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 ...

Protein motions are essential for function. Comparing protein processes with the dielectric fluctuations of the surrounding solvent shows that they fall into two classes: nonslaved and slaved. Nonslaved processes are independent of the solvent motions; their rates are determined by the protein conformation and vibrational dynamics. Slaved processes are tightly coupled to the solvent; their rates have approximately the same temperature dependence as the rate of the solvent fluctuations, but they are smaller. Because the temperature dependence is determined by the activation enthalpy, we propose that the solvent is responsible for the activation enthalpy, whereas the protein and the hydration shell control the activation entropy through the energy landscape. Bond formation is the prototype of nonslaved processes; opening and closing of channels are quintessential slaved motions. The prevalence of slaved motions highlights the importance of the environment in cells and membranes for the function of proteins.. . . everything that living things do can be understood in terms of the jigglings and wigglings of atoms.R. P. Feynman (1) P roteins perform most of the functions of living things, from metabolism to thinking. Textbooks usually show proteins naked, neglect fluctuations, and take little notice of the protein environment. Real proteins, however, are wiggling and jiggling, dressed by the hydration shell, and embedded in a cell or cell membrane. Feynman (1) stated the central problem succinctly, namely understanding protein functions in terms of the atomic motions. We are still very far from this goal, but progress is being made. Here we consider the effect of solvent fluctuations on protein processes. We will show that protein motions can be nonslaved or slaved. Nonslaved motions are independent of the solvent fluctuations. Slaved motions have rates that are proportional to the fluctuation rate of the solvent, but are smaller. We introduce a model, based on the energy landscape of the protein, that suggests how the protein controls its slaved dynamics. We use myoglobin (Mb) as a prototype, but the concepts apply also to many other proteins. The Dichotomy of MotionsThe main result of the present article emerges when the temperature dependences of protein processes are compared with the dielectric relaxation rate coefficient k diel (T) (2) of the solvent, essentially the average tumbling rate of the solvent water molecules. Fig. 1 shows k diel (T) (2) and the rate coefficients for various processes in Mb embedded in a 3:1 (vol͞vol) glycerol͞ water solvent (3-7). [We do not consider vibrations here, which can be described by normal modes (8).] We characterize the rate coefficients for selected processes by using the Inset in Fig. 1. The Inset shows a cross section through part of Mb with a heme group situated in the heme cavity and a major cavity called Xe-1 and labeled D. Small ligands such as carbon monoxide (CO) bind covalently at the heme iron. We denote the position of the CO by S if it is in the solvent, by A i...

Despite improved control measures, Ebola remains a serious public health risk in African regions where recurrent outbreaks have been observed since the initial epidemic in 1976. Using epidemic modeling and data from two well-documented Ebola outbreaks (Congo 1995 and Uganda 2000), we estimate the number of secondary cases generated by an index case in the absence of control interventions R0. Our estimate of R0 is 1.83 (SD 0.06) for Congo (1995) and 1.34 (SD 0.03) for Uganda (2000). We model the course of the outbreaks via an SEIR (susceptible-exposed-infectious-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. We perform an uncertainty analysis of the basic reproductive number R0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time interventions begin and provide a distribution for the final epidemic size. The control measures implemented during these two outbreaks (including education and contact tracing followed by quarantine) reduce the final epidemic size by a factor of 2 relative the final size with a 2-week delay in their implementation.

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). ...