Vibrational dynamics of myoglobin determined by the phonon-assisted Mössbauer effect

Temperature-dependent iron motion in extremophile rubredoxins - no need for 'corresponding states'

Extremophile organisms are known that can metabolize at temperatures down to - 25 °C (psychrophiles) and up to 122 °C (hyperthermophiles). Understanding viability under extreme conditions is relevant for human health, biotechnological applications, and our search for life elsewhere in the universe. Information about the stability and dynamics of proteins under environmental extremes is an important factor in this regard. Here we compare the dynamics of small Fe-S proteins - rubredoxins - from psychrophilic and hyperthermophilic microorganisms, using three different nuclear techniques as well as molecular dynamics calculations to quantify motion at the Fe site. The theory of 'corresponding states' posits that homologous proteins from different extremophiles have comparable flexibilities at the optimum growth temperatures of their respective organisms. Although 'corresponding states' would predict greater flexibility for rubredoxins that operate at low temperatures, we find that from 4 to 300 K, the dynamics of the Fe sites in these homologous proteins are essentially equivalent.

Water dynamics around T0 vs R4 of hemoglobin from local hydrophobicity analysis

The local hydration around tetrameric hemoglobin (Hb) in its T₀ and R₄ conformational substates is analyzed based on molecular dynamics simulations. Analysis of the local hydrophobicity (LH) for all residues at the α₁β₂ and α₂β₁ interfaces, responsible for the quaternary T → R transition, which is encoded in the Monod-Wyman-Changeux model, as well as comparison with earlier computations of the solvent accessible surface area, makes clear that the two quantities measure different aspects of hydration. Local hydrophobicity quantifies the presence and structure of water molecules at the interface, whereas "buried surface" reports on the available space for solvent. For simulations with Hb frozen in its T₀ and R₄ states, the correlation coefficient between LH and buried surface is 0.36 and 0.44, respectively, but it increases considerably if the 95% confidence interval is used. The LH with Hb frozen and flexible changes little for most residues at the interfaces but is significantly altered for a few select ones: Thr41α, Tyr42α, Tyr140α, Trp37β, Glu101β (for T₀) and Thr38α, Tyr42α, Tyr140α (for R₄). The number of water molecules at the interface is found to increase by ∼25% for T₀ → R₄, which is consistent with earlier measurements. Since hydration is found to be essential to protein function, it is clear that hydration also plays an essential role in allostery.

Stationary and Time-Dependent Carbon Monoxide Stretching Mode Features in Carboxy Myoglobin: A Theoretical-Computational Reappraisal

The stationary and time-dependent infrared spectrum (IR) of the CO stretching mode (ν_CO) in carboxymyoglobin (MbCO), a longstanding problem of biophysical chemistry, has been modeled through a theoretical-computational method specifically designed for simulating quantum observables in complex atomic-molecular systems and based on a combined application of long time scale molecular dynamics simulations and quantum-chemical calculations. This study is basically focused on two aspects: (i) the origin of the stationary IR substates (termed as A₀, A₁, and A₃) and (ii) the modeling and the interpretation of the ν_CO energy relaxation. The results, strengthened by a more than satisfactory agreement with the experimental data, concisely indicate that (i) the conformational His64-FeCO relevant substates, i.e., characterized by the formation-disruption of the H-bond between the above moieties, are the main responsible of the presence of two distinct and well separated (A₀ and A₁/A₃) spectroscopic regions; (ii) the characteristic bimodal shape of the A₁/A₃ spectral region, according to our model, is the result of the fluctuation of the electric field pattern as provided by the protein-solvent framework perturbing the bound His64-CO-Heme complex; and (iii) the electric field pattern, in conjunction with the relatively high density of MbCO vibrational states, is also the main determinant of the ν_CO energy relaxation, characterizing its kinetic efficiency.

Hard-X-Ray Spectroscopy with a Spectrographic Approach

Hard-x-ray spectroscopy relies on a suite of modern techniques for studies of vibrational, electronic, and magnetic excitations in condensed matter. At present, the energy resolution of these techniques can be improved only by decreasing the spectral window of the involved optics-monochromators and analyzers-thereby sacrificing the intensity. Here, we demonstrate hard-x-ray spectroscopy with greatly improved energy resolution without narrowing the spectral window by adapting principles of spectrographic imaging to the hard-x-ray regime. Similar to Newton's classical prism, the hard-x-ray spectrograph disperses different "colors"-i.e., energies-of x-ray photons in space. Then, selecting each energy component with a slit ensures high energy resolution, whereas measuring x-ray spectra with all components of a broad spectral window keeps the intensity. We employ the principles of spectrographic imaging for phonon spectroscopy. Here the new approach revealed anomalous soft atomic dynamics in α-iron, a phenomenon which was not previously reported in the literature. We argue that hard-x-ray spectrographic imaging also could be a path to discovering new physics in studies of electronic and magnetic excitations.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

