Tunneling in ligand binding to heme proteins

Electron Tunneling in Biology: When Does it Matter?

Electrons can tunnel between cofactor molecules positioned along biological electron transport chains up to a distance of ≃ 20 Å on the millisecond time scale of enzymatic turnover. This tunneling range determines the design of biological energy chains facilitating the cross-membrane transport of electrons. Tunneling distance and cofactors' redox potentials become the main physical parameters affecting the rate of electron transport. In addition, universal charge-transport properties are assigned to all proteins, making protein identity, flexibility, and dynamics insignificant. This paradigm is challenged by dynamical models of electron transfer, showing that the electron hopping rate is constant within the crossover distance R* ≃ 12 Å, followed with an exponential falloff at longer distances. If this hypothesis is fully confirmed, natural and man-made energy chains for electron transport should be best designed by placing redox cofactors near the crossover distance R*. Protein flexibility and dynamics affect the magnitude of the maximum hopping rate within the crossover distance. Changes in protein flexibility between forward and backward transitions contribute to vectorial charge transport. For biological energy chains, charge transport through proteins is not defined by universal parameters, and protein identity matters.

Chain-chain complexation and heme binding in haemoglobin with respect to the hydrophobic core structure

Heme binding by proteins and protein-protein complexation are the processes strongly related to the biological activity of proteins. The mechanism of these processes has not been still recognised. These phenomena are presented using haemoglobin as the example. Half of the mature haemoglobin (one α-chain and one β-chain) treated as a dissociation step in haemoglobin degradation reveals a specific change in heme binding after dissociation. This phenomenon is the object of analysis that interprets the structure of both complexes (tetramer and dimer) with respect to their hydrophobic core structure. The results suggest the higher stability of the complex in the form of one α-chain and one β-chain with respect to the hydrophobic core.

Ultrafast CO Kinetics in Heme Proteins: Adiabatic Ligand Binding and Heavy Atom Tunneling

The ultrafast kinetics of CO rebinding to carbon monoxide oxidation activator protein (ChCooA) are measured over a wide temperature range and compared with the kinetics of CO binding in other heme systems such as myoglobin (Mb) and hemoglobin (Hb). The Arrhenius prefactor for CO binding to ChCooA and protoheme (∼10¹¹ s^-1) is similar to what is found for spin-allowed NO binding to heme proteins and is several orders of magnitude larger than the prefactor of Mb and Hb (∼10⁹ s^-1). This indicates that the CO binding reaction is adiabatic, in contrast to the commonly held view that it is nonadiabatic due to spin-forbidden (ΔS = 2) selection rules. Under the adiabatic condition, entropic factors, rather than spin-selection rules, are the source of the reduced Arrhenius prefactors associated with CO binding in Mb and Hb. The kinetic response of ChCooA-CO is nonexponential at all temperatures, including 298 K, and is described quantitatively using a distribution of enthalpic rebinding barriers associated with heterogeneity in the heme doming conformation. Above the solvent glass transition (T_g ∼ 180 K), the rebinding progress slows as temperature increases, and this is ascribed to an evolution of the distribution toward increased heme doming and larger enthalpic barriers. Between T_g and ∼60 K, the nonexponential rebinding slows down as the temperature is lowered and the survival fraction follows the predictions expected for a quenched barrier distribution. Below ∼60 K the rebinding kinetics do not follow these predictions unless quantum mechanical tunneling along the heme doming coordinate is also included as an active channel for CO binding.

Proton transfer and protein conformation dynamics in photosensitive proteins by time-resolved step-scan Fourier-transform infrared spectroscopy

Monitoring the dynamics of protonation and protein backbone conformation changes during the function of a protein is an essential step towards understanding its mechanism. Protonation and conformational changes affect the vibration pattern of amino acid side chains and of the peptide bond, respectively, both of which can be probed by infrared (IR) difference spectroscopy. For proteins whose function can be repetitively and reproducibly triggered by light, it is possible to obtain infrared difference spectra with (sub)microsecond resolution over a broad spectral range using the step-scan Fourier transform infrared technique. With -10(2)-10(3) repetitions of the photoreaction, the minimum number to complete a scan at reasonable spectral resolution and bandwidth, the noise level in the absorption difference spectra can be as low as -10(-) (4), sufficient to follow the kinetics of protonation changes from a single amino acid. Lower noise levels can be accomplished by more data averaging and/or mathematical processing. The amount of protein required for optimal results is between 5-100 µg, depending on the sampling technique used. Regarding additional requirements, the protein needs to be first concentrated in a low ionic strength buffer and then dried to form a film. The protein film is hydrated prior to the experiment, either with little droplets of water or under controlled atmospheric humidity. The attained hydration level (g of water / g of protein) is gauged from an IR absorption spectrum. To showcase the technique, we studied the photocycle of the light-driven proton-pump bacteriorhodopsin in its native purple membrane environment, and of the light-gated ion channel channelrhodopsin-2 solubilized in detergent.

