Ligand binding to heme proteins: connection between dynamics and function

Interference between Franck-Condon and Herzberg-Teller Terms in the Condensed-Phase Molecular Spectra of Metal-Based Tetrapyrrole Derivatives

The commonly used Franck-Condon (FC) approximation is inadequate for explaining the electronic spectra of compounds that possess vibrations with substantial Herzberg-Teller (HT) couplings. Metal-based tetrapyrrole derivatives, which are ubiquitous natural pigments, often exhibit prominent HT activity. In this paper, we compare the condensed phase spectra of zinc-tetraphenylporphyrin (ZnTPP) and zinc-phthalocyanine (ZnPc), which exhibit vastly different spectral features in spite of sharing a common tetrapyrrole backbone. The absorption and emission spectra of ZnTPP are characterized by a lack of mirror symmetry and nontrivial temperature dependence. In contrast, mirror symmetry is restored, and the nontrivial temperature-dependent features disappear in ZnPc. We attribute these differences to FC-HT interference, which is less pronounced in ZnPc because of a larger FC component in the dipole moment that leads to FC-dominated transitions. A single minimalistic FC-HT vibronic model reproduces all the experimental spectral features of these molecules. These observations suggest that FC-HT interference is highly susceptible to chemical modification.

Modulation of free energy landscapes as a strategy for the design of antimicrobial peptides

Computational design of antimicrobial peptides (AMPs) is a promising area of research for developing novel agents against drug-resistant bacteria. AMPs are present naturally in many organisms, from bacteria to humans, a time-tested mechanism that makes them attractive as effective antibiotics. Depending on the environment, AMPs can exhibit α-helical or β-sheet conformations, a mix of both, or lack secondary structure; they can be linear or cyclic. Prediction of their structures is challenging but critical for rational design. Promising AMP leads can be developed using essentially two approaches: traditional modeling of the physicochemical mechanisms that determine peptide behavior in aqueous and membrane environments and knowledge-based, e.g., machine learning (ML) techniques, that exploit ever-growing AMP databases. Here, we explore the conformational landscapes of two recently ML-designed AMPs, characterize the dependence of these landscapes on the medium conditions, and identify features in peptide and membrane landscapes that mediate protein-membrane association. For both peptides, we observe greater conformational diversity in an aqueous solvent than in a less polar solvent, and one peptide is seen to alter its conformation more dramatically than the other upon the change of solvent. Our results support the view that structural rearrangement in response to environmental changes is central to the mechanism of membrane-structure disruption by linear peptides. We expect that the design of AMPs by ML will benefit from the incorporation of peptide conformational substates as quantified here with molecular simulations.

Dynamics of camel and human hemoglobin revealed by molecular simulations

Hemoglobin is one of the most widely studied proteins genetically, biochemically, and structurally. It is an oxygen carrying tetrameric protein that imparts the characteristic red color to blood. Each chain of hemoglobin harbors a heme group embedded in a hydrophobic pocket. Several studies have investigated structural variations present in mammalian hemoglobin and their functional implications. However, camel hemoglobin has not been thoroughly explored, especially from a structural perspective. Importantly, very little is known about how the heme group interacts with hemoglobin under varying conditions of osmolarity and temperature. Several experimental studies have indicated that the tense (T) state is more stable than the relaxed (R) state of hemoglobin under normal physiological conditions. Despite the fact that R state is less stable than the T state, no extensive structural dynamics studies have been performed to investigate global quaternary transitions of R state hemoglobin under normal physiological conditions. To evaluate this, several 500 ns all-atom molecular dynamics simulations were performed to get a deeper understanding of how camel hemoglobin behaves under stress, which it is normally exposed to, when compared to human hemoglobin. Notably, camel hemoglobin was more stable under physiological stress when compared to human hemoglobin. Additionally, when compared to camel hemoglobin, cofactor-binding regions of hemoglobin also exhibited more fluctuations in human hemoglobin under the conditions studied. Several differences were observed between the residues of camel and human hemoglobin that interacted with heme. Importantly, distal residues His58 of α hemoglobin and His63 of β hemoglobin formed more sustained interactions, especially at higher temperatures, in camel hemoglobin. These residues are important for oxygen binding to hemoglobin. Thus, this work provides insights into how camel and human hemoglobin differ in their interactions under stress.

Impact of Conformational Substates and Energy Landscapes on Understanding Hemoglobin Kinetics and Function

Hans Frauenfelder's discovery of conformational substates in studies of myoglobin carbon monoxide geminate rebinding kinetics at cryogenic temperatures (Austin RH, Beeson KW, Eisenstein L, Frauenfelder H, & Gunsalus IC (1975) Dynamics of Ligand Binding to Myoglobin. Biochemistry 14(24):5355-5373) followed by his introduction of energy landscape theory with Peter Wolynes (Frauenfelder H, Sligar SG, & Wolynes PG (1991) The Energy Landscapes and Motions of Proteins. Science 254(5038):1598-1603) marked the beginning of a new era in the physics and physical chemistry of proteins. Their work played a major role in demonstrating the power and importance of dynamics and of Kramers reaction rate theory for understanding protein function. The biggest impact of energy landscape theory has been in the protein folding field, which is well-known and has been documented in numerous articles and reviews, including a recent one of my own (Eaton WA (2021) Modern Kinetics and Mechanism of Protein Folding: a Retrospective. J. Phys. Chem. B. 125(14):3452-3467). Here I will describe the much less well-known impact of their modern view of proteins on both experimental and theoretical studies of hemoglobin kinetics and function. I will first describe how Frauenfelder's experiments motivated and influenced my own research on myoglobin, which were key ingredients to my work on understanding hemoglobin.

