Art, fact and artifact: reflections on the cross-talk between theory and experiment.

With the increasing sophistication of each, theory and experiment have become highly specialized endeavors conducted by separate research groups. A result has been a weakening of the coupling between them and occasional hostility. Examples are given and suggestions are offered for strengthening the traditional synergy between theory and experiment.

Emergence of Linnett's "double quartets" from a model of "Lewis dots".

Chemists routinely explicate molecular structures and chemical reactions in terms of the propensities of semiclassical valence electrons (aka "Lewis dots"). Typically, the electrons are viewed as forming spin pairs and recent efforts to translate this concise and intuitive qualitative picture into an efficient and relatable quantitative model have made good progress. But electrons are not always paired and advanced quantum calculations have shown that this is so even in small diamagnetic species such as dicarbon and benzene. Here we show that the latest semiclassical model for paired electrons can clarify the limitations on pairing simply by dissecting the elements of the interparticle potentials. Although not trained to do so, these elements produce a Linnett-like benzene, with three valence electrons in each CC bond, when the electrons are free to move singly. At the same time, sustaining higher order bonds with independently mobile electrons requires adjustments in the details of the model potentials at short distances. This is addressed with new training data and new forms for the contributions from Coulomb integrals. Although trained on hydrogen and carbon species separately, the combination applied to ethyne predicts the pairing of spins in the CH bonds and the dispersion of spins in the CC bond that is found in ab initio calculations. This adjusted force field is named LINNETT, in appreciation of Linnett's insightful double quartet interpretation of the Lewis octet.

A Carbon Is a Carbon Is a Carbon: Orbital-Free Simulations of Hydrocarbon Chemistry without Resort to Atom Types.

Semiclassical electrons (aka Lewis dots) have been a mainstay of chemists' thinking about molecular structure, polarizability, and reactivity for over a century. This utility has motivated the development of a corresponding quantitative description. Here we devise pairwise potentials that describe the behavior of valence electron pairs in hydrocarbons, including those in single, double, bridge, and bent bonds of linear, branched, and cyclic compounds, including anionic and cationic states. Beyond predicting structures and energies, the new subatomistic force field, dubbed LEWIS-B, efficiently simulates carbocation addition to a double bond and cation migration to a neighboring carbon. A crucial feature of the semiclassical electrons is variable spread, a fourth degree of freedom in addition to three Cartesian coordinates. In spontaneously adapting to different environments, the spread provides a signature of electron stability, with more contracted clouds where the electron interactions are favorable and expanded clouds where electrons are less tightly held. In addition, the pair potentials provide insight into the subtle trade-offs that govern isomerizations and reactions.

Primary Transfer Step in the Light-Driven Ion Pump Bacteriorhodopsin: An Irreversible U-Turn Revealed by Dynamic Nuclear Polarization-Enhanced Magic Angle Spinning NMR.

Despite much attention, the path of the highly consequential primary proton transfer in the light-driven ion pump bacteriorhodopsin (bR) remains mysterious. Here we use DNP-enhanced magic angle spinning (MAS) NMR to study critical elements of the active site just before the Schiff base (SB) deprotonates (in the L intermediate), immediately after the SB has deprotonated and Asp85 has become protonated (in the Mo intermediate), and just after the SB has reprotonated and Asp96 has deprotonated (in the N intermediate). An essential feature that made these experiments possible is the 75-fold signal enhancement through DNP. 15N(SB)-1H correlations reveal that the newly deprotonated SB is accepting a hydrogen bond from an alcohol and 13C-13C correlations show that Asp85 draws close to Thr89 before the primary proton transfer. Concurrently, 15N-13C correlations between the SB and Asp85 show that helices C and G draw closer together just prior to the proton transfer and relax thereafter. Together, these results indicate that Thr89 serves to relay the SB proton to Asp85 and that creating this pathway involves rapprochement between the C and G helices as well as chromophore torsion.

