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The glass transition is one of the few unsolved problems in condensed matter physics: agreement on the cause of the slowing down of structural relaxation in glass-forming liquids is lacking. Glasses are amorphous solids, which do not possess the long-range crystalline order, yet display arrested dynamics and the shear elastic modulus characteristic of equilibrium elasticity. It has been suggested that due to the influence of intramolecular interactions and chain connectivity, the nature of the glass transition in polymers and in standard glass-formers is fundamentally different. Here, we discuss the role of connectivity in polymer glasses, demonstrating that although covalent bonding promotes glass formation, bonding sequentiality that defines a polymer chain is not critical in the bulk: glassy dynamics is purely a result of the number of connections per particle, independently of how these connections are formed, agreeing with the classical Phillips-Thorpe topological constraint theory. We show that bonding sequentiality does play an important role in the surface effects of the glass, highlighting a major difference between polymeric and colloidal glasses. Further, we identify the heterogenous dynamics of model coarse-grained polymer chains both in ‘bulk’ and near the free surface, and demonstrate characteristic domain patterns in local displacement and connectivity.

Membrane fusion proteins are responsible for viral entry into host cells—a crucial first step in viral infection. These proteins undergo large conformational changes from pre-fusion to fusion-initiation structures, and, despite differences in viral genomes and disease etiology, many fusion proteins are arranged as trimers. Structural information for both pre-fusion and fusion-initiation states is critical for understanding virus neutralization by the host immune system. In the case of Ebola virus glycoprotein (EBOV GP) and Zika virus envelope protein (ZIKV E), pre-fusion state structures have been identified experimentally, but only partial structures of fusion-initiation states have been described. While the fusion-initiation structure is in an energetically unfavorable state that is difficult to solve experimentally, the existing structural information combined with computational approaches enabled the modeling of fusion-initiation state structures of both proteins. These structural models provide an improved understanding of four different neutralizing antibodies in the prevention of viral host entry.

Membrane fusion proteins are responsible for viral entry into host cells– a crucial first step in viral infection. These proteins undergo large conformational changes from pre-fusion to fusion initiation structures, and, despite differences in viral genomes and disease etiology, many fusion proteins are arranged as trimers. Structural information for both pre-fusion and fusion initiation states is critical for understanding virus neutralization by the host immune system. In the case of Ebola glycoprotein (GP) and Zika envelope protein (Zika E), pre-fusion state structures have been identified experimentally, but only partial structures of fusion initiation states have been described. While the fusion initiation structure is in an energetically unfavorable state that is difficult to solve experimentally, the existing structural information combined with computational approaches enabled the modeling of fusion initiation state structures of both proteins. These structural models provide an improved understanding of four different neutralizing antibodies in the prevention of viral host entry.

Proteins have evolved to perform numerous roles as specific catalysts and nano-machines. Some of the mechanisms exploited by evolution are clear. Hydrophobicity drives the stabilization energy of folding, charges mediate long-range interactions and facilitate catalysis, and specific geometries and hydrogen bonding patterns facilitate molecular recognition and catalysis. In this work, we examine the energy landscape of protein dynamics in terms of the continuous and discrete water structures that control protein dynamics. We observe that the internal structures at the active site of proteins are constantly shaped by strong interactions with hydration shell and bulk water motions. By describing the energy landscape of proteins in terms of its three component motions; conformational, hydration and protonation, and electronic structure, it is possible to systematically understand protein function.

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 ≈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.

Glasses, supercooled liquids and proteins share common properties, in particular the existence of an energy landscape and the presence of two types of fluctuations, alpha and beta. While the effect of alpha fluctuations on proteins has been known for a few years, the effect of beta fluctuations has not been fully understood. By comparing neutron-scattering data on the protein myoglobin with beta fluctuations in the hydration shell measured by dielectric relaxation spectroscopy, we show that the internal protein motions are slaved to these fluctuations. We also show that there is no 'dynamical transition' in proteins near 200 K. The rapid increase in the mean-square displacement with temperature in many neutron-scattering experiments can be quantitatively predicted by beta fluctuations in the hydration shell.

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.

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.

