Time- and temperature dependence of large-scale conformational transitions in myoglobin

Protoporphyrin IX iron(II) revisited. An overview of the Mössbauer spectroscopic parameters of low-spin porphyrin iron(II) complexes

Mössbauer parameters of low-spin six-coordinate [Fe(II)(Por)L2] complexes (where Por is a synthetic porphyrin; L is a nitrogenous aliphatic, an aromatic base or a heterocyclic ligand, a P-bonding ligand, CO or CN) and low-spin [Fe(Por)LX] complexes (where L and X are different ligands) are reported. A known point charge calculation approach was extended to investigate how the axial ligands and the four porphyrinato-N atoms generate the observed quadrupole splittings (ΔEQ) for the complexes. Partial quadrupole splitting (p.q.s.) and partial chemical shifts (p.c.s.) values were derived for all the axial ligands, and porphyrins reported in the literature. The values for each porphyrin are different emphasising the importance/uniqueness of the [Fe(PPIX)] moiety, (which is ubiquitous in nature). This new analysis enabled the construction of figures relating p.c.s and p.q.s values. The relationships presented in the figures indicates that strong field ligands such as CO can, and do change the sign of the electric field gradient in the [Fe(II)(Por)L2] complexes. The limiting p.q.s. value a ligand can have and still form a six-coordinate low-spin [Fe(II)(Por)L2] complex is established. It is shown that the control the porphyrin ligands exert on the low-spin Fe(II) atom limits its bonding to a defined range of axial ligands; outside this range the spin state of the iron is unstable and five-coordinate high-spin complexes are favoured. Amongst many conclusions, it was found that oxygen cannot form a stable low-spin [Fe(II)(Por)L(O2)] complex and that oxy-haemoglobin is best described as an [Fe(III)(Por)L(O2-)] complex, the iron is ferric bound to the superoxide molecule.

Studies on the binding of CO to low-spin [Fe(II)(Por)L2] complexes: an aid to understanding the binding of CO to haemoglobin and myoglobin

The visible and Mössbauer spectra of [Fe(II)(Por)L₂] and [Fe(II)(Por)L(CO)] complexes (where Por = protoporphyrin IX (PPIX) or tetra(p-sulfophenyl)porphyrin (TPPS) and L = an aliphatic or aromatic nitrogenous base) are reported and discussed. The results are compared to those of previously reported [Fe(II)(Por)L(CO)] complexes (where Por = PPIX, TPPS, PMXPP, TPP, OMTBP and OEP; L = a nitrogenous aromatic ligand) and HbCO (where Hb = haemoglobin) and MyCO (where My = myoglobin). A new approach, to extracting information from the Mössbauer parameters has been developed by plotting those of the [Fe(II)(Por)L₂] complexes against those of [Fe(II)(Por)L(CO)] complexes for the same ligands, has yielded a series of trend lines that show a significant dependence on both the nature of the porphyrin and also of the nitrogenous ligand. Different trend lines were found for aromatic nitrogenous ligands to aliphatic nitrogenous ligands showing that the porphyrins could donate different amounts of charge to the Fe(II) cations as the L ligand changed, and hence, they display electron sink properties. From the plots, it was shown that haemoglobin and myoglobin both bind CO very strongly compared to the model complexes studied herein. Using the reported structural and Mössbauer data for the [Fe(II)(Por)L₂] and [Fe(II)(Por)L(CO)] complexes, it proved possible and instructive to plot the Mössbauer parameters against a number of the bond lengths around the Fe(II) cations. The interpretation of the resulting trend lines both supported and facilitated the extension of our findings enabling further understanding of the geometry of the bonding in CO haemoglobin and CO myoglobin.

Studies on the binding of nitrogenous bases to protoporphyrin IX iron(II) in aqueous solution at high pH values

Studies are reported on the formation of low-spin six-coordinate [Fe(PPIX)L₂] complexes from iron(II) protoporphyrin where L is one of a series of nitrogenous ligands (aliphatic, aromatic or heterocyclic). The bonding constants have been determined by titration of the metal complex with these ligands and are compared in relation to previous studies. The adduct formation was monitored utilising optical spectroscopy. In addition, Mӧssbauer spectroscopic experiments were conducted to monitor the electronic environment around the central iron atom in these complexes. The two complementary spectroscopic methods indicated that all nitrogen ligands formed low-spin octahedral complexes. The magnitude of the overall binding constants (β₂ values) are discussed and related to (a) the pK_a values of the free ligands and (b) the Mössbauer parameter ΔE_Q, which represents the quadrupole splitting of the haem iron. The β₂ and ΔE_Q values are also discussed in terms of the structure of the ligand. Cooperative binding was observed for nearly all the ligands with Hill coefficients close to 2 for iron(II) protoporphyrin; one of these ligands displayed a much greater affinity than any we previously studied, and this was a direct consequence of the structure of the ligand. Overall conclusions on these and previous studies are drawn in terms of aliphatic ligands versus aromatic ring structures and the absence or presence of sterically hindered nitrogen atoms. The implications of the work for the greater understanding of haem proteins in general and in particular how the nitrogenous ligand binding results are relevant to and aid the understanding of the binding of inhibitor molecules to the cytochrome P₄₅₀ mono-oxygenases (for therapeutic purposes) are also discussed. Changes in the electronic absorption spectra of five-coordinate [Fe(II)(PPIX)(2-MeIm)] that occurred as the temperature was lowered from room temperature to 78° K.