Towards understanding non-equivalence of α and β subunits within human hemoglobin in conformational relaxation and molecular oxygen rebinding

Picosecond to millisecond laser time-resolved transient absorption spectroscopy was used to study molecular oxygen (O₂) rebinding and conformational relaxation following O₂ photodissociation in the α and β subunits within human hemoglobin in the quaternary R-like structure. Oxy-cyanomet valency hybrids, α₂(Fe²⁺-O₂)β₂(Fe³⁺-CN) and α₂(Fe³⁺-CN)β₂(Fe²⁺-O₂), were used as models for oxygenated R-state hemoglobin. An extended kinetic model for geminate O₂ rebinding in the ferrous hemoglobin subunits, ligand migration between the primary and secondary docking site(s), and nonexponential tertiary relaxation within the R quaternary structure, was introduced and discussed. Significant functional non-equivalence of the α and β subunits in both the geminate O₂ rebinding and concomitant structural relaxation was revealed. For the β subunits, the rate constant for the geminate O₂ rebinding to the unrelaxed tertiary structure and the tertiary transition rate were found to be greater than the corresponding values for the α subunits. The conformational relaxation following the O₂ photodissociation in the α and β subunits was found to decrease the rate constant for the geminate O₂ rebinding, this effect being more than one order of magnitude greater for the β subunits than for the α subunits. Evidence was provided for the modulation of the O₂ rebinding to the individual α and β subunits within human hemoglobin in the R-state structure by the intrinsic heme reactivity through a change in proximal constraints upon the relaxation of the tertiary structure on a picosecond to microsecond time scale. Our results demonstrate that, for native R-state oxyhemoglobin, O₂ rebinding properties and spectral changes following the O₂ photodissociation can be adequately described as the sum of those for the α and β subunits within the valency hybrids. The isolated β chains (hemoglobin H) show similar behavior to the β subunits within the valency hybrids and can be used as a model for the β subunits within the R-state oxyhemoglobin. At the same time, the isolated α chains behave differently to the α subunits within the valency hybrids.

Ultrafast Dynamics of Nonrigid Zinc-Porphyrin Arrays Mimicking the Photosynthetic "Special Pair"

Conjugated porphyrin arrays are heavily investigated as efficient molecular systems for photosynthesis and photocatalysis. Recently, a series of one-, two-, and six-zinc-porphyrin arrays, noncovalently linked through benzene-based hubs, have been synthesized with the aim of mimicking the structure and function of the bacteriochlorophyll "special pair" in photosynthetic reaction centers. The excitonically coupled porphyrin subunits are expected to activate additional excited state relaxation channels with respect to the monomer. Here, we unveil the appearance of such supramolecular electronic interactions using ultrafast transient absorption spectroscopy with sub-25 fs time resolution. Upon photoexcitation of the Soret band, we resolve energy trapping within ∼150 fs in a delocalized dark excitonic manifold. Moreover, excitonic interactions promote an additional fast internal conversion from the Q-band to the ground state with an efficiency of up to 60% in the hexamer. These relaxation pathways appear to be common loss channels that limit the lifetime of the exciton states in noncovalently bound molecular aggregates.

Nanosecond-Timescale Dynamics and Conformational Heterogeneity in Human GCK Regulation and Disease

Human glucokinase (GCK) is the prototypic example of an emerging class of proteins with allosteric-like behavior that originates from intrinsic polypeptide dynamics. High-resolution NMR investigations of GCK have elucidated millisecond-timescale dynamics underlying allostery. In contrast, faster motions have remained underexplored, hindering the development of a comprehensive model of cooperativity. Here, we map nanosecond-timescale dynamics and structural heterogeneity in GCK using a combination of unnatural amino acid incorporation, time-resolved fluorescence, and ¹⁹F nuclear magnetic resonance spectroscopy. We find that a probe inserted within the enzyme's intrinsically disordered loop samples multiple conformations in the unliganded state. Glucose binding and disease-associated mutations that suppress cooperativity alter the number and/or relative population of these states. Together, the nanosecond kinetics characterized here and the millisecond motions known to be essential for cooperativity provide a dynamical framework with which we address the origins of cooperativity and the mechanism of activated, hyperinsulinemia-associated, noncooperative variants.

O2 formation in cold environments

The diffusional dynamics of atomic oxygen in and on amorphous solid water (ASW) to form molecular oxygen is characterized. Reactive molecular dynamics simulations to study bond breaking and bond formation show that vibrational relaxation of the highly excited diatomic occurs on the 10 ns to 100 ns time scale. The relaxation process is highly nonexponential and can be characterized by a stretched exponential decay reminiscent of the dynamics of glasses. The stretched exponents range from β = 0.15 for relaxation on the surface to β = 0.21 for the dynamics in bulk. It is also found that coupling of the O2 relaxation to the internal water modes occurs which speeds up the vibrational relaxation by a factor of 4. Extrapolation of the stretched exponential decay to 1 μs yields a final vibrational quantum number v = 2 for O2(X3Σ-g), consistent with experimental results from photolysis of SO2 on ASW at 193 nm which find v ≤ 3. Desorption energies of water from the surface range from 1.5 to 2.0 kcal mol-1 compared with 1.8 kcal mol-1 found from experiment, depending on whether the water molecules are flexible or not.

