Structural Assignments and Dynamics of the A Substates of MbCO: Spectrally Resolved Vibrational Echo Experiments and Molecular Dynamics Simulations

Voltage fluctuations and probe frequency jitter in electric force microscopy of a conductor

Electric force microscopy probes the statistics of electric field fluctuations from a sample surface, both through measurement of the noncontact friction exerted on the oscillating charged probe and by determination of the power spectrum of stochastic probe frequency fluctuations, referred to as "jitter." Here we calculate the frequency jitter power spectrum determined over a conducting sample of finite thickness, whose response is characterized by a dielectric function that is wavevector-dependent. These calculations complement previous predictions of the coefficient of noncontact friction in an electric force microscopy measurement for the same model, and also previous predictions of the jitter power spectrum for a dielectric continuum. The inclusion both of a finite sample thickness and a wavevector-dependent dielectric response can significantly enhance the magnitude of the predicted jitter spectrum for a conductor, relative to a simpler model of an infinitely thick dielectric continuum. These calculations provide a baseline prediction of the jitter power spectrum generated by the dynamics of conduction electrons in a metal sample.

Molecular Simulation-Guided Spectroscopy of Imidazolium-Based Ionic Liquids and Effects of Methylation on Ion-Cage and -Pair Dynamics

Classical molecular dynamics simulations were performed to assess an atomistic interpretation of the ion-probe structural interactions in two typical ionic liquids (ILs), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [BMIm][NTf₂] and 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide [BDimIm][NTf₂] through computational ultrafast spectroscopy. The nitrile stretching vibrations of the thiocyanate anion, [SCN]^-, serve as the local mode of the ultrafast system dynamics within the imidazolium-based ionic liquid environment. The wavelet transform of classical trajectories determines the time-varying fluctuating frequencies and the stretch spectral signatures of SCN^- in the normalized distribution. However, computational modeling of the two-dimensional (2D) spectra from the wavelet-derived vibrational frequencies yields time evolution of the local molecular structure along with the varied time-dependent dynamics of the spectral diffusion process. We calculated the frequency-frequency correlation functions (FFCFs), time correlations associated with the ion-pair and -cage dynamics, and mean square displacements as a function of time, depicting diffusive dynamics. The calculated results based on the pair correlation functions and the distribution of atomic density suggest that the hydrogen and methylated carbon at the two-position of the imidazolium ring of [BMIm] and [BDimIm] cations, respectively, strongly interact with the probe through the N of the thiocyanate anion rather than the S atom. The center-of-mass center-of-mass (COM-COM) cation-probe radial distribution functions (RDFs) in conjunction with the site-specific structural analysis further reveal well-structured interactions of the thiocyanate ion and [BMIm]⁺ cation rather than the [BDimIm] cation. In contrast, the anion-probe COM-COM RDFs depict weak interactive associations within the vibrational probe [SCN]^- and [NTf₂]^- ions. Methylation at the two-position of the imidazolium ring predicts slower structural reorganization and breaking and reformation dynamics of the ion pairs and cages within the ionic liquid framework.

Multiple Ensembles of the Hydrogen-bonded Network in Ethylammonium Nitrate versus Water from Vibrational Spectral Dynamics of SCN- Probe

We performed classical molecular dynamics simulations to monitor the structural interactions and ultrafast dynamical and spectral response in the protic ionic liquid, ethylammonium nitrate (EAN) and water using the nitrile stretching mode of thiocyanate ion (SCN-) as the vibrational probe. The normalized stretch frequency distribution of nitrile stretch of SCN- attains an asymmetric shape in EAN, indicating the existence of more than one hydrogen-bonding environment in EAN. We computed the 2D IR spectrum from classical trajectories, applying the response function formalism. Spectral diffusion dynamics in EAN undergo an initial rattling of the SCN - inside the local ion-cage occurring at a timescale of 0.10 ps, followed by the breakup of the ion-cage activating molecular diffusion at 7.86 ps timescale. In contrast, the dynamics of structural reorganization occur at a timescale of 0.58 ps in H 2 O. Hence, the time dependence of the frequency-frequency correlation function decay hints at the local molecular structure and ultrafast ion dynamics of the SCN - probe. The loss of frequency correlation read from the peak shape changes in the 2D correlation spectrum as a function of waiting time is faster in H 2 O than in EAN due to the enhanced structural ordering and higher viscosity of the latter. We provide an atomic-level interpretation of the solvation environment around SCN - in EAN and water, which indicates the multiple ensembles of the hydrogen bond network in EAN.

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.