Protein and RNA dynamical fingerprinting

Protein structural vibrations impact biology by steering the structure to functional intermediate states; enhancing tunneling events; and optimizing energy transfer. Strong water absorption and a broad continuous vibrational density of states have prevented optical identification of these vibrations. Recently spectroscopic signatures that change with functional state were measured using anisotropic terahertz microscopy. The technique however has complex sample positioning requirements and long measurement times, limiting access for the biomolecular community. Here we demonstrate that a simplified system increases spectroscopic structure to dynamically fingerprint biomacromolecules with a factor of 6 reduction in data acquisition time. Using this technique, polarization varying anisotropy terahertz microscopy, we show sensitivity to inhibitor binding and unique vibrational spectra for several proteins and an RNA G-quadruplex. The technique’s sensitivity to anisotropic absorbance and birefringence provides rapid assessment of macromolecular dynamics that impact biology.

The characterization of biomacromolecule structural vibrations has been impeded by a broad continuous vibrational density of states obscuring molecule specific vibrations. A terahertz microscopy system using polarization control produces signatures to dynamically fingerprint proteins and a RNA G-quadruplex.

Ergodicity breaking of iron displacement in heme proteins

We present a model of the dynamical transition of atomic displacements in proteins. Increased mean-square displacement at higher temperatures is caused by the softening of the force constant for atomic/molecular displacements by electrostatic and van der Waals forces from the protein-water thermal bath. Displacement softening passes through a nonergodic dynamical transition when the relaxation time of the force-force correlation function enters, with increasing temperature, the instrumental observation window. Two crossover temperatures are identified. The lower crossover, presently connected to the glass transition, is related to the dynamical unfreezing of rotations of water molecules within nanodomains polarized by charged surface residues of the protein. The higher crossover temperature, usually assigned to the dynamical transition, marks the onset of water translations. All crossovers are ergodicity breaking transitions depending on the corresponding observation windows. Allowing stretched exponential relaxation of the protein-water thermal bath significantly improves the theory-experiment agreement when applied to solid protein samples studied by Mössbauer spectroscopy.

What Can Be Learned from Nuclear Resonance Vibrational Spectroscopy: Vibrational Dynamics and Hemes

Nuclear resonance vibrational spectroscopy (NRVS; also known as nuclear inelastic scattering, NIS) is a synchrotron-based method that reveals the full spectrum of vibrational dynamics for Mössbauer nuclei. Another major advantage, in addition to its completeness (no arbitrary optical selection rules), is the unique selectivity of NRVS. The basics of this recently developed technique are first introduced with descriptions of the experimental requirements and data analysis including the details of mode assignments. We discuss the use of NRVS to probe ⁵⁷Fe at the center of heme and heme protein derivatives yielding the vibrational density of states for the iron. The application to derivatives with diatomic ligands (O₂, NO, CO, CN^–) shows the strong capabilities of identifying mode character. The availability of the complete vibrational spectrum of iron allows the identification of modes not available by other techniques. This permits the correlation of frequency with other physical properties. A significant example is the correlation we find between the Fe–Im stretch in six-coordinate Fe(XO) hemes and the trans Fe–N(Im) bond distance, not possible previously. NRVS also provides uniquely quantitative insight into the dynamics of the iron. For example, it provides a model-independent means of characterizing the strength of iron coordination. Prediction of the temperature-dependent mean-squared displacement from NRVS measurements yields a vibrational “baseline” for Fe dynamics that can be compared with results from techniques that probe longer time scales to yield quantitative insights into additional dynamical processes.

Moving in the Right Direction: Protein Vibrations Steering Function

Nearly all protein functions require structural change, such as enzymes clamping onto substrates, and ion channels opening and closing. These motions are a target for possible new therapies; however, the control mechanisms are under debate. Calculations have indicated protein vibrations enable structural change. However, previous measurements found these vibrations only weakly depend on the functional state. By using the novel technique of anisotropic terahertz microscopy, we find that there is a dramatic change to the vibrational directionality with inhibitor binding to lysozyme, whereas the vibrational energy distribution, as measured by neutron inelastic scattering, is only slightly altered. The anisotropic terahertz measurements provide unique access to the directionality of the intramolecular vibrations, and immediately resolve the inconsistency between calculations and previous measurements, which were only sensitive to the energy distribution. The biological importance of the vibrational directions versus the energy distribution is revealed by our calculations comparing wild-type lysozyme with a higher catalytic rate double deletion mutant. The vibrational energy distribution is identical, but the more efficient mutant shows an obvious reorientation of motions. These results show that it is essential to characterize the directionality of motion to understand and control protein dynamics to optimize or inhibit function.

