The role of momentum transfer during incoherent neutron scattering is explained by the energy landscape model.

We recently introduced a model of incoherent quasielastic neutron scattering (QENS) that treats the neutrons as wave packets of finite length and the protein as a random walker in the free energy landscape. We call the model ELM for "energy landscape model." In ELM, the interaction of the wave packet with a proton in a protein provides the dynamic information. During the scattering event, the momentum [Formula: see text] is transferred by the wave packet to the struck proton and its moiety, exerting the force [Formula: see text] The resultant energy [Formula: see text] is stored elastically and returned to the neutron as it exits. The energy is given by [Formula: see text], where [Formula: see text] is the ambient temperature and [Formula: see text] ([Formula: see text] 91 K Å) is a new elastobaric coefficient. Experiments yield the scattering intensity (dynamic structure factor) [Formula: see text] as a function of [Formula: see text] and [Formula: see text] To test our model, we use published data on proteins where only thermal vibrations are active. ELM competes with the currently accepted theory, here called the spatial motion model (SMM), which explains [Formula: see text] by motions in real space. ELM is superior to SMM: It can explain the experimental angular and temperature dependence, whereas SMM cannot do so.

A wave-mechanical model of incoherent quasielastic scattering in complex systems.

Quasielastic incoherent neutron scattering (QENS) is an important tool for the exploration of the dynamics of complex systems such as biomolecules, liquids, and glasses. The dynamics is reflected in the energy spectra of the scattered neutrons. Conventionally these spectra are decomposed into a narrow elastic line and a broad quasielastic band. The band is interpreted as being caused by Doppler broadening due to spatial motion of the target molecules. We propose a quantum-mechanical model in which there is no separate elastic line. The quasielastic band is composed of sharp lines with twice the natural line width, shifted from the center by a random walk of the protein in the free-energy landscape of the target molecule. The walk is driven by vibrations and by external fluctuations. We first explore the model with the Mössbauer effect. In the subsequent application to QENS we treat the incoming neutron as a de Broglie wave packet. While the wave packet passes the protons in the protein and the hydration shell it exchanges energy with the protein during the passage time of about 100 ns. The energy exchange broadens the ensemble spectrum. Because the exchange involves the free-energy landscape of the protein, the QENS not only provides insight into the protein dynamics, but it may also illuminate the free-energy landscape of the protein-solvent system.

Ask not what physics can do for biology--ask what biology can do for physics.

Stan Ulam, the famous mathematician, said once to Hans Frauenfelder: 'Ask not what Physics can do for biology, ask what biology can do for physics'. The interaction between biologists and physicists is a two-way street. Biology reveals the secrets of complex systems, physics provides the physical tools and the theoretical concepts to understand the complexity. The perspective gives a personal view of the path to some of the physical concepts that are relevant for biology and physics (Frauenfelder et al 1999 Rev. Mod. Phys. 71 S419-S442). Schrödinger's book (Schrödinger 1944 What is Life? (Cambridge: Cambridge University Press)), loved by physicists and hated by eminent biologists (Dronamraju 1999 Genetics 153 1071-6), still shows how a great physicist looked at biology well before the first protein structure was known.

A unified model of protein dynamics.

Protein functions require conformational motions. We show here that the dominant conformational motions are slaved by the hydration shell and the bulk solvent. The protein contributes the structure necessary for function. We formulate a model that is based on experiments, insights from the physics of glass-forming liquids, and the concepts of a hierarchically organized energy landscape. To explore the effect of external fluctuations on protein dynamics, we measure the fluctuations in the bulk solvent and the hydration shell with broadband dielectric spectroscopy and compare them with internal fluctuations measured with the Mössbauer effect and neutron scattering. The result is clear. Large-scale protein motions are slaved to the fluctuations in the bulk solvent. They are controlled by the solvent viscosity, and are absent in a solid environment. Internal protein motions are slaved to the beta fluctuations of the hydration shell, are controlled by hydration, and are absent in a dehydrated protein. The model quantitatively predicts the rapid increase of the mean-square displacement above approximately 200 K, shows that the external beta fluctuations determine the temperature- and time-dependence of the passage of carbon monoxide through myoglobin, and explains the nonexponential time dependence of the protein relaxation after photodissociation.

