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Annu. Rev. PAys. Chern. 1991.42: 581-614 Copyright © 1991 by Annual Reviews Inc. All rights reserved
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VIBR�ATIONAL ENERGY RELl\XATION AND Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
STR1JCTURAL DYNAMICS OF flEME PROTEINS R. J. Dwayne Miller
Department of Chemistry and the Institute of Optics, University of Rochester, Rochester, New York 14627 KEY WORDS:
ultrafast optical studies, protein dynamics, energy transduction in proteins, biomechanics, deterministic protein motion
INTRODUCTION
One of the: great challenges in understanding the functionality of biological molecules from a microscopic perspective has been the development of a detailed understanding of the relative motion and exchange of energy among the enormous number of degrees of freedom in these systems. The three-dimensional structures of these systems have evolved to direct energy into highly specific motions, which are an integral part of the functionality of the molecule. The binding of small molecules at receptor sites can induce large amplitude motions of several angstroms that must be correlated through hundreds to thousands of atoms. The R --> T structure transition of hemoglobin, which controls the binding and release of oxygen, is the hallmark c�xample of these site-directed motions ( 1 -3). To understand deterministic protein motion, we must first understand the various energy exchange mechanisms that exist in protein systems. Vibrational energy relaxation studies provide a probe of the high frequency response of proteins. This relaxation process depends on the exact nature of the internuclear potentials, which, in turn, require structural infor mation. Herein lies one of the unique features of heme proteins in the study of vibrational energy relaxation processes. The structures of heme proteins, which have been well studied ( 1 -3), are not rigid, but undergo a range of dynamic motions (4-7). However, because they are highly 581 0066-426Xj9 1jllO l --058 1 $ 02.00
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
582
MILLER
constrained, the relative positions of the atoms are fairly well determined. As an example of a heme protein, Figure I illustrates the structure of myoglobin. This molecule is comprised of 1200 atoms, which correspond to a sequence of 153 amino acids. The prosthetic heme group is located approximately in the center of the protein. By optically exciting short-lived electronic states of the heme, one can selectively deposit large amounts of excess vibrational energy at the heme site. The vibrational energy transfer from the heme to the surrounding protein, and from the protein to the water layer, can be followed with optical methods to provide a spatial mapping of the vibrational energy relaxation pathways. The detailed struc tural information on these systems facilitates conceptual models of vibrational energy exchange and detailed theoretical modeling of the pro cess. Thus, heme proteins provide ideal model systems for understanding vibrational energy relaxation not only in proteins, but in general.
Figure 1 Structure of deoxymyoglobin with sequential amino acid residues numbered and the helical sections marked with capitallettas. The proximal histidine linkage to the heme is shown by the dottedline. (Reproduced with permission from I. Geis.)
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
VIBRATIONAL ENERGY RELAXATION
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In regard to the deterministic aspects of protein motion, heme proteins have played a central role in the development of concepts connected to the mechanism of molecular cooperativity and allosteric regulation of proteins (8). The primary reason for this role is again the detailed structural information available on these systems. In addition, the simple uptake of oxygen or other ligands can be used to follow the changes in structure as reflected in the binding efficiency for the ligands. Very early work in this area led to the Monod two-state description of molecular cooperativity (9), in which the state of occupancy (empty or filled ligation sites) is communicated through structure changes in the heme pocket. The entire system is set up so that the effect of a small ligand, the size of O2, can avalanche extensive changes in both the tertiary and quaternary structures of hemogllobin. The changes in structure and complementary changes in oxygen afIinity form a feedback loop that enhances the pickup and delivery of oxygen from the blood to the cells, as physiological conditions dictate. The exact mechanism by which these large amplitude-correlated struc ture changes occur and control binding has been an important, long standing issue in our general understanding of molecular cooperativity. As in the study of vibrational energy relaxation, heme proteins have unique optical properties that are well suited to the study of this problem. The oxy (ligated) to deoxy structure changes can be optically triggered by photodissociation of the ligand ( 1 0). This property has enabled direct, real-time studies of these functionally important protein dynamics. There is a wide range of time scales associated with these dynamics, which are discussed below. While the dynamics are becoming well defined, the mechanism of energy transduction, from the making or breaking of the iron-ligand bond into correlated motion, remains unresolved. In this review, we outline the progress made in understanding energy relaxation pathways and structure transitions in biological systems by using heme proteins as model systems. Both processes depend on energy exchange mechanisms and are related through the fluctuation and dis sipation theorems ( 1 1 ). A discussion of these two aspects of protein response will hopefully help strengthen this connection. This review focuses on time domain optical techniques, with an emphasis on picosecond phase grating spectroscopy, as probes of these dynamics. VIBRATIONAL ENERGY RELAXATION IN HEME PROTEINS General Considerations
There are regions of proteins, which have relatively large amplitude fluc tuations, that correspond to fluid-like environments; there are also rigid