Two-dimensional infrared spectroscopic study of cytochrome c peroxidase activity in deep eutectic solvent

Deep eutectic solvents (DESs) prepared by mixing hydrogen-bond donor and acceptor molecules have been found to be of use in several applications. Recently, it was shown that DESs can enhance the peroxidation activity of cytochrome c. Here, to elucidate the effects of DESs on the peroxidase activity of cytochrome c, we carried out linear and nonlinear infrared spectroscopic studies of the CO stretch mode of carbon monoxide cytochrome c (COCytc) in ethylammonium chloride (EAC)/urea DES. The FTIR spectrum of COCytc shows a significant spectral shift upon addition of the DES. The broadening and red-shifting of the CO band are observed in both urea and DES solutions, which are induced by the change of the distal ligands around the heme. Although the FTIR study is sensitive to structural changes in the active site, it does not provide quantitative information about structural dynamics related to the catalytic activity itself. Thus, we carried out two-dimensional IR spectroscopy of the CO mode, which suggests that there is a different conformer that could be related to the enhanced catalytic activity in DES. In particular, the spectral diffusion dynamics of that conformer exhibits quite different behavior. The experimental results lead us to propose a hypothesis that the DES increases the population of the conformer with distal ligand lysines close to the reaction center through the combining effect of urea and EAC, which results in the enhancement of the peroxidase activity of cytochrome c. We anticipate that the present experimental work stimulates future investigations of the effects of DES on biocatalysis.

Vibrational Stark spectroscopy for assessing ligand-binding strengths in a protein

Nitrile groups are potentially useful spectroscopic probes in the infrared to characterize the binding and dynamics of ligands in proteins. This opens the possibility of locating and determining the binding mode of suitably labelled ligands in proteins based on optical spectroscopy, without the need for determining an X-ray structure. However, relating structure and spectroscopy requires means to accurately compute infrared spectra. This is investigated for benzonitrile (PhCN) in water, wild type (WT) and two lysozyme mutants in solution. The force field is validated by comparing with experimental data for benzonitrile in water which is the basis for computing the Stark shift and time scale for spectral diffusion of PhCN in WT and the L99A and L99G mutants of T4 lysozyme. The 1-d spectra for PhCN in WT and the two mutant proteins differ in their maximum absorption by up to 4 cm^-1, which reflects the modified electrostatic environments in the three proteins. It is also tested whether extending from 1-d to 2-d infrared spectroscopy provides further discrimination in the ligand-binding modes. First, for PhCN in solution the frequency fluctuation correlation function (FFCF) decays to zero at short times whereas in the protein a pronounced static inhomogeneous component is found. Secondly, the decay time of the FFCF for the mutant to which PhCN binds most strongly has the longest decay time. It is demonstrated explicitly that the ligand-binding free energy with respect to the three protein variants correlates with the Stark shift. This makes 1-d infrared spectroscopy together with computations a valuable tool for characterizing binding modes and potentially binding locations in proteins.

Implications of short time scale dynamics on long time processes

This review provides a comprehensive overview of the structural dynamics in topical gas- and condensed-phase systems on multiple length and time scales. Starting from vibrationally induced dissociation of small molecules in the gas phase, the question of vibrational and internal energy redistribution through conformational dynamics is further developed by considering coupled electron/proton transfer in a model peptide over many orders of magnitude. The influence of the surrounding solvent is probed for electron transfer to the solvent in hydrated I-. Next, the dynamics of a modified PDZ domain over many time scales is analyzed following activation of a photoswitch. The hydration dynamics around halogenated amino acid side chains and their structural dynamics in proteins are relevant for iodinated TyrB26 insulin. Binding of nitric oxide to myoglobin is a process for which experimental and computational analyses have converged to a common view which connects rebinding time scales and the underlying dynamics. Finally, rhodopsin is a paradigmatic system for multiple length- and time-scale processes for which experimental and computational methods provide valuable insights into the functional dynamics. The systems discussed here highlight that for a comprehensive understanding of how structure, flexibility, energetics, and dynamics contribute to functional dynamics, experimental studies in multiple wavelength regions and computational studies including quantum, classical, and more coarse grained levels are required.

Reproducing kernel potential energy surfaces in biomolecular simulations: Nitric oxide binding to myoglobin

Multidimensional potential energy surfaces based on reproducing kernel-interpolation are employed to explore the energetics and dynamics of free and bound nitric oxide in myoglobin (Mb). Combining a force field description for the majority of degrees of freedom and the higher-accuracy representation for the NO ligand and the Fe out-of-plane motion allows for a simulation approach akin to a mixed quantum mechanics/molecular mechanics treatment. However, the kernel-representation can be evaluated at conventional force-field speed. With the explicit inclusion of the Fe-out-of-plane (Fe-oop) coordinate, the dynamics and structural equilibrium after photodissociation of the ligand are correctly described compared to experiment. Experimentally, the Fe-oop coordinate plays an important role for the ligand dynamics. This is also found here where the isomerization dynamics between the Fe-ON and Fe-NO state is significantly affected whether or not this co-ordinate is explicitly included. Although the Fe-ON conformation is metastable when considering only the bound (2)A state, it may disappear once the (4)A state is included. This explains the absence of the Fe-ON state in previous experimental investigations of MbNO.