Dynamical and orientational structural crossovers in low-temperature glycerol

Mean-square displacements of hydrogen atoms in glass-forming materials and proteins, as reported by incoherent elastic neutron scattering, show kinks in their temperature dependence. This crossover, known as the dynamical transition, connects two approximately linear regimes. It is often assigned to the dynamical freezing of subsets of molecular modes at the point of equality between their corresponding relaxation times and the instrumental observation window. The origin of the dynamical transition in glass-forming glycerol is studied here by extensive molecular dynamics simulations. We find the dynamical transition to occur for both the center-of-mass translations and the molecular rotations at the same temperature, insensitive to changes of the observation window. Both the translational and rotational dynamics of glycerol show a dynamic crossover from the structural to a secondary relaxation at the temperature of the dynamical transition. A significant and discontinuous increase in the orientational Kirkwood factor and in the dielectric constant is observed in the same range of temperatures. No indication is found of a true thermodynamic transition to an ordered low-temperature phase. We therefore suggest that all observed crossovers are dynamic in character. The increase in the dielectric constant is related to the dynamic freezing of dipolar domains on the time scale of simulations.

Time differentiated nuclear resonance spectroscopy coupled with pulsed laser heating in diamond anvil cells

Developments in pulsed laser heating applied to nuclear resonance techniques are presented together with their applications to studies of geophysically relevant materials. Continuous laser heating in diamond anvil cells is a widely used method to generate extreme temperatures at static high pressure conditions in order to study the structure and properties of materials found in deep planetary interiors. The pulsed laser heating technique has advantages over continuous heating, including prevention of the spreading of heated sample and/or the pressure medium and, thus, a better stability of the heating process. Time differentiated data acquisition coupled with pulsed laser heating in diamond anvil cells was successfully tested at the Nuclear Resonance beamline (ID18) of the European Synchrotron Radiation Facility. We show examples applying the method to investigation of an assemblage containing ε-Fe, FeO, and Fe3C using synchrotron Mössbauer source spectroscopy, FeCO3 using nuclear inelastic scattering, and Fe2O3 using nuclear forward scattering. These examples demonstrate the applicability of pulsed laser heating in diamond anvil cells to spectroscopic techniques with long data acquisition times, because it enables stable pulsed heating with data collection at specific time intervals that are synchronized with laser pulses.

Recent advances in biosynthetic modeling of nitric oxide reductases and insights gained from nuclear resonance vibrational and other spectroscopic studies

This Forum Article focuses on recent advances in structural and spectroscopic studies of biosynthetic models of nitric oxide reductases (NORs). NORs are complex metalloenzymes found in the denitrification pathway of Earth’s nitrogen cycle where they catalyze the proton-dependent two-electron reduction of nitric oxide (NO) to nitrous oxide (N₂O). While much progress has been made in biochemical and biophysical studies of native NORs and their variants, a clear mechanistic understanding of this important metalloenzyme related to its function is still elusive. We report herein UV–vis and nuclear resonance vibrational spectroscopy (NRVS) studies of mononitrosylated intermediates of the NOR reaction of a biosynthetic model. The ability to selectively substitute metals at either heme or nonheme metal sites allows the introduction of independent ⁵⁷Fe probe atoms at either site, as well as allowing the preparation of analogues of stable reaction intermediates by replacing either metal with a redox inactive metal. Together with previous structural and spectroscopic results, we summarize insights gained from studying these biosynthetic models toward understanding structural features responsible for the NOR activity and its mechanism. The outlook on NOR modeling is also discussed, with an emphasis on the design of models capable of catalytic turnovers designed based on close mimics of the secondary coordination sphere of native NORs.

New insights into nitric oxide reductases (NORs) are obtained. Using nuclear resonance vibrational spectroscopy, we probe both iron atoms in mononitrosylated intermediates of the NOR reaction in a biosynthetic protein model that reveal new insights into the structural and electronic features responsible for the NOR activity and its likely mechanism.