Double-exponential kinetics of binding and redistribution of the fluorescent dyes in cell membranes witness for the existence of lipid microdomains

New technique of detecting lateral heterogeneity of the plasma membrane of living cells by means of membrane-binding fluorescent dyes is proposed. The kinetics of dye incorporation into the membrane or its lateral diffusion inside the membrane is measured and decomposed into exponential components by means of the Maximum Entropy Method. Two distinct exponential components are obtained consistently in all cases for several fluorescent dyes, two different cell lines and in different types of experiments including spectroscopy, flow cytometry and fluorescence recovery after photobleaching. These components are attributed to the liquid-ordered and disordered phases in the plasma membrane of studied cells in their dynamic equilibrium.

Kinetic Study of Ligand Binding and Conformational Changes in Inducible Nitric Oxide Synthase

Nitric oxide synthases (NOSs) are heme enzymes that generate highly reactive nitric oxide from l-arginine (l-Arg) in a complex mechanism that is still only partially understood. We have studied carbon monoxide (CO) binding to the oxygenase domain of murine inducible NOS (iNOS) by using flash photolysis. The P420 and P450 forms of the enzyme, assigned to a protonated and unprotonated proximal cysteine, through which the heme is anchored to the protein, show markedly different CO rebinding properties. The data suggest that P420 has a widely open distal pocket that admits water. CO rebinding to the P450 form strongly depends on the presence of the substrate l-Arg, the intermediate N^ω-hydroxy-l-arginine, and the cofactor tetrahydrobiopterin. After adding these small molecules to the enzyme solution, the CO kinetics change slowly over the hours. This process can be described as a relaxation from a fast rebinding, metastable species to a slowly rebinding, thermodynamically stable species, which we associate with the enzymatically active form. Our results allow us to determine kinetic parameters of l-Arg binding to the ferrous deoxy iNOS protein for the first time and also provide clues regarding the nature of structural differences between the two interconverting species.

Modulating Enzyme Activity by Altering Protein Dynamics with Solvent

Optimal enzyme activity depends on a number of factors, including structure and dynamics. The role of enzyme structure is well recognized; however, the linkage between protein dynamics and enzyme activity has given rise to a contentious debate. We have developed an approach that uses an aqueous mixture of organic solvent to control the functionally relevant enzyme dynamics (without changing the structure), which in turn modulates the enzyme activity. Using this approach, we predicted that the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase (DHFR) from Escherichia coli in aqueous mixtures of isopropanol (IPA) with water will decrease by ∼3 fold at 20% (v/v) IPA concentration. Stopped-flow kinetic measurements find that the pH-independent k_hydride rate decreases by 2.2 fold. X-ray crystallographic enzyme structures show no noticeable differences, while computational studies indicate that the transition state and electrostatic effects were identical for water and mixed solvent conditions; quasi-elastic neutron scattering studies show that the dynamical enzyme motions are suppressed. Our approach provides a unique avenue to modulating enzyme activity through changes in enzyme dynamics. Further it provides vital insights that show the altered motions of DHFR cause significant changes in the enzyme's ability to access its functionally relevant conformational substates, explaining the decreased k_hydride rate. This approach has important implications for obtaining fundamental insights into the role of rate-limiting dynamics in catalysis and as well as for enzyme engineering.

Picosecond Solvation Dynamics in Nanoconfinement: Role of Water and Host-Guest Complexation

The dynamics of solvation of an excited chromophore, 5-(4″-dimethylaminophenyl)-2-(4'-sulfophenyl)oxazole, sodium salt (DMO), has been explored in confined nanoscopic environments of β-cyclodextrin (βCD) and heptakis(2,6-di- O-methyl)-β-cyclodextrin (DIMEB). Solvation occurs on a distinctly slower time scale (τ_S³ ∼ 47 ps, τ_S⁴ ∼ 517 ps) in the host cavity of DIMEB than in that of βCD (τ_S³ ∼ 20 ps, τ_S⁴ ∼ 174 ps). The calculated equilibrium solvation response of DMO was characterized by four relaxation components (τ_S¹ ∼ 0.46-0.48 ps, τ_S² ∼ 3.2-3.4 ps, τ_S³ ∼ 32.3-37.7 ps, and τ_S⁴ ∼ 232-485 ps), of which the longer ones (τ_S³, τ_S⁴) are well-consistent with experiments, whereas the ultrafast components (τ_S¹, τ_S²) are unresolved. The observed time constant (τ_S³) within the ∼20-47 ps range arises from slow water molecules in the primary hydration layers of the host CDs and is slower for DIMEB than for βCD presumably due to longer-lived and stronger hydrogen bonds that water forms with the former host relative to the latter. Decomposition of the calculated solvation response of DMO has revealed that conformational fluctuations of the macrocyclic hosts give rise to the observed long-time relaxation component (τ_S⁴), which is much slower for the inclusion complexes with DIMEB than for those with βCD because of slower conformational dynamics of the former host than that of the latter.