Vibrational ladder climbing in carboxy-hemoglobin: effects of the protein environment

We present simulations on vibrational ladder climbing in carboxy-hemoglobin. Motivated by recent experiments, we study the influence of different realistic pump probe parameters. To allow for a direct comparison with experimental results, transient absorption spectra obtained by a weak probe pulse following the strong, shaped pump pulse are calculated. The influence of the protein fluctuations is taken into account using a recently developed microscopic model. This model consists of a quantum Hamiltonian describing the CO vibration in carboxy-hemoglobin, together with a fluctuating potential, which is obtained by electronic structure calculation based on a large number of protein configurations. Using realistic pulse parameters, vibrational excitations to very high-lying states are possible, in qualitative agreement with experimental observations.

Dynamics in the interior of AOT lamellae investigated with two-dimensional infrared spectroscopy

The dynamics inside the organic regions of aerosol-OT (AOT)/water mixtures in the lamellar mesophase, bicontinuous cubic (BC) phase, and in an analogous molecule without the charged sulfonate headgroup are investigated by observing spectral diffusion, orientational relaxation and population relaxation using ultrafast two-dimensional infrared (2D IR) vibrational echo spectroscopy and IR pump-probe experiments on the asymmetric CO stretch of a vibrational probe, tungsten hexacarbonyl (W(CO)6). The water layer thickness between the bilayer planes in the lamellar phase was varied. For comparison, the dynamics of W(CO)6 in the normal liquid bis(2-ethylhexyl) succinate (EHS), which is analogous to AOT but has no charged sulfonate headgroup, were also studied. The 2D IR experiments measure spectral diffusion, which results from the structural evolution of the system. Spectral diffusion is quantified by the frequency-frequency correlation function (FFCF). In addition to a homogeneous component, the FFCFs are biexponential decays with fast and slow time components of ∼12.5 and ∼150 ps in the lamellar phase. Both components of the FFCF are independent of the number of water molecules per headgroup for the lamellae, but they slow somewhat in the BC phase. The dynamics in the ordered phases are in sharp contrast to the dynamics in EHS, which displays fast and slow components of the FFCF of 5 and 80 ps, respectively. As the hydration level of AOT increases, vibrational lifetime decreases, suggesting some change in the local environment of W(CO)6 with water content.

Oxygen migration pathways in NO-bound truncated hemoglobin

Atomistic simulations of dioxygen (O(2)) dynamics and migration in nitric oxide-bound truncated Hemoglobin N (trHbN) of Mycobacterium tuberculosis are reported. From more than 100 ns of simulations the connectivity network involving the metastable states for localization of the O(2) ligand is built and analyzed. It is found that channel I is the primary entrance point for O(2) whereas channel II is predominantly an exit path although access to the protein active site is also possible. For O(2) a new site compared to nitric oxide, from which reaction with the heme group can occur, was found. As this site is close to the heme iron, it could play an important role in the dioxygenation mechanism as O(2) can remain there for hundreds of picoseconds after which it can eventually leave the protein, while NO is localized in Xe2. The present study supports recent experimental work which proposed that O(2) docks in alternative pockets than Xe close to the reactive site. Similar to other proteins, a phenylalanine residue (Phe62) plays the role of a gate along the access route in channel I. The most highly connected site is the Xe3 pocket which is a "hub" and free energy barriers between the different metastable states are ≈1.5 kcal mol(-1) which allows facile O(2) migration within the protein.

Fast dynamics of HP35 for folded and urea-unfolded conditions

The changes in fast dynamics of HP35 with a double CN vibrational dynamics label (HP35-P(2)) as a function of the extent of denaturation by urea were investigated with two-dimensional infrared (2D IR) vibrational echo spectroscopy. Cyanophenylalanine (PheCN) replaces the native phenylalanine at two residues in the hydrophobic core of HP35, providing vibrational probes. NMR data show that HP35-P(2) maintains the native folded structure similar to wild type and that both PheCN residues share essentially the same environment within the peptide. A series of time-dependent 2D IR vibrational echo spectra were obtained for the folded peptide and the increasingly unfolded peptide. Analysis of the time dependence of the 2D spectra yields the system's spectral diffusion, which is caused by the sampling of accessible structures of the peptide under thermal equilibrium conditions. The structural dynamics become faster as the degree of unfolding is increased.

Quantifying the importance of protein conformation on ligand migration in myoglobin

Myoglobin (Mb) is a model system for ligand binding and migration. The energy barriers (ΔG) for ligand migration in Mb have been studied in the past by experiment and theory and significant differences between different approaches were found. From experiment, it is known that Mb can assume a large number of conformational substates. In this work, these substates are investigated as a possible source of the differences in migration barriers. We show that the initial structure significantly affects the calculated ΔG for a particular transition and that fluctuations in barrier heights δΔG are of similar magnitude as the free energy barriers themselves. The sensitivity of ΔG to the initial structure is compared to other sources of errors. Different protein structures can affect the calculated ΔG by up to 4 kcal/mol, whereas differences between simple point charge models and more elaborate multipolar charge models for the CO-ligand are smaller by a factor of two. Analysis of the structural changes underlying the large effect of the conformational substate reveals the importance of coupling between protein and ligand motion for migration.