Terahertz optical measurements of correlated motions with possible allosteric function

A suggested mechanism for allosteric response is the distortion of the energy landscape with agonist binding changing the protein structure's access to functional configurations. Intramolecular vibrations are indicative of the energy landscape and may have trajectories that enable functional conformational change. Here, we discuss the development of an optical method to measure the intramolecular vibrations in proteins, namely, crystal anisotropy terahertz microscopy, and the various approaches which can be used to identify the spectral data with specific structural motions.

A wave-mechanical model of incoherent quasielastic scattering in complex systems

Quasielastic incoherent neutron scattering (QENS) is an important tool for the exploration of the dynamics of complex systems such as biomolecules, liquids, and glasses. The dynamics is reflected in the energy spectra of the scattered neutrons. Conventionally these spectra are decomposed into a narrow elastic line and a broad quasielastic band. The band is interpreted as being caused by Doppler broadening due to spatial motion of the target molecules. We propose a quantum-mechanical model in which there is no separate elastic line. The quasielastic band is composed of sharp lines with twice the natural line width, shifted from the center by a random walk of the protein in the free-energy landscape of the target molecule. The walk is driven by vibrations and by external fluctuations. We first explore the model with the Mössbauer effect. In the subsequent application to QENS we treat the incoming neutron as a de Broglie wave packet. While the wave packet passes the protons in the protein and the hydration shell it exchanges energy with the protein during the passage time of about 100 ns. The energy exchange broadens the ensemble spectrum. Because the exchange involves the free-energy landscape of the protein, the QENS not only provides insight into the protein dynamics, but it may also illuminate the free-energy landscape of the protein-solvent system.

The dynamics of the non-heme iron in bacterial reaction centers from Rhodobacter sphaeroides

We investigate the dynamical properties of the non-heme iron (NHFe) in His-tagged photosynthetic bacterial reaction centers (RCs) isolated from Rhodobacter (Rb.) sphaeroides. Mössbauer spectroscopy and nuclear inelastic scattering of synchrotron radiation (NIS) were applied to monitor the arrangement and flexibility of the NHFe binding site. In His-tagged RCs, NHFe was stabilized only in a high spin ferrous state. Its hyperfine parameters (IS=1.06±0.01mm/s and QS=2.12±0.01mm/s), and Debye temperature (θ(D0)~167K) are comparable to those detected for the high spin state of NHFe in non-His-tagged RCs. For the first time, pure vibrational modes characteristic of NHFe in a high spin ferrous state are revealed. The vibrational density of states (DOS) shows some maxima between 22 and 33meV, 33 and 42meV, and 53 and 60meV and a very sharp one at 44.5meV. In addition, we observe a large contribution of vibrational modes at low energies. This iron atom is directly connected to the protein matrix via all its ligands, and it is therefore extremely sensitive to the collective motions of the RC protein core. A comparison of the DOS spectra of His-tagged and non-His-tagged RCs from Rb. sphaeroides shows that in the latter case the spectrum was overlapped by the vibrations of the heme iron of residual cytochrome c(2), and a low spin state of NHFe in addition to its high spin one. This enabled us to pin-point vibrations characteristic for the low spin state of NHFe.

Dissipative electro-elastic network model of protein electrostatics

We propose a dissipative electro-elastic network model to describe the dynamics and statistics of electrostatic fluctuations at active sites of proteins. The model combines the harmonic network of residue beads with overdamped dynamics of the normal modes of the network characterized by two friction coefficients. The electrostatic component is introduced to the model through atomic charges of the protein force field. The overall effect of the electrostatic fluctuations of the network is recorded through the frequency-dependent response functions of the electrostatic potential and electric field at the protein active site. We also consider the dynamics of displacements of individual residues in the network and the dynamics of distances between pairs of residues. The model is tested against loss spectra of residue displacements and the electrostatic potential and electric field at the heme's iron from all-atom molecular dynamics simulations of three hydrated globular proteins.

Nuclear resonance vibrational spectra of five-coordinate imidazole-ligated iron(II) porphyrinates

Nuclear resonance vibrational spectra have been obtained for six five-coordinate imidazole-ligated iron(II) porphyrinates, [Fe(Por)(L)] (Por = tetraphenylporphyrinate, octaethylporphyrinate, tetratolylporphyrinate, or protoporphyrinate IX and L = 2-methylimidazole or 1,2-dimethylimidazole). Measurements have been made on both powder and oriented crystal samples. The spectra are dominated by strong signals around 200-300 cm(-1). Although the in-plane and out-of-plane vibrations are seriously overlapped, oriented crystal spectra allow their deconvolution. Thus, oriented crystal experimental data, along with density functional theory (DFT) calculations, enable the assignment of key vibrations in the spectra. Molecular dynamics are also discussed. The nature of the Fe-N(Im) vibrations has been elaborated further than was possible from resonance Raman studies. Our study suggests that the Fe motions are coupled with the porphyrin core and peripheral groups motions. Both peripheral groups and their conformations have significant influence on the vibrational spectra (position and shape).