Solvent Composition Drives the Rebinding Kinetics of Nitric Oxide to Microperoxidase

The rebinding kinetics of NO after photodissociation from microperoxidase (Mp-9) is studied in different solvent environments. In mixed glycerol/water (G/W) mixtures the dissociating ligand rebinds with a yield close to 1 due to the cavities formed by the solvent whereas in pure water the ligand can diffuse into the solvent after photodissociation. In the G/W mixture, only geminate rebinding on the sub-picosecond and 5 ps time scales was found and the rebinding fraction is unity which compares well with available experiments. Contrary to that, simulations in pure water find two time scales – ~10 ps and ~200 ps - indicating that both, geminate rebinding and rebinding after diffusion of NO in the surrounding water contribute. The rebinding fraction is around 0.63 within 1 ns which is in stark contrast with experiment. Including ions (Na and Cl) at 0.15 M concentration in water leads to rebinding kinetics tending to that in the glycerol/water mixture and yields agreement with experiments. The effect of temperature is also probed and found to be non-negligible. The present simulations suggest that NO rebinding in Mp is primarily driven by thermal fluctuations which is consistent with recent resonance Raman spectroscopy experiments and simulations on MbNO.

Maximum entropy analysis of polarized fluorescence decay of (E)GFP in aqueous solution

The maximum entropy method (MEM) was used for the analysis of polarized fluorescence decays of enhanced green fluorescent protein (EGFP) in buffered water/glycerol mixtures, obtained with time-correlated single-photon counting (Visser et al 2016 Methods Appl. Fluoresc. 4 035002). To this end, we used a general-purpose software module of MEM that was earlier developed to analyze (complex) laser photolysis kinetics of ligand rebinding reactions in oxygen binding proteins. We demonstrate that the MEM software provides reliable results and is easy to use for the analysis of both total fluorescence decay and fluorescence anisotropy decay of aqueous solutions of EGFP. The rotational correlation times of EGFP in water/glycerol mixtures, obtained by MEM as maxima of the correlation-time distributions, are identical to the single correlation times determined by global analysis of parallel and perpendicular polarized decay components. The MEM software is also able to determine homo-FRET in another dimeric GFP, for which the transfer correlation time is an order of magnitude shorter than the rotational correlation time. One important advantage utilizing MEM analysis is that no initial guesses of parameters are required, since MEM is able to select the least correlated solution from the feasible set of solutions.

Predicting reaction coordinates in energy landscapes with diffusion anisotropy

We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For this we use our recently proposed method "spectral gap optimization of order parameters (SGOOP)" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. We show how available information about dynamical observables in addition to static information can be incorporated into SGOOP, which can then be used to accurately determine the "best" reaction coordinate for arbitrary anisotropies. We compare our results with transmission coefficient calculations and published benchmarks wherever applicable or available, respectively.

Following [FeFe] Hydrogenase Active Site Intermediates by Time-Resolved Mid-IR Spectroscopy

Time-resolved nanosecond mid-infrared spectroscopy is for the first time employed to study the [FeFe] hydrogenase from Chlamydomonas reinhardtii and to investigate relevant intermediates of the enzyme active site. An actinic 355 nm, 10 ns laser flash triggered photodissociation of a carbonyl group from the CO-inhibited state Hox-CO to form the state Hox, which is an intermediate of the catalytic proton reduction cycle. Time-resolved infrared spectroscopy allowed us to directly follow the subsequent rebinding of the carbonyl, re-forming Hox-CO, and determine the reaction half-life to be t1/2 ≈ 13 ± 5 ms at room temperature. This gives direct information on the dynamics of CO inhibition of the enzyme.

Rebinding dynamics of NO to microperoxidase-8 probed by time-resolved vibrational spectroscopy

Femtosecond vibrational spectroscopy was used to probe the rebinding kinetics of NO to microperoxidase-8 (Mp), an ideal model system for the active site of ligand-binding heme proteins, including myoglobin and hemoglobin, after the photodeligation of MpNO in glycerol/water (G/W) solutions at 294 K. The geminate rebinding (GR) of NO to Mp in viscous solutions was highly efficient and ultrafast and negligibly dependent on the solution viscosity, which was adjusted by changing the glycerol content from 65% to 90% by volume in G/W mixtures. The kinetics of the GR of NO to Mp in viscous solutions was well represented by an exponential function with a time constant of ca. 11 ps. Although the kinetic traces of the GR of NO to Mp in solutions with three different viscosities (18, 81, and 252 cP) almost overlap, they show a slight difference early in the decay process. The kinetic traces were also described by the diffusion-controlled reaction theory with a Coulomb potential. Since the ligand is deligated in a neutral form, an ionic pair of NO(-) and Mp(+) may be produced before forming the Mp-NO bond by an electron transfer from Mp to NO as the deligated NO is sufficiently near to the Fe atom of Mp. The strong reactivity between NO and ferrous heme may arise from the Coulomb interaction between the reacting pair, which is consistent with the harpooning mechanism for NO binding to heme.

Ligand and interfacial dynamics in a homodimeric hemoglobin

The structural dynamics of dimeric hemoglobin (HbI) from Scapharca inaequivalvis in different ligand-binding states is studied from atomistic simulations on the μs time scale. The intermediates are between the fully ligand-bound (R) and ligand-free (T) states. Tertiary structural changes, such as rotation of the side chain of Phe97, breaking of the Lys96-heme salt bridge, and the Fe-Fe separation, are characterized and the water dynamics along the R-T transition is analyzed. All these properties for the intermediates are bracketed by those determined experimentally for the fully ligand-bound and ligand-free proteins, respectively. The dynamics of the two monomers is asymmetric on the 100 ns timescale. Several spontaneous rotations of the Phe97 side chain are observed which suggest a typical time scale of 50-100 ns for this process. Ligand migration pathways include regions between the B/G and C/G helices and, if observed, take place in the 100 ns time scale.