Ribonuclease S dynamics measured using a nitrile label with 2D IR vibrational echo spectroscopy

A nitrile-labeled amino acid, p-cyanophenylalanine, is introduced near the active site of the semisynthetic enzyme ribonuclease S to serve as a probe of protein dynamics and fluctuations. Ribonuclease S is the limited proteolysis product of subtilisin acting on ribonuclease A, and consists of a small fragment including amino acids 1-20, the S-peptide, and a larger fragment including residues 21-124, the S-protein. A series of two-dimensional vibrational echo experiments performed on the nitrile-labeled S-peptide and the RNase S are described. The time-dependent changes in the two-dimensional infrared vibrational echo line shapes are analyzed using the center line slope method to obtain the frequency-frequency correlation function (FFCF). The observations show that the nitrile probe in the S-peptide has dynamics that are similar to, but faster than, those of the single amino acid p-cyanophenylalanine in water. In contrast, the dynamics of the nitrile label when the peptide is bound to form ribonuclease S are dominated by homogeneous dephasing (motionally narrowed) contributions with only a small contribution from very fast inhomogeneous structural dynamics. The results provide insights into the nature of the structural dynamics of the ribonuclease S complex. The equilibrium dynamics of the nitrile labeled S-peptide and the ribonuclease S complex are also investigated by molecular dynamics simulations. The experimentally determined FFCFs are compared to the FFCFs obtained from the molecular dynamics simulations, thereby testing the capacity of simulations to determine the amplitudes and time scales of protein structural fluctuations on fast time scales under thermal equilibrium conditions.

Two-dimensional IR spectroscopy of protein dynamics using two vibrational labels: a site-specific genetically encoded unnatural amino acid and an active site ligand

Protein dynamics and interactions in myoglobin (Mb) were characterized via two vibrational dynamics labels (VDLs): a genetically incorporated site-specific azide (Az) bearing unnatural amino acid (AzPhe43) and an active site CO ligand. The Az-labeled protein was studied using ultrafast two-dimensional infrared (2D IR) vibrational echo spectroscopy. CO bound at the active site of the heme serves as a second VDL located nearby. Therefore, it was possible to use Fourier transform infrared (FT-IR) and 2D IR spectroscopic experiments on the Az in unligated Mb and in Mb bound to CO (MbAzCO) and on the CO in MbCO and MbAzCO to investigate the environment and motions of different states of one protein from the perspective of two spectrally resolved VDLs. A very broad bandwidth 2D IR spectrum, encompassing both the Az and CO spectral regions, found no evidence of direct coupling between the two VDLs. In MbAzCO, both VDLs reported similar time scale motions: very fast homogeneous dynamics, fast, ∼1 ps dynamics, and dynamics on a much slower time scale. Therefore, each VDL reports independently on the protein dynamics and interactions, and the measured dynamics are reflective of the protein motions rather than intrinsic to the chemical nature of the VDL. The AzPhe VDL also permitted study of oxidized Mb dynamics, which could not be accessed previously with 2D IR spectroscopy. The experiments demonstrate that the combined application of 2D IR spectroscopy and site-specific incorporation of VDLs can provide information on dynamics, structure, and interactions at virtually any site throughout any protein.

Influence of histidine tag attachment on picosecond protein dynamics

Polyhistidine affinity tags are routinely employed as a convenient means of purifying recombinantly expressed proteins. A tacit assumption is commonly made that His tags have little influence on protein structure and function. Attachment of a His tag to the N-terminus of the robust globular protein myoglobin leads to only minor changes to the electrostatic environment of the heme pocket, as evinced by the nearly unchanged Fourier transform infrared spectrum of CO bound to the heme of His-tagged myoglobin. Experiments employing two-dimensional infrared vibrational echo spectroscopy of the heme-bound CO, however, find that significant changes occur to the short time scale (picoseconds) dynamics of myoglobin as a result of His tag incorporation. The His tag mainly reduces the dynamics on the 1.4 ps time scale and also alters protein motions of myoglobin on the slower, >100 ps time scale, as demonstrated by the His tag's influence on the fluctuations of the CO vibrational frequency, which reports on protein structural dynamics. The results suggest that affinity tags may have effects on protein function and indicate that investigators of affinity-tagged proteins should take this into consideration when investigating the dynamics and other properties of such proteins.