Exchange potentials for semi-classical electrons.

Semi-classical electrons offer access to efficient and intuitive simulations of chemical reactions. As for any treatment of fermions, the greatest difficulty is in accounting for anti-symmetry effects. Semi-classical efforts to-date either reference Slater-determinants from ab initio treatments or adopt a heuristic approach inspired by density functional treatments. Here we revisit the problem with a combined approach. We conclude that semi-classical electrons need to reference a non-conventional wave function and find that (1) contrary to earlier suppositions, contributions from the electrostatic terms in the Hamiltonian are of similar magnitude to those from the kinetic terms and (2) the former point to a need to supplement pair potentials with 3-body potentials. The first result explains features of reported heuristic potentials, and the second provides a firm footing for extending the transferability of potentials across a wider range of elements and bonding scenarios.

Transferable pseudoclassical electrons for aufbau of atomic ions.

Generalizing the LEWIS reactive force field from electron pairs to single electrons, we present LEWIS• in which explicit valence electrons interact with each other and with nuclear cores via pairwise interactions. The valence electrons are independently mobile particles, following classical equations of motion according to potentials modified from Coulombic as required to capture quantum characteristics. As proof of principle, the aufbau of atomic ions is described for diverse main group elements from the first three rows of the periodic table, using a single potential for interactions between electrons of like spin and another for electrons of unlike spin. The electrons of each spin are found to distribute themselves in a fashion akin to the major lobes of the hybrid atomic orbitals, suggesting a pointillist description of the electron density. The broader validity of the LEWIS• force field is illustrated by predicting the vibrational frequencies of diatomic and triatomic hydrogen species.

High frequency dynamic nuclear polarization.

During the three decades 1980-2010, magic angle spinning (MAS) NMR developed into the method of choice to examine many chemical, physical, and biological problems. In particular, a variety of dipolar recoupling methods to measure distances and torsion angles can now constrain molecular structures to high resolution. However, applications are often limited by the low sensitivity of the experiments, due in large part to the necessity of observing spectra of low-γ nuclei such as the I = 1/2 species (13)C or (15)N. The difficulty is still greater when quadrupolar nuclei, such as (17)O or (27)Al, are involved. This problem has stimulated efforts to increase the sensitivity of MAS experiments. A particularly powerful approach is dynamic nuclear polarization (DNP) which takes advantage of the higher equilibrium polarization of electrons (which conventionally manifests in the great sensitivity advantage of EPR over NMR). In DNP, the sample is doped with a stable paramagnetic polarizing agent and irradiated with microwaves to transfer the high polarization in the electron spin reservoir to the nuclei of interest. The idea was first explored by Overhauser and Slichter in 1953. However, these experiments were carried out on static samples, at magnetic fields that are low by current standards. To be implemented in contemporary MAS NMR experiments, DNP requires microwave sources operating in the subterahertz regime, roughly 150-660 GHz, and cryogenic MAS probes. In addition, improvements were required in the polarizing agents, because the high concentrations of conventional radicals that are required to produce significant enhancements compromise spectral resolution. In the last two decades, scientific and technical advances have addressed these problems and brought DNP to the point where it is achieving wide applicability. These advances include the development of high frequency gyrotron microwave sources operating in the subterahertz frequency range. In addition, low temperature MAS probes were developed that permit in situ microwave irradiation of the samples. And, finally, biradical polarizing agents were developed that increased the efficiency of DNP experiments by factors of ∼4 at considerably lower paramagnet concentrations. Collectively, these developments have made it possible to apply DNP on a routine basis to a number of different scientific endeavors, most prominently in the biological and material sciences. This Account reviews these developments, including the primary mechanisms used to transfer polarization in high frequency DNP, and the current choice of microwave sources and biradical polarizing agents. In addition, we illustrate the utility of the technique with a description of applications to membrane and amyloid proteins that emphasizes the unique structural information that is available in these two cases.

