Solution NMR techniques for large molecular and supramolecular structures

Transverse relaxation-optimized spectroscopy (TROSY) or generation of heteronuclear multiple quantum coherences during the frequency labeling period and TROSY during the acquisition period have been combined either with cross-correlated relaxation-induced polarization transfer (CRIPT) or cross-correlated relaxation-enhanced polarization transfer (CRINEPT) to obtain two-dimensional (2D) solution NMR correlation spectra of (15)N,(2)H-labeled homo-oligomeric macromolecules with molecular weights from 110 to 800 kDa. With the experimental conditions used, the line widths of the TROSY-components of the (1)H- and (15)N-signals were of the order of 60 Hz at 400 kDa, whereas, for structures of size 800 kDa, the line widths were about 75 Hz for (15)N and 110 Hz for (1)H. This paper describes the experimental schemes used and details of their setup for individual measurements. The performance of NMR experiments with large structures depends critically on the choice of the polarization transfer times, the relaxation delays between subsequent recordings, and the water-handling routines. Optimal transfer times for 2D [(15)N,(1)H]-CRIPT-TROSY experiments in H(2)O solutions were found to be 6 ms for a molecular weight of approximately 200 kDa, 2.8 ms for 400 kDa, and 1.4 ms for 800 kDa. These data validate theoretical predictions of inverse proportionality between optimal transfer time and size of the structure. The proton longitudinal relaxation times in H(2)O solution were found to be of the order of 0.8 s for structure sizes around 200 kDa, 0.4 s at 400 kDa, and 0.3 s at 800 kDa, which enabled the use of recycle times below 1 s. Since improper water handling results in severe signal loss, the water resonance was kept along the z-axis during the entire duration of the experiments by adjusting each water flip-back pulse individually.     

On p-Adic Heights in Families of Elliptic Curves

The non-degeneracy of the canonical p-adic height pairing definedby Perrin-Riou and Schneider on an elliptic curve over a numberfield with good, ordinary reduction is still unknown. Following the work done for the real-valued pairing, the behaviourof the p-adic height is analysed as a point varies on a sectionof a family of elliptic curves, and so new information is obtainedabout this pairing. In particular, the variation is p-adicallycontinuous and the non-degeneracy of a set of sections can bechecked simultaneously for almost all elements of the family.The paper contains some conjectures about the valuation of thep-adic regulator and its consequences for the growth of theMordell–Weil group in cyclotomic Z_p-extensions.