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
584
MILLER
areas, which form the core of helical and p-pleated sheet tertiary structures, that correspond more to crystalline environments (4, 12). The mechanical degrees of freedom cannot be categorized into either purely solid-state or liquid-state limits. This complexity is further compounded because these systems are also single, albeit gigantic, molecules in which there are covalent bonds threading a connective pathway for vibrational energy to flow between all the atoms. Despite the increased complexity, the vibrational energy relaxation pathways in proteins can be understood within current models for vibrational energy relaxation. There are two, fairly distinct reservoirs for vibrational energy that need to be considered in this problem: the intramolecular bath and the inter molecular bath. The intramolecular bath refers to the vibrational modes of the molecule, which are excited into a nonequilibrium condition. These modes are, in turn, coupled to the intermolecular bath through several energy transfer mechanisms. Despite the fact that heme proteins constitute a single molecule, the heme chromophore is relatively isolated from the rest of the protein and approximates a molecule in solution. For myoglobin and hemoglobin, the heme porphyrin ring is linked covalently to the surrounding globin through the proximal histidine, which serves as one of the iron ligation sites (see Figure 1). Motion along the histidine-Fe co ordinate is orthogonal and, to a first approximation, decoupled from the vibrational modes of the phorphyrin ring. The heme ring is primarily held in place by the ",90 van der Waals contacts in the heme pocket. For this reason, the vibrational energy exchange with the heme is expected to occur predominantly through the van der Waals contacts (13), in analogy to collisional exchange processes. For initial excess energy conditions local ized on the heme, the heme chromophore can be considered the intra molecular bath, and the surrounding protein and water, the intermolecular bath. The transfer of energy to the intermolecular bath involves primarily translational and rotational degrees of freedom. Other mechanisms of spatial redistribution of the energy into the intermolecular bath, such as dipolar coupling (V -+ V) and radiative relaxation, occur on a much longer time scale relative to collisional exchange processes (14, 15). Given the rigid structure of the heme pocket, the transfer of encrgy from the heme to the surrounding protein matrix is most similar to processes in molecular solids. For molecular solids, the translational and rotational motions are highly hindered. One molecule cannot be displaced without affecting the adjacent molecules. These types of motions involve collective dis placements of the molecules that couple to the long-range order of the crystal. The energy-accepting modes include librational modes and optical and acoustic phonons (16-20). These collective, wave-like modes must
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
VIBRATIONAL ENERGY RELAXATION
585
satisfy the boundary conditions of the unit cell and the macroscopic crystal boundary. There is a high frequency cutoff defined by the wave vector, which has the dimensions of the unit cell, typically on the order of 100 cm 1. Similarly, the protein has extended collective modes that span the entire protein structure. The finite dimensions of the protein create boun dary conditions that make the spectrum of these modes more discrete than a single crystal. Nevertheless, the collective modes of the protein bear similarities to solid-state phonons. The amino acid residues that line the heme pocket are covalently bonded through the skeletal carbon atoms and have numerous nonbonded interactions to the protein structure. Their motion is highly hindered and must be correlated to a certain degree. The relative translational motion of these residues with respect to the heme necessitates the involvement of collective modes of the protein (21). Energy transfer to translational degrees of freedom from the heme to the sur rounding globin is expected to occur to a significant degree through the collective modes of the protein ( 1 3). These same interactions are important in the protein response to the doming of the heme, which controls the oxy to deoxy tertiary structure changes. Thus, the vibrational energy transfer from the heme to the protein serves as a probe of the energy exchange processes that are relevant to the protein function. The full vibrational energy relaxation pathway from the heme involves redistribution of the excess vibrational energy within thc heme, followed by energy transfer to the protein and, finally, transfer to the water layer. A detailed understanding of vibrational energy relaxation pathways in heme proteins, and proteins in general, requires an understanding of vibrational' energy relaxation processes characteristic of liquids and solids. There is a vast literature devoted to nonradiative relaxation processes in the condensed phase. The formalisms that have been developed for vibrational energy relaxation in the solid state are different than those in the liquid state. The differences reflect the longer range order of the intermolecular bath in the solid state relative to the liquid state. However, the fundamental process of the vibrational energy relaxation or cooling are the same. The key general points are ( 1 3-20, 22-34):
I. The vibrational energy transfer rate from an initially excited mode depends on the anharmonic coupling between the donor and accepting modes. The magnitUde of the coupling is determined by the anharmonic components of all the atom-atom potentials that constitute the interacting modes. 2. For the excited vibrational population to decay, the energy transfer step from the initially excited vibrational mode(s) must be accompanied by subsequent transfer steps to other degrees of freedom that reestablish
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