We use Molecular Dynamics simulations to study single chain polymer dynamics and collapse to imitate the early stages of protein folding, as well as polymer brush collapse, to understand the physics and morphology of collapsing polymer brushes. Simulations of this nature can help us understand complex phenomena such as glass transition, molecular crowding and complex higher order organisation. As an example, we demonstrate a study of the physical origin of the polymer glass transition from the point of view of marginal rigidity, which is achieved above a certain number of intermolecular contacts. We find that when the average number of contacts per monomer (covalent and non-covalent) exceeds the critical value z∗=4, the system becomes solid and the dynamics arrested - a state that we declare the glass. We also look at polymer brushes and describe spinodal decomposition-like processes that take place upon brush collapse. It is often impossible to simulate large systems without a certain level of sophisticated coarse graining. We introduce a possible model for studying higher order organisation of chromatin, a biological complex of DNA and histone proteins within the nucleus of a cell. Chromatin organisation is a fascinating topic that resembles protein folding, however, it is much more complex due to multiple levels at which chromatin folding and dynamics have to be understood. Using a simplified force field, we also study helical structures formed by peptoids, small peptidomimetic molecules that are of importance to the pharmacological industry.

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 Mossbauer 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.

The Mossbauer 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.

In a tour de force in this issue of PNAS, Bourgeois et al. (1) have used 2.2-ns x-ray pulses to observe the motion of carbon monoxide (CO) through myoglobin (Mb) and the relaxation of the protein from 3.2 ns to 3 ms after photodissociation. This work follows the pioneering experiments of Moffat and collaborators (2). It demonstrates how far advances in x-ray sources and computers have moved the field of protein structure determination since the path-breaking work of Kendrew et al . and Perutz (3, 4). The recent breakthrough shows how careful studies of proteins, in particular of Mb, impact many different fields. Mb is a monomeric protein that gives muscle its red color. Thirty years ago the textbook function of Mb, storage of dioxygen at the heme iron, was considered to be simple, fully understood, and consequently boring. Mb was essentially written off as a topic of serious research. Since then, the situation has changed: Mb is no longer fully understood. It plays roles other than O2 storage, serves as a prototype for complex systems, and yields insight into the chemistry and physics of soft matter and of chemical reactions. Mb consists of 153 amino acids that fold into a structure that is ≈3 nm in diameter, as depicted in Fig. 1 a . Fig. 1 b gives a schematic cross section through Mb that shows the active center: a heme group with a central iron atom. Surrounding the heme group are five cavities, the heme cavity and four cavities denoted by Xe1 to Xe4 (5). The amino acids lining the xenon cavities are much more conserved than other amino acids in mammalian Mb; they are thus likely to be important for function. A major part of Mb is taken up by amino acids that do not appear to …

We review the concepts of protein dynamics developed over the last 35years and extend applications of the unified model of protein dynamics to heat flow and spatial fluctuations in hydrated myoglobin (Mb) powders. Differential scanning calorimetry (DSC) and incoherent neutron scattering (INS) data on hydration Mb powders are explained by the temperature-dependence of the hydration-shell β(h) process measured by dielectric relaxation spectroscopy (DRS). The unified model explains the temperature dependence of DSC and INS data as a kinetic effect due to a fixed experimental time window and a broad distribution of hydration-shell β(h) fluctuation rates. We review the slaving of large scale protein motions to the bulk solvent α process, and the metastability of Mb molecules in glass forming bulk solvent at low temperatures. This article is part of a Special Issue entitled: "Protein Dynamics: Experimental and Computational Approaches".

Bacterial RNA polymerase (RNAP) is responsible for transcribing genes into messenger-RNAs. RNAP is a multi-components protein complex consisting of α, β, β′, Ω-subunits. RNAP, together with one or more initiation factor(s), binds to promoter DNA to yield an RNAP-DNA initiation complex. While many attempts were made to solve structures of various components of the transcription complex, the detailed structure of the RNAP-transcription factor-DNA complex is still not available. We have engaged in an exercise to develop a detailed model structure for an RNAP-σ70-DNA complex. The detailed structure of the complex (as shown in the attached figure) is modeled using a structure and sequence-based approach developed in our laboratory utilizing the low-resolution crystal structure of T. aquaticus RNAP- σ70-DNA (PDB: 1L9Z) as a scaffold and information derived from high-resolution crystal structures of the polymerases (minus the σ-subunit and the promoter DNA duplex) from T. aquaticus (PDB: 1HQM) and T. thermophilus (PDB: 2O5J). The physical constraints for the C-terminal domains of the α-subunits binding to DNA with and/or without other factors (e.g., MarA, CAP) in the presence of the RNAP-σ70-DNA are discussed.View Large Image | View Hi-Res Image | Download PowerPoint Slide