Conformational adaptation in drug-target interactions and residence time

Although drug-target interactions are commonly illustrated in terms of structurally static binding and dissociation events, such descriptions are inadequate to explain the impact of conformational dynamics on these processes. For high-affinity interactions, both the association and dissociation of drug molecules to and from their targets are often controlled by conformational changes of the target. Conformational adaptation can greatly influence the residence time of a drug on its target (i.e., the lifetime of the binary drug-target complex); long residence time can lead to sustained pharmacology and may also mitigate off-target toxicity. In this perspective, the kinetics of drug-target association and dissociation reactions are explored, with particular emphasis on the impact of conformational adaptation on drug-target residence time.

Ligand dynamics in heme proteins observed by Fourier transform infrared-temperature derivative spectroscopy

Fourier transform infrared (FTIR) spectroscopy is a powerful tool for the investigation of protein-ligand interactions in heme proteins. Nitric oxide and carbon monoxide are attractive physiologically relevant ligands because their bond stretching vibrations give rise to strong mid-infrared absorption bands that can be measured with exquisite sensitivity and precision using photolysis difference spectroscopy at cryogenic temperatures. These stretching bands are fine-tuned by electrostatic interactions with the environment and, therefore, ligands can be utilized as local probes of structure and dynamics. Bound to the heme iron, the ligand stretching bands are susceptible to changes in the iron-ligand bond and the electric field at the active site. Upon photolysis, the vibrational bands display changes due to ligand relocation to docking sites within the protein, rotational motions of the ligand in these sites and protein conformational changes. Photolysis difference spectra taken over a wide temperature range (3-300K) using specific temperature protocols for sample photodissociation can provide detailed insights into both protein and ligand dynamics. Moreover, temperature-derivative spectroscopy (TDS) has proven to be a particularly powerful technique to study protein-ligand interactions. The FTIR-TDS technique has been extensively applied to studies of carbon monoxide binding to heme proteins, whereas measurements with nitric oxide are still scarce. Here we describe infrared cryo-spectroscopy and present a variety of applications to the study of protein-ligand interactions in heme proteins. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Spin-Forbidden Ligand Binding to the Ferrous−Heme Group: Ab Initio and DFT Studies

The potential energy surfaces (PESs) and associated energy barriers that characterize the spin-forbidden recombination reactions of the gas-phase ferrous deoxy-heme group with CO, NO, and H2O ligands have been calculated using density functional theory (DFT). The bond energy for binding of O2 has also been calculated. Extensive large basis set CCSD(T) calculations on two small models of the heme group have been used to calibrate the accuracy of different DFT functionals for treating these systems. Pure functionals are shown to overestimate the stability of the low-spin forms of the deoxy-heme model, and to overestimate the binding energy of H2O and CO, whereas hybrid functionals such as B3PW91 and B3LYP yield accurate results. Accordingly, the latter functionals have been used to explore the PESs for binding. CO binding is found to involve a significant barrier of ca. 3 kcal mol-1 due to the need to change from the deoxy-heme quintet ground state to the bound singlet state. Binding of water does not involve a barrier, but the resulting bond is weak and may be further weakened in the protein environment, which should explain why water binding is not usually observed in heme proteins such as myoglobin. NO binding involves a low barrier, which is consistent with observed rapid geminate recombination. The calculated bond energies are in good agreement with previous reported values and in fair agreement with experiment for CO and O2. The value for NO is significantly lower than the experimentally derived bond energy, suggesting that B3LYP is less accurate in this case.

