De novo design of proteins housing excitonically coupled chlorophyll special pairs.

Natural photosystems couple light harvesting to charge separation using a 'special pair' of chlorophyll molecules that accepts excitation energy from the antenna and initiates an electron-transfer cascade. To investigate the photophysics of special pairs independently of the complexities of native photosynthetic proteins, and as a first step toward creating synthetic photosystems for new energy conversion technologies, we designed C2-symmetric proteins that hold two chlorophyll molecules in closely juxtaposed arrangements. X-ray crystallography confirmed that one designed protein binds two chlorophylls in the same orientation as native special pairs, whereas a second designed protein positions them in a previously unseen geometry. Spectroscopy revealed that the chlorophylls are excitonically coupled, and fluorescence lifetime imaging demonstrated energy transfer. The cryo-electron microscopy structure of a designed 24-chlorophyll octahedral nanocage with a special pair on each edge closely matched the design model. The results suggest that the de novo design of artificial photosynthetic systems is within reach of current computational methods.

Equivalence of quantum and classical third order response for weakly anharmonic coupled oscillators.

Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light-matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Accurate prediction of mutation-induced frequency shifts in chlorophyll proteins with a simple electrostatic model.

Photosynthetic pigment-protein complexes control local chlorophyll (Chl) transition frequencies through a variety of electrostatic and steric forces. Site-directed mutations can modify this local spectroscopic tuning, providing critical insight into native photosynthetic functions and offering the tantalizing prospect of creating rationally designed Chl proteins with customized optical properties. Unfortunately, at present, no proven methods exist for reliably predicting mutation-induced frequency shifts in advance, limiting the method's utility for quantitative applications. Here, we address this challenge by constructing a series of point mutants in the water-soluble chlorophyll protein of Lepidium virginicum and using them to test the reliability of a simple computational protocol for mutation-induced site energy shifts. The protocol uses molecular dynamics to prepare mutant protein structures and the charge density coupling model of Adolphs et al. [Photosynth. Res. 95, 197-209 (2008)] for site energy prediction; a graphical interface that implements the protocol automatically is published online at http://nanohub.org/tools/pigmenthunter. With the exception of a single outlier (presumably due to unexpected structural changes), we find that the calculated frequency shifts match the experiment remarkably well, with an average error of 1.6 nm over a 9 nm spread in wavelengths. We anticipate that the accuracy of the method can be improved in the future with more advanced sampling of mutant protein structures.

Distinct electrostatic frequency tuning rates for amide I and amide I' vibrations.

Amide I spectroscopy probes the backbone C=O stretch vibrations of peptides and proteins. Amide I spectra are often collected in deuterated water (D2O) since this provides a cleaner background in the amide I frequency range; such data are often referred to as amide I' spectra since deuteration induces changes in the mode structure, including a roughly ∼10 cm-1 redshift. For biological samples, however, deuteration is often not possible. As amide I frequency maps are increasingly applied to quantitative protein structural analysis, this raises the interesting challenge of drawing direct connections between amide I and amide I' data. We here analyze amide I and amide I' peak frequencies for a series of dipeptides and related compounds. Changes in protonation state induce large electrostatic shifts in the peak frequencies, allowing us to amass a sizable library of data points for direct amide I/amide I' comparison. While we find an excellent linear correlation between amide I and amide I' peak frequencies, the deuteration-induced shift is smaller for more red-shifted vibrations, indicating different electrostatic tuning rates in the two solvents. H2O/D2O shifts were negligible for proline-containing dipeptides that lack exchangeable amide hydrogens, indicating that the intrinsic properties of the solvent do not strongly influence the H/D shift. These findings indicate that the distinct tuning rates observed for the two vibrations arise from modifications to the intrinsic properties of the amide bond and provide (at least for solvated dipeptides) a simple, linear "map" for translating between amide I and amide I' frequencies.

Quantumness in light harvesting is determined by vibrational dynamics.

We demonstrate for the multi-level spin-boson (MLSB) Hamiltonian, typically used to describe biological light-harvesting, that the distinction between quantum and classical dynamics is determined entirely by the thermal environment. In particular, any MLSB model featuring classical interactions with a classical bath is exactly equivalent in its absorption and energy transfer dynamics to a classical model involving coupled harmonic oscillators. This result holds in the linear response regime for both pulsed and incoherent excitation. In the biological context, this finding highlights the centrality of vibrational dynamics in determining the "quantumness" of photosynthetic light-harvesting, particularly in the creation of the photosynthetic energy funnel where excitation energy concentrates near the reaction center via a series of downhill energy transfer events. These findings support the idea that this energy funnel is exclusively quantum-mechanical in origin, although it need not rely on entanglement.