Exploring the energy landscape of a SAM-I riboswitch

SAM-I riboswitches regulate gene expression through transcription termination upon binding a S-adenosyl-L-methionine (SAM) ligand. In previous work, we characterized the conformational energy landscape of the full-length Bacillus subtilis yitJ SAM-I riboswitch as a function of Mg²⁺ and SAM ligand concentrations. Here, we have extended this work with measurements on a structurally similar ligand, S-adenosyl-l-homocysteine (SAH), which has, however, a much lower binding affinity. Using single-molecule Förster resonance energy transfer (smFRET) microscopy and hidden Markov modeling (HMM) analysis, we identified major conformations and determined their fractional populations and dynamics. At high Mg²⁺ concentration, FRET analysis yielded four distinct conformations, which we assigned to two terminator and two antiterminator states. In the same solvent, but with SAM added at saturating concentrations, four states persisted, although their populations, lifetimes and interconversion dynamics changed. In the presence of SAH instead of SAM, HMM revealed again four well-populated states and, in addition, a weakly populated ‘hub’ state that appears to mediate conformational transitions between three of the other states. Our data show pronounced and specific effects of the SAM and SAH ligands on the RNA conformational energy landscape. Interestingly, both SAM and SAH shifted the fractional populations toward terminator folds, but only gradually, so the effect cannot explain the switching action. Instead, we propose that the noticeably accelerated dynamics of interconversion between terminator and antiterminator states upon SAM binding may be essential for control of transcription.

Characterization of Metalloporphines: Iron(II) Carbonyls and Environmental Effects on νCO

The synthesis and characterization of two new iron(II) porphine complexes is described. Porphine, the simplest porphyrin derivative, has been studied less than other synthetic porphyrins owing to synthetic difficulties and solubility issues. The subjects of this study are two six-coordinate iron(II) species further coordinated by CO and an imidazole ligand (either 1-methylimidazole or 2-methylimidazole). The two species have very different CO stretching frequencies, with the 2-methylimidazole complex having a very low stretching frequency of 1923 cm^-1 compared to the more usual 1957 cm^-1 for the 1-methylimidazole derivative. The very low frequency is the result of environmental effects; the oxygen atom of the carbonyl forms a hydrogen bond with an adjacent coordinated imidazole with a hydrogen atom from the N-H group. The two species, with their differing C-O stretches, also display substantial differences in the values of the Fe-C and C-O bond distances, as determined by their X-ray structures. The two bond distances are strongly correlated ( R = 0.98) in the direction expected for the classical π-backbonding model. The two bond distances are also strongly correlated with the C-O stretching frequencies. We can conclude that the Fe-C and C-O stretches are quite representative of the observed bond distances; their stretching frequencies are not affected by substantial mode mixing.

Atomistic Simulation of Adiabatic Reactive Processes Based on Multi-State Potential Energy Surfaces

The adiabatic reactive molecular dynamics (ARMD) method provides a framework to study chemical reactions using molecular dynamics simulations with minimal computational overhead. Here, ARMD is generalized to an arbitrary reactive process between two states in which reactants and products can be treated by an atomistic force field. The implementation is described, and the method is applied to two systems: the kinetics of NO rebinding to myoglobin (Mb) as a validation system and the conformational transition in neuroglobin (Ngb) which explores the full functionality of ARMD. For MbNO, the nonexponential kinetics observed both in experiment and earlier ARMD studies is reproduced. Furthermore, the sensitivity of the results with respect to the asymptotic separation between the two potential energy surfaces (NO bound and unbound) is studied.

Ligand migration and binding in nonsymbiotic hemoglobins of Arabidopsis thaliana

We have studied carbon monoxide (CO) migration and binding in the nonsymbiotic hemoglobins AHb1 and AHb2 of Arabidopsis thaliana using Fourier transform infrared (FTIR) spectroscopy combined with temperature derivative spectroscopy (TDS) at cryogenic temperatures. Both proteins have similar amino acid sequences but display pronounced differences in ligand binding properties, at both physiological and cryogenic temperatures. Near neutral pH, the distal HisE7 side chain is close to the heme-bound ligand in the majority of AHb1-CO molecules, as indicated by a low CO stretching frequency at 1921 cm(-1). In this fraction, two CO docking sites can be populated, the primary site B and the secondary site C. When the pH is lowered, a high-frequency stretching band at approximately 1964 cm(-1) grows at the expense of the low-frequency band, indicating that HisE7 protonates and, concomitantly, moves away from the bound ligand. Geminate rebinding barriers are markedly different for the two conformations, and docking site C is not accessible in the low-pH conformation. Rebinding of NO ligands was observed only from site B of AHb1, regardless of conformation. In AHb2, the HisE7 side chain is removed from the bound ligand; rebinding barriers are low, and CO molecules can populate only primary docking site B. These results are interpreted in terms of differences in the active site structures and physiological functions.

