a number of characteristic frequencies
(low frequency, = wx, = WH)' These values contain contributions from both
overall and intramolecular dynamics. This procedure is especially powerful in
application to disordered molecules in which the assumption of the LipariSzabo method is not valid any more. For example a protein with a flexible end
(see van Heijenoort et al. 1998 for an illustration): as compared to the structured core, residues in this part are characterized by larger values of the spectral density function at high frequency and smaller ones at low frequency.
The information obtained from the analysis of relaxation data is manifold. Internal mobility can be analyzed for parts of proteins which look disordered after
NMR structure refinement: if ns-ps internal motions are detected for these residues, one can conclude that the lack of a unique conformation is genuine and not
just an NMR artifact due to the lack of experimental constraints, spectral overlap
or line broadening. From the anisotropy of the overall tumbling (compare 3.5.1.
and 4.2), insights can be obtained into the shape of the protein in solution including the solvation layer and possible multimerization. An easy application of
relaxation is the comparison of mutant proteins with a wild-type and the study of
a macromolecule in presence or absence of a ligand: when used in a relative manner, these measurements become less prone to possible experimental or processing artefacts.
B. BERSCH et al.
relaxation rate constant). Three mechanisms contribute to the measurable
parameter: the dipolar interaction, the chemical shift anisotropy (see above) and
the chemical exchange. Relaxation measurements on proteins have generally
focused on nearly ideal systems such as lSN_1H on labeled proteins and 13C u _ 1 H at
natural abundance, in which cases the relaxation of the nucleus of interest is governed by only one other spin. In order to interpret the relaxation data in terms of
the motion of the vector connecting the two spins, a few assumptions on the CSA
are made which we will not discuss here. It also is important to keep in mind that
relaxation data do not contain information about internal motion much slower
than rotational diffusion. An exception to this rule are chemical or conformational exchange processes. These effects, which only contribute to transverse
relaxation, provide information on [!s-ms range motions, but unfortunately, it is
rather difficult to assess if the chemical shift for each conformation is not known
(see below).
As far as the data analysis is concerned, there are basically two approaches:
1. the modellree formalism (proposed by Lipari and Szabo 1982) supposes a separation between overall rotational diffusion and internal motion. There are
few cases, such as a protein made of a string of modules, where its validity has
been questioned. For each vector, an internal correlation time ('tj, typically in
the picosecond time range) and an order parameter (S2, varying between 1.0
for completely restricted and 0.0 for completely unrestricted motion) are
derived: in regular a-helices or ~-sheets, typical S2 are usually found between
0.8 and 0.9 corresponding to the restricted mobility in the secondary structure
elements.
2. the spectral density mapping method (Peng and Wagner 1992) analyzes the
frequency spectrum of the motions at a number of characteristic frequencies
(low frequency, = wx, = WH)' These values contain contributions from both
overall and intramolecular dynamics. This procedure is especially powerful in
application to disordered molecules in which the assumption of the LipariSzabo method is not valid any more. For example a protein with a flexible end
(see van Heijenoort et al. 1998 for an illustration): as compared to the structured core, residues in this part are characterized by larger values of the spectral density function at high frequency and smaller ones at low frequency.
The information obtained from the analysis of relaxation data is manifold. Internal mobility can be analyzed for parts of proteins which look disordered after
NMR structure refinement: if ns-ps internal motions are detected for these residues, one can conclude that the lack of a unique conformation is genuine and not
just an NMR artifact due to the lack of experimental constraints, spectral overlap
or line broadening. From the anisotropy of the overall tumbling (compare 3.5.1.
and 4.2), insights can be obtained into the shape of the protein in solution including the solvation layer and possible multimerization. An easy application of
relaxation is the comparison of mutant proteins with a wild-type and the study of
a macromolecule in presence or absence of a ligand: when used in a relative manner, these measurements become less prone to possible experimental or processing artefacts.