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thermal equilibrium. The overall rate of vibrational energy relaxation depends on both the initial energy transfer step and the spatial transport of energy among the system modes. 3. Thc vibrational relaxation rate depends on the density of states of the system. As the density of states of a system increases with size, there is a higher probability of energy-conserving pathways between interacting modes and more total relaxation pathways that speed up the relaxation process. 4. An increase in the density of states, with the size of the system, spatially extends the modes and decreases the anharmonic coupling, i.e. there are fewer atoms that spatially overlap (point 1). There is a density of states independent decay rate reached at some point, after which the increase in density of states or accepting modes is cancelled exactly by the decrease in anharmonic coupling. Because the intermolecular bath is in this limit, the density of states dependence (point 3) refers primarily to the intramolecular bath. The above generalizations refieet the view that the vibrational energy transfer is initiated from nonstationary states that involve localized vibrational motion. This initial condition occurs with impulsive excitation (e.g. pulsed optical excitation or collisions), which tends to prepare states that involve the motion of only a few atoms. Such local motions clearly do not correspond to normal modes, but this initial state can be written as a superposition of normal mode eigenfunctions. The vibrational en ergy relaxation process involves the transfer of energy from this local atomic motion to the other degrees of freedom. A local mode basis can be constructed to describe this motion, in which the energy is trans ferred to adjacent modes through the anharmonic coupling between the zeroth-order basis. The energy decays into lower frequency com binations and overtones of these modes. The important point is that this energy transfer process can only occur through anharmonic contribu tions to the interaction potentials (point I). If the interatomic potentials were purely harmonic, the normal modes of the molecule would form an orthogonal set of vibrational eigenfunctions with no possibility of interaction or energy exchange at either the intramolecular or intermol ecular level. Ultimately, it is the interatomic potentials that define the anhar monicities, such that this is the primary fundamental information needed to understand energy flow in biological molecules. However, correctly modeling the statistics of the spatial transport of the energy remains a central part of the problem and is perhaps the most important point regarding vibrational energy relaxation or cooling. The largest anharmonic coupling exists between vibrational modes or other degrees of freedom that
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
VIBRATIONAL ENERGY RELAXATION
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involve adjacent atoms (point 1). Thus, the energy transfers to spatially adjacent degrees of freedom first (23). These excited motions, in turn, transfer energy to other spatially adjacent degrees of freedom, which leads to propagation of the energy away from the initial site. The total rate for cooling depends on the transport of the excess energy relative to the back transfer rate. It is the spatial dispersion of the vibrational energy among the system modes that leads to cooling. The second general point concerning energy transport represents the greatest difference between vibrational energy relaxation processes in liquids relative to solids. For the solid state, once energy is transferred from the iintramolecular manifold to the lattice phonons, the energy is rapidly transported away from the source. The excited intramolecular atomic motions decay into various phonon frequency combinations. These newly exciited impulsively propagate away from the source at their group velocity. The collective nature of the atomic motion associated with the phonon dis placement disperses the energy over many atomic degrees of freedom. In this manner, the overall vibrational cooling process is primarily limited by the rate of transmission to the phonon bath and not by transport. The same would be true for energy transfer from the heme to the collective modes of the protein. In contrast, there is no long-range order in liquids such that the energy transferred eollisionally is highly localized as excess kinetic energy in the first solvation shell surrounding the molecule. The energy is exchanged dynamically through collisions with the first solvation shell, the first solv ation shell with the second layer of solvation molecules, etc. In other words, the transport of this excess energy, away from the vibration ally hot molecule, occurs through thermal diffusion. This relatively slow transport can lead to back transfer of energy through collisional exchange that retards the rate of cooling. However, large molecules (>40 atoms) with initial exc(:ss energies of 3000 cm- , exhibit relaxation times of less than 1 0 ps, largely independent of solvent (15). In this case, the heat capacity of the surrounding solvation shell is not saturated, and the collisional exchange process occurs in the classic acoustic limit ( 1 4). For heme proteins, even excess vibrational energy conditions, which correspond to nonradiatiive relaxation of an absorbed optical photon ( 20,000 cm- I ) , should occur in the acoustic limit. The volume and heat capacity of the solvation shell around heme proteins is at least an order of magnitude larger than that of previously used molecular probes of vibrational energy relaxation. As long as the energy is redistributed uniformly throughout the protein, the vibrational energy exchange with the water layer should occur on a picosecond time scale. �
�
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
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MILLER
