Coupling Vector-host Dynamics with Weather Geography and Mitigation Measures to Model Rift Valley Fever in Africa.

We present and characterize a multi-host epidemic model of Rift Valley fever (RVF) virus in East Africa with geographic spread on a network, rule-based mitigation measures, and mosquito infection and population dynamics. Susceptible populations are depleted by disease and vaccination and are replenished with the birth of new animals. We observe that the severity of the epidemics is strongly correlated with the duration of the rainy season and that even severe epidemics are abruptly terminated when the rain stops. Because naturally acquired herd immunity is established, total mortality across 25 years is relatively insensitive to many mitigation approaches. Strong reductions in cattle mortality are expected, however, with sufficient reduction in population densities of either vectors or susceptible (ie. unvaccinated) hosts. A better understanding of RVF epidemiology would result from serology surveys to quantify the importance of herd immunity in epidemic control, and sequencing of virus from representative animals to quantify the realative importance of transportation and local reservoirs in nucleating yearly epidemics. Our results suggest that an effective multi-layered mitigation strategy would include vector control, movement control, and vaccination of young animals yearly, even in the absence of expected rainfall.

Protein folding is slaved to solvent motions.

Proteins, the workhorses of living systems, are constructed from chains of amino acids, which are synthesized in the cell based on the instructions of the genetic code and then folded into working proteins. The time for folding varies from microseconds to hours. What controls the folding rate is hotly debated. We postulate here that folding has the same temperature dependence as the alpha-fluctuations in the bulk solvent but is much slower. We call this behavior slaving. Slaving has been observed in folded proteins: Large-scale protein motions follow the solvent fluctuations with rate coefficient k(alpha) but can be slower by a large factor. Slowing occurs because large-scale motions proceed in many small steps, each determined by k(alpha). If conformational motions of folded proteins are slaved, so a fortiori must be the motions during folding. The unfolded protein makes a Brownian walk in the conformational space to the folded structure, with each step controlled by k(alpha). Because the number of conformational substates in the unfolded protein is extremely large, the folding rate coefficient, k(f), is much smaller than k(alpha). The slaving model implies that the activation enthalpy of folding is dominated by the solvent, whereas the number of steps n(f) = k(alpha)/k(f) is controlled by the number of accessible substates in the unfolded protein and the solvent. Proteins, however, undergo not only alpha- but also beta-fluctuations. These additional fluctuations are local protein motions that are essentially independent of the bulk solvent fluctuations and may be relevant at late stages of folding.

Bulk-solvent and hydration-shell fluctuations, similar to alpha- and beta-fluctuations in glasses, control protein motions and functions.

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 Mossbauer and neutron-scattering experiments, that fluctuations in the hydration shell control fast fluctuations in the protein. We call the first type solvent-slaved or alpha-fluctuations and the second type hydration-shell-coupled or beta-fluctuations. Solvent-slaved motions are similar to the alpha-fluctuations in glasses. Their temperature dependence can be approximated by a Vogel-Tammann-Fulcher relation and they are absent in a solid environment. Hydration-shell-coupled fluctuations are similar to the beta-relaxation in glasses. They can be approximated by a Ferry or an Arrhenius relation, are much reduced or absent in dehydrated proteins, and occur in hydrated proteins even if embedded in a solid. They can be responsible for internal processes such as the migration of ligands within myoglobin. The existence of two functionally important fluctuations in proteins, one slaved to bulk motions and the other coupled to hydration-shell fluctuations, implies that the environment can control protein functions through different avenues and that no real protein transition occurs at approximately 200 K. The large number of conformational substates is essential; proteins cannot function without this reservoir of entropy, which resides mainly in the hydration shell.

Slaving: solvent fluctuations dominate protein dynamics and functions.

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.

Hydration, slaving and protein function.

Protein dynamics is crucial for protein function. Proteins in living systems are not isolated, but operate in networks and in a carefully regulated environment. Understanding the external control of protein dynamics is consequently important. Hydration and solvent viscosity are among the salient properties of the environment. Dehydrated proteins and proteins in a rigid environment do not function properly. It is consequently important to understand the effect of hydration and solvent viscosity in detail. We discuss experiments that separate the two effects. These experiments have predominantly been performed with wild-type horse and sperm whale myoglobin, using the binding of carbon monoxide over a broad range of temperatures as a tool. The experiments demonstrate that data taken only in the physiological temperature range are not sufficient to understand the effect of hydration and solvent on protein relaxation and function. While the actual data come from myoglobin, it is expected that the results apply to most or all globular proteins.

Relaxations and fluctuations in myoglobin.

One major goal of biological physics is the discovery and understanding of the concepts and laws that govern biomolecules, in particular proteins. Since there exist at least 10(5) different proteins, the choice of a suitable prototype is necessary. Myoglobin (Mb) has for many years played the role of such a prototype. It appears to be simple enough so that many of its properties can be understood, yet it is complex enough to display many of the fascinating characteristics of biomolecules. One major achievement in the study of any protein would be the establishment of convincing connections among structure, kinetics, energy landscape, dynamics, and function. We believe that this goal has not yet been reached in any protein, but the present knowledge of Mb gives some hope that the end is near in this case. Here, we sketch some of the results that have been obtained in the past 50 or more years in the research on Mb, obtained by an army of investigators.