Ultrafast proteinquake dynamics in cytochrome c

We report here our systematic studies of the heme dynamics and induced protein conformational relaxations in two redox states of ferric and ferrous cytochrome c upon femtosecond excitation. With a wide range of probing wavelengths from the visible to the UV and a site-directed mutation we unambiguously determined that the protein dynamics in the two states are drastically different. For the ferrous state the heme transforms from 6-fold to 5-fold coordination with ultrafast ligand dissociation in less than 100 fs, followed by vibrational cooling within several picoseconds, but then recombining back to its original 6-fold coordination in 7 ps. Such impulsive bond breaking and late rebinding generate proteinquakes and strongly perturb the local heme site and shake global protein conformation, which were found to completely recover in 13 and 42 ps, respectively. For the ferric state the heme however maintains its 6-fold coordination. The dynamics mainly occur at the local site, including ultrafast internal conversion in hundreds of femtoseconds, vibrational cooling on the similar picosecond time scale, and complete ground-state recovery in 10 ps, and no global conformation relaxation was observed.

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.

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.

Influence of distal residue B10 on CO dynamics in myoglobin and neuroglobin

For many years, myoglobin has served as a paradigm for structure-function studies in proteins. Ligand binding and migration within myoglobin has been studied in great detail by crystallography and spectroscopy, showing that gaseous ligands such as O(2), CO, and NO not only bind to the heme iron but may also reside transiently in three internal ligand docking sites, the primary docking site B and secondary sites C and D. These sites affect ligand association and dissociation in specific ways. Neuroglobin is another vertebrate heme protein that also binds small ligands. Ligand migration pathways in neuroglobin have not yet been elucidated. Here, we have used Fourier transform infrared temperature derivative spectroscopy at cryogenic temperatures to compare the influence of the side chain volume of amino acid residue B10 on ligand migration to and rebinding from docking sites in myoglobin and neuroglobin.

Ultrafast dynamics of myoglobin without the distal histidine: stimulated vibrational echo experiments and molecular dynamics simulations

Ultrafast protein dynamics of the CO adduct of a myoglobin mutant with the polar distal histidine replaced by a nonpolar valine (H64V) have been investigated by spectrally resolved infrared stimulated vibrational echo experiments and molecular dynamics (MD) simulations. In aqueous solution at room temperature, the vibrational dephasing rate of CO in the mutant is reduced by approximately 50% relative to the native protein. This finding confirms that the dephasing of the CO vibration in the native protein is sensitive to the interaction between the ligand and the distal histidine. The stimulated vibrational echo observable is calculated from MD simulations of H64V within a model in which vibrational dephasing is driven by electrostatic forces. In agreement with experiment, calculated vibrational echoes show slower dephasing for the mutant than for the native protein. However, vibrational echoes calculated for H64V do not show the quantitative agreement with measurements demonstrated previously for the native protein.

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.

Cytochrome c552 Mutants: Structure and Dynamics at the Active Site Probed by Multidimensional NMR and Vibration Echo Spectroscopy

Spectrally resolved infrared stimulated vibrational echo experiments are used to measure the vibrational dephasing of a CO ligand bound to the heme cofactor in two mutated forms of the cytochrome c552 from Hydrogenobacter thermophilus. The first mutant (Ht-M61A) is characterized by a single mutation of Met61 to an Ala (Ht-M61A), while the second variant is doubly modified to have Gln64 replaced by an Asn in addition to the M61A mutation (Ht-M61A/Q64N). Multidimensional NMR experiments determined that the geometry of residue 64 in the two mutants is consistent with a non-hydrogen-bonding and hydrogen-bonding interaction with the CO ligand for Ht-M61A and Ht-M61A/Q64N, respectively. The vibrational echo experiments reveal that the shortest time scale vibrational dephasing of the CO is faster in the Ht-M61A/Q64N mutant than that in Ht-M61A. Longer time scale dynamics, measured as spectral diffusion, are unchanged by the Q64N modification. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to confirm that the dynamical difference induced by the Q64N mutation is primarily an increase in the fast (hundreds of femtoseconds) frequency fluctuations, while the slower (tens of picoseconds) dynamics are nearly unaffected. We conclude that the faster dynamics in Ht-M61A/Q64N are due to the location of Asn64, which is a hydrogen bond donor, above the heme-bound CO. A similar difference in CO ligand dynamics has been observed in the comparison of the CO derivative of myoglobin (MbCO) and its H64V variant, which is caused by the difference in axial residue interactions with the CO ligand. The results suggest a general trend for rapid ligand vibrational dynamics in the presence of a hydrogen bond donor.

