Neil A. Farrow

Spectral density function mapping using 15N relaxation data exclusively

SummaryA method is presented for the determination of values of the spectral density function, J(ω), describing the dynamics of amide bond vectors from 15N relaxation parameters alone. Assuming that the spectral density is given by the sum of Lorentzian functions, the approach allows values of J(ω) to be obtained at ω=0, ωN and 0.870ωH, where ωN and ωH are Larmor frequencies of nitrogen and proton nuclei, respectively, from measurements of 15N T1, T2 and 1H−15N steady-state NOE values at a single spectrometer frequency. Alternatively, when measurements are performed at two different spectrometer frequencies of i and j MHz, J(ω) can be mapped at ω=0, ωiN, ωjN, 0.870ωiH and 0.870ωjH, where ωiN, for example, is the 15N Larmor frequency for a spectrometer operating at i MHz. Additionally, measurements made at two different spectrometer frequencies enable contributions to trasverse relaxation from motions on millisecond-microsecond time scales to be evaluated and permit assessment of whether a description of the internal dynamics is consistent with a correlation function consisting of a sum of exponentials. No assumptions about the specific form of the spectral density function describing the dynamics of the 15N−NH bond vector are necessary, provided that dJ(ω)/dω is relatively constant between ω=ωH+ωN to ω=ωH−ωN. Simulations demonstrate that the method is accurate for a wide range of protein motions and correlation times, and experimental data establish the validity of the methodology. Results are presented for a folded and an unfolded form of the N-terminal SH3 domain of the protein drk.

A heteronuclear correlation experiment for simultaneous determination of 15N longitudinal decay and chemical exchange rates of systems in slow equilibrium

SummaryA heteronuclear correlation experiment is described which permits simultaneous characterization of both 15N longitudinal decay rates and slow conformational exchange rates. Data pertaining to the exchange between folded and unfolded forms of an SH3 domain is used to illustrate the technique. Because the unfolded form of the molecule, on average, shows significantly higher NH exchange rates than the folded form, and approach which minimizes the degree of water saturation is employed, enabling the extraction of accurate rate constants.

A posteriori determination of relative projection directions of arbitrarily oriented macromolecules

For the generation of three-dimensional structures from two-dimensional projections a fundamental requirement is knowledge of the individual projection directions. In electron microscopy of single macromolecules the molecular projection directions are not known and must be determined a posteriori from the projection images themselves. The algorithm presented achieves such a determination by using the central-section theorem, geometrical techniques, and quaternion mathematics. The quality of the solution is tested in relation to image noise, angular error in the input data, number of intercompared projections used to generate common-axis data, and number of iterations. Correct determination of mutual alignments is achieved despite significant errors in the input data, indicating that the method should be applicable to electron microscopy problems.

Pulse schemes for the measurement of3 JC′Cγ and3 JNCγ scalar couplings in 15N,13C uniformly labeled proteins

Pulse sequences are presented for the measurement of3JC′Cγ and3JNCγ scalar couplings for allCγ containing residues in15N,13C uniformly labeled proteins. The methodsdescribed are based on quantitative J correlation spectroscopy pioneered byBax and co-workers [Bax et al. (1994) Methods Enzymol., 239, 79–105].The combination of 3JC′Cγ and3JNCγ scalar coupling constants allows theassignment of discrete rotameric states about the χ1 torsion angle in cases where such states exist or, alternatively,facilitates the establishment of noncanonical χ1conformations or the presence of rotameric averaging. The methods areapplied to a 1.5 mM sample of staphylococcal nuclease.

Rapid corepressor exchange from the trp-repressor/operator complex: An NMR study of [ul-13C/15N]-l-tryptophan

Summary[ul-13C/15N]-l-tryptophan was prepared biosynthetically and its dynamic properties and intermolecular interaction with a complex of Escherichia coli trp-repressor and a 20 base-pair operator DNA were studied by heteronuclear isotope-edited NMR experiments. The resonances of the free and bound corepressor (l-Trp) were unambiguously identified from gradient-enhanced 15N−1H HSQC, 13C−1H HSQC, 13C-and 15N-edited 2D NOESY spectra. The exchange off-rate of the corepressor between the bound and free states was determined to be 3.4±0.52 s−1 at 45°C, almost three orders of magnitude faster than the dissociation of the protein-DNA complex. Examination of the experimental NOE buildup curves indicates that it may be desirable to use longer mixing times than would normally be used for a large molecule, in order to detect weak intermolecular NOEs in the presence of exchange. Intermolecular NOEs from bound corepressor to trp-repressor and DNA were analyzed with respect to the mechanism of ligand exchange. This analysis suggests that, in order for the ligand to diffuse out of the complex, there must be significant movement or ‘breathing’ of the protein and/or DNA.

Maximum entropy methods and dark field microscopy images

Abstract Maximum entropy methods are examined for the removal of noise from dark field electron microscope images. A number of maximum entropy algorithms, including χ 2 and E 2 constraints, are examined. Failure of conventional maximum entropy methods led to the inclusion of an autocovariance constraint in the algorithm. Under this constraint the noise removed from the images has a more realistic spatial distribution than under conventional constraints. This constraint, when combined with a simulated annealing algorithm, led to successful removal of noise from small test data sets.

Structural, Dynamic, and Folding Studies of SH2 and SH3 Domains

Recent advances in NMR methodology have made it a powerful approach for the study of biomolecular structure and dynamics (Bax and Grzesiek, 1993; Bax, 1994; Farrow et al., 1994a). In addition to NMR being a structural tool, as a solution spectroscopy it is exquisitely sensitive to dynamic processes - not only fast, low amplitude motions which can often be described by analysis of X-ray crystallographic B factors (Ringe and Petsko, 1985), but also slower, larger amplitude motions. These may include conformational exchange on millisecond time-scales or longer between states as dissimilar as folded and unfolded states of proteins and reflecting motions of tens of angstroms. We have exploited this distinguishing capability of NMR spectroscopy to describe the dynamic processes observed during structural studies of two isolated domains of signal transduction proteins, a Src Homology 2 (SH2) domain of phospholipase Cγ in complex with a phosphopeptide from the platelet-derived growth factor receptor (PDGFR) and an isolated Src Homology 3 (SH3) domain from the drosophila protein Drk1.