An amyloid organelle, solid-state NMR evidence for cross-ß assembly of gas vesicles.

Functional amyloids have been identified in a wide range of organisms, taking on a variety of biological roles and being controlled by remarkable mechanisms of directed assembly. Here, we report that amyloid fibrils constitute the ribs of the buoyancy organelles of Anabaena flos-aquae. The walls of these gas-filled vesicles are known to comprise a single protein, GvpA, arranged in a low pitch helix. However, the tertiary and quaternary structures have been elusive. Using solid-state NMR correlation spectroscopy we find detailed evidence for an extended cross-ß structure. This amyloid assembly helps to account for the strength and amphiphilic properties of the vesicle wall. Buoyancy organelles thus dramatically extend the scope of known functional amyloids.

Efficient resonance assignment of proteins in MAS NMR by simultaneous intra- and inter-residue 3D correlation spectroscopy.

Resonance assignment is the first step in NMR structure determination. For magic angle spinning NMR, this is typically achieved with a set of heteronuclear correlation experiments (NCaCX, NCOCX, CONCa) that utilize SPECIFIC-CP (15)N-(13)C transfers. However, the SPECIFIC-CP transfer efficiency is often compromised by molecular dynamics and probe performance. Here we show that one-bond ZF-TEDOR (15)N-(13)C transfers provide simultaneous NCO and NCa correlations with at least as much sensitivity as SPECIFIC-CP for some non-crystalline samples. Furthermore, a 3D ZF-TEDOR-CC experiment provides heteronuclear sidechain correlations and robustness with respect to proton decoupling and radiofrequency power instabilities. We demonstrate transfer efficiencies and connectivities by application of 3D ZF-TEDOR-DARR to a model microcrystalline protein, GB1, and a less ideal system, GvpA in intact gas vesicles.

Selectively dispersed isotope labeling for protein structure determination by magic angle spinning NMR.

The power of nuclear magnetic resonance spectroscopy derives from its site-specific access to chemical, structural and dynamic information. However, the corresponding multiplicity of interactions can be difficult to tease apart. Complimentary approaches involve spectral editing on the one hand and selective isotope substitution on the other. Here we present a new "redox" approach to the latter: acetate is chosen as the sole carbon source for the extreme oxidation numbers of its two carbons. Consistent with conventional anabolic pathways for the amino acids, [1-(13)C] acetate does not label α carbons, labels other aliphatic carbons and the aromatic carbons very selectively, and labels the carboxyl carbons heavily. The benefits of this labeling scheme are exemplified by magic angle spinning spectra of microcrystalline immunoglobulin binding protein G (GB1): the elimination of most J-couplings and one- and two-bond dipolar couplings provides narrow signals and long-range, intra- and inter-residue, recoupling essential for distance constraints. Inverse redox labeling, from [2-(13)C] acetate, is also expected to be useful: although it retains one-bond couplings in the sidechains, the removal of CA-CO coupling in the backbone should improve the resolution of NCACX spectra.

Natural polarizability and flexibility via explicit valency: the case of water.

As the dominant physiological solvent, water drives the folding of biological macromolecules, influences conformational changes, determines the ionization states of surface groups, actively participates in catalytic events, and provides "wires" for long-range proton transfer. Elucidation of all these roles calls for atomistic simulations. However, currently available methods do not lend themselves to efficient simulation of proton transfer events, or even polarizability and flexibility. Here, we report that an explicit account of valency can provide a unified description for the polarizability, flexibility, and dissociability of water in one intuitive and efficient setting. We call this approach LEWIS, after the chemical theory that inspires the use of valence electron pairs. In this paper, we provide details of the method, the choice of the training set, and predictions for the neat ambient liquid, with emphasis on structure, dynamics, and polarization. LEWIS water provides a good description of bulk properties, and dipolar and quadrupolar responses.