Dynamics of proteins encapsulated in silica sol-gel glasses studied with IR vibrational echo spectroscopy

Spectrally resolved infrared stimulated vibrational echo spectroscopy is used to measure the fast dynamics of heme-bound CO in carbonmonoxy-myoglobin (MbCO) and -hemoglobin (HbCO) embedded in silica sol-gel glasses. On the time scale of approximately 100 fs to several picoseconds, the vibrational dephasing of the heme-bound CO is measurably slower for both MbCO and HbCO relative to that of aqueous protein solutions. The fast structural dynamics of MbCO, as sensed by the heme-bound CO, are influenced more by the sol-gel environment than those of HbCO. Longer time scale structural dynamics (tens of picoseconds), as measured by the extent of spectral diffusion, are the same for both proteins encapsulated in sol-gel glasses compared to that in aqueous solutions. A comparison of the sol-gel experimental results to viscosity-dependent vibrational echo data taken on various mixtures of water and fructose shows that the sol-gel-encapsulated MbCO exhibits dynamics that are the equivalent of the protein in a solution that is nearly 20 times more viscous than bulk water. In contrast, the HbCO dephasing in the sol-gel reflects only a 2-fold increase in viscosity. Attempts to alter the encapsulating pore size by varying the molar ratio of silane precursor to water (R value) used to prepare the sol-gel glasses were found to have no effect on the fast or steady-state spectroscopic results. The vibrational echo data are discussed in the context of solvent confinement and protein-pore wall interactions to provide insights into the influence of a confined environment on the fast structural dynamics experienced by a biomolecule.

Temperature-dependent studies of NO recombination to heme and heme proteins

The rebinding kinetics of NO to the heme iron of myoglobin (Mb) is investigated as a function of temperature. Below 200 K, the transition-state enthalpy barrier associated with the fastest (approximately 10 ps) recombination phase is found to be zero and a slower geminate phase (approximately 200 ps) reveals a small enthalpic barrier (approximately 3 +/- 1 kJ/mol). Both of the kinetic rates slow slightly in the myoglobin (Mb) samples above 200 K, suggesting that a small amount of protein relaxation takes place above the solvent glass transition. When the temperature dependence of the NO recombination in Mb is studied under conditions where the distal pocket is mutated (e.g., V68W), the rebinding kinetics lack the slow phase. This is consistent with a mechanism where the slower (approximately 200 ps) kinetic phase involves transitions of the NO ligand into the distal heme pocket from a more distant site (e.g., in or near the Xe4 cavity). Comparison of the temperature-dependent NO rebinding kinetics of native Mb with that of the bare heme (PPIX) in glycerol reveals that the fast (enthalpically barrierless) NO rebinding process observed below 200 K is independent of the presence or absence of the proximal histidine ligand. In contrast, the slowing of the kinetic rates above 200 K in MbNO disappears in the absence of the protein. Generally, the data indicate that, in contrast to CO, the NO ligand binds to the heme iron through a "harpoon" mechanism where the heme iron out-of-plane conformation presents a negligible enthalpic barrier to NO rebinding. These observations strongly support a previous analysis (Srajer et al. J. Am. Chem. Soc. 1988, 110, 6656-6670) that primarily attributes the low-temperature stretched exponential rebinding of MbCO to a quenched distribution of heme geometries. A simple model, consistent with this prior analysis, is presented that explains a variety of MbNO rebinding experiments, including the dependence of the kinetic amplitudes on the pump photon energy.

The Influence of Aqueous versus Glassy Solvents on Protein Dynamics: Vibrational Echo Experiments and Molecular Dynamics Simulations

Spectrally resolved infrared stimulated vibrational echo measurements are used to measure the vibrational dephasing of the CO stretching mode of carbonmonoxy-hemoglobin (HbCO), a myoglobin mutant (H64V), and a bacterial cytochrome c(552) mutant (Ht-M61A) in aqueous solution and trehalose glasses. The vibrational dephasing of the heme-bound CO is significantly slower for all three proteins embedded in trehalose glasses compared to that of aqueous protein solutions. All three proteins exhibit persistent but notably slower spectral diffusion when the protein surface is fixed by the glassy solvent. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to reveal that the structural dynamics, as sensed by the CO, of the three proteins in trehalose and aqueous solution are dominated by fast (tens of femtoseconds), motionally narrowed fluctuations. MD simulations of H64V in dynamic and "static" water are presented as models of the aqueous and glassy environments. FFCFs are calculated from the H64V simulations and qualitatively reproduce the important features of the experimentally extracted FFCFs. The suppression of long time scale (picoseconds to tens of picoseconds) frequency fluctuations (spectral diffusion) in the glassy solvent is the result of a damping of atomic displacements throughout the protein structure and is not limited to structural dynamics that occur only at the protein surface. The analysis provides evidence that some dynamics are coupled to the hydration shell of water, supporting the idea that the bioprotection offered by trehalose is due to its ability to immobilize the protein surface through a thin, constrained layer of water.