The density of states dependence (points 3 and 4) focuses on the large differences in vibrational relaxation rates that one should expect from one molecule to another and one vibrational mode to another, even on the same molecule. The level density must be considered when trying to under stand the large variability observed for vibrational relaxation. Vibrational lifetimes and intramolecular vibrational redistribution (IVR) dynamics for different systems range from nanoseconds for small molecules (24) or isolated high frequency modes (23, 25) to subpicosecond for large mol ecules directly excited into a high density of states region ( 1 5, 26, 27). The small molecule and large molecule limits defining the time scales for vibrational energy redistribution can be quantified in terms of an average anharmonic coupling < V) and density of states PV' < V) Pv « 1 corresponds to the small molecule limit; < V) Pv 1 is the intermediate case; and < V) Pv » I corresponds to the statistical large molecule limit for I VR . Biological molecules are certainIy in the large molecules category. However, some sites are not strongly coupled with the modes of the rest of the molecule. The spatial modulation of vibrational coupling with structure can be treated as a variation in the local density of states (pv/volume). For example, the local density ofstates for the heme porphyrin ring should be very similar to free iron porphyrin molecules. At these sites in the protein, one should expect a dependence on the amount of excess energy and mode dependent relaxation rates. Three separate energy regimes can be identified for vibrational energy relaxation processes based on the density of states of the intermolecular bath ( 1 6). Figure 2 schematically illustrates these regimes in terms of an energy level diagram for vibrational energy relaxation originating at the heme. In this figure, the approximate dynamics, which depict the spatial redistribution of the excess vibrational energy, are based on numerous experimental studies of analogous systems ( 14--2 0, 23-27). At high enough vibrational energies, the intramolecular vibrational energy is rapidly redis tributed statistically among all the modes of the molecule. The dynamics of this process are in the 1 00 femtosecond to picosecond range for typical anharmonic couplings in large organic molecules (26, 27). After redis tribution, the population of the various vibrational modes can be defined by a Boltzman distribution, which corresponds to a higher temperature than the ambient. This statistical distribution leads to a concept of an internal temperature for the intramolecular bath ( 1 5). The vibrational relaxation into the intermolecular bath proceeds through the lowest fre quencies of the intramolecular coordinate, which can be rationalized based on the density of states of the accepting modes of the intermolecular bath. The low frequency modes of the molecule act as the doorway states to the intermolecular manifold. As energy leaks out of the low frequency modes, =
VIBRATIONAL ENERGY RELAXATION
} 1 III
100ern" 1
fast
-=�=- _ lHRESHOLD
]1II : __
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
589
impulsive excitation
heme porphyrin
i
globin
water
Figure 2 Energy level diagram schematically representing the local density of states depen dence for vibrational energy relaxation as a function of spatial position from the heme center. Impulsive excitation creates a nonstationary state centered on the heme porphyrin. There is a maximum in the acceptor mode density fur transfer from the heme to the surrounding globin at 100 em-I, which extends past 400 cm-I (21). The most efficient energy transfer and transport channel is to these extended modes of the protein. The fastest relaxation rates are for energy regimes above the IVR threshold (III) and the low frequency regime (I) in which these short-lived modes are populated and act as doorway states to the globin and surrounding water. (Adapted from Ref. 16.)
rapid IVR maintains a statistical distribution among all the modes as the molecule cools. These low frequency modes are rapidly repopulated until the distribution of excited vibrational modes, with frequencies above the threshold for rapid IVR, are depleted. This threshold depends strongly on the molecular structure. For porphyrins, it is approximately 700 cm I, which should be representative of the heme porphyrin (16, 28a,b). For excited vibrational modes below this threshold, the low frequency modes are only slowly repopulated by IVR. In addition, there are fewer energy-conserving pathways that enable an excited vibrational mode to decay into two lower frequency components. The net effect is that vibrational relaxation is slowest in the energy regime bracketed by the threshold for rapid IVR and twice the phonon cutoff frequency, I or the -
I
The vibrational mode decays into two phonons.
590
MILLER
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
highest frequency combination of collective modes in the case of proteins. This regime is typically 200-1000 em- , for molecular solids. Time scales for vibrational relaxation can vary from tens to hundreds of picoseconds in this energy regime (16). At low excess energies, below the two phonon cutoff frequency for solids (:::::; 200 em-I), the density of states of the intermolecular bath coordinate is again very large. In this limit, the vibrational lifetime of low frequency modes is extremely short, picosecond to subpicosecond, as a result of dirl�ct transfer to the phonon bath. Theoretical Treatments
Numerous theoretical models have been developed to handle vibrational energy relaxation processes in the condensed phase (29-34). They all involve a low order, time-dependent treatment of the anharmonic coupling. For the purposes of this review, the above discussion can be formulated mathematically by considering the dynamics of the excited modes in the initial distribution. The T I decay time of an excited mode (Wi) as a function of the temperature (T) can be written in terms of a Fermi Golden Rule expression, i.e. (16, 1 7) [2ncT,(T)r'
=
(18n/li)
I I
j�' k� I
{IlIMt>E
.-+>�
1
� r"
�
.8
.6
.4
.2
(J
Figure 3
2
4
6 TIME (NSEC>
8
10
Transient thermal phase grating data for cytochrome c, which use� narrow angle excitation at 355 um (A "" 2.2 ,utYl) and a }l('(jbe at S32 nm. This method measure:; tlle ViI> 'J' ener$Y trantfe( j}!'ocess to the intermolecular bath directly. The: solid curve it; a fit to it biexponentia!, with a rise time in the lhermal grating �n