Functional and shunt states of bacteriorhodopsin resolved by 250 GHz dynamic nuclear polarization-enhanced solid-state NMR.

Observation and structural studies of reaction intermediates of proteins are challenging because of the mixtures of states usually present at low concentrations. Here, we use a 250 GHz gyrotron (cyclotron resonance maser) and cryogenic temperatures to perform high-frequency dynamic nuclear polarization (DNP) NMR experiments that enhance sensitivity in magic-angle spinning NMR spectra of cryo-trapped photocycle intermediates of bacteriorhodopsin (bR) by a factor of approximately 90. Multidimensional spectroscopy of U-(13)C,(15)N-labeled samples resolved coexisting states and allowed chemical shift assignments in the retinylidene chromophore for several intermediates not observed previously. The correlation spectra reveal unexpected heterogeneity in dark-adapted bR, distortion in the K state, and, most importantly, 4 discrete L substates. Thermal relaxation of the mixture of L's showed that 3 of these substates revert to bR(568) and that only the 1 substate with both the strongest counterion and a fully relaxed 13-cis bond is functional. These definitive observations of functional and shunt states in the bR photocycle provide a preview of the mechanistic insights that will be accessible in membrane proteins via sensitivity-enhanced DNP NMR. These observations would have not been possible absent the signal enhancement available from DNP.

Proton defect solvation and dynamics in aqueous acid and base.

Easy come, easy go: LEWIS, a new model of reactive and polarizable water that enables the simulation of a statistically reliable number of proton hopping events in aqueous acid and base at concentrations of practical interest, is used to evaluate proton transfer intermediates in aqueous acid and base (picture, left and right, respectively).

Microspherules from sugars in the absence of nitrogen.

Reactions of short sugars under mild, plausibly prebiotic conditions yield organic microspherules that may have played a role in prebiotic chemistry as primitive reaction vessels. It has been widely thought that nitrogen chemistry, in particular Amadori rearrangement, is central to this process, Here we show that microspherules form in the absence of any nitrogen compounds if the pH is sufficiently low. In particular, while the microspherule formation induced by ammonium acetate (pH 7) is not reproduced by ammonium chloride (pH 5), it is reproduced by oxalic acid and by hydrochloric acid (pH 1). The formation of microspherules in the presence of oxalic acid is similar to that in the presence of ammonium acetate: aqueous reactions of D-erythrose, D-ribose, 2-deoxy-D-ribose and D-fructose in the presence of oxalic acid produce microspherules ranging in size from approximately 1-5 µm after eight weeks incubation at 65°C, while the aldohexoses D-glucose, D-galactose and D-mannose do not. This pattern correlates with the occurrence of furanose forms in these sugars.

Energy transformations early in the bacteriorhodopsin photocycle revealed by DNP-enhanced solid-state NMR.

By exploiting dynamic nuclear polarization (DNP) at 90 K, we observe the first NMR spectrum of the K intermediate in the ion-motive photocycle of bacteriorhodopsin. The intermediate is identified by its reversion to the resting state of the protein in red light and by its thermal decay to the L intermediate. The (15)N chemical shift of the Schiff base in K indicates that contact has been lost with its counterion. Under these circumstances, the visible absorption of K is expected to be more red-shifted than is observed and this suggests torsion around single bonds of the retinylidene chromophore. This is in contrast to the development of a strong counterion interaction and double bond torsion in L. Thus, photon energy is stored in electrostatic modes in K and is transferred to torsional modes in L. This transfer is facilitated by the reduction in bond alternation that occurs with the initial loss of the counterion interaction, and is driven by the attraction of the Schiff base to a new counterion. Nevertheless, the process appears to be difficult, as judged by the multiple L substates, with weaker counterion interactions, that are trapped at lower temperatures. The double-bond torsion ultimately developed in the first half of the photocycle is probably responsible for enforcing vectoriality in the pump by causing a decisive switch in the connectivity of the active site once the Schiff base and its counterion are neutralized by proton transfer.