Dynamics of hemoglobin in human erythrocytes and in solution: influence of viscosity studied by ultrafast vibrational echo experiments

Ultrafast spectrally resolved stimulated vibrational echo experiments are used to measure the vibrational dephasing of the CO stretching mode of hemoglobin-CO (HbCO) inside living human erythrocytes (red blood cells), in liquid solutions, and in a glassy matrix. A method is presented to overcome the adverse impact on the vibrational echo signal from the strong light scattering caused by the cells. The results from the cytoplasmic HbCO are compared to experiments on aqueous HbCO samples prepared in different buffers, solutions containing low and high concentrations of glycerol, and in a solid trehalose matrix. Measurements are also presented that provide an accurate determination of the viscosity at the very high Hb concentration that is found inside the cells. It is demonstrated that the dynamics of the protein, as sensed by the CO ligand, are the same inside the erythrocytes and in aqueous solution and are independent of the viscosity. In solutions that are predominantly glycerol, the dynamics are modified somewhat but are still independent of viscosity. The experiments in trehalose give the dynamics at infinite viscosity and are used to separate the viscosity-dependent dynamics from the viscosity-independent dynamics. Although the HbCO dynamics are the same in the red blood cell and in the equivalent aqueous solutions, differences in the absorption spectra show that the distribution of a protein's equilibrium substates is sensitive to small pH differences.

Structural dynamics of myoglobin: ligand migration among protein cavities studied by Fourier transform infrared/temperature derivative spectroscopy

Fourier transform infrared (FTIR) spectroscopy in the CO stretch bands combined with temperature derivative spectroscopy (TDS) was used to characterize intermediate states obtained by photolysis of two sperm whale mutant myoglobins, YQR (L29(B10)Y, H64(E7)Q, T67(E10)R) and YQRF (with an additional I107(G8)F replacement). Both mutants assume two different bound-state conformations, A(0) and A(3), which can be distinguished by their different CO bands near 1965 and 1933 cm(-1). They most likely originate from different conformations of the Gln-64 side chain. Within each A substate, a number of photoproduct states have been characterized on the basis of the temperature dependence of recombination in TDS experiments. Different locations and orientations of the ligand within the protein can be distinguished by the infrared spectra of the photolyzed CO. Recombination from the primary docking site, B, near the heme dominates below 50 K. Above 60 K, ligand rebinding occurs predominantly from a secondary docking site, C', in which the CO is trapped in the Xe4 cavity on the distal side, as shown by crystallography of photolyzed YQR and L29W myoglobin CO. Another kinetic state (C") has been identified from which rebinding occurs around 130 K. Moreover, a population appearing above the solvent glass transition at approximately 180 K (D state) is assigned to rebinding from the Xe1 cavity, as suggested by the photoproduct structure of the L29W sperm whale myoglobin mutant. For both the YQR and YQRF mutants, rebinding from the B sites near the heme differs for the two A substates, supporting the view that the return of the ligand from the C', C", and D states is not governed by the recombination barrier at the heme iron but rather by migration to the active site. Comparison of YQR and YQRF shows that access to the Xe4 site (C') is severely restricted by introduction of the bulky Phe side chain at position 107.

Modeling the "glass" transition in proteins

A model of a protein as a disordered system of identical spherical particles (which imitate protein side chains) interacting with each other via a repulsive soft sphere potential U(r) infinity r(-beta) is constructed. The particles undergo the conformational motion (CM) within their own harmonic conformational potentials around some mean equilibrium positions ascribed by the tertiary structure of the protein. A first principles calculation of the positional correlation functions for the CM is carried out. The general analysis is exemplified by the case in which the mean equilibrium positions of the particles form a cubic tightly-packed (face- centered) lattice (each particle has 12 nearest neighbors) with the step b(hydr) =6.6 A (the average distance between the centers of mass of hydrated protein subunits). The model yields dramatic slowing down of the relaxation with the decrease of temperature followed by a sharp glass transition at some crossover temperature T(c) < 200 K. At the transition the liquid-like dynamic behavior (the correlation functions tend to zero with time) is altered by the glass-like one (the correlation functions tend with time to some non-zero limit). In the liquid-like region above the crossover temperature the relaxation exhibits distinct alpha-process following the beta-one. The glass transition results from the interaction of the particles. Thus the model suggests that namely direct interactions of the fragments of protein structure rather than protein-solvent interactions are the origin of the phenomenon of the glass transition. The known increase of T(c) up to 300 K at dehydration of the protein is attributed to the known concomitant compression of the globule upon drying by about 4-6% so that positions of individual atoms displace by about 0.6 A (modeled by the decrease of the step of the lattice b by 0.6 A so that b(dehydr)=6 A). The model suggests that the solvent influences the phenomenon of the glass transition indirectly determining the tertiary structure of the protein rather than via own freezing. In the model the transition from the liquid-like dynamic behavior to the glass-like one can be obtained even in a cluster containing a few particles. Thus the results of the model can be considered as an argument in favor of the point of view that the transition to the glassy behavior can take place for a very small domains of the protein comprising only several constituting fragments of its structure. The model predicts that for the dehydrated protein the alpha-relaxation process is strongly repressed.

On the nature of a glassy state of matter in a hydrated protein: Relation to protein function

Diverse biochemical and biophysical experiments indicate that all proteins, regardless of size or origin, undergo a dynamic transition near 200 K. The cause of this shift in dynamic behavior, termed a "glass transition," and its relation to protein function are important open questions. One explanation postulated for the transition is solidification of correlated motions in proteins below the transition. We verified this conjecture by showing that crambin's radius of gyration (Rg) remains constant below approximately 180 K. We show that both atom position and dynamics of protein and solvent are physically coupled, leading to a novel cooperative state. This glassy state is identified by negative slopes of the Debye-Waller (B) factor vs. temperature. It is composed of multisubstate side chains and solvent. Based on generalization of Adam-Gibbs' notion of a cooperatively rearranging region and decrease of the total entropy with temperature, we calculate the slope of the Debye-Waller factor. The results are in accord with experiment.