Comparison of the kinetics of different Markov models for ligand binding under varying conditions

We recently derived a Markov model for macromolecular ligand binding dynamics from few physical assumptions and showed that its stationary distribution is the grand canonical ensemble [J. W. R. Martini, M. Habeck, and M. Schlather, J. Math. Chem. 52, 665 (2014)]. The transition probabilities of the proposed Markov process define a particular Glauber dynamics and have some similarity to the Metropolis-Hastings algorithm. Here, we illustrate that this model is the stochastic analog of (pseudo) rate equations and the corresponding system of differential equations. Moreover, it can be viewed as a limiting case of general stochastic simulations of chemical kinetics. Thus, the model links stochastic and deterministic approaches as well as kinetics and equilibrium described by the grand canonical ensemble. We demonstrate that the family of transition matrices of our model, parameterized by temperature and ligand activity, generates ligand binding kinetics that respond to changes in these parameters in a qualitatively similar way as experimentally observed kinetics. In contrast, neither the Metropolis-Hastings algorithm nor the Glauber heat bath reflects changes in the external conditions correctly. Both converge rapidly to the stationary distribution, which is advantageous when the major interest is in the equilibrium state, but fail to describe the kinetics of ligand binding realistically. To simulate cellular processes that involve the reversible stochastic binding of multiple factors, our pseudo rate equation model should therefore be preferred to the Metropolis-Hastings algorithm and the Glauber heat bath, if the stationary distribution is not of only interest.

Full kinetics of CO entry, internal diffusion, and exit in myoglobin from transition-path theory simulations

We use Markovian milestoning molecular dynamics (MD) simulations on a tessellation of the collective variable space for CO localization in myoglobin to estimate the kinetics of entry, exit, and internal site-hopping. The tessellation is determined by analysis of the free-energy surface in that space using transition-path theory (TPT), which provides criteria for defining optimal milestones, allowing short, independent, cell-constrained MD simulations to provide properly weighted kinetic data. We coarse grain the resulting kinetic model at two levels: first, using crystallographically relevant internal cavities and their predicted interconnections and solvent portals; and second, as a three-state side-path scheme inspired by similar models developed from geminate recombination experiments. We show semiquantitative agreement with experiment on entry and exit rates and in the identification of the so-called "histidine gate" at position 64 through which ≈90% of flux between solvent and the distal pocket passes. We also show with six-dimensional calculations that the minimum free-energy pathway of escape through the histidine gate is a "knock-on" mechanism in which motion of the ligand and the gate are sequential and interdependent. In total, these results suggest that such TPT simulations are indeed a promising approach to overcome the practical time-scale limitations of MD to allow reliable estimation of transition mechanisms and rates among metastable states.

Probing the electronic and geometric structure of ferric and ferrous myoglobins in physiological solutions by Fe K-edge absorption spectroscopy

We present an iron K-edge X-ray absorption study of carboxymyoglobin (MbCO), nitrosylmyoglobin (MbNO), oxymyoglobin (MbO2), cyanomyoglobin (MbCN), aquomet myoglobin (metMb) and unligated myoglobin (deoxyMb) in physiological media. The analysis of the XANES region is performed using the full-multiple scattering formalism, implemented within the MXAN package. This reveals trends within the heme structure, absent from previous crystallographic and X-ray absorption analysis. In particular, the iron-nitrogen bond lengths in the porphyrin ring converge to a common value of about 2 Å, except for deoxyMb whose bigger value is due to the doming of the heme. The trends of the Fe-Nε (His93) bond length is found to be consistent with the effect of ligand binding to the iron, with the exception of MbNO, which is explained in terms of the repulsive trans effect. We derive a high resolution description of the relative geometry of the ligands with respect to the heme and quantify the magnitude of the heme doming in the deoxyMb form. Finally, time-dependent density functional theory is used to simulate the pre-edge spectra and is found to be in good agreement with the experiment. The XAS spectra typically exhibit one pre-edge feature which arises from transitions into the unoccupied dσ and dπ - πligand* orbitals. 1s → dπ transitions contribute weakly for MbO2, metMb and deoxyMb. However, despite this strong Fe d contribution these transitions are found to be dominated by the dipole (1s → 4p) moment due to the low symmetry of the heme environment.

Coupled protein-ligand dynamics in truncated hemoglobin N from atomistic simulations and transition networks

BACKGROUND

The nature of ligand motion in proteins is difficult to characterize directly using experiment. Specifically, it is unclear to what degree these motions are coupled.

METHODS

All-atom simulations are used to sample ligand motion in truncated Hemoglobin N. A transition network analysis including ligand- and protein-degrees of freedom is used to analyze the microscopic dynamics.

RESULTS

Clustering of two different subsets of MD trajectories highlights the importance of a diverse and exhaustive description to define the macrostates for a ligand-migration network. Monte Carlo simulations on the transition matrices from one particular clustering are able to faithfully capture the atomistic simulations. Contrary to clustering by ligand positions only, including a protein degree of freedom yields considerably improved coarse grained dynamics. Analysis with and without imposing detailed balance agree closely which suggests that the underlying atomistic simulations are converged with respect to sampling transitions between neighboring sites.

CONCLUSIONS

Protein and ligand dynamics are not independent from each other and ligand migration through globular proteins is not passive diffusion.