Annu. Rev. PAys. Chern. 1991.42: 581-614 Copyright © 1991 by Annual Reviews Inc. All rights reserved
Further
Quick links to online content
VIBR�ATIONAL ENERGY RELl\XATION AND Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
STR1JCTURAL DYNAMICS OF flEME PROTEINS R. J. Dwayne Miller
Department of Chemistry and the Institute of Optics, University of Rochester, Rochester, New York 14627 KEY WORDS:
ultrafast optical studies, protein dynamics, energy transduction in proteins, biomechanics, deterministic protein motion
INTRODUCTION
One of the: great challenges in understanding the functionality of biological molecules from a microscopic perspective has been the development of a detailed understanding of the relative motion and exchange of energy among the enormous number of degrees of freedom in these systems. The three-dimensional structures of these systems have evolved to direct energy into highly specific motions, which are an integral part of the functionality of the molecule. The binding of small molecules at receptor sites can induce large amplitude motions of several angstroms that must be correlated through hundreds to thousands of atoms. The R --> T structure transition of hemoglobin, which controls the binding and release of oxygen, is the hallmark c�xample of these site-directed motions ( 1 -3). To understand deterministic protein motion, we must first understand the various energy exchange mechanisms that exist in protein systems. Vibrational energy relaxation studies provide a probe of the high frequency response of proteins. This relaxation process depends on the exact nature of the internuclear potentials, which, in turn, require structural infor mation. Herein lies one of the unique features of heme proteins in the study of vibrational energy relaxation processes. The structures of heme proteins, which have been well studied ( 1 -3), are not rigid, but undergo a range of dynamic motions (4-7). However, because they are highly 581 0066-426Xj9 1jllO l --058 1 $ 02.00
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
582
MILLER
constrained, the relative positions of the atoms are fairly well determined. As an example of a heme protein, Figure I illustrates the structure of myoglobin. This molecule is comprised of 1200 atoms, which correspond to a sequence of 153 amino acids. The prosthetic heme group is located approximately in the center of the protein. By optically exciting short-lived electronic states of the heme, one can selectively deposit large amounts of excess vibrational energy at the heme site. The vibrational energy transfer from the heme to the surrounding protein, and from the protein to the water layer, can be followed with optical methods to provide a spatial mapping of the vibrational energy relaxation pathways. The detailed struc tural information on these systems facilitates conceptual models of vibrational energy exchange and detailed theoretical modeling of the pro cess. Thus, heme proteins provide ideal model systems for understanding vibrational energy relaxation not only in proteins, but in general.
Figure 1 Structure of deoxymyoglobin with sequential amino acid residues numbered and the helical sections marked with capitallettas. The proximal histidine linkage to the heme is shown by the dottedline. (Reproduced with permission from I. Geis.)
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
VIBRATIONAL ENERGY RELAXATION
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In regard to the deterministic aspects of protein motion, heme proteins have played a central role in the development of concepts connected to the mechanism of molecular cooperativity and allosteric regulation of proteins (8). The primary reason for this role is again the detailed structural information available on these systems. In addition, the simple uptake of oxygen or other ligands can be used to follow the changes in structure as reflected in the binding efficiency for the ligands. Very early work in this area led to the Monod two-state description of molecular cooperativity (9), in which the state of occupancy (empty or filled ligation sites) is communicated through structure changes in the heme pocket. The entire system is set up so that the effect of a small ligand, the size of O2, can avalanche extensive changes in both the tertiary and quaternary structures of hemogllobin. The changes in structure and complementary changes in oxygen afIinity form a feedback loop that enhances the pickup and delivery of oxygen from the blood to the cells, as physiological conditions dictate. The exact mechanism by which these large amplitude-correlated struc ture changes occur and control binding has been an important, long standing issue in our general understanding of molecular cooperativity. As in the study of vibrational energy relaxation, heme proteins have unique optical properties that are well suited to the study of this problem. The oxy (ligated) to deoxy structure changes can be optically triggered by photodissociation of the ligand ( 1 0). This property has enabled direct, real-time studies of these functionally important protein dynamics. There is a wide range of time scales associated with these dynamics, which are discussed below. While the dynamics are becoming well defined, the mechanism of energy transduction, from the making or breaking of the iron-ligand bond into correlated motion, remains unresolved. In this review, we outline the progress made in understanding energy relaxation pathways and structure transitions in biological systems by using heme proteins as model systems. Both processes depend on energy exchange mechanisms and are related through the fluctuation and dis sipation theorems ( 1 1 ). A discussion of these two aspects of protein response will hopefully help strengthen this connection. This review focuses on time domain optical techniques, with an emphasis on picosecond phase grating spectroscopy, as probes of these dynamics. VIBRATIONAL ENERGY RELAXATION IN HEME PROTEINS General Considerations
There are regions of proteins, which have relatively large amplitude fluc tuations, that correspond to fluid-like environments; there are also rigid
