beta process ͉ dielectric ͉ hydration ͉ solvent P roteins are dynamic systems that interact strongly with their environment (1). Most texts and publications show proteins in unique conformations and naked, without hydration shell and bulk solvent, while fluctuations are rarely mentioned. The unified model of protein dynamics presented here is a radical departure from this picture. In this model, the protein provides the structure for the biological function, but it is dynamically passive. The fluctuations in the bulk solvent power and control the large-scale motions and shape changes of the protein in a diffusive manner (2-4), whereas the fluctuations in the hydration shell power and control the internal protein motions such as ligand migration (5, 6). The hydration shell consists of Ϸ2 layers of water that surround proteins as shown in Fig. 1 (7-12). Protein functions depend on the degree of hydration, h, defined as the weight ratio of water to protein. Dehydrated proteins do not function. Some proteins begin to work at h Ϸ 0.2 (11) but full function may require h Ͼ 1. The controls exerted by the bulk solvent and the hydration shell are possible because the protein interior is fluid-like (13); the intrinsic viscosity of a protein is small, about like water (14-16). The image of the protein being essentially passive and being slaved to the environment is not an idle speculation. It is based on experiments using myoglobin (Mb) that led to the seminal concepts that underlie the present work: (i) Proteins do not exist in a unique conformation; they can assume a very large number of conformational substates (CS) (17, 18). (ii) The CS can be described by an energy landscape (17). (iii) The landscape is organized in a hierarchy; there are energy valleys within energy valleys within energy valleys (19). The description of the effects of the bulk solvent and the hydration shell is based on these concepts. Because knowledge of the fluctuations in glass-forming liquids and of the energy landscape of proteins is essential for understanding these results, we discuss these topics first.The ␣ and  Processes (20, 21) Glass-forming liquids have two types of equilibrium fluctuations, ␣ and .* One tool to study these fluctuations is dielectric relaxation spectroscopy (21). The sample is placed in a capacitor, a sine-wave voltage U 1 ( ) of frequency is applied, and the resulting current is converted into a voltage U 2 ( ) that characterizes the dielectric spectrum. Our spectra exhibit two prominent peaks that characterize ␣, or primary, and , or secondary, relaxations. The ␣ process describes structural fluctuations. The mechanical Maxwell relation,connects the rate coefficient k ␣ (T) for the ␣ fluctuations to the viscosity (T). Here, G 0 is the infinite-frequency shear modulus that depends only weakly on temperature and on the material.Author contributions: H.F., G.C., J.B., P.W.F., H.J., B.H.M., I.R.S., J.S., and R.D.Y. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote ...
After photodissociation of carbon monoxide bound to myoglobin, the protein relaxes to the deoxy equilibrium structure in a quake-like motion. Investigation of the proteinquake and of related intramolecular equilibrium motions shows that states and motions have a hierarchical glasslike structure.The dynamic aspects of proteins have been studied extensively in recent years and a picture of ever increasing complexity has emerged. To bring some order into the complexity, we have introduced a model that classifies states and motions (1). In the present paper, we describe the model and its experimental basis in more detail. STATES, SUBSTATES, AND MOTIONSWe consider myoglobin (Mb), an oxygen storage protein, consisting of 153 amino acids, with molecular weight of 17,900 and approximate dimensions of2.5 x 4.4 x 4.4 nm (2). Embedded in the protein matrix is a heme group with a central iron atom, which binds small ligands such as dioxygen (02) or carbon monoxide (CO) reversibly. Thus, two states are involved in the function of Mb, deoxyMb and liganded Mb (e.g., MbCO). In the liganded state, the heme is planar and the iron has spin 0 and lies close to the mean heme plane. In the unliganded state, the heme group is domed, the iron has spin 2 and lies =0.5 A away from the mean heme plane, and the globin structure differs somewhat from the liganded one (3).A protein molecule in a particular state can assume a very large number of conformational substates (CS) (4-6). Different substates have the same overall structure, but they differ in details; they perform the same function, but with different rates. equilibrium (10). Return to equilibrium occurs through a proteinquake: the released strain energy is dissipated through waves [phonons (11) or solitons (12)1 and through the propagation of a deformation (2, 3). HIERARCHY OF SUBSTATESThe experiments described in the next section imply that the proteinquake released by photodissociation of MbCO propagates sequentially: Fig. 2, consequently is much more complex than we originally anticipated (4).The valley in the top diagram of Fig. 2a represents one state, say MbCO. MbCO can exist in a large number of conformational substates, CS1, separated by high barriers.Each valley in the first tier is structured into substates (CS2) with smaller barriers. The furcation continues through two more tiers, with decreasing barrier heights. The dynamic