The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin

The grail of protein science is the connection between structure and function. For myoglobin (Mb) this goal is close. Described as only a passive dioxygen storage protein in texts, we argue here that Mb is actually an allosteric enzyme that can catalyze reactions among small molecules. Studies of the structural, spectroscopic, and kinetic properties of Mb lead to a model that relates structure, energy landscape, dynamics, and function. Mb functions as a miniature chemical reactor, concentrating and orienting diatomic molecules such as NO, CO, O(2), and H(2)O(2) in highly conserved internal cavities. Reactions can be controlled because Mb exists in distinct taxonomic substates with different catalytic properties and connectivities of internal cavities.

Time-resolved hole-burning study on myoglobin: fluctuation of restricted water within distal pocket

We have studied the equilibrium fluctuation dynamics of Zn-substituted myoglobin and its His64-->Leu (H64L) mutant in the pH range from 5 to 9 by using time-resolved transient-hole-burning (TRTHB) spectroscopy. In the H64L mutant, we have observed a largely reduced width of the absorption spectrum and only a slight temporal shift of the hole-burning spectrum. These observations both reflect the suppressed conformational fluctuation in the mutant. On the other hand, the pH-dependent change in the absorption spectrum could not be solely explained by the change in the protonation state of His64 induced by the pH change. These results suggest that although the fluctuation dynamics observed by the TRTHB experiment of the native sample mainly reflects the conformational motion around His64, the interconversion process of His64 between its protonated and unprotonated states has a minor contribution. Instead, we have proposed a tentative interpretation that the motion of the water molecule around His64 is the main source of the observed dynamics in the TRTHB technique.

Kinetics of diffusion-assisted reactions in microheterogeneous systems

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.

Modeling the correlation functions of conformational motions in proteins

A first principles calculation of the correlation function for conformational motion (CM) in proteins is carried out within the framework of a microscopic model of a protein as a heterogeneous system. The fragments of the protein are assumed to be identical hard spheres undergoing the CM within their conformational potentials about some mean equilibrium positions assigned by the tertiary structure. The memory friction function (MFF) for the generalized Langevin equation describing the CM of the particle is obtained on the basis of the direct calculation which is feasible for the present model of the protein due to the existence of a natural large parameter, viz. the ratio of the minimal distance between the mean equilibrium positions of the particles (approximately 7A) to the amplitude of their CM (<1A). A relationship between the MFF and the correlation functions of the CM of the particles is derived which makes their calculation to be a self-consistent mathematical problem. The general analysis of the MFF is exemplified by a simple model case in which the mean equilibrium positions of the particles form a regular lattice so that the correlation functions for all particles are the same. In this case the MFF is shown to be an infinite series of the powers of the auto-correlation function whose coefficients are independent on temperature. The latter is a result of the abstraction of the interaction potential by that of hard spheres which actually corresponds to the high temperature limit. On the examples of cubic and triangular lattices the coefficients are shown to be non-negative values which increase with the increase of the packing density of the particles and quickly tend to zero with the increase of their index. Thus the MFF can be approximated by a polynomial of the correlation function and the resulting mathematical equation is analogous to the one from the dynamic theory of liquids. The correlation function of the CM is obtained by numerical solution of the equation. At realistic packing densities for proteins it exhibits transparent non-exponential decay and includes two relaxation processes: the first one on the intermediate timescale (tens of picoseconds) and the second on the long timescale (its characteristic time is about tens of nanoseconds at small values of the friction coefficient and increases by orders of the magnitude with the increase of the latter). Thus the present approach provides the microscopic basis for previous phenomenological models of cooperative dynamics in proteins.

Crystal structures of myoglobin-ligand complexes at near-atomic resolution

We have used x-ray crystallography to determine the structures of sperm whale myoglobin (Mb) in four different ligation states (unligated, ferric aquomet, oxygenated, and carbonmonoxygenated) to a resolution of better than 1.2 A. Data collection and analysis were performed in as much the same way as possible to reduce model bias in differences between structures. The structural differences among the ligation states are much smaller than previously estimated, with differences of <0.25 A root-mean-square deviation among all atoms. One structural parameter previously thought to vary among the ligation states, the proximal histidine (His-93) azimuthal angle, is nearly identical in all the ferrous complexes, although the tilt of the proximal histidine is different in the unligated form. There are significant differences, however, in the heme geometry, in the position of the heme in the pocket, and in the distal histidine (His-64) conformations. In the CO complex the majority conformation of ligand is at an angle of 18 +/- 3 degrees with respect to the heme plane, with a geometry similar to that seen in encumbered model compounds; this angle is significantly smaller than reported previously by crystallographic studies on monoclinic Mb crystals, but still significantly larger than observed by photoselection. The distal histidine in unligated Mb and in the dioxygenated complex is best described as having two conformations. Two similar conformations are observed in MbCO, in addition to another conformation that has been seen previously in low-pH structures where His-64 is doubly protonated. We suggest that these conformations of the distal histidine correspond to the different conformational substates of MbCO and MbO(2) seen in vibrational spectra. Full-matrix refinement provides uncertainty estimates of important structural parameters. Anisotropic refinement yields information about correlated disorder of atoms; we find that the proximal (F) helix and heme move approximately as rigid bodies, but that the distal (E) helix does not.