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
584
MILLER
areas, which form the core of helical and p-pleated sheet tertiary structures, that correspond more to crystalline environments (4, 12). The mechanical degrees of freedom cannot be categorized into either purely solid-state or liquid-state limits. This complexity is further compounded because these systems are also single, albeit gigantic, molecules in which there are covalent bonds threading a connective pathway for vibrational energy to flow between all the atoms. Despite the increased complexity, the vibrational energy relaxation pathways in proteins can be understood within current models for vibrational energy relaxation. There are two, fairly distinct reservoirs for vibrational energy that need to be considered in this problem: the intramolecular bath and the inter molecular bath. The intramolecular bath refers to the vibrational modes of the molecule, which are excited into a nonequilibrium condition. These modes are, in turn, coupled to the intermolecular bath through several energy transfer mechanisms. Despite the fact that heme proteins constitute a single molecule, the heme chromophore is relatively isolated from the rest of the protein and approximates a molecule in solution. For myoglobin and hemoglobin, the heme porphyrin ring is linked covalently to the surrounding globin through the proximal histidine, which serves as one of the iron ligation sites (see Figure 1). Motion along the histidine-Fe co ordinate is orthogonal and, to a first approximation, decoupled from the vibrational modes of the phorphyrin ring. The heme ring is primarily held in place by the ",90 van der Waals contacts in the heme pocket. For this reason, the vibrational energy exchange with the heme is expected to occur predominantly through the van der Waals contacts (13), in analogy to collisional exchange processes. For initial excess energy conditions local ized on the heme, the heme chromophore can be considered the intra molecular bath, and the surrounding protein and water, the intermolecular bath. The transfer of energy to the intermolecular bath involves primarily translational and rotational degrees of freedom. Other mechanisms of spatial redistribution of the energy into the intermolecular bath, such as dipolar coupling (V -+ V) and radiative relaxation, occur on a much longer time scale relative to collisional exchange processes (14, 15). Given the rigid structure of the heme pocket, the transfer of encrgy from the heme to the surrounding protein matrix is most similar to processes in molecular solids. For molecular solids, the translational and rotational motions are highly hindered. One molecule cannot be displaced without affecting the adjacent molecules. These types of motions involve collective dis placements of the molecules that couple to the long-range order of the crystal. The energy-accepting modes include librational modes and optical and acoustic phonons (16-20). These collective, wave-like modes must
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
VIBRATIONAL ENERGY RELAXATION
585
satisfy the boundary conditions of the unit cell and the macroscopic crystal boundary. There is a high frequency cutoff defined by the wave vector, which has the dimensions of the unit cell, typically on the order of 100 cm 1. Similarly, the protein has extended collective modes that span the entire protein structure. The finite dimensions of the protein create boun dary conditions that make the spectrum of these modes more discrete than a single crystal. Nevertheless, the collective modes of the protein bear similarities to solid-state phonons. The amino acid residues that line the heme pocket are covalently bonded through the skeletal carbon atoms and have numerous nonbonded interactions to the protein structure. Their motion is highly hindered and must be correlated to a certain degree. The relative translational motion of these residues with respect to the heme necessitates the involvement of collective modes of the protein (21). Energy transfer to translational degrees of freedom from the heme to the sur rounding globin is expected to occur to a significant degree through the collective modes of the protein ( 1 3). These same interactions are important in the protein response to the doming of the heme, which controls the oxy to deoxy tertiary structure changes. Thus, the vibrational energy transfer from the heme to the protein serves as a probe of the energy exchange processes that are relevant to the protein function. The full vibrational energy relaxation pathway from the heme involves redistribution of the excess vibrational energy within thc heme, followed by energy transfer to the protein and, finally, transfer to the water layer. A detailed understanding of vibrational energy relaxation pathways in heme proteins, and proteins in general, requires an understanding of vibrational' energy relaxation processes characteristic of liquids and solids. There is a vast literature devoted to nonradiative relaxation processes in the condensed phase. The formalisms that have been developed for vibrational energy relaxation in the solid state are different than those in the liquid state. The differences reflect the longer range order of the intermolecular bath in the solid state relative to the liquid state. However, the fundamental process of the vibrational energy relaxation or cooling are the same. The key general points are ( 1 3-20, 22-34):
I. The vibrational energy transfer rate from an initially excited mode depends on the anharmonic coupling between the donor and accepting modes. The magnitUde of the coupling is determined by the anharmonic components of all the atom-atom potentials that constitute the interacting modes. 2. For the excited vibrational population to decay, the energy transfer step from the initially excited vibrational mode(s) must be accompanied by subsequent transfer steps to other degrees of freedom that reestablish
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
586
MILLER