Predicting Nuclear Resonance Vibrational Spectra of [Fe(OEP)(NO)]

Nuclear Resonance Vibrational Spectroscopy (NRVS) is a sensitive vibrational probe for biologically important heme complexes. The exquisite sensitivity of the NRVS data to the electronic structure provides detailed insights into the nature of these interesting compounds, but requires highly accurate computational methods for the mode assignments. To determine the best combinations of density functionals and basis sets, a series of benchmark DFT calculations on the previously characterized complex [Fe(OEP)NO] (OEP(2-)=octaethylporphyrinatio dianion) were performed. A test set of 21 methodology combinations including 8 functionals (BP86, mPWPW91, B3LYP, PBE1PBE, M062X, M06L, LC-BP86 and ωB97X-D) and 5 basis set (VTZ, TZVP, Lanl2DZ for iron and 6-31G*, 6-31+G* for other atoms) was carried out to calculate electronic structures and vibrational frequencies. We also implemented the conversion of frequency calculations into orientation-selective mode composition factors (e(2)), which can used to simulate the Vibrational Density Of States (VDOS) using Gaussian normal distribution functions. These use a series of user-friendly scripts for their application to NRVS. The structures as well as the isotropic and anisotropic NRVS of [Fe(OEP)NO] obtained with the M06L functional with a variety of basis sets are found to best reproduce the available experimental data, followed by B3LYP/LanL2DZ calculations. Other density functionals and basis sets do not produce the same level of accuracy. The noticeably worse agreement between theory and experiment for the out-plane NRVS compared with the excellent performance of the M06L functional for the in-plane prediction is attributed to deficiencies of the physical model rather than the computational methodology.

Electrostatics of the protein-water interface and the dynamical transition in proteins

Atomic displacements of hydrated proteins are dominated by phonon vibrations at low temperatures and by dissipative large-amplitude motions at high temperatures. A crossover between the two regimes is known as a dynamical transition. Recent experiments indicate a connection between the dynamical transition and the dielectric response of the hydrated protein. We analyze two mechanisms of the coupling between the protein atomic motions and the protein-water interface. The first mechanism considers viscoelastic changes in the global shape of the protein plasticized by its coupling to the hydration shell. The second mechanism involves modulations of the local motions of partial charges inside the protein by electrostatic fluctuations. The model is used to analyze mean-square displacements of iron of metmyoglobin reported by Mössbauer spectroscopy. We show that high displacement of heme iron at physiological temperatures is dominated by electrostatic fluctuations. Two onsets, one arising from the viscoelastic response and the second from electrostatic fluctuations, are seen in the temperature dependence of the mean-square displacements when the corresponding relaxation times enter the instrumental resolution window.

Evidence of protein collective motions on the picosecond timescale

We investigate the presence of structural collective motions on a picosecond timescale for the heme protein, cytochrome c, as a function of oxidation and hydration, using terahertz (THz) time domain spectroscopy and molecular dynamics simulations. The THz response dramatically increases with oxidation, with the largest increase for lowest hydrations, and highest frequencies. For both oxidation states the THz response rapidly increases with hydration saturating above ∼25% (g H(2)O/g protein). Quasiharmonic vibrational modes and dipole-dipole correlation functions were calculated from molecular dynamics trajectories. The collective mode density of states alone reproduces the measured hydration dependence, providing strong evidence of the existence of these motions. The large oxidation dependence is reproduced only by the dipole-dipole correlation function, indicating the contrast arises from diffusive motions consistent with structural changes occurring in the vicinity of buried internal water molecules. This source for the observed oxidation dependence is consistent with the lack of an oxidation dependence in nuclear resonant vibrational spectroscopy measurements.

Dynamical transition in proteins and non-Gaussian behavior of low-frequency modes in self-consistent normal mode analysis

Self-consistent normal mode analysis (SCNMA) is applied to heme c type cytochrome f to study temperature-dependent protein motion. Classical normal mode analysis assumes harmonic behavior and the protein mean-square displacement has a linear dependence on temperature. This is only consistent with low-temperature experimental results. To connect the protein vibrational motions between low and physiological temperatures, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, quantum harmonic-oscillator theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests that it may be the cause of the non-Gaussian behavior of the protein motions probed by elastic incoherent neutron scattering. The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low-frequency regime ( <50 cm(-1) or <6 meV or >0.6 ps). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.

