13C nuclear magnetic resonance relaxation studies of uniformly 13C and 15N labelled proteins

This thesis examines the problems of making 13C NMR relaxation measurements in proteins uniformly enriched with 13C and 15N isotopes and it presents a solution in the form of a new method of analysing 13C relaxation data.;In uniformly doubly-labelled proteins a particular 13C spin can undergo relaxation due to its own CSA and its dipolar interactions with bonded 13C atoms and bonded and non-bonded protons. The non-bonded protons can be on the same amino acid residue or on other residues which are close in space. To quantify the dipolar interactions the internuclear vector needs to be known to a significant degree of accuracy because of the 1/r6 proportionality (where r is the internuclear vector). The non-bonded 13CH distances cannot usually be determined to such a precision and additionally these distances are constantly changing as a consequence of molecular dynamics. This makes the conventional 13C T1 and NOE measurements difficult to analyse. Furthermore, homonuclear 13C scalar coupling evolution renders the traditional T2 measurement problematic.;In this study we have developed a method of analysis which, taking account of all the numerous and difficult to quantify interactions, isolates the mutual dipolar interaction of a set of active spins from all other interactions in an n-spin system. This method involves taking a linear combination of the longitudinal relaxation matrix elements pertaining to the relaxation decay rates of various longitudinal modes. This method can be used in conjunction with conventional 15N relaxation measurements and suitable motional models to model the spectral density function. Alternatively, the isolated 13C dipolar interactions may be used in conjunction with a less rigorous method of analysis to map the spectral density function.;The new method of analysis involves making five relaxation measurements: 13C T1, proton T1, 13CH and HH longitudinal two spin order and 13CHH longitudinal three spin order. Of these only the 13C T1 was reported in the literature but it needed to be modified for use on uniformly 13C labelled samples. The design and development of two-dimensional heteronuclear experiments to make the five necessary measurements as precisely as possible is presented in this thesis.;Relaxation data for a small model molecular and a 64 residue protein are presented and the dynamics information which can be obtained is discussed.