Thr-E11 regulates O2 affinity in Cerebratulus lacteus mini-hemoglobin

The mini-hemoglobin from Cerebratulus lacteus (CerHb) belongs to a class of globins containing the polar Tyr-B10/Gln-E7 amino acid pair that normally causes low rates of O2 dissociation and ultra-high O2 affinity, which suggest O2 sensing or NO scavenging functions. CerHb, however, has high rates of O2 dissociation (kO2 = 200-600 s(-1)) and moderate O2 affinity (KO2) approximately 1 microm(-1)) as a result of a third polar amino acid in its active site, Thr-E11. When Thr-E11 is replaced by Val, kO2 decreases 1000-fold and KO2 increases 130-fold at pH 7.0, 20 degrees C. The mutation also shifts the stretching frequencies of both heme-bound and photodissociated CO, indicating marked changes of the electrostatic field at the active site. The crystal structure of Thr-E11 --> Val CerHbO2 at 1.70 A resolution is almost identical to that of the wild-type protein (root mean square deviation of 0.12 A). The dramatic functional and spectral effects of the Thr-E11 --> Val mutation are due exclusively to changes in the hydrogen bonding network in the active site. Replacing Thr-E11 with Val "frees" the Tyr-B10 hydroxyl group to rotate toward and donate a strong hydrogen bond to the heme-bound ligand, causing a selective increase in O2 affinity, a decrease of the rate coefficient for O2 dissociation, a 40 cm(-1) decrease in nuCO of heme-bound CO, and an increase in ligand migration toward more remote intermediate sites.

Of spherical cows, cloudy crystal balls, and proteins

Although proteins perform a vast multitude of tasks in living organisms, perhaps the most fascinating and least well understood is the nanoengine aspect of protein action, where chemical energy is turned into mechanical motion. In order for this to happen a protein must change chemical bond energy into physical displacement via some sort of a conformational change of the protein. The critical first step of this process must be the transient storage (self-trapping) of chemical energy into some metastable strained conformation of the protein. We discuss how the early work of Irwin C. "Gunny" Gunsalus with Hans Frauenfelder and Peter Debrunner led to insights into the picosecond dynamics of proteins, the initial functionally important motions.

Ligand binding and protein dynamics in neuroglobin

Neuroglobin (Ngb) is a recently discovered protein in vertebrate brain tissue that belongs to the globin family of proteins. It has been implicated in the neuronal response to hypoxia or ischemia, although its physiological role has been hitherto unknown. Ngb is hexacoordinate in the ferrous deoxy form under physiological conditions. To bind exogenous ligands like O(2) and CO, the His E7 endogenous ligand is displaced from the sixth coordination. By using infrared spectroscopy and nanosecond time-resolved visible spectroscopy, we have investigated the ligand-binding reaction over a wide temperature range (3-353 K). Multiple, intrinsically heterogeneous distal heme pocket conformations exist in NgbCO. Photolysis at cryogenic temperatures creates a five-coordinate deoxy species with very low geminate-rebinding barriers. The photodissociated CO is observed to migrate within the distal heme pocket even at 20 K. Flash photolysis near physiological temperature (275-353 K) exhibits four sequential kinetic features: (i) geminate rebinding (t < 1 micros); (ii) extremely fast bimolecular exogenous ligand binding (10 micros < t < 1 ms) with a nontrivial temperature dependence; (iii) endogenous ligand binding (100 micros < t < 10 ms), which can be studied by using flash photolysis on deoxy Ngb; and (iv) displacement of the endogenous by the exogenous ligand (10 ms < t < 10 ks). All four processes are markedly nonexponential, suggesting that Ngb fluctuates among different conformations on surprisingly long time scales.

Heavy-atom skeleton quantization and proton tunneling in "intermediate-barrier" hydrogen bonds

Quantum effects on proton transfer through barriers of several kcal/mol in hydrogen bonds are investigated theoretically in malonaldehyde. Such "intermediate-barrier" proton transfer processes play a key role in the catalytic activity of some enzymes. Tunneling is shown to be significant in this reaction even at room temperature. More importantly, the quantum nature of the heavy molecular frame atoms is found to substantially enhance proton tunneling. These findings have far-reaching implications for common modeling strategies of proton transfer in complex systems such as biomolecules.

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.