Classical coherent two-dimensional vibrational spectroscopy.

Two-dimensional (2D) ultrafast spectroscopy is a powerful tool for studying the electronic and vibrational structures of complex systems. Unfortunately, the physical interpretation of these experiments is obscured by conceptual problems in classical response theory, i.e., the divergence of classical nonlinear response functions. We demonstrate that these difficulties are avoided by modeling classical 2D experiments nonperturbatively, illustrating that nonlinear spectroscopy and nonlinear response are not synonymous. Numerical simulations allow a direct comparison between classical and quantum 2D spectra for simple, weakly anharmonic systems relevant to vibrational spectroscopy. We find that nonperturbative classical theory-although differing in quantitative details-accurately captures the key qualitative features of the quantum 2D spectrum, including the separation of the signal into wavevector-selected pathways, formation of cross peaks between coupled vibrational modes, and coherent beating in the signal as a function of waiting time (so-called "quantum beats"). These results are discussed in terms of a simple analytical model which captures the key physical features of classical 2D spectroscopy and provides a link between classical and quantum descriptions. One interesting conclusion from this comparison is that the "coherence" observed in ultrafast spectroscopy may (at least in vibrational experiments) be understood as a purely classical phenomenon, without reference to quantum mechanics.

Computational Amide I 2D IR Spectroscopy as a Probe of Protein Structure and Dynamics.

Two-dimensional infrared spectroscopy of amide I vibrations is increasingly being used to study the structure and dynamics of proteins and peptides. Amide I, a primarily carbonyl stretching vibration of the protein backbone, provides information on secondary structures as a result of vibrational couplings and on hydrogen-bonding contacts when isotope labeling is used to isolate specific sites. In parallel with experiments, computational models of amide I spectra that use atomistic structures from molecular dynamics simulations have evolved to calculate experimental spectra. Mixed quantum-classical models use spectroscopic maps to translate the structural information into a quantum-mechanical Hamiltonian for the spectroscopically observed vibrations. This allows one to model the spectroscopy of large proteins, disordered states, and protein conformational dynamics. With improvements in amide I models, quantitative modeling of time-dependent structural ensembles and of direct feedback between experiments and simulations is possible. We review the advances in developing these models, their theoretical basis, and current and future applications.

Communication: Quantitative multi-site frequency maps for amide I vibrational spectroscopy.

An accurate method for predicting the amide I vibrational spectrum of a given protein structure has been sought for many years. Significant progress has been made recently by sampling structures from molecular dynamics simulations and mapping local electrostatic variables onto the frequencies of individual amide bonds. Agreement with experiment, however, has remained largely qualitative. Previously, we used dipeptide fragments and isotope-labeled constructs of the protein G mimic NuG2b as experimental standards for developing and testing amide I frequency maps. Here, we combine these datasets to test different frequency-map models and develop a novel method to produce an optimized four-site potential (4P) map based on the CHARMM27 force field. Together with a charge correction for glycine residues, the optimized map accurately describes both experimental datasets, with average frequency errors of 2-3 cm(-1). This 4P map is shown to be convertible to a three-site field map which provides equivalent performance, highlighting the viability of both field- and potential-based maps for amide I spectral modeling. The use of multiple sampling points for local electrostatics is found to be essential for accurate map performance.

Isotope-enriched protein standards for computational amide I spectroscopy.

We present a systematic isotope labeling study of the protein G mutant NuG2b as a step toward the production of reliable, structurally stable, experimental standards for amide I infrared spectroscopic simulations. By introducing isotope enriched amino acids into a minimal growth medium during bacterial expression, we induce uniform labeling of the amide bonds following specific amino acids, avoiding the need for chemical peptide synthesis. We use experimental data to test several common amide I frequency maps and explore the influence of various factors on map performance. Comparison of the predicted absorption frequencies for the four maps tested with empirical assignments to our experimental spectra yields a root-mean-square error of 6-12 cm(-1), with outliers of at least 12 cm(-1) in all models. This means that the predictions may be useful for predicting general trends such as changes in hydrogen bonding configuration; however, for finer structural constraints or absolute frequency assignments, the models are unreliable. The results indicate the need for careful testing of existing literature maps and shed light on possible next steps for the development of quantitative spectral maps.

Comments on the optical lineshape function: application to transient hole-burned spectra of bacterial reaction centers.