Vibrational dynamics of iron in cytochrome C

Nuclear resonance vibrational spectroscopy (NRVS) and Raman spectroscopy on (54)Fe- and (57)Fe-enriched cytochrome c (cyt c) identify multiple bands involving vibrations of the heme Fe. Comparison with predictions from Fe isotope shifts reveals that 70% of the NRVS signal in the 300-450 cm(-1) frequency range corresponds to vibrations resolved in Soret-enhanced Raman spectra. This frequency range dominates the "stiffness", an effective force constant determined by the Fe vibrational density of states (VDOS), which measures the strength of nearest-neighbor interactions with Fe. The stiffness of the low-spin Fe environment in both oxidation states of cyt c significantly exceeds that for the high-spin Fe in deoxymyoglobin, where the 200-300 cm(-1) frequency range dominates the VDOS. This situation is reflected in the shorter Fe-ligand bond lengths in the former with respect to the latter. The longer Fe-S(Met80) in oxidized cyt c with respect to reduced cyt c leads to a decrease in the stiffness of the iron environment upon oxidation. Comparison with NRVS measurements allows us to assess assignments for vibrational modes resolved in this region of the heme Raman spectrum. We consider the possibility that the 372 cm(-1) band in reduced cyt c involves the Fe-S(Met80) bond.

Resilience of the iron environment in heme proteins

Conformational flexibility is essential to the functional behavior of proteins. We use an effective force constant introduced by Zaccai, the resilience, to quantify this flexibility. Site-selective experimental and computational methods allow us to determine the resilience of heme protein active sites. The vibrational density of states of the heme Fe determined using nuclear resonance vibrational spectroscopy provides a direct experimental measure of the resilience of the Fe environment, which we compare quantitatively with values derived from the temperature dependence of atomic mean-squared displacements in molecular dynamics simulations. Vibrational normal modes in the THz frequency range dominate the resilience. Both experimental and computational methods find a higher resilience for cytochrome c than for myoglobin, which we attribute to the increased number of covalent links to the peptide in the former protein. For myoglobin, the resilience of the iron environment is larger than the average resilience previously determined for hydrogen sites using neutron scattering. Experimental results suggest a slightly reduced resilience for cytochrome c upon oxidation, although the change is smaller than reported in previous Mössbauer investigations on a bacterial cytochrome c, and is not reproduced by the simulations. Oxidation state also has no significant influence on the compressibility calculated for cyt c, although a slightly larger compressibility is predicted for myoglobin.

Intermolecular dynamics in crystalline iron octaethylporphyrin (FeOEP)

The new technique of nuclear resonance vibrational spectroscopy (NRVS) has increased the range and quality of dynamical data from Fe-containing molecules that when combined with Raman and infrared spectroscopies impose stricter constraints on normal mode simulations, especially at lower frequencies. Going beyond the usual single molecule approximation, a classical normal-mode analysis that includes intermolecular coupling and the full crystalline symmetry is found to produce a better fit with fewer free parameters for the heme compound iron octaethylporphyrin (FeOEP), using NRVS data from polycrystalline material. Off-diagonal force constants were completely unnecessary, indicating that their role in previous single molecule fits was just to emulate intermolecular coupling. Sound velocities deduced from the calculated phonon dispersion curves are compared to NRVS measurements to further constrain the intermolecular force constants. The NRVS data by themselves are insufficient to rigorously determine all unknown force constants for molecules of this size, but the improved crystal model fit indicates the necessity of including intermolecular interactions for normal-mode analyses.

A physical picture of protein dynamics and conformational changes

A physical model is reviewed which explains different aspects of protein dynamics consistently. At low temperatures, the molecules are frozen in conformational substates. Their average energy is 3/2RT. Solid-state vibrations occur on a time scale of femtoseconds to nanoseconds. Above a characteristic temperature, often called the dynamical transition temperature, slow modes of motions can be observed occurring on a time scale between about 140 and 1 ns. These motions are overdamped, quasidiffusive, and involve collective motions of segments of the size of an alpha-helix. Molecules performing these types of motion are in the "flexible state". This state is reached by thermal activation. It is shown that these motions are essential for conformational relaxation. Based on this picture, a new approach is proposed to understand conformational changes. It connects structural fluctuations and conformational transitions.