Bending the Curve: Molecular Manifestations of Electron Antisymmetry.

As very light fermions, electrons are governed by antisymmetric wave functions that lead to exchange integrals in the evaluation of the energy. Here we use the localized representation of orbitals to decompose the electronic energy in a fashion that isolates the enigmatic exchange contributions and characterizes their distinctive control over electron distributions. The key to this completely general analysis is considering the electrons in groups of three, drawing attention to the curvatures of pair potentials, rather than just their amplitudes and slopes. We show that a positive curvature at short distances is essential for the mutual distancing of electrons and a negative curvature at longer distances is essential to account for the influence of lone pairs on bond torsion. Neither curvature is available in the absence of the exchange contributions. Thus, although exchange energies are much shorter range than Coulomb energies, their influence on molecular geometry is profound and readily understood.

Solid-state NMR characterization of gas vesicle structure.

Gas vesicles are gas-filled buoyancy organelles with walls that consist almost exclusively of gas vesicle protein A (GvpA). Intact, collapsed gas vesicles from the cyanobacterium Anabaena flos-aquae were studied by solid-state NMR spectroscopy, and most of the GvpA sequence was assigned. Chemical shift analysis indicates a coil-α-ß-ß-α-coil peptide backbone, consistent with secondary-structure-prediction algorithms, and complementary information about mobility and solvent exposure yields a picture of the overall topology of the vesicle subunit that is consistent with its role in stabilizing an air-water interface.

Resolution and polarization distribution in cryogenic DNP/MAS experiments.

This contribution addresses four potential misconceptions associated with high-resolution dynamic nuclear polarization/magic angle spinning (DNP/MAS) experiments. First, spectral resolution is not generally compromised at the cryogenic temperatures at which DNP experiments are performed. As we demonstrate at a modest field of 9 T (380 MHz (1)H), 1 ppm linewidths are observed in DNP/MAS spectra of a membrane protein in its native lipid bilayer, and <0.4 ppm linewidths are reported in a crystalline peptide at 85 K. Second, we address the concerns about paramagnetic broadening in DNP/MAS spectra of proteins by demonstrating that the exogenous radical polarizing agents utilized for DNP are distributed in the sample in such a manner as to avoid paramagnetic broadening and thus maintain full spectral resolution. Third, the enhanced polarization is not localized around the polarizing agent, but rather is effectively and uniformly dispersed throughout the sample, even in the case of membrane proteins. Fourth, the distribution of polarization from the electron spins mediated via spin diffusion between (1)H-(1)H strongly dipolar coupled spins is so rapid that shorter magnetization recovery periods between signal averaging transients can be utilized in DNP/MAS experiments than in typical experiments performed at ambient temperature.

Spectroscopy by integration of frequency and time domain information for fast acquisition of high-resolution dark spectra.

A simple and effective method, SIFT (spectroscopy by integration of frequency and time domain information), is introduced for processing nonuniformly sampled multidimensional NMR data. Applying the computationally efficient Gerchberg-Papoulis (G-P) algorithm, used previously in picture processing and medical imaging, SIFT supplements data at nonuniform points in the time domain with the information carried by known "dark" points (i.e., empty regions) in the frequency domain. We demonstrate that this rapid integration not only removes the severe pseudonoise characteristic of the Fourier transforms of nonuniformly sampled data, but also provides a robust procedure for using frequency information to replace time measurements. The latter can be used to avoid unnecessary sampling in sampling-limited experiments, and the former can be used to take advantage of the ability of nonuniformly sampled data to minimize trade-offs between the signal-to-noise ratio and the resolution in sensitivity-limited experiments. Processing 2D and 3D data sets takes about 0.1 and 2 min, respectively, on a personal computer. With these several attractive features, SIFT offers a novel, model-independent, flexible, and user-friendly tool for efficient and accurate processing of multidimensional NMR data.