The vibrational spectral density is an important physical parameter needed to describe both linear and non-linear spectra of multi-chromophore systems such as photosynthetic complexes. Low-temperature techniques such as hole burning (HB) and fluorescence line narrowing are commonly used to extract the spectral density for a given electronic transition from experimental data. We report here that the lineshape function formula reported by Hayes et al. [J. Phys. Chem. 98, 7337 (1994)] in the mean-phonon approximation and frequently applied to analyzing HB data contains inconsistencies in notation, leading to essentially incorrect expressions in cases of moderate and strong electron-phonon (el-ph) coupling strengths. A corrected lineshape function L(ω) is given that retains the computational and intuitive advantages of the expression of Hayes et al. [J. Phys. Chem. 98, 7337 (1994)]. Although the corrected lineshape function could be used in modeling studies of various optical spectra, we suggest that it is better to calculate the lineshape function numerically, without introducing the mean-phonon approximation. New theoretical fits of the P870 and P960 absorption bands and frequency-dependent resonant HB spectra of Rb. sphaeroides and Rps. viridis reaction centers are provided as examples to demonstrate the importance of correct lineshape expressions. Comparison with the previously determined el-ph coupling parameters [Johnson et al., J. Phys. Chem. 94, 5849 (1990); Lyle et al., ibid. 97, 6924 (1993); Reddy et al., ibid. 97, 6934 (1993)] is also provided. The new fits lead to modified el-ph coupling strengths and different frequencies of the special pair marker mode, ωsp, for Rb. sphaeroides that could be used in the future for more advanced calculations of absorption and HB spectra obtained for various bacterial reaction centers.

Direct observation of intermolecular interactions mediated by hydrogen bonding.

Although intermolecular interactions are ubiquitous in physicochemical phenomena, their dynamics have proven difficult to observe directly, and most experiments rely on indirect measurements. Using broadband two-dimensional infrared spectroscopy (2DIR), we have measured the influence of hydrogen bonding on the intermolecular vibrational coupling between dimerized N-methylacetamide molecules. In addition to strong intramolecular coupling between N-H and C=O oscillators, cross-peaks in the broadband 2DIR spectrum appearing upon dimerization reveal strong intermolecular coupling that changes the character of the vibrations. In addition, dimerization changes the effects of intramolecular coupling, resulting in Fermi resonances between high and low-frequency modes. These results illustrate how hydrogen bonding influences the interplay of inter- and intramolecular vibrations, giving rise to correlated nuclear motions and significant changes in the vibrational structure of the amide group. These observations have direct impact on modeling and interpreting the IR spectra of proteins. In addition, they illustrate a general approach to direct molecular characterization of intermolecular interactions.

Modeling of fluorescence line-narrowed spectra in weakly coupled dimers in the presence of excitation energy transfer.

This work describes simple analytical formulas to describe the fluorescence line-narrowed (FLN) spectra of weakly coupled chromophores in the presence of excitation energy transfer (EET). Modeling studies for dimer systems (assuming low fluence and weak coupling) show that the FLN spectra (including absorption and emission spectra) calculated for various dimers using our model are in good agreement with spectra calculated by: (i) the simple convolution method and (ii) the more rigorous treatment using the Redfield approach [T. Renger and R. A. Marcus, J. Chem. Phys. 116, 9997 (2002)]. The calculated FLN spectra in the presence of EET of all three approaches are very similar. We argue that our approach provides a simplified and computationally more efficient description of FLN spectra in the presence of EET. This method also has been applied to FLN spectra obtained for the CP47 antenna complex of Photosystem II reported by Neupane et al. [J. Am. Chem. Soc. 132, 4214 (2010)], which indicated the presence of uncorrelated EET between pigments contributing to the two lowest energy (overlapping) exciton states, each mostly localized on a single chromophore. Calculated and experimental FLN spectra for CP47 complex show very good qualitative agreement.

Feeling the Strain: Quantifying Ligand Deformation in Photosynthesis.

Structural distortion of protein-bound ligands can play a critical role in enzyme function by tuning the electronic and chemical properties of the ligand molecule. However, quantifying these effects is difficult due to the limited resolution of protein structures and the difficulty of generating accurate structural restraints for nonprotein ligands. Here, we seek to quantify these effects through a statistical analysis of ligand distortion in chlorophyll proteins (CP), where ring deformation is thought to play a role in energy and electron transfer. To assess the accuracy of ring-deformation estimates from available structural data, we take advantage of the C2 symmetry of photosystem II (PSII), comparing ring-deformation estimates for equivalent sites both within and between 113 distinct X-ray and cryogenic electron microscopy PSII structures. Significantly, we find that several deformation modes exhibit considerable variability in predictions, even for equivalent monomers, down to a 2 Å resolution, to an extent that probably prevents their utilization in optical calculations. We further find that refinement restraints play a critical role in determining deformation values to resolution as low as 2 Å. However, for those modes that are well-resolved in the structural data, ring deformation in PSII is strongly conserved across all species tested from cyanobacteria to algae. These results highlight both the opportunities and limitations inherent in structure-based analyses of the bioenergetic and optical properties of CPs and other protein-ligand complexes.