GENERAL SIGNIFICANCE

Transition network analysis is a powerful tool to analyze and characterize the microscopic dynamics in complex systems. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

The importance of individual protein molecule dynamics in developing and assessing solid state protein preparations

Processing protein solutions into the solid state is a common approach for generating stable amorphous protein mixtures that are suitable for long-term storage. Great care is typically given to protecting the protein native structure during the various drying steps that render it into the amorphous solid state. However, many studies illustrate that chemical and physical degradations still occur in spite of this amorphous material having good glassy properties and it being stored at temperatures below its glass transition temperature (Tg). Because of these persistent issues and recent biophysical studies that have refined the debate ascribing meaning to the molecular dynamical transition temperature and Tg of protein molecules, we provide an updated discussion on the impact of assessing and managing localized, individual protein molecule nondiffusive motions in the context of proteins being prepared into bulk amorphous mixtures. Our aim is to bridge the pharmaceutical studies addressing bulk amorphous preparations and their glassy behavior, with the biophysical studies historically focused on the nondiffusive internal protein dynamics and a protein's activity, along with their combined efforts in assessing the impact of solvent hydrogen-bonding networks on local stability. We also provide recommendations for future research efforts in solid-state formulation approaches.

Long-range electron transfer with myoglobin immobilized at Au/mixed-SAM junctions: mechanistic impact of the strong protein confinement

Horse muscle myoglobin (Mb) was tightly immobilized at Au-deposited ~15-Å-thick mixed-type (1:1) alkanethiol SAMs, HS-(CH₂)₁₁-COOH/HS-(CH₂)₁₁-OH, and placed in contact with buffered H₂O or D₂O solutions. Fast-scan cyclic voltammetry (CV) and a Marcus-equation-based analysis were applied to determine unimolecular standard rate constants and reorganization free energies for electron transfer (ET), under variable-temperature (15-55 °C) and -pressure (0.01-150 MPa) conditions. The CV signal was surprisingly stable and reproducible even after multiple temperature and pressure cycles. The data analysis revealed the following values: standard rate constant, 33 s⁻¹ (25 °C, 0.01 MPa, H₂O); reorganization free energy, 0.5 ± 0.1 eV (throughout); activation enthalpy, 12 ± 3 kJ mol⁻¹; activation volume, -3.1 ± 0.2 cm³ mol⁻¹; and pH-dependent solvent kinetic isotope effect (k(H)⁰/k(D)⁰), 0.7-1.4. Furthermore, the values for the rate constant and reorganization free energy are very similar to those previously found for cytochrome c electrostatically immobilized at the monocomponent Au/HS-(CH₂)₁₁-COOH junction. In vivo, Mb apparently forms a natural electrostatic complex with cytochrome b₅ (cyt-b₅) through the "dynamic" (loose) docking pattern, allowing for a slow ET that is intrinsically coupled to the water's removal from the "defective" heme iron (altogether shaping the biological repair mechanism for Mb's "met" form). In contrary, our experiments rather mimic the case of a "simple" (tight) docking of the redesigned (mutant) Mb with cyt-b₅ (Nocek et al. J. Am. Chem. Soc. 2010, 132, 6165-6175). According to our analysis, in this configuration, Mb's distal pocket (linked to the "ligand channel") seems to be arrested within the restricted configuration, allowing the rate-determining reversible ET process to be coupled only to the inner-sphere reorganization (minimal elongation/shortening of an Fe-OH₂ bond) rather than the pronounced detachment (rebinding) of water and, hence, to be much faster.

Functional consequences of the open distal pocket of dehaloperoxidase-hemoglobin observed by time-resolved X-ray crystallography

Using time-resolved X-ray crystallography, we contrast a bifunctional dehaloperoxidase-hemoglobin (DHP) with previously studied examples of myoglobin and hemoglobin to understand the functional role of the distal pocket of globins. One key functional difference between DHP and other globins is the requirement that H2O2 enter the distal pocket of oxyferrous DHP to displace O2 from the heme Fe atom and thereby activate the heme for the peroxidase function. The open architecture of DHP permits more than one molecule to simultaneously enter the distal pocket of the protein above the heme to facilitate the unique peroxidase cycle starting from the oxyferrous state. The time-resolved X-ray data show that the distal pocket of DHP lacks a protein valve found in the two other globins that have been studied previously. The photolyzed CO ligand trajectory in DHP does not have a docking site; rather, the CO moves immediately to the Xe-binding site. From there, CO can escape but can also recombine an order of magnitude more rapidly than in other globins. The contrast with DHP dynamics and function more precisely defines the functional role of the multiple conformational states of myoglobin. Taken together with the high reduction potential of DHP, the open distal site helps to explain how a globin can also function as a peroxidase.

Internal friction in enzyme reactions

The empirical concept of internal friction was introduced 20 years ago. This review summarizes the results of experimental and theoretical studies that help to uncover the nature of internal friction. After the history of the concept, we describe the experimental challenges in measuring and interpreting internal friction based on the viscosity dependence of enzyme reactions. We also present speculations about the structural background of this viscosity dependence. Finally, some models about the relationship between the energy landscape and internal friction are outlined. Alternative concepts regarding the viscosity dependence of enzyme reactions are also discussed.