Open-state conformation of the KcsA K+ channel: Monte Carlo normal mode following simulations

Potassium channels fluctuate between closed and open states. The detailed mechanism of the conformational changes opening the intracellular pore in the K+ channel from Streptomyces lividans (KcsA) is unknown. Applying Monte Carlo normal mode following, we find that gating involves rotation and unwinding of the TM2 bundle, lateral movement of the TM2 helices away from the channel axis, and disappearance of the TM2 bundle. The open-state conformation of KcsA exhibits a very wide inner vestibule, with a radius approximately 5-7 A and inner helices bent at the A98-G99 hinge. Computed conformational changes demonstrate that spin labeling and X-ray experiments illuminate different stages in gating: transition begins with clockwise rotation of the TM2 helices ending at a final state with the TM2 bend hinged near residues A98-G99. The concordance between the computational and experimental results provides atomic-level insights into the structural rearrangements of the channel's inner pore.

Quantitative vibrational dynamics of iron in carbonyl porphyrins

We use nuclear resonance vibrational spectroscopy and computational predictions based on density functional theory (DFT) to explore the vibrational dynamics of (57)Fe in porphyrins that mimic the active sites of histidine-ligated heme proteins complexed with carbon monoxide. Nuclear resonance vibrational spectroscopy yields the complete vibrational spectrum of a Mössbauer isotope, and provides a valuable probe that is not only selective for protein active sites but quantifies the mean-squared amplitude and direction of the motion of the probe nucleus, in addition to vibrational frequencies. Quantitative comparison of the experimental results with DFT calculations provides a detailed, rigorous test of the vibrational predictions, which in turn provide a reliable description of the observed vibrational features. In addition to the well-studied stretching vibration of the Fe-CO bond, vibrations involving the Fe-imidazole bond, and the Fe-N(pyr) bonds to the pyrrole nitrogens of the porphyrin contribute prominently to the observed experimental signal. All of these frequencies show structural sensitivity to the corresponding bond lengths, but previous studies have failed to identify the latter vibrations, presumably because the coupling to the electronic excitation is too small in resonance Raman measurements. We also observe the FeCO bending vibrations, which are not Raman active for these unhindered model compounds. The observed Fe amplitude is strongly inconsistent with three-body oscillator descriptions of the FeCO fragment, but agrees quantitatively with DFT predictions. Over the past decade, quantum chemical calculations have suggested revised estimates of the importance of steric distortion of the bound CO in preventing poisoning of heme proteins by carbon monoxide. Quantitative agreement with the predicted frequency, amplitude, and direction of Fe motion for the FeCO bending vibrations provides direct experimental support for the quantum chemical description of the energetics of the FeCO unit.

Vibrational Dynamics of Biological Molecules: Multi-quantum Contributions

High-resolution X-ray measurements near a nuclear resonance reveal the complete vibrational spectrum of the probe nucleus. Because of this, nuclear resonance vibrational spectroscopy (NRVS) is a uniquely quantitative probe of the vibrational dynamics of reactive iron sites in proteins and other complex molecules. Our measurements of vibrational fundamentals have revealed both frequencies and amplitudes of (57)Fe vibrations in proteins and model compounds. Information on the direction of Fe motion has also been obtained from measurements on oriented single crystals, and provides an essential test of normal mode predictions. Here, we report the observation of weaker two-quantum vibrational excitations (overtones and combinations) for compounds that mimic the active site of heme proteins. The predicted intensities depend strongly on the direction of Fe motion. We compare the observed features with predictions based on the observed fundamentals, using information on the direction of Fe motion obtained either from DFT predictions or from single crystal measurements. Two-quantum excitations may become a useful tool to identify the directions of the Fe oscillations when single crystals are not available.