Role of the distal hydrogen-bonding network in regulating oxygen affinity in the truncated hemoglobin III from Campylobacter jejuni

Oxygen affinity in heme-containing proteins is determined by a number of factors, such as the nature and conformation of the distal residues that stabilize the heme bound-oxygen via hydrogen-bonding interactions. The truncated hemoglobin III from Campylobacter jejuni (Ctb) contains three potential hydrogen-bond donors in the distal site: TyrB10, TrpG8, and HisE7. Previous studies suggested that Ctb exhibits an extremely slow oxygen dissociation rate due to an interlaced hydrogen-bonding network involving the three distal residues. Here we have studied the structural and kinetic properties of the G8(WF) mutant of Ctb and employed state-of-the-art computer simulation methods to investigate the properties of the O(2) adduct of the G8(WF) mutant, with respect to those of the wild-type protein and the previously studied E7(HL) and/or B10(YF) mutants. Our data indicate that the unique oxygen binding properties of Ctb are determined by the interplay of hydrogen-bonding interactions between the heme-bound ligand and the surrounding TyrB10, TrpG8, and HisE7 residues.

Temperature dependent equilibrium native to unfolded protein dynamics and properties observed with IR absorption and 2D IR vibrational echo experiments

Dynamic and structural properties of carbonmonoxy (CO)-coordinated cytochrome c(552) from Hydrogenobacter thermophilus (Ht-M61A) at different temperatures under thermal equilibrium conditions were studied with infrared absorption spectroscopy and ultrafast two-dimensional infrared (2D IR) vibrational echo experiments using the heme-bound CO as the vibrational probe. Depending on the temperature, the stretching mode of CO shows two distinct bands corresponding to the native and unfolded proteins. As the temperature is increased from low temperature, a new absorption band for the unfolded protein grows in and the native band decreases in amplitude. Both the temperature-dependent circular dichroism and the IR absorption area ratio R(A)(T), defined as the ratio of the area under the unfolded band to the sum of the areas of the native and unfolded bands, suggest a two-state transition from the native to the unfolded protein. However, it is found that the absorption spectrum of the unfolded protein increases its inhomogeneous line width and the center frequency shifts as the temperature is increased. The changes in line width and center frequency demonstrate that the unfolding does not follow simple two-state behavior. The temperature-dependent 2D IR vibrational echo experiments show that the fast dynamics of the native protein are virtually temperature independent. In contrast, the fast dynamics of the unfolded protein are slower than those of the native protein, and the unfolded protein fast dynamics and at least a portion of the slower dynamics of the unfolded protein change significantly, becoming faster as the temperature is raised. The temperature dependence of the absorption spectrum and the changes in dynamics measured with the 2D IR experiments confirm that the unfolded ensemble of conformers continuously changes its nature as unfolding proceeds, in contrast to the native state, which displays a temperature-independent distribution of structures.

Protein dynamics in cytochrome P450 molecular recognition and substrate specificity using 2D IR vibrational echo spectroscopy

Cytochrome (cyt) P450s hydroxylate a variety of substrates that can differ widely in their chemical structure. The importance of these enzymes in drug metabolism and other biological processes has motivated the study of the factors that enable their activity on diverse classes of molecules. Protein dynamics have been implicated in cyt P450 substrate specificity. Here, 2D IR vibrational echo spectroscopy is employed to measure the dynamics of cyt P450(cam) from Pseudomonas putida on fast time scales using CO bound at the active site as a vibrational probe. The substrate-free enzyme and the enzyme bound to both its natural substrate, camphor, and a series of related substrates are investigated to explicate the role of dynamics in molecular recognition in cyt P450(cam) and to delineate how the motions may contribute to hydroxylation specificity. In substrate-free cyt P450(cam), three conformational states are populated, and the structural fluctuations within a conformational state are relatively slow. Substrate binding selectively stabilizes one conformational state, and the dynamics become faster. Correlations in the observed dynamics with the specificity of hydroxylation of the substrates, the binding affinity, and the substrates' molecular volume suggest that motions on the hundreds of picosecond time scale contribute to the variation in activity of cyt P450(cam) toward different substrates.

Relationship between protein structural fluctuations and rebinding dynamics in ferric haem nitrosyls

The interaction of nitric oxide (NO) with haem proteins is widespread in biology. In the current paper, we present the first ultrafast 2D-IR (two-dimensional infrared) spectroscopic analysis of haem nitrosylation, which has been combined with time-resolved IR pump–probe studies to investigate the relationship between equilibrium vibrational dynamics of the haem environment and ligand rebinding behaviour following photolysis of NO from the Fe(III)–NO site. Studies of two haem proteins, Mb (myoglobin) and Cc (cytochrome c), which play different physiological roles, reveal marked contrasts in the ultrafast fluctuations of the protein pockets containing the haem, showing that the Mb pocket is somewhat more flexible than that of Cc. This correlates strongly with slower observed photolysis rebinding kinetics of Mb–NO compared with Cc–NO, and indicates a direct link between ultrafast fluctuations and biological functionality. Furthermore, this indicates the validity of linear response theories in relation to protein ligand binding. Finally, 2D-IR shows that Cc–NO displays two distinct structural sub-sites at room temperature that do not exchange on the timescales accessible via the NO vibrational lifetime.

