Glassy behavior of a protein

Metastability of Protein Solution Structures in the Absence of a Solvent: Rugged Energy Landscape and Glass-like Behavior

Native ion mobility/mass spectrometry is well-poised to structurally screen proteomes but characterizes protein structures in the absence of a solvent. This raises long-standing unanswered questions about the biological significance of protein structures identified through ion mobility/mass spectrometry. Using newly developed computational and experimental ion mobility/ion mobility/mass spectrometry methods, we investigate the unfolding of the protein ubiquitin in a solvent-free environment. Our data suggest that the folded, solvent-free ubiquitin observed by ion mobility/mass spectrometry exists in a largely native fold with an intact β-grasp motif and α-helix. The ensemble of folded, solvent-free ubiquitin ions can be partitioned into kinetically stable subpopulations that appear to correspond to the structural heterogeneity of ubiquitin in solution. Time-resolved ion mobility/ion mobility/mass spectrometry measurements show that folded, solvent-free ubiquitin exhibits a strongly stretched-exponential time dependence, which simulations trace to a rugged energy landscape with kinetic traps. Unfolding rate constants are estimated to be approximately 800 to 20,000 times smaller than in the presence of water, effectively quenching the unfolding process on the time scale of typical ion mobility/mass spectrometry measurements. Our proposed unfolding pathway of solvent-free ubiquitin shares substantial characteristics with that established for the presence of solvent, including a polarized transition state with significant native content in the N-terminal β-hairpin and α-helix. Our experimental and computational data suggest that (1) the energy landscape governing the motions of folded, solvent-free proteins is rugged in analogy to that of glassy systems; (2) large-scale protein motions may at least partially be determined by the amino acid sequence of a polypeptide chain; and (3) solvent facilitates, rather than controls, protein motions.

Main role of fractal-like nature of conformational space in subdiffusion in proteins

Protein dynamics involves a myriad of mechanical movements happening at different time and space scales, which make it highly complex. One of the less understood features of protein dynamics is subdiffusivity, defined as sublinear dependence between displacement and time. Here, we use all-atoms molecular dynamics (MD) simulations to directly interrogate an already well-established theory and demonstrate that subdiffusivity arises from the fractal nature of the network of metastable conformations over which the dynamics, thought of as a diffusion process, takes place.

Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586-599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head-tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes.

Variations in the Protein Hydration and Hydrogen-Bond Network of Water Molecules Induced by the Changes in the Secondary Structures of Proteins Studied through Near-Infrared Spectroscopy

This study investigated how the secondary structural changes of proteins in aqueous solutions affect their hydration and the hydrogen-bond network of water molecules using near-infrared (NIR) spectroscopy. The aqueous solutions of three types of proteins, i.e., ovalbumin, β-lactoglobulin, and bovine serum albumin, were denatured by heating, and changes in the NIR bands of water reflecting the states of hydrogen bonds induced via protein secondary structural changes were investigated. On heating, the intermolecular hydrogen bonds between water molecules as well as between water and protein molecules were broken, and protein molecules were no longer strongly bound by the surrounding water molecules. Consequently, the denaturation was observed to proceed depending on the thermodynamic properties of the proteins. When the aqueous solutions of proteins were cooled after denaturation, the hydrogen-bond network was reformed. However, the state of protein hydration was changed owing to the secondary structural changes of proteins, and the variation patterns were different depending on the protein species. These changes in protein hydration may be derived from the differences in the surface charges of proteins. The elucidation of the mechanism of protein hydration and the formation of the hydrogen-bond network of water molecules will afford a comprehensive understanding of the protein functioning and dysfunctioning derived from the structural changes in proteins.

On the Rapid Calculation of Binding Affinities for Antigen and Antibody Design and Affinity Maturation Simulations