Dynamic properties of monomeric insect erythrocruorin III from Chironomus thummi-thummi: relationships between structural flexibility and functional complexity

We have investigated the kinetics of geminate carbon monoxide binding to the monomeric component III of Chironomus thummi-thummi erythrocruorin, a protein that undergoes pH-induced conformational changes linked to a pronounced Bohr effect. Measurements were performed from cryogenic temperatures to room temperature in 75% glycerol and either 0.1 M potassium phosphate (pH 7) or 0.1 potassium borate (pH 9) after nanosecond laser photolysis. The distributions of the low temperature activation enthalpy g(H) for geminate ligand binding derived from the kinetic traces are quite narrow and are influenced by temperature both below and above approximately 170 K, the glass transition temperature. The thermal evolution of the CO binding kinetics between approximately 50 K and approximately 170 K indicates the presence of some degree of structural relaxation, even in this temperature range. Above approximately 220 K the width of the g(H) progressively decreases, and at 280 K geminate CO binding becomes exponential in time. Based on a comparison with analogous investigations of the homodimeric hemoglobin from Scapharca inaequivalvis, we propose a link between dynamic properties and functional complexity.

Ultrafast rotation and trapping of carbon monoxide dissociated from myoglobin

The nature of ligand motion within proteins has been investigated by measuring femtosecond time-resolved infrared (IR) spectra of CO photodissociated from the haem of myoglobin. Upon dissociation, the CO rotates approximately 90 degrees and becomes trapped within a ligand docking site located near the binding site. Two trajectories, distinguished spectroscopically and kinetically with time constants of 0.20 +/- 0.05 ps and 0.52 +/- 0.10 ps, lead to CO located within the docking site with opposite orientations. The protein reorganizes about the "docked' CO with a time constant of 1.6 +/- 0.3 ps and quickly establishes an energetic barrier that inhibits the reverse rebinding process.

Ligand binding to heme proteins: III. FTIR studies of His-E7 and Val-E11 mutants of carbonmonoxymyoglobin

Fouier-transform infrared (FTIR) difference spectra of several His-E7 and Val-E11 mutants of sperm whale carbonmonoxymyoglobin were obtained by photodissociation at cryogenic temperatures. The IR absorption of the CO ligand shows characteristic features for each of the mutants, both in the ligand-bound (A) state and in the photodissociated (B) state. For most of the mutants, a single A substate band is observed, which points to the crucial role of the His-E7 residue in determining the A substrate spectrum of the bound CO in the native structure. The fact that some of the mutants show more than one stretch band of the bound CO indicates that the appearance of multiple A substates is not exclusively connected to the presence of His-E7. In all but one mutant, multiple stretch bands of the CO in the photodissociated state are observed; these B substates are thought to arise from discrete positions and/or orientations of the photodissociated ligand in the heme pocket. The red shifts of the B bands with respect to the free-gas frequency indicate weak binding in the heme pocket. The observation of similar red shifts in microperoxidase (MP-8), where there is no residue on the distal side, suggests that the photodissociated ligand is still associated with the heme iron. Photoselection experiments were performed to determine the orientation of the bound ligand with respect to the heme normal by photolyzing small fractions of the sample with linearly polarized light at 540 nm. The resulting linear dichroism in the CO stretch spectrum yielded angles alpha > 20 degrees between the CO molecular axis and the heme normal for all of the mutants. We conclude that the off-axis position of the CO ligand in the native structure does not arise from steric constraints imposed by the distal histidine. There is no clear correlation between the size of the distal residue and the alpha of the CO ligand.

Vibrationally enhanced tunneling as a mechanism for enzymatic hydrogen transfer

We present a theory of enzymatic hydrogen transfer in which hydrogen tunneling is mediated by thermal fluctuations of the enzyme's active site. These fluctuations greatly increase the tunneling rate by shortening the distance the hydrogen must tunnel. The average tunneling distance is shown to decrease when heavier isotopes are substituted for the hydrogen or when the temperature is increased, leading to kinetic isotope effects (KIEs)--defined as the factor by which the reaction slows down when isotopically substituted substrates are used--that need be no larger than KIEs for nontunneling mechanisms. Within this theory we derive a simple KIE expression for vibrationally enhanced ground state tunneling that is able to fit the data for the bovine serum amine oxidase (BSAO) system, correctly predicting the large temperature dependence of the KIEs. Because the KIEs in this theory can resemble those for nontunneling dynamics, distinguishing the two possibilities requires careful measurements over a range of temperatures, as has been done for BSAO.