Dynamics of a myoglobin mutant enzyme: 2D IR vibrational echo experiments and simulations

Myoglobin (Mb) double mutant T67R/S92D displays peroxidase enzymatic activity in contrast to the wild type protein. The CO adduct of T67R/S92D shows two CO absorption bands corresponding to the A(1) and A(3) substates. The equilibrium protein dynamics for the two distinct substates of the Mb double mutant are investigated by using two-dimensional infrared (2D IR) vibrational echo spectroscopy and molecular dynamics (MD) simulations. The time-dependent changes in the 2D IR vibrational echo line shapes for both of the substates are analyzed using the center line slope (CLS) method to obtain the frequency-frequency correlation function (FFCF). The results for the double mutant are compared to those from the wild type Mb. The experimentally determined FFCF is compared to the FFCF obtained from molecular dynamics simulations, thereby testing the capacity of a force field to determine the amplitudes and time scales of protein structural fluctuations on fast time scales. The results provide insights into the nature of the energy landscape around the free energy minimum of the folded protein structure.

Conformational switching between protein substates studied with 2D IR vibrational echo spectroscopy and molecular dynamics simulations

Myoglobin is an important protein for the study of structure and dynamics. Three conformational substates have been identified for the carbonmonoxy form of myoglobin (MbCO). These are manifested as distinct peaks in the IR absorption spectrum of the CO stretching mode. Ultrafast 2D IR vibrational echo chemical exchange experiments are used to observed switching between two of these substates, A(1) and A(3), on a time scale of <100 ps for two mutants of wild-type Mb. The two mutants are a single mutation of Mb, L29I, and a double mutation, T67R/S92D. Molecular dynamics (MD) simulations are used to model the structural differences between the substates of the two MbCO mutants. The MD simulations are also employed to examine the substate switching in the two mutants as a test of the ability of MD simulations to predict protein dynamics correctly for a system in which there is a well-defined transition over a significant potential barrier between two substates. For one mutant, L29I, the simulations show that translation of the His64 backbone may differentiate the two substates. The simulations accurately reproduce the experimentally observed interconversion time for the L29I mutant. However, MD simulations exploring the same His64 backbone coordinate fail to display substate interconversion for the other mutant, T67R/S92D, thus pointing to the likely complexity of the underlying protein interactions. We anticipate that understanding conformational dynamics in MbCO via ultrafast 2D IR vibrational echo chemical exchange experiments can help to elucidate fast conformational switching processes in other proteins.

Imaging protein statistical substate occupancy in a spectrum-function phase space

Hemeprotein ligand rebinding studies reveal varying IR absorbance and rebinding functions across a cryogenic ensemble. Since IR-active vibrations and rebinding barriers couple to structural coordinates, spectral and functional heterogeneity arise from conformational heterogeneity. Modeling rebinding data as a spectrally resolved superposition of first-order rate processes and employing maximum entropy regularization, protein heterogeneity is imaged as an ensemble occupancy of a spectrum-function phase space. Results from myoglobin rebinding carbon monoxide are discussed.

Integrated and dispersed photon echo studies of nitrile stretching vibration of 4-cyanophenol in methanol

By means of integrated and dispersed IR photon echo measurement methods, the vibrational dynamics of C-N stretch modes in 4-cyanophenol and 4-cyanophenoxide in methanol is investigated. The vibrational frequency-frequency correlation function (FFCF) is retrieved from the integrated photon echo signals by assuming that the FFCF is described by two exponential functions with about 400 fs and a few picosecond components. The excited state lifetimes of the C-N stretch modes of neutral and anionic 4-cyanophenols are 1.45 and 0.91 ps, respectively, and the overtone anharmonic frequency shifts are 25 and 28 cm(-1). At short waiting times, a notable underdamped oscillation, which is attributed to a low-frequency intramolecular vibration coupled to the CN stretch, in the integrated and dispersed vibrational echo as well as transient grating signals was observed. The spectral bandwidths of IR absorption and dispersed vibrational echo spectra of the 4-cyanophenoxide are significantly larger than those of its neutral form, indicating that the strong interaction between phenoxide and methanol causes large frequency fluctuation and rapid population relaxation. The resonance effects in a paradisubstituted aromatic compound would be of interest in understanding the conjugation effects and their influences on chemical reactivity of various aromatic compounds in organic solvents.

