Eric R. Henry

Is cooperative oxygen binding by hemoglobin really understood

The enormous success of structural biology challenges the physical scientist. Can biophysical studies provide a truly deeper understanding of how a protein works than can be obtained from static structures and qualitative analysis of biochemical data? We address this question in a case study by presenting the key concepts and experimental results that have led to our current understanding of cooperative oxygen binding by hemoglobin, the paradigm of structure function relations in multisubunit proteins. We conclude that the underlying simplicity of the two-state allosteric mechanism could not have been demonstrated without novel physical experiments and a rigorous quantitative analysis.

Geminate recombination of carbon monoxide to myoglobin.

Transient absorption spectra of myoglobin, following photolysis of the carbon monoxide complex at room temperature, were measured using a newly developed, sensitive nanosecond absorption spectrometer. The Soret spectrum of the immediate photoproduct is almost identical to that of deoxymyoglobin at equilibrium, suggesting that the heme group has changed from a planar to a domed structure in less than about 3 ns. About 4% of the photodissociated carbon monoxide molecules rebind to the hemes to which they were initially bound, with a relaxation time of 180 ns. Duddell et al. (1980) observed a geminate yield of 27% and a relaxation time of approximately 55 ns for the photolysis of oxymyoglobin. Comparison of the two results using the simplest kinetic model suggests that the 30-fold more rapid overall association rate for the reaction of oxygen with myoglobin compared to carbon monoxide results mainly from faster binding at the heme, with a small contribution from more rapid entry of oxygen into the protein from the solvent. The data on carbon monoxide are also compared with predictions from low-temperature studies of Frauenfelder and co-workers. This comparison points to the need for further experiments to demonstrate the correspondence between the ligand rebinding processes observed at high and low temperatures.

Influence of vibrational motion on solid state line shapes and NMR relaxation

The influence of vibrational motion on bond lengths and quadrupole constants obtained from dipolar and quadrupolar solid state line shapes is considered. It is shown that such motions average both the magnitude and the orientation of the intrinsic interaction tensor. Explicit expressions for the effective coupling constants that can be conveniently evaluated using the results of a normal mode analysis are derived. When the vibrationally averaged interaction tensor is axially symmetric, it is shown that the effect of vibrational motion on relaxation can be rigorously incorporated into an effective coupling constant which is formally identical to the one that determines the line shape. Illustrative calculations for several alkanes, in both the gas and solid phases, are presented. The relative contributions of stretching and bending vibrations and the effect of anharmonicity on the effective C–H bond lengths and deuterium quadrupole constants are examined. The influence of vibrational averaging on the magnit...

A kinetic mechanism for nicotinic acetylcholine receptors based on multiple allosteric transitions

Abstract. Nicotinic acetylcholine receptors are transmembrane oligomeric proteins that mediate interconversions between open and closed channel states under the control of neurotransmitters. Fast in vitro chemical kinetics and in vivo electrophysiological recordings are consistent with the following multi-step scheme. Upon binding of agonists, receptor molecules in the closed but activatable resting state (the Basal state, B) undergo rapid transitions to states of higher affinities with either open channels (the Active state, A) or closed channels (the initial Inactivatable and fully Desensitized states, I and D). In order to represent the functional properties of such receptors, we have developed a kinetic model that links conformational interconversion rates to agonist binding and extends the general principles of the Monod-Wyman-Changeux model of allosteric transitions. The crucial assumption is that the linkage is controlled by the position of the interconversion transition states on a hypothetical linear reaction coordinate. Application of the model to the peripheral nicotinic acetylcholine receptor (nAChR) accounts for the main properties of ligand-gating, including single-channel events, and several new relationships are predicted. Kinetic simulations reveal errors inherent in using the dose-response analysis, but justify its application under defined conditions. The model predicts that (in order to overcome the intrinsic stability of the B state and to produce the appropriate cooperativity) channel activation is driven by an A state with a Kd in the 50 nM range, hence some 140-fold stronger than the apparent affinity of the open state deduced previously. According to the model, recovery from the desensitized states may occur via rapid transit through the A state with minimal channel opening, thus without necessarily undergoing a distinct recovery pathway, as assumed in the standard ‘cyclic’ model. Transitions to the desensitized states by low concentration ‘pre-pulses’ are predicted to occur without significant channel opening, but equilibrium values of IC50 can be obtained only with long pre-pulse times. Predictions are also made concerning allosteric effectors and their possible role in coincidence detection. In terms of future developments, the analysis presented here provides a physical basis for constructing more biologically realistic models of synaptic modulation that may be applied to artificial neural networks.

Chemical, physical, and theoretical kinetics of an ultrafast folding protein

An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein—the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models—a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 105 possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 105 microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models.

Measuring internal friction of an ultrafast-folding protein

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.

Watching a Signaling Protein Function in Real Time Via 100-Ps Time-Resolved Laue Crystallography.

To understand how signaling proteins function, it is crucial to know the time-ordered sequence of events that lead to the signaling state. We recently developed on the BioCARS 14-IDB beamline at the Advanced Photon Source the infrastructure required to characterize structural changes in protein crystals with near-atomic spatial resolution and 150-ps time resolution, and have used this capability to track the reversible photocycle of photoactive yellow protein (PYP) following trans-to-cis photoisomerization of its p-coumaric acid (pCA) chromophore over 10 decades of time. The first of four major intermediates characterized in this study is highly contorted, with the pCA carbonyl rotated nearly 90° out of the plane of the phenolate. A hydrogen bond between the pCA carbonyl and the Cys69 backbone constrains the chromophore in this unusual twisted conformation. Density functional theory calculations confirm that this structure is chemically plausible and corresponds to a strained cis intermediate. This unique structure is short-lived (∼600 ps), has not been observed in prior cryocrystallography experiments, and is the progenitor of intermediates characterized in previous nanosecond time-resolved Laue crystallography studies. The structural transitions unveiled during the PYP photocycle include trans/cis isomerization, the breaking and making of hydrogen bonds, formation/relaxation of strain, and gated water penetration into the interior of the protein. This mechanistically detailed, near-atomic resolution description of the complete PYP photocycle provides a framework for understanding signal transduction in proteins, and for assessing and validating theoretical/computational approaches in protein biophysics.