Mössbauer effect in proteins.

In proteins, the Mössbauer effect and neutron scattering show a broad line and a rapid increase of the conformational mean-square displacement above about 180 K. The increase, dubbed the "dynamical transition," is controversial. We introduce a new interpretation of the Mössbauer effect in proteins and demonstrate that no dynamical transition is required. The increase in the mean-square displacement and the broad line are caused by fluctuations in the protein's hydration shell. Using the dielectric spectrum of these fluctuations, we predict the shape of the Mössbauer spectrum from 80 to 295 K with one dimensionless coefficient.

Neutron scattering and protein dynamics.

Neutrons play an important role in the study of proteins. The best known example is the determination of protein structures using neutron diffraction. Less well known, but possibly even more important in the future, is the determination of protein fluctuations using neutron scattering. Here, the background is sketched and some recent measurements are described that show how a relevant and revealing range of relaxation rates can be explored.

Mosaic energy landscapes of liquids and the control of protein conformational dynamics by glass-forming solvents.

Using recent advances in the Random First-Order Transition (RFOT) Theory of glass-forming liquids, we explain how the molecular motions of a glass-forming solvent distort the protein's boundary and slave some of the protein's conformational motions. Both the length and time scales of the solvent imposed constraints are provided by the RFOT theory. Comparison of the protein relaxation rate to that of the solvent provides an explicit lower bound on the size of the conformational space explored by the protein relaxation. Experimental measurements of slaving of myoglobin motions indicate that a major fraction of functionally important motions have significant entropic barriers.

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.

Dynamics and the free-energy landscape of proteins, explored with the Mössbauer effect and quasi-elastic neutron scattering.

The Mössbauer effect and quasi-elastic neutron scattering (QENS) from hydrated proteins yield sharp elastic lines that are accompanied by broad wings. Conventionally, the elastic line and the broad wings are treated as separate phenomena. We show that there is no separation; the entire spectrum consists of Lorentzians with the natural line width. In protein crystals, the shifts of the individual lines from the elastic center above about 150 K are caused by beta fluctuations in the hydration shell. Vibrations cause shifts in the entire temperature range but are best seen below about 150 K. We construct a microscopic model for the dynamics that is based on a random walk of the proteins in their free-energy landscape. The model yields approximate values for the steps in the energy landscape. Remarkably, the quantum electrodynamic concept of gamma rays is needed to justify the model.

Protein dynamics and function: insights from the energy landscape and solvent slaving.

Protein motions are complex and a good way to describe them is in terms of a very high-dimensional conformation space. We give here a simple explanation of the conformation space and the energy landscape, the conformational motions and protein reactions, based on an analogy to a traffic problem. The analogy provides insight into the slaving of protein processes to bulk solvent fluctuations, in both the native and unfolded states.

Energy landscape and dynamics of biomolecules extended abstract.

Proteins are not isolated homogeneous systems. Each protein can exist in a very large number of conformations (conformational substates) that are characterized by an energy landscape. The main conformational motions, similar to the α and ß fluctuations in glasses, are linked to fluctuations in the bulk solvent and the hydration shell.

Picosecond thermometer in the amide I band of myoglobin.

The amide I and II bands in myoglobin show a heterogeneous temperature dependence, with bands at 6.17 and 6.43 microm which are more intense at low temperatures. The amide I band temperature dependence is on the long wavelength edge of the band, while the short wavelength side has almost no temperature dependence. We compare concepts of anharmonic solid-state crystal physics and chemical physics for the origins of these bands. We suggest that the long wavelength side is composed of those amino acids which hydrogen bond to the hydration shell of the protein, and that temperature dependent bands can be used to determine the time it takes vibrational energy to flow into the hydration shell. We determine that vibrational energy flow to the hydration shell from the amide I takes approximately 20 ps to occur.

Proteins: paradigms of complexity.

Proteins are the working machines of living systems. Directed by the DNA, of the order of a few hundred building blocks, selected from 20 different amino acids, are covalently linked into a linear polypeptide chain. In the proper environment, the chain folds into the working protein, often a globule of linear dimensions of a few nanometers. The biologist considers proteins units from which living systems are built. Many physical scientists look at them as systems in which the laws of complexity can be studied better than anywhere else. Some of the results of such studies will be sketched.

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.