Modeling, calculating, and analyzing multidimensional vibrational spectroscopies

Spectral line shapes in a condensed phase contain information from various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. Because nonlinear response functions are sensitive to the complex dynamics of chemical processes, multidimensional vibrational spectroscopies can separate these processes. In multidimensional vibrational spectroscopy, the nonlinear response functions of a molecular dipole or polarizability are measured using ultrashort pulses to monitor inter- and intramolecular vibrational motions. Because a complex profile of such signals depends on the many dynamic and structural aspects of a molecular system, researchers would like to have a theoretical understanding of these phenomena. In this Account, we explore and describe the roles of different physical phenomena that arise from the peculiarities of the system-bath coupling in multidimensional spectra. We also present simple analytical expressions for a weakly coupled multimode Brownian system, which we use to analyze the results obtained by the experiments and simulations. To calculate the nonlinear optical response, researchers commonly use a particular form of a system Hamiltonian fit to the experimental results. The optical responses of molecular vibrational motions have been studied in either an oscillator model or a vibration energy state model. In principle, both models should give the same results as long as the energy states are chosen to be the eigenstates of the oscillator model. The energy state model can provide a simple description of nonlinear optical processes because the diagrammatic Liouville space theory that developed in the electronically resonant spectroscopies can easily handle three or four energy states involved in high-frequency vibrations. However, the energy state model breaks down if we include the thermal excitation and relaxation processes in the dynamics to put the system in a thermal equilibrium state. The roles of these excitation and relaxation processes are different and complicated compared with those in the resonant spectroscopy. Observing the effects of such thermal processes is more intuitive with the oscillator model because the bath modes, which cause the fluctuation and dissipation processes, are also described in the coordinate space. This coordinate space system-bath approach complements a realistic full molecular dynamics simulation approach. By comparing the calculated 2D spectra from the coordinate space model and the energy state model, we can examine the role of thermal processes and anharmonic mode-mode couplings in the energy state model. For this purpose, we employed the Brownian oscillator model with the nonlinear system-bath interaction. Using the hierarchy formalism, we could precisely calculate multidimensional spectra for a single and multimode anharmonic system for inter- and intramolecular vibrational modes.

Structural assignment of spectra by characterization of conformational substates in bound MbCO

Residue motions of the distal heme pocket and bound CO ligand of carbonmonoxy Myoglobin are studied using a combination of molecular dynamics simulations and quantum chemical methods. Using mixed quantum mechanics/molecular mechanics calculations together with sampling from molecular dynamics simulations (QM/MM(MD)), the experimentally observed spectroscopic A(0) and A(1) substates of the bound CO ligand are assigned to the open and closed conformation of His(64) and the His(epsilon)(64) tautomer, respectively. Several previously proposed origins of the A(3) substate, including rotamers of the doubly protonated His(64)H(+) side chain, His(64)H(+) inside the distal pocket, and cooperative motions with Arg(45), are investigated with QM/MM(MD). However, the signatures of the calculated infrared spectra do not agree with the experimentally observed ones. For additional insight on this, extensive molecular dynamics simulations are used together with improved electrostatics for the bound ligand. A CO fluctuating charge model is developed to describe the ab initio dipole and quadrupole moments of the bound ligand. CO absorption spectra are then obtained directly from the dynamics simulations. Finally, the electrostatics of the heme pocket is examined in detail in an attempt to determine the structural origins of the observed spectroscopic A-states from MD simulations. However, contrary to related simulations for unbound CO in myoglobin, the shifts and splittings for carbonmonoxy Myoglobin are generally small and difficult to relate to structural change. This suggests that coupling of the CO motion to other degrees of freedom, such as the Fe-CO stretching and bending, is important to correctly describe the dynamics of bound CO in myoglobin.

Exploring the molecular origins of protein dynamics in the active site of human carbonic anhydrase II

We present three-pulse vibrational echo measurements of azide ion bound to the active site Zn of human carbonic anhydrase II (HCA II) and of two separate active-site mutants Thr199 --> Ala (T199A) and Leu198 --> Phe (L198F). Because structural motions of the protein active site influence the frequency of bound ligands, the differences in the time scales of the frequency-frequency correlation functions (FFCFs) obtained from global fits to each set of data allow us to make inferences about the time scales of the active site dynamics of HCA II. Surprisingly, the deletion of a potential electrostatic interaction in results in very little change in the FFCF, but the insertion of the bulky phenylalanine ring in causes much faster dynamics. We conclude that the fast, sub-picosecond time scale in the correlation function is attributable to hydrogen bond dynamics, and the slow, apparently static contribution is due to the conformational flexibility of Zn-bound azide in the active site.

Dynamic fluctuation of proteins watched in real time

The dynamic nature of protein function is a fundamental concept in the physics of proteins. Although the basic general ideas are well accepted most experimental evidence has an indirect nature. The detailed characterization of the dynamics is necessary for the understanding in detail. The dynamic fluctuations thought crucial for the function span an extremely broad time, starting from the picosecond regime. Recently, a few new experimental techniques emerged that permit the observation of dynamical phenomena directly. Notably, pulsed infrared (IR) spectroscopy has been applied with great success to observe structural changes with picosecond time resolution. Using two-dimensional-IR vibrational echo chemical exchange spectroscopy Ishikawa and co-workers [Ishikawa et al. (2008), Proc. Natl. Acad. Sci. U.S.A. 101, 14402-14407] managed to observe the transition between well defined conformational substrates of carbonmonoxy myoglobin directly. This is an important step in improving our insight into the details of protein function.