Inhomogeneous broadening and kinetic carbon monoxide isotope effects in low-temperature carbon monoxide recombination with myoglobin and hemoglobin

We have analyzed the non-exponential kinetics, the temperature variation, and the CO isotope effects of the CO recombination reactions with myoglobin and single-chain hemoglobin. The analysis rests on multiphonon quantum-mechanical chemical-rate theory combined with static inhomogeneous broadening of either the reorganization free energy or the reaction Gibbs free energy. The simplest specific model which can account for all the data contains an inhomogeneous distribution function of width 0.2-0.3 eV, independent of temperature down to the tunnel transition at about 20 K, two discrete nuclear coordinates of low vibrational frequency (60-150 cm-1) representing iron-heme and CO bending motion, the CO stretching motion of frequency about 2000 cm-1, and additional inhomogeneous broadening of the protein and CO bending configuration below the tunnel transition temperature. The model appears somewhat involved but in return provides corresponding insight in the dynamics of this important class of processes.

Determination of rate distributions from kinetic experiments

Rate processes in proteins are often not adequately described by simple exponential kinetics. Instead of modeling the kinetics in the time domain, it can be advantageous to perform a numerical inversion leading to a rate distribution function f(lambda). The features observed in f(lambda) (number, positions, and shapes of peaks) can then be interpreted. We discuss different numerical techniques for obtaining rate distribution functions, with special emphasis on the maximum entropy method. Examples are given for the application of these techniques to flash photolysis data of heme proteins.

E.p.r. studies of photolysis of nitrosyl haemoglobin at low temperatures: effects of quaternary structure

Photolysis of nitrosyl haemoglobin (HbNO) has been studied from 6.5 K to 20 K for different NO saturation conditions. The kinetic curves are fitted equally well by a biphasic exponential and a distribution of activation energies. The parameters are straightforwardly related to the quaternary structure of the protein. The biphasic model indicates that two germinate processes in the NO reassociation to Hb dominate at low temperatures independent of the protein conformation.

E.p.r. studies of photolysis of nitrosyl haemoglobin at low temperatures

Photolysis of HbNO has been studied from 6.2 K to 15.5 K by electron spin resonance during and after continuous illumination. Non-exponential kinetics of both dissociation and reassociation of NO was observed. The prolonged illumination separates the fast and slow ligands. This picture is consistent with NO tunnelling from two sites at different distances from the bound position. This result is obtained using a model of a sum of two exponentials or of conformational substates.

Cytochrome oxidation in bacterial photosynthesis

In this paper we propose that the reduction of the bacteriochlorophyl dimer cation (P(+)) by cytochrome c in the photosynthetic bacteria Rps. viridis and Chromatium vinosum proceeds via two parallel electron transfer (ET) processes from two distinct cytochrome c molecules. The dominating ET process at high temperatures involves the activated oxidation of the high-potential cytochrome c at closest proximity to P, while the dominating low-temperature process involves activationless ET from a low-potential cytochrome c, which is further away from P. The available data for the effects of blocking the low-potential cytochrome c on ET dynamics are consistent with this model, which results in reasonable nuclear reorganization and electronic coupling parameters for the parallel cytochrome oxidation processes. The lack of universality in the cytochrome oxidation in reaction centres of various bacteria is emphasized.

Protein dynamics and reaction rates: mode-specific chemistry in large molecules?

Reactive events in proteins may be strongly coupled to a few specific modes of protein motion or they may couple nonspecifically to the dense continuum of protein and solvent modes. We summarize the evidence that at least some biologically important reactions can be described in terms of a few specific modes, and we propose experiments to quantify the strength of coupling to the continuum. We also show that large entropic effects--solvent ordering, for example--can be rigorously incorporated in few-mode models without losing mode specificity. Within our description, the dynamics that determine chemical reaction rates can be summarized by a small number of parameters directly related to spectroscopic and thermodynamic data. Mode specificity allows protein dynamics to contribute directly to the control and specificity of biochemical reaction rates.