The accurate and efficient calculation of protein-protein binding affinities is an essential component in antibody and antigen design and optimization, and in computer modeling of antibody affinity maturation. Such calculations remain challenging despite advances in computer hardware and algorithms, primarily because proteins are flexible molecules, and thus, require explicit or implicit incorporation of multiple conformational states into the computational procedure. The astronomical size of the amino acid sequence space further compounds the challenge by requiring predictions to be computed within a short time so that many sequence variants can be tested. In this study, we compare three classes of methods for antibody/antigen (Ab/Ag) binding affinity calculations: (i) a method that relies on the physical separation of the Ab/Ag complex in equilibrium molecular dynamics (MD) simulations, (ii) a collection of 18 scoring functions that act on an ensemble of structures created using homology modeling software, and (iii) methods based on the molecular mechanics-generalized Born surface area (MM-GBSA) energy decomposition, in which the individual contributions of the energy terms are scaled to optimize agreement with the experiment. When applied to a set of 49 antibody mutations in two Ab/HIV gp120 complexes, all of the methods are found to have modest accuracy, with the highest Pearson correlations reaching about 0.6. In particular, the most computationally intensive method, i.e., MD simulation, did not outperform several scoring functions. The optimized energy decomposition methods provided marginally higher accuracy, but at the expense of requiring experimental data for parametrization. Within each method class, we examined the effect of the number of independent computational replicates, i.e., modeled structures or reinitialized MD simulations, on the prediction accuracy. We suggest using about ten modeled structures for scoring methods, and about five simulation replicates for MD simulations as a rule of thumb for obtaining reasonable convergence. We anticipate that our study will be a useful resource for practitioners working to incorporate binding affinity calculations within their protein design and optimization process.

Modulation of free energy landscapes as a strategy for the design of antimicrobial peptides

Computational design of antimicrobial peptides (AMPs) is a promising area of research for developing novel agents against drug-resistant bacteria. AMPs are present naturally in many organisms, from bacteria to humans, a time-tested mechanism that makes them attractive as effective antibiotics. Depending on the environment, AMPs can exhibit α-helical or β-sheet conformations, a mix of both, or lack secondary structure; they can be linear or cyclic. Prediction of their structures is challenging but critical for rational design. Promising AMP leads can be developed using essentially two approaches: traditional modeling of the physicochemical mechanisms that determine peptide behavior in aqueous and membrane environments and knowledge-based, e.g., machine learning (ML) techniques, that exploit ever-growing AMP databases. Here, we explore the conformational landscapes of two recently ML-designed AMPs, characterize the dependence of these landscapes on the medium conditions, and identify features in peptide and membrane landscapes that mediate protein-membrane association. For both peptides, we observe greater conformational diversity in an aqueous solvent than in a less polar solvent, and one peptide is seen to alter its conformation more dramatically than the other upon the change of solvent. Our results support the view that structural rearrangement in response to environmental changes is central to the mechanism of membrane-structure disruption by linear peptides. We expect that the design of AMPs by ML will benefit from the incorporation of peptide conformational substates as quantified here with molecular simulations.

Effects of cryo-EM cooling on structural ensembles

Structure determination by cryo electron microscopy (cryo-EM) provides information on structural heterogeneity and ensembles at atomic resolution. To obtain cryo-EM images of macromolecules, the samples are first rapidly cooled down to cryogenic temperatures. To what extent the structural ensemble is perturbed during cooling is currently unknown. Here, to quantify the effects of cooling, we combined continuum model calculations of the temperature drop, molecular dynamics simulations of a ribosome complex before and during cooling with kinetic models. Our results suggest that three effects markedly contribute to the narrowing of the structural ensembles: thermal contraction, reduced thermal motion within local potential wells, and the equilibration into lower free-energy conformations by overcoming separating free-energy barriers. During cooling, barrier heights below 10 kJ/mol were found to be overcome, which is expected to reduce B-factors in ensembles imaged by cryo-EM. Our approach now enables the quantification of the heterogeneity of room-temperature ensembles from cryo-EM structures.

The rapid temperature drop during plunge-freezing affects the structural ensembles obtained by cryo-EM. To quantify the extent of perturbation, Bock and Grubmüller combined continuum calculations, MD simulations, and kinetic models.

Multiscale relaxation dynamics and diffusion of myelin basic protein in solution studied by quasielastic neutron scattering