Ligand migration through hemeprotein cavities: insights from laser flash photolysis and molecular dynamics simulations

The presence of cavities and tunnels in the interior of proteins, in conjunction with the structural plasticity arising from the coupling to the thermal fluctuations of the protein scaffold, has profound consequences on the pathways followed by ligands moving through the protein matrix. In this perspective we discuss how quantitative analysis of experimental rebinding kinetics from laser flash photolysis, trapping of unstable conformational states by embedding proteins within the nanopores of silica gels, and molecular simulations can synergistically converge to gain insight into the migration mechanism of ligands. We show how the evaluation of the free energy landscape for ligand diffusion based on the outcome of computational techniques can assist the definition of sound reaction schemes, leading to a comprehensive understanding of the broad range of chemical events and time scales that encompass the transport of small ligands in hemeproteins.

Dynamics of geminate rebinding of CO to cytochrome c in guanidine HCl probed by femtosecond vibrational spectroscopy

Femtosecond vibrational spectroscopy was used to probe the rebinding dynamics of CO to cytochrome c (Cytc) in 1.8 and 7 M guanidine HCl (GdnHCl) after photodeligation of the corresponding CO-bound protein in D2O buffer (pD = 7.4) at 283 K. Geminate rebinding (GR) dynamics of CO to the folded Cytc in 1.8 M GdnHCl (nCytc) is similar to that to chemically modified cytochrome c (cCytc), suggesting that the overall conformations of nCytcCO and cCytcCO are similar. About 86% of the dissociated CO molecules were geminately rebound to nCytc nonexponentially within 1 ns. The efficient GR of CO to the folded Cytc can be attributed to the organized protein matrix near the active site of nCytc that provides an efficient trap for the diffusing CO ligand after photodissociation. Although the concentration of nCytc did not affect its GR yield of CO, GR yield of CO to the unfolded Cytc in 7 M GdnHCl (uCytc) increased from 5 to 30% as the protein concentration increased from 0.3 to 9 mM. Time-resolved spectra of the (13)CO dissociated from both 9 mM nCytc(13)CO and 9 mM uCytc(13)CO showed a growing band with a peak at 2090 cm(-1) on the picosecond time scale, which was assigned to (13)CO in D2O solvent. At 1 ns, the fraction of the CO band in the solvent was about 10% of the nascent photodeligated protein in nCytc and more than 50% in the concentrated uCytc. Whereas a small opening in the active site of nCytc is responsible for the ultrafast escape of CO to solution in the folded protein, a large fraction of the CO escape to the solvent in uCytc results from the denatured structure of the active site in the unfolded protein. The spectrum of the CO dissociated from the concentrated uCytcCO contained a band that decayed as efficiently as that for the folded protein, suggesting that some fraction of uCytcCO might form aggregates even in 7 M denaturant, such that the aggregate acts as an efficient trap for the diffusing CO after deligation. No hint of precipitate in the concentrated uCytcCO and protein refolding upon dilution of the GdnHCl indicate that the aggregate does not grow continuously but remains as a soluble oligomer. The delayed appearance of the solvated CO and the inefficient GR of CO in uCytcCO suggest that the monomeric unfolded CytcCO so loosely arranged that the protein matrix cannot trap CO efficiently but the bound CO is still buried within hydrophobic residues even under the harsh denaturation condition.

Geminate rebinding dynamics of nitric oxide to ferric hemoglobin in D2O solution

Femtosecond mid-infrared (mid-IR) spectroscopy was used to probe geminate rebinding (GR) dynamics of photo-released nitric oxide (NO) to ferric hemoglobin (Hb(III)) in D2O solution at room temperature. Time-resolved vibrational spectra exhibit two overlapping NO bands for NO-bound Hb(III) (Hb(III)NO), a major band at 1925 cm(-1) (89%) and a minor one at 1905 cm(-1) (11%), suggesting that Hb(III)NO has at least two conformational substates. Both bands decay nonexponentially, each with a different time scale, and the decays are described by a stretched exponential function; the major band's decay is described by 0.96 exp(-t/40 ps)(0.86) + 0.04 and the minor band's decay is described by exp(-t/85 ps)(0.75). These decays arise mainly from the GR of the photo-released NO to Hb(III), indicating that the bound state's conformer influences the NO binding. In particular, the His64 residue, known to have inward conformation in the major band and outward conformation in the minor band, plays a significant role in controlling the binding of NO to Hb(III). The GR of NO to ferric Hb is slower than that to ferrous Hb, which shows fast and efficient GR due to the high reactivity of NO to the heme Fe(ii). The slower GR of NO to Hb(III) may be caused by the lower reactivity of NO to the heme Fe(iii).

A spectroscopic study of structural heterogeneity and carbon monoxide binding in neuroglobin

Neuroglobin (Ngb) is a small globular protein that binds diatomic ligands like oxygen, carbon monoxide (CO) and nitric oxide at a heme prosthetic group. We have performed FTIR spectroscopy in the infrared stretching bands of CO and flash photolysis with monitoring in the electronic heme absorption bands to investigate structural heterogeneity at the active site of Ngb and its effects on CO binding and migration at cryogenic temperatures. Four CO stretching bands were identified; they correspond to discrete conformations that differ in structural details and CO binding properties. Based on a comparison of bound-state and photoproduct IR spectra of the wild-type protein, Ngb distal pocket mutants and myoglobin, we have provided structural interpretations of the conformations associated with the different CO bands. We have also studied ligand migration to the primary docking site, B. Rebinding from this site is governed by very low enthalpy barriers (∼1 kJ/mol), indicating an extremely reactive heme iron. Moreover, we have observed ligand migration to a secondary docking site, C, from which CO rebinding involves higher enthalpy barriers.