Quantitative vibrational dynamics of iron in nitrosyl porphyrins

We use quantitative experimental and theoretical approaches to characterize the vibrational dynamics of the Fe atom in porphyrins designed to model heme protein active sites. Nuclear resonance vibrational spectroscopy (NRVS) yields frequencies, amplitudes, and directions for 57Fe vibrations in a series of ferrous nitrosyl porphyrins, which provide a benchmark for evaluation of quantum chemical vibrational calculations. Detailed normal mode predictions result from DFT calculations on ferrous nitrosyl tetraphenylporphyrin Fe(TPP)(NO), its cation [Fe(TPP)(NO)]+, and ferrous nitrosyl porphine Fe(P)(NO). Differing functionals lead to significant variability in the predicted Fe-NO bond length and frequency for Fe(TPP)(NO). Otherwise, quantitative comparison of calculated and measured Fe dynamics on an absolute scale reveals good overall agreement, suggesting that DFT calculations provide a reliable guide to the character of observed Fe vibrational modes. These include a series of modes involving Fe motion in the plane of the porphyrin, which are rarely identified using infrared and Raman spectroscopies. The NO binding geometry breaks the four-fold symmetry of the Fe environment, and the resulting frequency splittings of the in-plane modes predicted for Fe(TPP)(NO) agree with observations. In contrast to expectations of a simple three-body model, mode energy remains localized on the FeNO fragment for only two modes, an N-O stretch and a mode with mixed Fe-NO stretch and FeNO bend character. Bending of the FeNO unit also contributes to several of the in-plane modes, but no primary FeNO bending mode is identified for Fe(TPP)(NO). Vibrations associated with hindered rotation of the NO and heme doming are predicted at low frequencies, where Fe motion perpendicular to the heme is identified experimentally at 73 and 128 cm-1. Identification of the latter two modes is a crucial first step toward quantifying the reactive energetics of Fe porphyrins and heme proteins.

RF absorption involving biological macromolecules

The fundamental intramolecular frequency of a globular protein can be obtained from the measurements of acoustic velocities of bulk protein matter. This lowest frequency for common size molecules is shown to be above several hundred GHz. All modes below this frequency would then be intermolecular modes or bulk modes of the molecule and surrounding matter or tissue. The lowest frequency modes of an extended DNA double helix are also shown to be bulk modes because of interaction with water. Only DNA modes, whose frequency is well above 4 GHz, can be intrahelical modes, that is, confined to the helix rather than in the helix plus surroundings. Near 4 GHz, they are heavily damped and, therefore, not able to resonantly absorb. Modes that absorb radio frequency (RF) below this frequency are bulk modes of the supporting matter. Bulk modes rapidly thermalize all absorbed energy. The implication of these findings for the possibility of athermal RF effects is considered. The applicability of these findings for other biological molecules is discussed.

Direct determination of the complete set of iron normal modes in a porphyrin-imidazole model for carbonmonoxy-heme proteins: [Fe(TPP)(CO)(1-MeIm)]

Detailed Fe vibrational spectra have been obtained for the heme model complex [Fe(TPP)(CO)(1-MeIm)] using a new, highly selective and quantitative technique, Nuclear Resonance Vibrational Spectroscopy (NRVS). This spectroscopy measures the complete vibrational density of states for iron atoms, from which normal modes can be calculated via refinement of the force constants. These data and mode assignments can reveal previously undetected vibrations and are useful for validating predictions based on optical spectroscopies and density functional theory, for example. Vibrational modes of the iron porphyrin-imidazole compound [Fe(TPP)(CO)(1-MeIm)] have been determined by refining normal mode calculations to NRVS data obtained at an X-ray synchrotron source. Iron dynamics of this compound, which serves as a useful model for the active site in the six-coordinate heme protein, carbonmonoxy-myoglobin, are discussed in relation to recently determined dynamics of a five-coordinate deoxy-myoglobin model, [Fe(TPP)(2-MeHIm)]. For the first time in a six-coordinate heme system, the iron-imidazole stretch mode has been observed, at 226 cm(-)(1). The heme in-plane modes with large contributions from the nu(42), nu(49), nu(50), and nu(53) modes of the core porphyrin are identified. In general, the iron modes can be attributed to coupling with the porphyrin core, the CO ligand, the imidazole ring, and/or the phenyl rings. Other significant findings are the observation that the porphyrin ring peripheral substituents are strongly coupled to the iron doming mode and that the Fe-C-O tilting and bending modes are related by a negative interaction force constant.

Iron normal mode dynamics in a porphyrin-imidazole model for deoxyheme proteins

Iron vibrational modes of a deoxyheme protein model (2-methylimidazole)(tetraphenylporphinato)iron(II), [Fe(TPP)(2-MeImH)], have been studied by refining normal mode calculations to nuclear resonance vibrational spectroscopy (NRVS) data. The NRVS measurements give quantitative frequencies and iron amplitudes of all modes with significant Fe vibrational motion. Modes with in-plane displacement of iron are distinguished from those involving out-of-plane motion by measurements on oriented single-crystal samples. Normal modes having large overlaps with in-plane nu(42), nu(50), and nu(53) modes of the porphyrin core are identified, as well as several modes with large iron-imidazole stretch components. An out-of-plane mode at 78 cm(-1) shows significant doming of the porphyrin core, but the largest Fe doming motion arises from the coupling of phenyls and imidazole at 25 cm(-1).