Connection between the taxonomic substates and protonation of histidines 64 and 97 in carbonmonoxy myoglobin

Infrared spectra of heme-bound CO in sperm whale carbonmonoxy myoglobin and two mutants (H64L and H97F) were studied in the pH range from 4.2 to 9.5. Comparison of the native protein with the mutants shows that the observed pH effects can be traced to protonations of two histidine residues, H64 and H97, near the active site. Their imidazole sidechains experience simple, uncoupled Henderson-Hasselbalch type protonations, giving rise to four different protonation states. Because two of the protonation states are linked by a pH-independent equilibrium, the overall pH dependence of the spectra is described by a linear combination of three independent components. Global analysis, based on singular value decomposition and matrix least-squares algorithms enabled us to extract the pK values of the two histidines and the three basis spectra of the protonating species. The basis spectra were decomposed into the taxonomic substates A(0), A(1), and A(3), previously introduced in a heuristic way to analyze CO stretch spectra in heme proteins at fixed pH (see for instance, Biophys. J. 71:1563-1573). Moreover, an additional, weakly populated substate, called A(x), was identified. Protonation of H97 gives rise to a blue shift of the individual infrared lines by about 2 cm(-1), so that the A substates actually appear in pairs, such as A(0) and A(0)(+). The blue shift can be explained by reduced backbonding from the heme iron to the CO. Protonation of the distal histidine, H64, leads to a change of the infrared absorption from the A(1) or A(3) substate lines to A(0). This behavior can be explained by a conformational change upon protonation that moves the imidazole sidechain of H64 away from the CO into the high-dielectric solvent environment, which avoids the energetically unfavorable situation of an uncompensated electric charge in the apolar, low-dielectric protein interior. Our results suggest that protonation reactions serve as an important mechanism to create taxonomic substates in proteins.

Smoluchowski dynamics of the vnd/NK-2 homeodomain from Drosophila melanogaster: first-order mode-coupling approximation

This work is the first in a series devoted to applying mode coupling diffusion theory to the derivation of local dynamics properties of proteins in solution. The first-order mode-coupling approximation, or optimized Rouse-Zimm local dynamics (ORZLD), is applied here to derive the rotational dynamics of the bonds and compare the calculated with the experimental nmr 15N spin-lattice relaxation time behavior of the vnd/NK-2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three-dimensional structure of the homeodomain determined by multidimensional nmr spectroscopy. The results of the computations are compared with experimentally measured 15N spin-lattice relaxation times T1, at 34.5 and 60.8 MHz, to check the first-order approximation. To estimate the relative importance of internal and overall rotation, both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics (MD) simulations. The correlation times for the fundamental bond vector time correlation function and for the second-order bond orientational TCF are obtained as a function of the residue number for vnd/NK-2. The stability of the corresponding local dynamics pattern for the fluctuating structure as a function of the length of the MD trajectory is presented. Diffusive dynamics, which is essentially free of model parameters even at first order in the mode-coupling diffusion approach, confirm that local dynamics of proteins can be described in terms of rotational diffusion of a fluctuating quasi-rigid structure. The comparison with the nmr data shows that the first-order mode coupling diffusion approximation accounts for the correct order of magnitude of the results and of important qualitative aspects of the data sensitive to conformational changes. Indications are obtained from this study to efficiently extend the theory to higher order in the mode-coupling expansion. These results demonstrate the promise of the mode-coupling approach, where the local dynamics of proteins is described in terms of rotational diffusion of a fluctuating quasi-rigid structure, to analyze nmr spin-lattice relaxation behavior.

Low temperature photolysis of denatured nitrosyl hemoproteins

Photolysis of denatured HbNO were carried out at temperatures below 26 K. The normalized kinetic curves were fitted using either two exponentials or a conformational substate energy distribution or a fractal model. The parameters are related to the protein structure. The two exponentials model assumes the existence of two fractions of photolysed molecules that rebind with slow and fast reaction rates. Only the slow reaction rate is sensitive to the denaturation process. The pre-exponential factor and the peak energy of the substate distribution values suggest an increase in the entropy and a decrease of the flexibility in the denatured samples, respectively. The fractal model parameters strengthened the functional relevance of the flexibility of the protein chain.

