Magic-angle spinning solid-state NMR spectroscopy of the beta1 immunoglobulin binding domain of protein G (GB1): 15N and 13C chemical shift assignments and conformational analysis

Magic-angle spinning solid-state NMR (SSNMR) studies of the beta1 immunoglobulin binding domain of protein G (GB1) are presented. Chemical shift correlation spectra at 11.7 T (500 MHz 1H frequency) were employed to identify signals specific to each amino acid residue type and to establish backbone connectivities. High sensitivity and resolution facilitated the detection and assignment of every 15N and 13C site, including the N-terminal (M1) 15NH3, the C-terminal (E56) 13C', and side-chain resonances from residues exhibiting fast-limit conformational exchange near room temperature. The assigned spectra lend novel insight into the structure and dynamics of microcrystalline GB1. Secondary isotropic chemical shifts report on conformation, enabling a detailed comparison of the microcrystalline state with the conformation of single crystals and the protein in solution; the consistency of backbone conformation in these three preparations is the best among proteins studied so far. Signal intensities and line widths vary as a function of amino acid position and temperature. High-resolution spectra are observed near room temperature (280 K) and at <180 K, whereas resolution and sensitivity greatly degrade substantially near 210 K; the magnitude of this effect is greatest among the side chains of residues at the intermolecular interface of the microcrystal lattice, which we attribute to intermediate-rate translational diffusion of solvent molecules near the glass transition. These features of GB1 will enable its use as an excellent model protein not only for SSNMR methods development but also for fundamental studies of protein thermodynamics in the solid state.     

Long-range 19F-15N distance measurements in highly-13C, 15N-enriched solid proteins with 19F-dephased REDOR shift (FRESH) spectroscopy

We present a novel rotational-echo double resonance (REDOR) method for detection of multiple (19)F-(15)N distances in solid proteins. The method is applicable to protein samples containing a single (19)F label, in addition to high levels of (13)C and (15)N enrichment. REDOR dephasing pulses are applied on the (19)F channel during an indirect constant time chemical shift evolution period on (15)N, and polarization is then transferred to (13)C for detection, with high-power (1)H decoupling throughout the sequence. This four-channel experiment reports site-specifically on (19)F-(15)N distances, with highly accurate determinations of approximately 5 A distances and detection of correlations arising from internuclear distances of at least 8 A. We demonstrate the method on the well-characterized 56-residue model protein GB1, where the sole tryptophan residue (Trp-43) has been labeled with 5-(19)F-Trp, in a bacterial growth medium also including (13)C-glucose and (15)N ammonium chloride. In GB1, 11 distances are determined, all agreeing within 20% of the X-ray structure distances. We envision the experiment will be utilized to measure quantitative long-range distances for protein structure determination.     

Sensitivity and resolution in proton solid-state NMR at intermediate deuteration levels: quantitative linewidth characterization and applications to correlation spectroscopy

We present a systematic study of proton linewidths in rigid solids as a function of sample spinning frequency and proton density, with the latter controlled by the ratio of protonated and perdeuterated model compounds. We find that the linewidth correlates more closely with the overall proton density (rho(H)) than the size of local clusters of (1)H spins. At relatively high magic-angle spinning (MAS) rates, the linewidth depends linearly upon the inverse MAS rate. In the limit of infinite spinning rate and/or zero proton concentration, the linewidth extrapolates to a non-zero value, owing to contributions from scalar couplings, chemical shift dispersion, and B(0) field inhomogeneity. The slope of this line depends on the overall concentration of unexchangeable protons in the sample and the spinning rate. At up to 30% protonation levels ( approximately 2 (1)H/100A(3)), proton detection experiments are demonstrated to have a substantial (2- to 3-fold) sensitivity gain over corresponding (13)C-detected experiments. Within this range, the absolute sensitivity increases with protonation level; the optimal compromise between sensitivity and resolution is in the range of 20-30% protonation. We illustrate the use of dilute protons for polarization transfer to and from low-gamma spins within 5A, and to be utilized as both magnetization source and detection spins. The intermediate protonation regime enhances relaxation properties, which we expect will enable new types of (1)H correlation pulse sequences to be implemented with improved resolution and sensitivity.     

Minimum length from quantum mechanics and classical general relativity

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.     

New Reflection Generator for Simulated Annealing in Mixed-Integer/Continuous Global Optimization

To reduce the well-known jamming problem in global optimization algorithms, we propose a new generator for the simulated annealing algorithm based on the idea of reflection. Furthermore, we give conditions under which the sequence of points generated by this simulated annealing algorithm converges in probability to the global optimum for mixed-integer/continuous global optimization problems. Finally, we present numerical results on some artificial test problems as well as on a composite structural design problem.