The concept that proteins exist in numerous different conformations or conformational substates, described by an energy landscape, is now accepted, but the dynamics is incompletely explored. We have previously shown that large-scale protein motions, such as the exit of a ligand from the protein interior, follow the dielectric fluctuations in the bulk solvent. Here, we demonstrate, by using mean-square displacements (msd) from Mö ssbauer and neutron P roteins are the molecules that perform most biological functions, from storage of dioxygen (O 2 ) to enzyme catalysis. A central goal of protein science is to relate structure, dynamics, and function. Although investigations of protein structures and functions are well organized industries, protein dynamics is still in its infancy. Dynamics studies are best performed on proteins whose structures and functions are well known, e.g., myoglobin (Mb), the protein that gives muscles their red color. A hybrid picture of Mb is shown in Fig. 1. The lower part displays a piece of the protein backbone, namely, three ␣-helices. The upper part presents a space-filling view of the protein atoms. The active center, a heme group with a central iron atom, is red. Two cavities are also shown, Xe1 and the heme cavity. The protein is surrounded by the hydration shell, one to two layers of water, and is embedded in the bulk solvent. In Mb's role as an oxygenstorage protein, O 2 enters the protein, stays some time in Xe1, then binds at the heme iron (1). CO follows a similar path through the protein. The structure of Mb shows no permanent channel that leads from the outside to either Xe1 or the heme pocket or from Xe1 to the heme pocket. Thus, structural fluctuations are necessary for function (2).Fluctuations imply that Mb possesses numerous different conformations, called conformational substates (CS) (3). The different CS can be described by an energy landscape (EL) (4), the central concept in the folding (5), dynamics, and function of proteins. The EL is a construct in Ϸ3N dimensions, where N is the number of atoms forming the protein and the hydration shell. A substate is a point in this hyperspace, and structural fluctuations are represented by jumps between points. Initially, we assumed that protein conformations could be organized into a simple, rough EL (1). Experiments showed, however, that there are wells within wells within wells, and an organization of the EL with several tiers of decreasing free-energy barriers ensued (6). The top tier, denoted by CS0, contains a small number of CS with different structures that can have different functions: in A 0 Mb is involved in NO enzymatics; in A 1 it acts as an oxygen-storage system (7). Each of the CS0 substates can assume a very large number of CS1, called statistical substates. They perform the same function but with different rates. Here, we will show that the statistical substates comprise two tiers, CS1␣ and CS1. Fluctuations between CS1␣ substates are slaved to the solvent motions and involve sizeable structural changes (8). ...
Ligand binding to heme proteins is studied by using flash photolysis over wide ranges in time (100 ns-1 ks) and temperature (10-320 K). Below about 200 K in 75% glycerol/water solvent, ligand rebinding occurs from the heme pocket and is nonexponential in time. The kinetics is explained by a distribution, g(H), of the enthalpic barrier of height H between the pocket and the bound state. Above 170 K rebinding slows markedly. Previously we interpreted the slowing as a "matrix process" resulting from the ligand entering the protein matrix before rebinding. Experiments on band III, an inhomogeneously broadened charge-transfer band near 760 nm (approximately 13,000 cm-1) in the photolyzed state (Mb*) of (carbonmonoxy)myoglobin (MbCO), force us to reinterpret the data. Kinetic hole-burning measurements on band III in Mb* establish a relation between the position of a homogeneous component of band III and the barrier H. Since band III is red-shifted by 116 cm-1 in Mb* compared with Mb, the relation implies that the barrier in relaxed Mb is 12 kJ/mol higher than in Mb*. The slowing of the rebinding kinetics above 170 K hence is caused by the relaxation Mb*----Mb, as suggested by Agmon and Hopfield [(1983) J. Chem. Phys. 79, 2042-2053]. This conclusion is supported by a fit to the rebinding data between 160 and 290 K which indicates that the entire distribution g(H) shifts. Above about 200 K, equilibrium fluctuations among conformational substates open pathways for the ligands through the protein matrix and also narrow the rate distribution. The protein relaxations and fluctuations are nonexponential in time and non-Arrhenius in temperature, suggesting a collective nature for these protein motions. The relaxation Mb*----Mb is essentially independent of the solvent viscosity, implying that this motion involves internal parts of the protein. The protein fluctuations responsible for the opening of the pathways, however, depend strongly on the solvent viscosity, suggesting that a large part of the protein participates. While the detailed studies concern MbCO, similar data have been obtained for MbO2 and CO binding to the beta chains of human hemoglobin and hemoglobin Zürich. The results show that protein dynamics is essential for protein function and that the association coefficient for binding from the solvent at physiological temperatures in all these heme proteins is governed by the barrier at the heme.
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