Amide I two-dimensional infrared spectroscopy: methods for visualizing the vibrational structure of large proteins.

Network layouts are introduced as a method to visualize couplings between local amide I vibrations in proteins. The method is used to identify groups of strongly coupled oscillators to block-diagonalize the Hamiltonians, considerably reducing the expense associated with computing infrared spectra of large proteins. The quality of linear and nonlinear spectra generated from block-diagonal Hamiltonians is demonstrated by comparison with spectra generated from full Hamiltonian trajectories. A library of six proteins reveals that vibrational couplings within hydrogen-bonded residues in specific secondary structures give rise to the characteristic amide I line shapes whereas other couplings play a minor role. Exciton delocalization analyses indicate that amide I vibrations in proteins remain largely localized to groups of less than ten residues.

Electrostatic frequency shifts in amide I vibrational spectra: direct parameterization against experiment.

The interpretation of protein amide I infrared spectra has been greatly assisted by the observation that the vibrational frequency of a peptide unit reports on its local electrostatic environment. However, the interpretation of spectra remains largely qualitative due to a lack of direct quantitative connections between computational models and experimental data. Here, we present an empirical parameterization of an electrostatic amide I frequency map derived from the infrared absorption spectra of 28 dipeptides. The observed frequency shifts are analyzed in terms of the local electrostatic potential, field, and field gradient, evaluated at sites near the amide bond in molecular dynamics simulations. We find that the frequency shifts observed in experiment correlate very well with the electric field in the direction of the C=O bond evaluated at the position of the amide oxygen atom. A linear best-fit mapping between observed frequencies and electric field yield sample standard deviations of 2.8 and 3.7 cm(-1) for the CHARMM27 and OPLS-AA force fields, respectively, and maximum deviations (within our data set) of 9 cm(-1). These results are discussed in the broader context of amide I vibrational models and the effort to produce quantitative agreement between simulated and experimental absorption spectra.

Bioexcitons by Design: How Do We Get There?

Biological pigment-protein complexes (PPCs) exhibit a remarkable ability to tune the optical properties of biological excitons (bioexcitons) through specific pigment-protein interactions. While such fine-tuning allows natural systems (e.g., photosynthetic proteins) to carry out their native functions with near-optimal performance, native function itself is often suboptimal for applications such as biofuel production or quantum technology development. This perspective offers a look at near-term prospects for the rational reoptimization of PPC bioexcitons for new functions using site-directed mutagenesis. The primary focus is on the "structure-spectrum" challenge of understanding the relationships between structural features and spectroscopic properties. While recent examples demonstrate that site-directed mutagenesis can be used to tune nearly all key bioexciton parameters (e.g., site energies, interpigment couplings, and electronic-vibrational interactions), critical challenges remain before we achieve truly rational design of bioexciton properties.

De novo design of energy transfer proteins housing excitonically coupled chlorophyll special pairs.

Natural photosystems couple light harvesting to charge separation using a "special pair" of chlorophyll molecules that accepts excitation energy from the antenna and initiates an electron-transfer cascade. To investigate the photophysics of special pairs independent of complexities of native photosynthetic proteins, and as a first step towards synthetic photosystems for new energy conversion technologies, we designed C2-symmetric proteins that precisely position chlorophyll dimers. X-ray crystallography shows that one designed protein binds two chlorophylls in a binding orientation matching native special pairs, while a second positions them in a previously unseen geometry. Spectroscopy reveals excitonic coupling, and fluorescence lifetime imaging demonstrates energy transfer. We designed special pair proteins to assemble into 24-chlorophyll octahedral nanocages; the design model and cryo-EM structure are nearly identical. The design accuracy and energy transfer function of these special pair proteins suggest that de novo design of artificial photosynthetic systems is within reach of current computational methods.

Identifying residual structure in intrinsically disordered systems: a 2D IR spectroscopic study of the GVGXPGVG peptide.

The peptide amide-I vibration of a proline turn encodes information on the turn structure. In this study, FTIR, two-dimensional IR spectroscopy and molecular dynamics simulations were employed to characterize the varying turn conformations that exist in the GVGX(L)PGVG family of disordered peptides. This analysis revealed that changing the size of the side chain at the X amino acid site from Gly to Ala to Val substantially alters the conformation of the peptide. To quantify this effect, proline peak shifts and intensity changes were compared to a structure-based spectroscopic model. These simulated spectra were used to assign the population of type-II ß turns, bulged turns, and irregular ß turns for each peptide. Of particular interest was the Val variant commonly found in the protein elastin, which contained a 25% population of irregular ß turns containing two peptide hydrogen bonds to the proline C═O.