Simone Ulzega

Boosting the Sensitivity of Ligand−Protein Screening by NMR of Long-Lived States

A new NMR method for the study of ligand-protein interactions exploits the unusual lifetimes of long-lived states (LLSs). The new method provides better contrast between bound and free ligands and requires a protein-ligand ratio ca. 25 times lower than for established T(1ρ) methods, thus saving on costly proteins. The new LLS method was applied to the screening of inhibitors of urokinase-type plasminogen activator (uPA), which is a prototypical target of cancer research. With only 10 μM protein, a dissociation constant (K(D)) of 180 ± 20 nM was determined for the strong ligand (inhibitor) UK-18, which can be compared with K(D) = 157 ± 39 nM determined by the established surface plasmon resonance method.

Time Scales of Slow Motions in Ubiquitin Explored by Heteronuclear Double Resonance

Understanding how proteins function at the atomic level relies in part on a detailed characterization of their dynamics. Ubiquitin, a small single-domain protein, displays rich dynamic properties over a wide range of time scales. In particular, several regions of ubiquitin show the signature of chemical exchange, including the hydrophobic patch and the β4-α2 loop, which are both involved in many interactions. Here, we use multiple-quantum relaxation techniques to identify the extent of chemical exchange in ubiquitin. We employ our recently developed heteronuclear double resonance method to determine the time scales of motions that give rise to chemical exchange. Dispersion profiles are obtained for the backbone NH(N) pairs of several residues in the hydrophobic patch and the β4-α2 loop, as well as the C-terminus of helix α1. We show that a single time scale (ca. 50 μs) can be used to fit the data for most residues. Potential mechanisms for the propagation of motions and the possible extent of correlation of these motions are discussed.

Evidence for Dynamics on a 100 ns Time Scale from Single-and Double-Quantum Nitrogen-14 NMR in Solid Peptides

The indirect detection of 14N spectra via protons in the manner of heteronuclear multiple-quantum correlation (HMQC) allows one to obtain single- (SQ) and double-quantum (DQ) 14N spectra in solids. A comparison of the SQ and DQ line widths as a function of temperature with simulations reveals motions in the tripeptide AAG with rates on the order of 107 s(-1) at 49 degrees C.

Broadband excitation in solid-state NMR using interleaved DANTE pulse trains with N pulses per rotor period

We analyze the direct excitation of wide one-dimensional spectra of nuclei with spin I=1/2 or 1 in rotating solids submitted to pulse trains in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE), either with one short rotor-synchronized pulse of duration τp in each of K rotor periods (D1(K)) or with N interleaved equally spaced pulses τp in each rotor period, globally also extending over K rotor periods (D(N)(K)). The excitation profile of D(N)(K) scheme is a comb of rf-spikelets with Nν(R)=N/T(R) spacing from the carrier frequency, and a width of each spikelet inversely proportional to the length, KT(R), of D(N)(K) scheme. Since the individual pulse lengths, τp, are typically of a few hundreds of ns, D(N)(K) scheme can readily excite spinning sidebands families covering several MHz, provided the rf carrier frequency is close enough to the resonance frequency of one the spinning sidebands. If the difference of isotropic chemical shifts between distinct chemical sites is less than about 1.35/(KT(R)), D(N)(K) scheme can excite the spinning sidebands families of several sites. For nuclei with I=1/2, if the homogeneous and inhomogeneous decays of coherences during the DANTE sequence are neglected, the K pulses of a D1(K) train have a linearly cumulative effect, so that the total nutation angle is θ(tot)=K2πν1τp, where ν1 is the rf-field amplitude. This allows obtaining nearly ideal 90° pulses for excitation or 180° rotations for inversion and refocusing across wide MAS spectra comprising many spinning sidebands. If one uses interleaved DANTE trains D(N)(K) with N>1, only spinning sidebands separated by intervals of Nν(R) with respect to the carrier frequency are observed as if the effective spinning speed was Nν(R). The other sidebands have vanishing intensities because of the cancellation of the N contributions with opposite signs. However, the intensities of the remaining sidebands obey the same rules as in spectra obtained with νR. With increasing N, the intensities of the non-vanishing sidebands increase, but the total intensity integrated over all sidebands decreases. Furthermore, the NK pulses in a D(N)(K) train do not have a simple cumulative effect and the optimal cumulated flip angle for optimal excitation, θ(tot)(opt)=NK2πν1τp, exceeds 90°. Such D(N)(K) pulse trains allow achieving efficient broadband excitation, but they are not recommended for broadband inversion or refocusing as they cannot provide proper 180° rotations. Since D(N)(K) pulse trains with N>1 are shorter than basic D1(K) sequences, they are useful for broadband excitation in samples with rapid homogeneous or inhomogeneous decay. For nuclei with I=1 (e.g., for (14)N), the response to basic D1(K) pulse train is moreover affected by inhomogeneous decay due to 2nd-order quadrupole interactions, since these are not of rank 2 and therefore cannot be eliminated by spinning about the magic angle. For large quadrupole interactions, the signal decay produced by second-order quadrupole interaction can be minimized by (i) reducing the length of D(N)(K) pulse trains using N>1, (ii) fast spinning, (iii) large rf-field, and (iv) using high magnetic fields to reduce the 2nd-order quadrupole interaction.

Control of Cross Relaxation of Multiple-Quantum Coherences Induced by Fast Chemical Exchange under Heteronuclear Double-Resonance Irradiation

A fully analytical description of the control of the cross-correlated cross relaxation of multiple-quantum coherences in the presence of local dynamics under heteronuclear double-resonance radio-frequency (RF) irradiation is presented. The contribution of chemical exchange to relaxation can be partly or fully quenched by RF fields. We assume a correlated two-site chemical exchange model with arbitrary populations, and show that in the limit of fast exchange the dependence of the effective multiple-quantum cross-relaxation rate on the applied RF amplitude can be described by a compact analytical expression. Numerical simulations and preliminary experiments support our theoretical results. The relaxation dispersion as a function of RF amplitude can provide accurate information on the kinetics of correlated processes.

High-resolution two-field nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance (NMR) is a ubiquitous branch of spectroscopy that can explore matter at the scale of an atom. Significant improvements in sensitivity and resolution have been driven by a steady increase of static magnetic field strengths. However, some properties of nuclei may be more favourable at low magnetic fields. For example, transverse relaxation due to chemical shift anisotropy increases sharply at higher magnetic fields leading to line-broadening and inefficient coherence transfers. Here, we present a two-field NMR spectrometer that permits the application of rf-pulses and acquisition of NMR signals in two magnetic centres. Our prototype operates at 14.1 T and 0.33 T. The main features of this system are demonstrated by novel NMR experiments, in particular a proof-of-concept correlation between zero-quantum coherences at low magnetic field and single quantum coherences at high magnetic field, so that high resolution can be achieved in both dimensions, despite a ca. 10 ppm inhomogeneity of the low-field centre. Two-field NMR spectroscopy offers the possibility to circumvent the limits of high magnetic fields, while benefiting from their exceptional sensitivity and resolution. This approach opens new avenues for NMR above 1 GHz.

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.