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.

Ligand binding to heme proteins: a comparison of cytochrome c variants with globins

We have studied the binding of carbon monoxide (CO) in mutants of Cyt c having its methionine at position 80 replaced by alanine, aspartate, and arginine, so that the sixth coordination is available for ligand binding. We have employed Fourier transform infrared (FTIR) photolysis difference spectroscopy to examine interactions of the heme-bound and photolyzed CO (and also nitric oxide, NO) in the small heme pocket created by the mutations. By using FTIR temperature derivative spectroscopy (TDS) and nanosecond flash photolysis, the enthalpy barrier distributions for CO rebinding were determined. In flash photolysis experiments, the majority of ligands rebind to the heme iron on picosecond time scales so that only the high-barrier tail of the distributions is visible on the nanosecond scale. By continuous wave excitation prior to TDS characterization of the barriers, however, each Cyt c molecule is photoexcited multiple times and complete photodissociation can be achieved, which likely arises from a rotation of the CO within the heme pocket so that the oxygen faces the heme iron. Apparently, reorientation prior to rebinding constitutes an additional and significant contribution to the rebinding barrier. Our experiments reveal that the compact, rigid structure of Cyt c offers no alternative binding sites for photodissociated ligands in the protein matrix. A comparison of ligand binding in these Cyt c mutants and hemoglobins underscores the importance of internal ligand docking sites and ligand migration routes for conveying a ligand binding function to heme proteins.

Filtering artifacts from lifetime distributions when maximizing entropy using a bootstrapped model

The maximum entropy method (MEM) has been used in many studies to reliably recover effective lifetimes from kinetics, whether measured experimentally or simulated computationally. Here, recent claims made by Mulligan et al. regarding MEM analyses of kinetics (Anal. Biochem. 421 (2012) 181-190) are shown to be unfounded. Their assertion that their software allows "analysis of datasets too noisy to process by existing iterative search algorithms" is refuted with a MEM analysis of their triexponential test case with increased noise. In addition, it is shown that lifetime distributions recovered from noisy kinetics data with the MEM can be improved by using a simple filter when bootstrapping the prior model. When deriving the bootstrapped model from the lifetime distribution obtained using a uniform model, only the slower processes are represented as Gaussians in the bootstrapped model. Using this new approach, results are clearly superior to those of Mulligan et al. despite the presence of increased noise. In a second example, ambiguity in the interpretation of Poisson kinetics in the presence of scattered excitation light is resolved by filtering the prior model.

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.

Using spectroscopic tools to probe porphyrin deformation and porphyrin-protein interactions

The reactivity and functionality of heme proteins are to a significant extent determined by the conformation of their functional heme groups and by the interaction of axial ligands with their protein environment. This review focuses on experimental methods and theoretical concepts for elucidating symmetry lowering perturbations of the heme induced by the protein environment of the heme pocket. First, we discuss a variety of methods which can be used to probe the electric field at the heme, including spectral hole burning as well as low temperature absorption and room temperature circular dichroism spectroscopy. Second, we show how heme deformations can be described as superposition of deformations along normal coordinates, thereby using the irreducible representations of the D4h point group as a classification tool. Finally, resonance Raman spectroscopy is introduced as a tool to probe the deformations of metalloprophyrins in solution and in protein matrices by measuring and comparing intensities and depolarization properties rather than wavenumber positions.

Local structure and dynamics of hemeproteins by X-ray absorption near edge structure spectroscopy

X-ray absorption near edge structure (XANES) spectroscopy is a synchrotron radiation technique sensitive to the local structure and dynamics around the metal site of a heme containing protein. Advances in detection techniques and theoretical/computational platforms in the last 15 years allowed the use of XANES as a quantitative probe of the key structural determinants driving functional changes, both in a concerted way with protein crystallography and EXAFS (extended X-ray absorption fine structure), or as a stand-alone method to apply in the crystal state as well as in solution. Moreover, the local dynamics of the heme site has been deeply investigated, on one hand, coupling XANES to classical photolysis experiments at cryogenic temperatures; on the other hand, the intrinsic property of the synchrotron radiation to induce radiolysis events, has been exploited to investigate specific cryotrapped intermediates, using X-rays both as a pump and a probe. Insights on the XANES method and some specific examples are presented to illustrate these topics.

The role of atomic level steric effects and attractive forces in protein folding

Protein folding into tertiary structures is controlled by an interplay of attractive contact interactions and steric effects. We investigate the balance between these contributions using structure-based models using an all-atom representation of the structure combined with a coarse-grained contact potential. Tertiary contact interactions between atoms are collected into a single broad attractive well between the C(β) atoms between each residue pair in a native contact. Through the width of these contact potentials we control their tolerance for deviations from the ideal structure and the spatial range of attractive interactions. In the compact native state dominant packing constraints limit the effects of a coarse-grained contact potential. During folding, however, the broad attractive potentials allow an early collapse that starts before the native local structure is completely adopted. As a consequence the folding transition is broadened and the free energy barrier is decreased. Eventually two-state folding behavior is lost completely for systems with very broad attractive potentials. The stabilization of native-like residue interactions in non-perfect geometries early in the folding process frequently leads to structural traps. Global mirror images are a notable example. These traps are penalized by the details of the repulsive interactions only after further collapse. Successful folding to the native state requires simultaneous guidance from both attractive and repulsive interactions.

Fractal symmetry of protein interior: what have we learned?

The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/β class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/β-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.