The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin.

The grail of protein science is the connection between structure and function. For myoglobin (Mb) this goal is close. Described as only a passive dioxygen storage protein in texts, we argue here that Mb is actually an allosteric enzyme that can catalyze reactions among small molecules. Studies of the structural, spectroscopic, and kinetic properties of Mb lead to a model that relates structure, energy landscape, dynamics, and function. Mb functions as a miniature chemical reactor, concentrating and orienting diatomic molecules such as NO, CO, O(2), and H(2)O(2) in highly conserved internal cavities. Reactions can be controlled because Mb exists in distinct taxonomic substates with different catalytic properties and connectivities of internal cavities.

Structure of a ligand-binding intermediate in wild-type carbonmonoxy myoglobin.

Small molecules such as NO, O2, CO or H2 are important biological ligands that bind to metalloproteins to function crucially in processes such as signal transduction, respiration and catalysis. A key issue for understanding the regulation of reaction mechanisms in these systems is whether ligands gain access to the binding sites through specific channels and docking sites, or by random diffusion through the protein matrix. A model system for studying this issue is myoglobin, a simple haem protein. Myoglobin has been studied extensively by spectroscopy, crystallography, computation and theory. It serves as an aid to oxygen diffusion but also binds carbon monoxide, a byproduct of endogenous haem catabolism. Molecular dynamics simulations, random mutagenesis and flash photolysis studies indicate that ligand migration occurs through a limited number of pathways involving docking sites. Here we report the 1.4 A resolution crystal structure of a ligand-binding intermediate in carbonmonoxy myoglobin that may have far-reaching implications for understanding the dynamics of ligand binding and catalysis.

Connection between the taxonomic substates and protonation of histidines 64 and 97 in carbonmonoxy myoglobin.

Infrared spectra of heme-bound CO in sperm whale carbonmonoxy myoglobin and two mutants (H64L and H97F) were studied in the pH range from 4.2 to 9.5. Comparison of the native protein with the mutants shows that the observed pH effects can be traced to protonations of two histidine residues, H64 and H97, near the active site. Their imidazole sidechains experience simple, uncoupled Henderson-Hasselbalch type protonations, giving rise to four different protonation states. Because two of the protonation states are linked by a pH-independent equilibrium, the overall pH dependence of the spectra is described by a linear combination of three independent components. Global analysis, based on singular value decomposition and matrix least-squares algorithms enabled us to extract the pK values of the two histidines and the three basis spectra of the protonating species. The basis spectra were decomposed into the taxonomic substates A(0), A(1), and A(3), previously introduced in a heuristic way to analyze CO stretch spectra in heme proteins at fixed pH (see for instance, Biophys. J. 71:1563-1573). Moreover, an additional, weakly populated substate, called A(x), was identified. Protonation of H97 gives rise to a blue shift of the individual infrared lines by about 2 cm(-1), so that the A substates actually appear in pairs, such as A(0) and A(0)(+). The blue shift can be explained by reduced backbonding from the heme iron to the CO. Protonation of the distal histidine, H64, leads to a change of the infrared absorption from the A(1) or A(3) substate lines to A(0). This behavior can be explained by a conformational change upon protonation that moves the imidazole sidechain of H64 away from the CO into the high-dielectric solvent environment, which avoids the energetically unfavorable situation of an uncompensated electric charge in the apolar, low-dielectric protein interior. Our results suggest that protonation reactions serve as an important mechanism to create taxonomic substates in proteins.

Electron transfer and protein dynamics in the photosynthetic reaction center.

We have measured the kinetics of electron transfer (ET) from the primary quinone (Q(A)) to the special pair (P) of the reaction center (RC) complex from Rhodobacter sphaeroides as a function of temperature (5-300 K), illumination protocol (cooled in the dark and under illumination from 110, 160, 180, and 280 K), and warming rate (1.3 and 13 mK/s). The nonexponential kinetics are interpreted with a quantum-mechanical ET model (Fermi's golden rule and the spin-boson model), in which heterogeneity of the protein ensemble, relaxations, and fluctuations are cast into a single coordinate that relaxes monotonically and is sensitive to all types of relaxations caused by ET. Our analysis shows that the structural changes that occur in response to ET decrease the free energy gap between donor and acceptor states by 120 meV and decrease the electronic coupling between donor and acceptor states from 2.7 x 10(-4) cm(-1) to 1.8 x 10(-4) cm(-1). At cryogenic temperatures, conformational changes can be slowed or completely arrested, allowing us to monitor relaxations on the annealing time scale (approximately 10(3)-10(4) s) as well as the time scale of ET (approximately 100 ms). The relaxations occur within four broad tiers of conformational substates with average apparent Arrhenius activation enthalpies of 17, 50, 78, and 110 kJ/mol and preexponential factors of 10(13), 10(15), 10(21), and 10(25) s(-1), respectively. The parameterization provides a prediction of the time course of relaxations at all temperatures. At 300 K, relaxations are expected to occur from 1 ps to 1 ms, whereas at lower temperatures, even broader distributions of relaxation times are expected. The weak dependence of the ET rate on both temperature and protein conformation, together with the possibility of modeling heterogeneity and dynamics with a single conformational coordinate, make RC a useful model system for probing the dynamics of conformational changes in proteins.