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

Real-time observation of conformational fluctuations in Zn-substituted myoglobin by time-resolved transient hole-burning spectroscopy

Equilibrium fluctuations of the protein conformation have been studied in myoglobin by a novel method of time-resolved transient hole-burning spectroscopy over a temperature range of 180-300 K and a time range of 10 ns to 10 ms. The temporal shift of the hole spectrum has been observed in a wide temperature region of 200-300 K. It has been found that the time behavior of the peak position of the hole is highly nonexponential and can be expressed by a stretched exponential function with a beta value of 0.22. As compared with the results for a dye solution sample, the time scale of the fluctuation of the protein conformation is much more weakly dependent on temperature. The time scale of the observed conformational dynamics shows a temperature dependence similar to that associated with the ligand escape process of myoglobin.

Electron transfer and protein dynamics in the photosynthetic reaction center

We have measured the kinetics of electron transfer (ET) from the primary quinone (Q(A)) to the special pair (P) of the reaction center (RC) complex from Rhodobacter sphaeroides as a function of temperature (5-300 K), illumination protocol (cooled in the dark and under illumination from 110, 160, 180, and 280 K), and warming rate (1.3 and 13 mK/s). The nonexponential kinetics are interpreted with a quantum-mechanical ET model (Fermi's golden rule and the spin-boson model), in which heterogeneity of the protein ensemble, relaxations, and fluctuations are cast into a single coordinate that relaxes monotonically and is sensitive to all types of relaxations caused by ET. Our analysis shows that the structural changes that occur in response to ET decrease the free energy gap between donor and acceptor states by 120 meV and decrease the electronic coupling between donor and acceptor states from 2.7 x 10(-4) cm(-1) to 1.8 x 10(-4) cm(-1). At cryogenic temperatures, conformational changes can be slowed or completely arrested, allowing us to monitor relaxations on the annealing time scale (approximately 10(3)-10(4) s) as well as the time scale of ET (approximately 100 ms). The relaxations occur within four broad tiers of conformational substates with average apparent Arrhenius activation enthalpies of 17, 50, 78, and 110 kJ/mol and preexponential factors of 10(13), 10(15), 10(21), and 10(25) s(-1), respectively. The parameterization provides a prediction of the time course of relaxations at all temperatures. At 300 K, relaxations are expected to occur from 1 ps to 1 ms, whereas at lower temperatures, even broader distributions of relaxation times are expected. The weak dependence of the ET rate on both temperature and protein conformation, together with the possibility of modeling heterogeneity and dynamics with a single conformational coordinate, make RC a useful model system for probing the dynamics of conformational changes in proteins.

A ligand-gated, hinged loop rearrangement opens a channel to a buried artificial protein cavity

Conformational changes that gate the access of substrates or ligands to an active site are important features of enzyme function. In this report, we describe an unusual example of a structural rearrangement near a buried artificial cavity in cytochrome c peroxidase that occurs on binding protonated benzimidazole. A hinged main-chain rotation at two residues (Pro 190 and Asn 195) results in a surface loop rearrangement that opens a large solvent-accessible channel for the entry of ligands to an otherwise inaccessible binding site. The trapping of this alternate conformational state provides a unique view of the extent to which protein dynamics can allow small molecule penetration into buried protein cavities.

Using buried water molecules to explore the energy landscape of proteins

Buried water molecules constitute a highly conserved, integral part of nearly all known protein structures. Such water molecules exchange with external solvent as a result of protein conformational fluctuations. We report here the results of water (17)O and (2)H magnetic relaxation dispersion measurements on wild-type and mutant bovine pancreatic trypsin inhibitor in aqueous solution at 4-80 degrees C. These data lead to the first determination of the exchange rate of a water molecule buried in a protein. The strong temperature dependence of this rate is ascribed to large-scale conformational fluctuations in an energy landscape with a statistical ruggedness of approximately 10 kJ mol(-1).

Ligand binding and protein dynamics in cupredoxins

Type 1 copper sites bind nitric oxide (NO) in a photolabile complex. We have studied the NO binding properties of the type 1 copper sites in two cupredoxins, azurin and halocyanin, by measuring the temperature dependence of the ligand binding equilibria and the kinetics of the association reaction after photodissociation over a wide range of temperature (80-280 K) and time (10(-6)-10(2) s). In both proteins, we find nonexponential kinetics below 200 K that do not depend on the NO concentration. Consequently, this process is interpreted as geminate recombination. In azurin, the rebinding can be modeled with the Arrhenius law using a single pre-exponential factor of 10(8.3) s-1 and a Gaussian distribution of enthalpy barriers centered at 22 kJ/mol with a width [full width at half-maximum (FWHM)] of 11 kJ/mol. In halocyanin, a more complex behavior is observed. About 97% of the rebinding population can also be characterized by a Gaussian distribution of enthalpy barriers at 12 kJ/mol with a width of 6.0 kJ/mol (FWHM). The pre-exponential of this population is 1.6 x 10(12) s-1 at 100 K. After the majority population has rebound, a power-law phase that can be modeled with a gamma-distribution of enthalpy barriers is observed. Between 120 and 180 K, an additional feature that can be interpreted as a relaxation of the barrier distribution toward higher barriers shows up in the kinetics. Above 200 K, a slower, exponential rebinding appears in both cupredoxins. Since the kinetics depend on the NO concentration, this process is identified as bimolecular rebinding.(ABSTRACT TRUNCATED AT 250 WORDS)