We report an analysis of high-resolution quasielastic neutron scattering spectra from Myelin Basic Protein (MBP) in solution, comparing the spectra at three different temperatures (283, 303, and 323 K) for a pure D₂O buffer and a mixture of D₂O buffer with 30% of deuterated trifluoroethanol (TFE). Accompanying experiments with dynamic light scattering and Circular Dichroism (CD) spectroscopy have been performed to obtain, respectively, the global diffusion constant and the secondary structure content of the molecule for both buffers as a function of temperature. Modeling the decay of the neutron intermediate scattering function by the Mittag-Leffler relaxation function, ϕ(t) = E_α(-(t/τ)^α) (0 < α < 1), we find that trifluoroethanol slows down the relaxation dynamics of the protein at 283 K and leads to a broader relaxation rate spectrum. This effect vanishes with increasing temperature, and at 323 K, its relaxation dynamics is identical in both solvents. These results are coherent with the data from dynamic light scattering, which show that the hydrodynamic radius of MBP in TFE-enriched solutions does not depend on temperature and is only slightly smaller compared to the pure D₂O buffer, except for 283 K, where it is much reduced. In accordance with these observations, the CD spectra reveal that TFE induces essentially a partial transition from β-strands to α-helices, but only a weak increase in the total secondary structure content, leaving about 50% of the protein unfolded. The results show that MBP is for all temperatures and in both buffers an intrinsically disordered protein and that TFE essentially induces a reduction in its hydrodynamic radius and its relaxation dynamics at low temperatures.

Stationary and Time-Dependent Carbon Monoxide Stretching Mode Features in Carboxy Myoglobin: A Theoretical-Computational Reappraisal

The stationary and time-dependent infrared spectrum (IR) of the CO stretching mode (ν_CO) in carboxymyoglobin (MbCO), a longstanding problem of biophysical chemistry, has been modeled through a theoretical-computational method specifically designed for simulating quantum observables in complex atomic-molecular systems and based on a combined application of long time scale molecular dynamics simulations and quantum-chemical calculations. This study is basically focused on two aspects: (i) the origin of the stationary IR substates (termed as A₀, A₁, and A₃) and (ii) the modeling and the interpretation of the ν_CO energy relaxation. The results, strengthened by a more than satisfactory agreement with the experimental data, concisely indicate that (i) the conformational His64-FeCO relevant substates, i.e., characterized by the formation-disruption of the H-bond between the above moieties, are the main responsible of the presence of two distinct and well separated (A₀ and A₁/A₃) spectroscopic regions; (ii) the characteristic bimodal shape of the A₁/A₃ spectral region, according to our model, is the result of the fluctuation of the electric field pattern as provided by the protein-solvent framework perturbing the bound His64-CO-Heme complex; and (iii) the electric field pattern, in conjunction with the relatively high density of MbCO vibrational states, is also the main determinant of the ν_CO energy relaxation, characterizing its kinetic efficiency.

Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3  nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.

Origin of subdiffusions in proteins: Insight from peptide systems

Subdiffusive kinetics are popular in proteins and peptides as observed in experiments and simulations. For protein systems with diverse interactions, are there multiple mechanisms to produce the common subdiffusion behavior? To approach this problem, long trajectories of two model peptides are simulated to study the mechanism of subdiffusion and the relations with their interactions. The free-energy profiles and the subdiffusive kinetics are observed for these two peptides. A hierarchical plateau analysis is employed to extract the features of the landscape from the mean square of displacement. The mechanism of subdiffusions can be postulated by comparing the exponents by simulations with those based on various models. The results indicate that the mechanisms of these two peptides are different and are related to the characteristics of their energy landscapes. The subdiffusion of the flexible peptide is mainly caused by depth distribution of traps on the energy landscape, while the subdiffusion of the helical peptide is attributed to the fractal topology of local minima on the landscape. The emergence of these different mechanisms reflects different kinetic scenarios in peptide systems though the peptides behave in a similar way of diffusion. To confirm these ideas, the transition networks between various conformations of these peptides are generated. Based on the network description, the controlled kinetics based only on the topology of the networks are calculated and compared with the results based on simulations. For the flexible peptide, the feature of controlled diffusion is distinct from that of simulation, and for the helical peptide, two kinds of kinetics have a similar exponent of subdiffusion. These results further exemplify the importance of the landscape topology in the kinetics of structural proteins and the effect of depth distribution of traps for the subdiffusion of disordered peptides.

Fluid Phase Coexistence in Biological Membrane: Insights from Local Nonaffine Deformation of Lipids

Lateral heterogeneities in biomembranes play a crucial role in various physiological functions of the cell. Such heterogeneities lead to demixing of lipid constituents and formation of distinct liquid domains in the membrane. We study lateral heterogeneities in terms of topological rearrangements of lipids to identify the liquid-liquid phase coexistence in model membranes. Using ideas from the physics of amorphous systems and glasses, we calculate the degree of nonaffine deformation associated with individual lipids to characterize the liquid-ordered (L_o) and liquid-disordered (L_d) regions in model lipid bilayers. We explore the usage of this method on all-atom and coarse-grained lipid bilayer trajectories. This method is helpful in defining the instantaneous L_o-L_d domain boundaries in complex multicomponent bilayer systems. The characterization is also used to highlight the effect of line-active molecules on the phase boundaries and domain mixing. Overall, we propose a framework to explore the molecular origin of spatial and dynamical heterogeneity in biomembrane systems, which can be exploited not only in computer simulations but also in experiments.