Evolution of allosteric models for hemoglobin

We compare various allosteric models that have been proposed to explain cooperative oxygen binding to hemoglobin, including the two‐state allosteric model of Monod, Wyman, and Changeux (MWC), the Cooperon model of Brunori, the model of Szabo and Karplus (SK) based on the stereochemical mechanism of Perutz, the generalization of the SK model by Lee and Karplus (SKL), and the Tertiary Two‐State (TTS) model of Henry, Bettati, Hofrichter and Eaton. The preponderance of experimental evidence favors the TTS model which postulates an equilibrium between high (r)‐ and low (t)‐affinity tertiary conformations that are present in both the T and R quaternary structures. Cooperative oxygenation in this model arises from the shift of T to R, as in MWC, but with a significant population of both r and t conformations in the liganded T and in the unliganded R quaternary structures. The TTS model may be considered a combination of the SK and SKL models, and these models provide a framework for a structural interpretation of the TTS parameters. The most compelling evidence in favor of the TTS model is the nanosecond ‐ millisecond carbon monoxide (CO) rebinding kinetics in photodissociation experiments on hemoglobin encapsulated in silica gels. The polymeric network of the gel prevents any tertiary or quaternary conformational changes on the sub‐second time scale, thereby permitting the subunit conformations prior to CO photodissociation to be determined from their ligand rebinding kinetics. These experiments show that a large fraction of liganded subunits in the T quaternary structure have the same functional conformation as liganded subunits in the R quaternary structure, an experimental finding inconsistent with the MWC, Cooperon, SK, and SKL models, but readily explained by the TTS model as rebinding to r subunits in T. We propose an additional experiment to test another key prediction of the TTS model, namely that a fraction of subunits in the unliganded R quaternary structure has the same functional conformation (t) as unliganded subunits in the T quaternary structure.

Time-resolved optical spectroscopy and structural dynamics following photodissociation of carbonmonoxyhemoglobin

A summary is presented of our current understanding of the kinetics of ligand rebinding and conformational changes at room temperature following photodissociation of the carbon monoxide complex of hemoglobin with pulsed lasers. The events which occur subsequent to excitation have been followed over 12 decades in time, from about 100 fs to the completion of ligand rebinding at about 100 ms. Experiments with picosecond and subpicosecond lasers by others, together with molecular dynamics simulations, indicate that by 1 ns the deoxyhemoglobin photoproduct is in a thermally equilibrated ground electronic state, so that subsequent processes are unaffected by the initial laser excitation. The principal results have been obtained from time-resolved optical absorption spectroscopy using a sensitive nanosecond laser spectrometer. Five relaxations have been observed which are interpreted as geminate rebinding at about 50 ns that competes with motion of the ligand away from the heme which produces a tertiary conformational change, a second tertiary conformational change at 0.5-1 microseconds, transition from the R to T quaternary structure at about 20 microseconds, and overall bimolecular rebinding of ligands from the solvent to the R and T quaternary structures at about 200 microseconds and 10 ms. Assuming that the dissociation pathway in photolysis experiments is the reverse of the association pathway, we find that for the R state there is a 40% probability that the ligand will bind to the heme after entering the protein, and a 60% probability that it will return to the solvent. Studies on the alpha-subunit of an iron-cobalt hybrid hemoglobin indicate that carbon monoxide enters the protein at the same rate for both R and T quaternary structures. For the alpha-subunit in the T state the probability of binding after entry is much lower, and the ligand returns to the solvent more than 99% of the time, accounting for the 60-fold overall lower association rate. This decreased probability of binding results from a decreased rate of binding to the heme from within the protein, and not an increased rate of return to the solvent. There are still unresolved problems on the basic structural description of carbon monoxide binding and dissociation, particularly the functional significance of the tertiary relations in both the R and T states, and the precise number of kinetic barriers within the protein.

The Use of Matrix Methods in the Modeling of Spectroscopic Data Sets

We describe a general approach to the model-based analysis of sets of spectroscopic data that is built upon the techniques of matrix analysis. A model hypothesis may often be expressed by writing a matrix of measured spectra as the product of a matrix of spectra of individual molecular species and a matrix of corresponding species populations as a function of experimental conditions. The modeling procedure then requires the simultaneous determination of a set of species spectra and a set of model parameters (from which the populations are derived), such that this product yields an optimal description of the measured spectra. This procedure may be implemented as an optimization problem in the space of the (possibly nonlinear) model parameters alone, coupled with the efficient solution of a corollary linear optimization problem using matrix decomposition methods to obtain a set of species spectra corresponding to any set of model parameters. Known species spectra, as well as other information and assumptions about spectral shapes, may be incorporated into this general framework, using parametrized analytical functional forms and basis-set techniques. The method by which assumed relationships between global features (e.g., peak positions) of different species spectra may be enforced in the modeling without otherwise specifying the shapes of the spectra will be shown. We also consider the effect of measurement errors on this approach and suggest extensions of the matrix-based least-squares procedures applicable to situations in which measurement errors may not be assumed to be normally distributed. A generalized analysis procedure is introduced for cases in which the species spectra vary with experimental conditions.