thermal equilibrium. The overall rate of vibrational energy relaxation depends on both the initial energy transfer step and the spatial transport of energy among the system modes. 3. Thc vibrational relaxation rate depends on the density of states of the system. As the density of states of a system increases with size, there is a higher probability of energy-conserving pathways between interacting modes and more total relaxation pathways that speed up the relaxation process. 4. An increase in the density of states, with the size of the system, spatially extends the modes and decreases the anharmonic coupling, i.e. there are fewer atoms that spatially overlap (point 1). There is a density of states independent decay rate reached at some point, after which the increase in density of states or accepting modes is cancelled exactly by the decrease in anharmonic coupling. Because the intermolecular bath is in this limit, the density of states dependence (point 3) refers primarily to the intramolecular bath. The above generalizations refieet the view that the vibrational energy transfer is initiated from nonstationary states that involve localized vibrational motion. This initial condition occurs with impulsive excitation (e.g. pulsed optical excitation or collisions), which tends to prepare states that involve the motion of only a few atoms. Such local motions clearly do not correspond to normal modes, but this initial state can be written as a superposition of normal mode eigenfunctions. The vibrational en ergy relaxation process involves the transfer of energy from this local atomic motion to the other degrees of freedom. A local mode basis can be constructed to describe this motion, in which the energy is trans ferred to adjacent modes through the anharmonic coupling between the zeroth-order basis. The energy decays into lower frequency com binations and overtones of these modes. The important point is that this energy transfer process can only occur through anharmonic contribu tions to the interaction potentials (point I). If the interatomic potentials were purely harmonic, the normal modes of the molecule would form an orthogonal set of vibrational eigenfunctions with no possibility of interaction or energy exchange at either the intramolecular or intermol ecular level. Ultimately, it is the interatomic potentials that define the anhar monicities, such that this is the primary fundamental information needed to understand energy flow in biological molecules. However, correctly modeling the statistics of the spatial transport of the energy remains a central part of the problem and is perhaps the most important point regarding vibrational energy relaxation or cooling. The largest anharmonic coupling exists between vibrational modes or other degrees of freedom that
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VIBRATIONAL ENERGY RELAXATION
587
involve adjacent atoms (point 1). Thus, the energy transfers to spatially adjacent degrees of freedom first (23). These excited motions, in turn, transfer energy to other spatially adjacent degrees of freedom, which leads to propagation of the energy away from the initial site. The total rate for cooling depends on the transport of the excess energy relative to the back transfer rate. It is the spatial dispersion of the vibrational energy among the system modes that leads to cooling. The second general point concerning energy transport represents the greatest difference between vibrational energy relaxation processes in liquids relative to solids. For the solid state, once energy is transferred from the iintramolecular manifold to the lattice phonons, the energy is rapidly transported away from the source. The excited intramolecular atomic motions decay into various phonon frequency combinations. These newly exciited impulsively propagate away from the source at their group velocity. The collective nature of the atomic motion associated with the phonon dis placement disperses the energy over many atomic degrees of freedom. In this manner, the overall vibrational cooling process is primarily limited by the rate of transmission to the phonon bath and not by transport. The same would be true for energy transfer from the heme to the collective modes of the protein. In contrast, there is no long-range order in liquids such that the energy transferred eollisionally is highly localized as excess kinetic energy in the first solvation shell surrounding the molecule. The energy is exchanged dynamically through collisions with the first solvation shell, the first solv ation shell with the second layer of solvation molecules, etc. In other words, the transport of this excess energy, away from the vibration ally hot molecule, occurs through thermal diffusion. This relatively slow transport can lead to back transfer of energy through collisional exchange that retards the rate of cooling. However, large molecules (>40 atoms) with initial exc(:ss energies of 3000 cm- , exhibit relaxation times of less than 1 0 ps, largely independent of solvent (15). In this case, the heat capacity of the surrounding solvation shell is not saturated, and the collisional exchange process occurs in the classic acoustic limit ( 1 4). For heme proteins, even excess vibrational energy conditions, which correspond to nonradiatiive relaxation of an absorbed optical photon ( 20,000 cm- I ) , should occur in the acoustic limit. The volume and heat capacity of the solvation shell around heme proteins is at least an order of magnitude larger than that of previously used molecular probes of vibrational energy relaxation. As long as the energy is redistributed uniformly throughout the protein, the vibrational energy exchange with the water layer should occur on a picosecond time scale. �
�
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MILLER