Void distributions reveal structural link between jammed packings and protein cores

Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction ϕ≈0.56, which is the same as dense, random packing of amino-acid-shaped particles. In this article, we compare the structural properties of protein cores and jammed packings of amino-acid-shaped particles in much greater depth by measuring their local and connected void regions. We find that the distributions of surface Voronoi cell volumes and local porosities obey similar statistics in both systems. We also measure the probability that accessible, connected void regions percolate as a function of the size of a spherical probe particle and show that both systems possess the same critical probe size. We measure the critical exponent τ that characterizes the size distribution of connected void clusters at the onset of percolation. We find that the cluster size statistics are similar for void percolation in packings of amino-acid-shaped particles and randomly placed spheres, but different from that for void percolation in jammed sphere packings. We propose that the connected void regions are a defining structural feature of proteins and can be used to differentiate experimentally observed proteins from decoy structures that are generated using computational protein design software. This work emphasizes that jammed packings of amino-acid-shaped particles can serve as structural and mechanical analogs of protein cores, and could therefore be useful in modeling the response of protein cores to cavity-expanding and -reducing mutations.

Temperature Induced Dynamical Transition of Biomolecules in Polarizable and Nonpolarizable TIP3P Water

Temperature induced dynamical transition (DT), associated with a sharp rise in molecular flexibility, is well-known to be exhibited between 270 and 280 K in glycerol to 200-230 K in hydrated biomolecules and is controlled by diffusivity (viscosity) of the solvation layer. In the molecular dynamics (MD) community, especially for water as a solvent, this has been an intense area of research despite decades of investigations. However, in general, water in these studies is described by empirical nonpolarizable force fields in which electronic polarizability is treated implicitly with effective charges and related parameters. This might have led to the present trait of discovery that DTs of biomolecules, irrespective of the potential functions for water models used, occur within a narrow band of temperature variation (30-40 K). Whereas a water molecule in a biomolecular surface and one in bulk are polarized differently, therefore explicit treatment of water polarizability would be a powerful approach toward the treatment of hydration water, believed to cause the DT manifestation. Using MD simulations, we investigated the effects of polarizable water on the DT of biomolecules and the dynamic properties of hydration water. We chose two types of solutes: globular protein (lysozyme) and more open and flexible RNAs (a hairpin and a riboswitch) with different natures of hydrophilic sites than proteins in general. We found that the characteristic temperature of DT ( T_DT) for the solutes in polarizable water is always higher than that in its nonpolarizable counterpart. In particular, for RNAs, the variations are found to be ∼45 K between the two water models, whereas for the more compact lysozyme, it is only ∼4 K. The results are discussed in light of the enormous increase in relaxation times of a liquid upon cooling in the paradigm of dynamic switchover in hydration water with liquid-liquid phase transition, derived from the existence of the second critical point. Our result supports the idea that structures of biomolecules and their interactions with the hydration water determines T_DT and provides evidence for the decisive role of polarizable water on the onset of DT, which has been hitherto ignored.

Redox chemistry in the pigment eumelanin as a function of temperature using broadband dielectric spectroscopy

We demonstrate on synthetic eumelanin that biomolecular conductivity models should account for temperature and hydration effects coherently.

Hydrogen-bond dynamics at the bio-water interface in hydrated proteins: a molecular-dynamics study

