Theoretical analysis of the geometrical isotope effect on the hydrogen bonds in photoactive yellow protein with multi-component density functional theory

Perturbation of Short Hydrogen Bonds in Photoactive Yellow Protein via Noncanonical Amino Acid Incorporation

Photoactive yellow protein (PYP) is a small photoreceptor protein that has two unusually short hydrogen bonds between the deprotonated p-coumaric acid chromophore and two amino acids, a tyrosine and a glutamic acid. This has led to considerable debate as to whether the glutamic acid-chromophore hydrogen bond is a low barrier hydrogen bond, with conflicting results in the literature. We have modified the p Ka of the tyrosine by amber suppression and of the chromophore by chemical substitution. X-ray crystal structures of these modified proteins are nearly identical to the wild-type protein, so the heavy atom distance between proton donor and acceptor is maintained, even though these modifications change the relative proton affinity between donor and acceptor. Despite a considerable change in relative proton affinity, the NMR chemical shifts of the hydrogen-bonded protons are only moderately affected. QM/MM calculations were used to explore the protons' potential energy surface and connect the calculated proton position with empirically measured proton chemical shifts. The results are inconsistent with a low barrier hydrogen bond but in all cases are consistent with a localized proton, suggesting an ionic hydrogen bond rather than a low barrier hydrogen bond.

Effective electronic-only Kohn-Sham equations for the muonic molecules

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

Observation of α-Helical Hydrogen-Bond Cooperativity in an Intact Protein

The presence and extent of hydrogen-bonding (H-bonding) cooperativity in proteins remains a fundamental question, which in the past has been studied extensively, mostly by infrared and fluorescence measurements on model peptides. We demonstrate that such cooperativity can be studied in an intact protein by hydrogen/deuterium exchange NMR spectroscopy. The method is based on the fact that substitution of NH by ND in a backbone amide group slightly weakens the N-H···O═C hydrogen bond. Our results show that such substitution at position i in an α-helix impacts the (1)H and (15)N chemical shifts of the amide sites of residues i - 3 to i + 3. Quantum mechanical calculations indicate that the upfield shifts of (1)H and (15)N resonances at site i, observed upon H/D exchanges at sites i - 3, i + 1, i + 2, and i + 3, correspond to a decrease of the ith backbone amide electric dipole moment, which weakens its H-bonding and long-range electrostatic interactions with other backbone amides in the α-helix. These results provide new quantitative insights into the cooperativity of H-bonding in protein α-helices.

Vibrational analysis on the revised potential energy curve of the low-barrier hydrogen bond in photoactive yellow protein

Photoactive yellow protein (PYP) has a characteristic hydrogen bond (H bond) between p-coumaric acid chromophore and Glu46, whose OH bond length has been observed to be 1.21 Å by the neutron diffraction technique [Proc. Natl. Acad. Sci. 106, 440-4]. Although it has been expected that such a drastic elongation of the OH bond could be caused by the quantum effect of the hydrogen nucleus, previous theoretical computations including the nuclear quantum effect have so far underestimated the bond length by more than 0.07 Å. To elucidate the origin of the difference, we performed a vibrational analysis of the H bond on potential energy curve with O…O distance of 2.47 Å on the equilibrium structure, and that with O…O distance of 2.56 Å on the experimental crystal structure. While the vibrationally averaged OH bond length for equilibrium structure was underestimated, the corresponding value for crystal structure was in reasonable agreement with the corresponding experimental values. The elongation of the O…O distance by the quantum mechanical or thermal fluctuation would be indispensable for the formation of a low-barrier hydrogen bond in PYP.

Theoretical analysis of geometry and NMR isotope shift in hydrogen-bonding center of photoactive yellow protein by combination of multicomponent quantum mechanics and ONIOM scheme

Multicomponent quantum mechanical (MC_QM) calculation has been extended with ONIOM (our own N-layered integrated molecular orbital + molecular mechanics) scheme [ONIOM(MC_QM:MM)] to take account of both the nuclear quantum effect and the surrounding environment effect. The authors have demonstrated the first implementation and application of ONIOM(MC_QM:MM) method for the analysis of the geometry and the isotope shift in hydrogen-bonding center of photoactive yellow protein. ONIOM(MC_QM:MM) calculation for a model with deprotonated Arg52 reproduced the elongation of O-H bond of Glu46 observed by neutron diffraction crystallography. Among the unique isotope shifts in different conditions, the model with protonated Arg52 with solvent effect reasonably provided the best agreement with the corresponding experimental values from liquid NMR measurement. Our results implied the availability of ONIOM(MC_QM:MM) to distinguish the local environment around hydrogen bonds in a biomolecule.

Hidden aspects of the Structural theory of chemistry: MC-QTAIM analysis reveals "alchemical" transformation from a triatomic to a diatomic structure

The Structural theory of chemistry introduces chemical/molecular structure as a combination of relative arrangement and bonding patterns of atoms in a molecule. Nowadays, the structure of atoms in molecules is derived from the topological analysis of the quantum theory of atoms in molecules (QTAIM). In this context, a molecular structure is varied by large geometrical variations and concomitant reorganization of electronic structure that usually take place in chemical reactions or under extreme hydrostatic pressure. In this report, a new mode of structural variation is introduced within the context of the newly proposed multi-component QTAIM (MC-QTAIM) that originates from the mass variation of nuclei. Accordingly, XCN and CNX series of species are introduced where X stands for a quantum particle with a unit of positive charge and a variable mass that is varied in discrete steps between the mass of a proton and a positron. Ab initio non-Born-Oppenheimer (non-BO) calculations are done on both series of species and the resulting non-BO wavefunctions are used for the MC-QTAIM analysis, revealing a triatomic structure for the proton mass and a diatomic structure for the positron mass. In both series of species, a critical mass between that of proton and positron mass is discovered where the transition from triatomic to diatomic structure takes place. This abrupt structural transformation has a topological nature resembling the usual phase transitions in thermodynamics. The discovered mass-induced structural transformation is a hidden aspect of the Structural theory which is revealed only beyond the BO paradigm, when nuclei are treated as quantum waves instead of clamped point charges.

Strong ionic hydrogen bonding causes a spectral isotope effect in photoactive yellow protein

Standard hydrogen bonds are of great importance for protein structure and function. Ionic hydrogen bonds often are significantly stronger than standard hydrogen bonds and exhibit unique properties, but their role in proteins is not well understood. We report that hydrogen/deuterium exchange causes a redshift in the visible absorbance spectrum of photoactive yellow protein (PYP). We expand the range of interpretable isotope effects by assigning this spectral isotope effect (SIE) to a functionally important hydrogen bond at the active site of PYP. The inverted sign and extent of this SIE is explained by the ionic nature and strength of this hydrogen bond. These results show the relevance of ionic hydrogen bonding for protein active sites, and reveal that the inverted SIE is a novel, to our knowledge, tool to probe ionic hydrogen bonds. Our results support a classification of hydrogen bonds that distinguishes the properties of ionic hydrogen bonds from those of both standard and low barrier hydrogen bonds, and show how this classification helps resolve a recent debate regarding active site hydrogen bonding in PYP.