Rebinding and relaxation in the myoglobin pocket

The infrared stretching bands of carboxymyoglobin (MbCO) and the rebinding of CO to Mb after photodissociation have been studied in the temperature range 10-300 K in a variety of solvents. Four stretching bands imply that MbCO can exist in four substates, A0-A3. The temperature dependences of the intensities of the four bands yield the relative binding enthalpies and and entropies. The integrated absorbances and pH dependences of the bands permit identification of the substates with the conformations observed in the X-ray data (Kuriyan et al., J. Mol. Biol. 192 (1986) 133). At low pH, A0 is hydrogen-bonded to His E7. The substates A0-A3 interconvert above about 180 K in a 75% glycerol/water solvent and above 270 K in buffered water. No major interconversion is seen at any temperature if MbCO is embedded in a solid polyvinyl alcohol matrix. The dependence of the transition on solvent characteristics is explained as a slaved glass transition. After photodissociation at low temperature the CO is in the heme pocket B. The resulting CO stretching bands which are identified as B substates are blue-shifted from those of the A substates. At 40 K, rebinding after flash photolysis has been studied in the Soret, the near-infrared, and the integrated A and B substates. All data lie on the same rebinding curve and demonstrate that rebinding is nonexponential in time from at least 100 ns to 100 ks. No evidence for discrete exponentials is found. Flash photolysis with monitoring in the infrared region shows four different pathways within the pocket B to the bound substates Ai. Rebinding in each of the four pathways B----A is nonexponential in time to at least 10 ks and the four pathways have different kinetics below 180 K. From the time and temperature dependence of the rebinding, activation enthalpy distributions g(HBA) and preexponentials ABA are extracted. No pumping from one A substate to another, or one B substate to another, is observed below the transition temperature of about 180 K. If MbCO is exposed to intense white light for 10-10(3) s before being fully photolyzed by a laser flash, the amplitude of the long-lived states increases. The effect is explained in terms of a hierarchy of substates and substate symmetry breaking. The characteristics of the CO stretching bands and of the rebinding processes in the heme pocket depend strongly on the external parameters of solvent, pH and pressure. This sensitivity suggests possible control mechanisms for protein reactions.

Recombination of carbon monoxide to ferrous horseradish peroxidase types A and C

The recombination of carbon monoxide to isoenzymes A2 and C of horseradish peroxidase (HRP) was studied as a function of temperature (2 to 320 K) and pH (5 to 8.3) with flash photolysis and infrared difference absorption. At low temperatures three geminate recombination processes are observed. One of these internal processes, denoted by I*, is exponential in time with a rate coefficient that deviates strongly from an Arrhenius behavior below 100 K, implying phonon-assisted tunneling. The two other processes, denoted by I, are non-exponential in time and related to different carbonyl isomers, as shown by the infrared difference spectra. The existence of three internal processes indicates that HRP differs considerably from myoglobin where only one internal process, I, is seen. Moreover, the internal processes in HRP are faster than process I in myoglobin. At 300 K, only one recombination process from the solvent is observed and it is very slow (lambda s approximately 1 s-1 at 1 atm CO (1 atm = 101,325 Pa)), much slower than the corresponding association process in myoglobin. Since process I is fast, but binding from the solvent is slow, the barrier at the heme cannot be responsible for the small association rate. The infrared absorption difference spectra of the amide I/II bands indicate that photolysis and recombination trigger a two-step structural change. The slow recombination rate at 300 K can thus be explained by the large Gibbs energy of the conformational transition that is necessary to let CO move into the heme pocket. The partition coefficient for the CO in the heme pocket and the solvent is extremely small, while bond formation with the heme iron occurs in less than 100 nanoseconds.

Rate theories and puzzles of hemeprotein kinetics

The binding of dioxygen and carbon monoxide to heme proteins such as myoglobin and hemoglobin has been studied with flash photolysis. At temperatures below 200 K, binding occurs from within the heme pocket and, contrary to expectation, with nearly equal rates for both ligands. This observation has led to a reexamination of the theory of the association reaction taking into account friction, protein structure, and the nature of electronic transitions. The rate coefficients for the limiting cases of large and small friction are found with simple arguments that use characteristic lengths and times. The arguments indicate how transition state theory as well as calculations based on nonadiabatic perturbation theory, which is called the Golden Rule, may fail. For ligand-binding reactions the data suggest the existence of intermediate states not directly observed so far. The general considerations may also apply to other biomolecular processes such as electron transport.