Water is fundamental to the biochemistry of enzymes. It is well known that without a minimum amount of water, enzymes are not biologically active. Bare minimal solvation for biological function corresponds to about a single layer of water covering enzymes' surfaces. Many contradictory studies on protein-hydration-water-coupled dynamics have been published in recent decades. Following prevailing wisdom, a dynamical crossover in hydration water (at around 220 K for hydrated lysozymes) can trigger larger-amplitude motions of the protein, activating, in turn, biological functions. Here, we present a molecular-dynamics-simulation study on a solvated model protein (hen egg-white lysozyme), in which we determine, inter alia, the relaxation dynamics of the hydrogen-bond network between the protein and its hydration water molecules on a residue-per-residue basis. Hydrogen-bond breakage/formation kinetics is rather heterogeneous in temperature dependence (due to the heterogeneity of the free-energy surface), and is driven by the magnitude of thermal motions of various different protein residues which provide enough thermal energy to overcome energy barriers to rupture their respective hydrogen bonds with water. In particular, arginine residues exhibit the highest number of such hydrogen bonds at low temperatures, losing almost completely such bonding above 230 K. This suggests that hydration water's dynamical crossover, observed experimentally for hydrated lysozymes at ∼220 K, lies not at the origin of the protein residues' larger-amplitude motions, but rather arises as a consequence thereof. This highlights the need for new experimental investigations, and new interpretations to link protein dynamics to functions, in the context of key interrelationships with the solvation layer.

Observation of dielectric universalities in albumin, cytochrome C and Shewanella oneidensis MR-1 extracellular matrix

The electrodynamics of metals is well understood within the Drude conductivity model; properties of insulators and semiconductors are governed by a gap in the electronic states. But there is a great variety of disordered materials that do not fall in these categories and still respond to external field in an amazingly uniform manner. At radiofrequencies delocalized charges yield a frequency-independent conductivity σ 1(ν) whose magnitude exponentially decreases while cooling. With increasing frequency, dispersionless conductivity starts to reveal a power-law dependence σ 1(ν)∝ν s with s < 1 caused by hopping charge carriers. At low temperatures, such Universal Dielectric Response can cross over to another universal regime with nearly constant loss ε″∝σ1/ν = const. The powerful research potential based on such universalities is widely used in condensed matter physics. Here we study the broad-band (1-1012 Hz) dielectric response of Shewanella oneidensis MR-1 extracellular matrix, cytochrome C and serum albumin. Applying concepts of condensed matter physics, we identify transport mechanisms and a number of energy, time, frequency, spatial and temperature scales in these biological objects, which can provide us with deeper insight into the protein dynamics.

Weak nanoscale chaos and anomalous relaxation in DNA

Anomalous nonexponential relaxation in hydrated biomolecules is commonly attributed to the complexity of the free-energy landscapes, similarly to polymers and glasses. It was found recently that the hydrogen-bond breathing of terminal DNA base pairs exhibits a slow power-law relaxation attributable to weak Hamiltonian chaos, with parameters similar to experimental data. Here, the relationship is studied between this motion and spectroscopic signals measured in DNA with a small molecular photoprobe inserted into the base-pair stack. To this end, the earlier computational approach in combination with an analytical theory is applied to the experimental DNA fragment. It is found that the intensity of breathing dynamics is strongly increased in the internal base pairs that flank the photoprobe, with anomalous relaxation quantitatively close to that in terminal base pairs. A physical mechanism is proposed to explain the coupling between the relaxation of base-pair breathing and the experimental response signal. It is concluded that the algebraic relaxation observed experimentally is very likely a manifestation of weakly chaotic dynamics of hydrogen-bond breathing in the base pairs stacked to the photoprobe and that the weak nanoscale chaos can represent an ubiquitous hidden source of nonexponential relaxation in ultrafast spectroscopy.

Coexisting origins of subdiffusion in internal dynamics of proteins

Subdiffusion in conformational dynamics of proteins is observed both experimentally and in simulations. Although its origin has been attributed to multiple mechanisms, including trapping on a rugged energy landscape, fractional Brownian noise, or a fractal topology of the energy landscape, it is unclear which of these, if any, is most relevant. To obtain insights into the actual mechanism, we introduce an analytically tractable hierarchical trapping model and apply it to molecular dynamics simulation trajectories of three proteins in solution. The analysis of the simulations introduces a subdiffusive exponent that varies with time and associates plateaus in the mean-squared displacement with traps on the energy landscape. This analysis permits us to separate the component of subdiffusion due to a trapping mechanism from that due to an underlying fluctuating process, such as fractional Brownian motion. The present results thus provide insights concerning the physical origin of subdiffusion in the dynamics of proteins.