Native and unfolded cytochrome c--comparison of dynamics using 2D-IR vibrational echo spectroscopy

Unfolded vs native CO-coordinated horse heart cytochrome c (h-cyt c) and a heme axial methionine mutant cyt c552 from Hydrogenobacter thermophilus ( Ht-M61A) are studied by IR absorption spectroscopy and ultrafast 2D-IR vibrational echo spectroscopy of the CO stretching mode. The unfolding is induced by guanidinium hydrochloride (GuHCl). The CO IR absorption spectra for both h-cyt c and Ht-M61A shift to the red as the GuHCl concentration is increased through the concentration region over which unfolding occurs. The spectra for the unfolded state are substantially broader than the spectra for the native proteins. A plot of the CO peak position vs GuHCl concentration produces a sigmoidal curve that overlays the concentration-dependent circular dichroism (CD) data of the CO-coordinated forms of both Ht-M61A and h-cyt c within experimental error. The coincidence of the CO peak shift curve with the CD curves demonstrates that the CO vibrational frequency is sensitive to the structural changes induced by the denaturant. 2D-IR vibrational echo experiments are performed on native Ht-M61A and on the protein in low- and high-concentration GuHCl solutions. The 2D-IR vibrational echo is sensitive to the global protein structural dynamics on time scales from subpicosecond to greater than 100 ps through the change in the shape of the 2D spectrum with time (spectral diffusion). At the high GuHCl concentration (5.1 M), at which Ht-M61A is essentially fully denatured as judged by CD, a very large reduction in dynamics is observed compared to the native protein within the approximately 100 ps time window of the experiment. The results suggest the denatured protein may be in a glassy-like state involving hydrophobic collapse around the heme.

Exploring a free energy landscape by means of multidimensional infrared and terahertz spectroscopies

A model for the dipolar crystal system is employed to explore a role of free energy landscape (FEL), in which dipolar molecules are posted on two-dimensional lattice sites with two-state libratinal dynamics. All dipole-dipole interactions are included to have frustrated interactions among the dipoles. For the regular and distorted lattice cases, the FEL is calculated from the interaction energies and the total polarizations for all possible dipolar states at various temperatures. At high temperatures, the shape of the calculated FEL is smooth and parabolic, while it becomes bumpy at low temperatures exhibiting multiple local minima. To study dynamical aspects of the system, the single flip dynamics and the single-double mixed flips dynamics of dipoles are examined from a master equation approach. As the observables of linear absorption and two-dimensional (2D) infrared, far infrared, and terahertz spectroscopies, the first- and third-order response functions of polarization are calculated for different physical conditions characterized by the FEL. While the linear absorption signals decay in time in a similar manner regardless of the FEL profiles, the 2D signals exhibit prominent differences for those profiles. This indicates that we may differentiate the FEL profiles by changing two-time valuables in 2D spectroscopy. As illustrated in the single-double flips case, the FEL study by means of 2D spectroscopy, however, relies on the dynamics which is set independently from the FEL. The Smoluchowski equation is applied to examine the description of the collective dynamics on the microscopically calculated FEL. We found that the one-dimensional and 2D signals calculated from the Smoluchowski equation agree with those from master equation only at temperatures where the FEL becomes parabolic shape.

The role of higher CO-multipole moments in understanding the dynamics of photodissociated carbonmonoxide in myoglobin

The influence of electrostatic multipole moments up to hexadecapole on the dynamics of photodissociated carbon monoxide (CO) in myoglobin is investigated. The CO electrostatic potential is expressed as an expansion into atomic multipole moments of increasing order up to octopole which are obtained from a distributed multipole analysis. Three models with increasingly accurate molecular multipoles (accurate quadrupole, octopole, and hexadecapole moments, respectively) are developed and used in molecular dynamics simulations. All models with a fluctuating quadrupole moment correctly describe the location of the B-state whereas the sign of the octopole moment differentiates between the Fe...CO and Fe...OC orientation. For the infrared spectrum of photodissociated CO, considerable differences between the three electrostatic models are found. The most detailed electrostatic model correctly reproduces the splitting, shift, and width of the CO spectrum in the B-state. From an analysis of the trajectories, the spectroscopic B(1) and B(2) states are assigned to the Fe...CO and Fe...OC substates, respectively.

Fast enzyme dynamics at the active site of formate dehydrogenase

The role of femtosecond-picosecond structural dynamics of proteins in enzyme-catalyzed reactions is a hotly debated topic. We report infrared photon echo measurement of the formate dehydrogenase-NAD+-azide ternary complex. In contrast to earlier studies of protein dynamics, the data show complete spectral diffusion on the femtosecond-picosecond time scale with no static heterogeneity. This result indicates that this transition-state analogue complex completely samples the distribution of structures that determine the distribution of azide vibrational frequencies within a few picoseconds and that there are no slower motions that perturb the H-bond network at the active site.