The density of states dependence (points 3 and 4) focuses on the large differences in vibrational relaxation rates that one should expect from one molecule to another and one vibrational mode to another, even on the same molecule. The level density must be considered when trying to under stand the large variability observed for vibrational relaxation. Vibrational lifetimes and intramolecular vibrational redistribution (IVR) dynamics for different systems range from nanoseconds for small molecules (24) or isolated high frequency modes (23, 25) to subpicosecond for large mol ecules directly excited into a high density of states region ( 1 5, 26, 27). The small molecule and large molecule limits defining the time scales for vibrational energy redistribution can be quantified in terms of an average anharmonic coupling < V) and density of states PV' < V) Pv « 1 corresponds to the small molecule limit; < V) Pv 1 is the intermediate case; and < V) Pv » I corresponds to the statistical large molecule limit for I VR . Biological molecules are certainIy in the large molecules category. However, some sites are not strongly coupled with the modes of the rest of the molecule. The spatial modulation of vibrational coupling with structure can be treated as a variation in the local density of states (pv/volume). For example, the local density ofstates for the heme porphyrin ring should be very similar to free iron porphyrin molecules. At these sites in the protein, one should expect a dependence on the amount of excess energy and mode dependent relaxation rates. Three separate energy regimes can be identified for vibrational energy relaxation processes based on the density of states of the intermolecular bath ( 1 6). Figure 2 schematically illustrates these regimes in terms of an energy level diagram for vibrational energy relaxation originating at the heme. In this figure, the approximate dynamics, which depict the spatial redistribution of the excess vibrational energy, are based on numerous experimental studies of analogous systems ( 14--2 0, 23-27). At high enough vibrational energies, the intramolecular vibrational energy is rapidly redis tributed statistically among all the modes of the molecule. The dynamics of this process are in the 1 00 femtosecond to picosecond range for typical anharmonic couplings in large organic molecules (26, 27). After redis tribution, the population of the various vibrational modes can be defined by a Boltzman distribution, which corresponds to a higher temperature than the ambient. This statistical distribution leads to a concept of an internal temperature for the intramolecular bath ( 1 5). The vibrational relaxation into the intermolecular bath proceeds through the lowest fre quencies of the intramolecular coordinate, which can be rationalized based on the density of states of the accepting modes of the intermolecular bath. The low frequency modes of the molecule act as the doorway states to the intermolecular manifold. As energy leaks out of the low frequency modes, =
VIBRATIONAL ENERGY RELAXATION
} 1 III
100ern" 1
fast
-=�=- _ lHRESHOLD
]1II : __
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
589
impulsive excitation
heme porphyrin
i
globin
water
Figure 2 Energy level diagram schematically representing the local density of states depen dence for vibrational energy relaxation as a function of spatial position from the heme center. Impulsive excitation creates a nonstationary state centered on the heme porphyrin. There is a maximum in the acceptor mode density fur transfer from the heme to the surrounding globin at 100 em-I, which extends past 400 cm-I (21). The most efficient energy transfer and transport channel is to these extended modes of the protein. The fastest relaxation rates are for energy regimes above the IVR threshold (III) and the low frequency regime (I) in which these short-lived modes are populated and act as doorway states to the globin and surrounding water. (Adapted from Ref. 16.)
rapid IVR maintains a statistical distribution among all the modes as the molecule cools. These low frequency modes are rapidly repopulated until the distribution of excited vibrational modes, with frequencies above the threshold for rapid IVR, are depleted. This threshold depends strongly on the molecular structure. For porphyrins, it is approximately 700 cm I, which should be representative of the heme porphyrin (16, 28a,b). For excited vibrational modes below this threshold, the low frequency modes are only slowly repopulated by IVR. In addition, there are fewer energy-conserving pathways that enable an excited vibrational mode to decay into two lower frequency components. The net effect is that vibrational relaxation is slowest in the energy regime bracketed by the threshold for rapid IVR and twice the phonon cutoff frequency, I or the -
I
The vibrational mode decays into two phonons.
590
MILLER
Annu. Rev. Phys. Chem. 1991.42:581-614. Downloaded from www.annualreviews.org by Colorado State University on 09/30/13. For personal use only.
highest frequency combination of collective modes in the case of proteins. This regime is typically 200-1000 em- , for molecular solids. Time scales for vibrational relaxation can vary from tens to hundreds of picoseconds in this energy regime (16). At low excess energies, below the two phonon cutoff frequency for solids (:::::; 200 em-I), the density of states of the intermolecular bath coordinate is again very large. In this limit, the vibrational lifetime of low frequency modes is extremely short, picosecond to subpicosecond, as a result of dirl�ct transfer to the phonon bath. Theoretical Treatments
Numerous theoretical models have been developed to handle vibrational energy relaxation processes in the condensed phase (29-34). They all involve a low order, time-dependent treatment of the anharmonic coupling. For the purposes of this review, the above discussion can be formulated mathematically by considering the dynamics of the excited modes in the initial distribution. The T I decay time of an excited mode (Wi) as a function of the temperature (T) can be written in terms of a Fermi Golden Rule expression, i.e. (16, 1 7) [2ncT,(T)r'
=
(18n/li)
I I
j�' k� I
{IlIMt>E
.-+>�
1
� r"
�
.8
.6
.4
.2
(J
Figure 3
2
4
6 TIME (NSEC>
8
10
Transient thermal phase grating data for cytochrome c, which use� narrow angle excitation at 355 um (A "" 2.2 ,utYl) and a }l('(jbe at S32 nm. This method measure:; tlle ViI> 'J' ener$Y trantfe( j}!'ocess to the intermolecular bath directly. The: solid curve it; a fit to it biexponentia!, with a rise time in the lhermal grating �n