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 α-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 α but can be slower by a large factor. Slowing occurs because large-scale motions proceed in many small steps, each determined by k α . 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 α . Because the number of conformational substates in the unfolded protein is extremely large, the folding rate coefficient, k f , is much smaller than k α . The slaving model implies that the activation enthalpy of folding is dominated by the solvent, whereas the number of steps n f = k α / k f is controlled by the number of accessible substates in the unfolded protein and the solvent. Proteins, however, undergo not only α- but also β-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.

Atomic motions and energetics for a phosphate transfer reaction catalyzed by the cAMP-dependent protein kinase (PKA) are calculated by plane-wave density functional theory, starting from structures of proteins crystallized in both the reactant conformation (RC) and the transition-state conformation (TC). In the TC, we calculate that the reactants and products are nearly isoenergetic with a 0.2 eV barrier; while phosphate transfer is unfavorable by over 1.2 eV in the RC, with an even higher barrier. With the protein in the TC, the motions involved in reaction are small, with only P$_\gamma$ and the catalytic proton moving more than 0.5 \AA. Examination of the structures reveals that in the RC the active site cleft is not completely closed and there is insufficient space for the phosphorylated serine residue in the product state. Together, these observations imply that the phosphate transfer reaction occurs rapidly and reversibly in a particular conformation of the protein, and that the reaction can be gated by changes of a few tenths of an \AA in the catalytic site., Comment: revtex4, 7 pages, 4 figures, to be submitted to Science

The science of complexity has moved to center stage within the past few decades. Complex systems range from glasses to the immune system and the brain. Glasses are too simple to possess all aspects of complexity; brains are too complex to expose common concepts and laws of complexity. Proteins, however, are systems where many concepts and laws of complexity can be explored experimentally, theoretically, and computationally. Such studies have elucidated crucial aspects. The energy landscape has emerged as one central concept; it describes the free energy of a system as a function of temperature and the coordinates of all relevant atoms. A second concept is that of fluctuations. Without fluctuations, proteins would be dead and life impossible. A third concept is slaving. Proteins are not isolated systems; they are embedded in cells and membranes. Slaving arises when the fluctuations in the surroundings of a protein dominate many of the motions of the protein proper.

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.

The temperature dependence of functional kinetics of hydrated proteins has been related to changes in dynamic behaviour on the microscopic level, as reflected by the transition like variation of the mean square displacement u2 of the hydrogen atoms. We have extended these explorations by a detailed study of the whole quasielastic and inelastic neutron scattering spectra over the broad energy transfer domain of 50 neV to 20 meV by the combination of high precision time-of-flight neutron spectroscopy (TOF) and neutron spin echo (NSE) experiments in H2O and D2O hydrated myoglobin. This allowed us to identify the basic character of the dynamic processes behind the observed un-harmonic variation of u2. We have found that these processes are fully compatible with the extensively studied glassy type β fluctuations, which enter with increasing temperature the 0.2 ps – 10 ns combined TOF – NSE time window of the present study.

A wide variety of protein dynamics are accounted for by two classes of solvent processes: the bulk-solvent viscosity and hydration-shell dynamics. In glass-forming solvents the bulk viscosity arises from the well-characterized microscopic alpha relaxation; in liquid solvents that freeze the alpha process is essentially molecular reorientation. In past work we showed that the solvent alpha relaxation determines the activation enthalpy of alpha-slaved protein motions.We have now measured the dielectric spectrum of the hydration-shell dynamics in myoglobin solutions as a function of hydration, temperature and frequency. These hydration-shell data and a minimal model of protein-solvent coupling predict the temperature- and hydration-dependence of the Mossbauer effect. Furthermore, we show agreement between incoherent neutron scattering data and our measurements of hydration dynamics.These improvements in understanding protein-solvent dynamical coupling will be discussed in terms of earlier work describing the slaving of many protein functional motions to the solvent alpha-process and the slaving of protein folding. We demonstrate that many enthalpy barriers to protein motion arise almost entirely from solvent dynamical processes.