Role of Hydration Layer in Dynamical Transition in Proteins: Insights from Translational Self-Diffusivity

Elucidation of the role of hydration water underpinning dynamical crossover in proteins has proven challenging. Indeed, many contradictory findings in the literature seek to establish either causal or correlative links between water and protein behavior. Here, via molecular dynamics, we compute the temperature dependence of mean-square displacement and translational self-diffusivities for both hen egg white lysozyme and its hydration layer from 190 to 300 K. We find that the protein's mobility increases sharply at ∼230 K, indicating dynamical onset; concerted motion with hydration-water molecules is evident up to ∼285 K, confirming dynamical correlation between them. Exploring underlying mechanisms of such concerted motion, we scrutinize the water-protein hydrogen-bonding network as a function of temperature, noting sharp deviation from linearity of the hydrogen bond number's profile with temperature originating near the protein dynamical transition. Our studies reveal a common temperature profile/dependence of self-diffusivity values of the protein, hydration water, and the bulk solvent, originating from a common dependence on the bulk solvent viscosity, η_S. The key mechanistic role adopted by the protein-water hydrogen bond network in relation to the onset of proteins' dynamical transition is also discussed.

The logarithmic relaxation process and the critical temperature of liquids in nano-confined states

The logarithmic relaxation process is the slowest of all relaxation processes and is exhibited by only a few molecular liquids and proteins. Bulk salol, which is a glass-forming liquid, is known to exhibit logarithmic decay of intermediate scattering function for the β-relaxation process. In this article, we report the influence of nanoscale confinements on the logarithmic relaxation process and changes in the microscopic glass-transition temperature of salol in the carbon and silica nanopores. The generalized vibrational density-of-states of the confined salol indicates that the interaction of salol with ordered nanoporous carbon is hydrophilic in nature whereas the interaction with silica surfaces is more hydrophobic. The mode-coupling theory critical temperature derived from the QENS data shows that the dynamic transition occurs at much lower temperature in the carbon pores than in silica pores. The results of this study indicate that, under nano-confinements, liquids that display logarithmic β-relaxation phenomenon undergo a unique glass transition process.

THz frequency spectrum of protein-solvent interaction energy using a recurrence plot-based Wiener-Khinchin method

The dynamics of a protein and the water surrounding it are coupled via nonbonded energy interactions. This coupling can exhibit a complex, nonlinear, and nonstationary nature. The THz frequency spectrum for this interaction energy characterizes both the vibration spectrum of the water hydrogen bond network, and the frequency range of large amplitude modes of proteins. We use a Recurrence Plot based Wiener-Khinchin method RPWK to calculate this spectrum, and the results are compared to those determined using the classical auto-covariance-based Wiener-Khinchin method WK. The frequency spectra for the total nonbonded interaction energy extracted from molecular dynamics simulations between the β-Lactamase Inhibitory Protein BLIP, and water molecules within a 10 Å distance from the protein surface, are calculated at 150, 200, 250, and 310 K, respectively. Similar calculations are also performed for the nonbonded interaction energy between the residues 49ASP, 53TYR, and 142PHE in BLIP, with water molecules within 10 Å from each residue respectively at 150, 200, 250, and 310 K. A comparison of the results shows that RPWK performs better than WK, and is able to detect some frequency data points that WK fails to detect. This points to the importance of using methods capable of taking the complex nature of the protein-solvent energy landscape into consideration, and not to rely on standard linear methods. In general, RPWK can be a valuable addition to the analysis tools for protein molecular dynamics simulations. Proteins 2016; 84:1549-1557. © 2016 Wiley Periodicals, Inc.

Criteria to Extract High-Quality Protein Data Bank Subsets for Structure Users

It is often necessary to build subsets of the Protein Data Bank to extract structural trends and average values. For this purpose it is mandatory that the subsets are non-redundant and of high quality. The first problem can be solved relatively easily at the sequence level or at the structural level. The second, on the contrary, needs special attention. It is not sufficient, in fact, to consider the crystallographic resolution and other feature must be taken into account: the absence of strings of residues from the electron density maps and from the files deposited in the Protein Data Bank; the B-factor values; the appropriate validation of the structural models; the quality of the electron density maps, which is not uniform; and the temperature of the diffraction experiments. More stringent criteria produce smaller subsets, which can be enlarged with more tolerant selection criteria. The incessant growth of the Protein Data Bank and especially of the number of high-resolution structures is allowing the use of more stringent selection criteria, with a consequent improvement of the quality of the subsets of the Protein Data Bank.

Effects of pressure on the dynamics of an oligomeric protein from deep-sea hyperthermophile

Inorganic pyrophosphatase (IPPase) from Thermococcus thioreducens is a large oligomeric protein derived from a hyperthermophilic microorganism that is found near hydrothermal vents deep under the sea, where the pressure is up to 100 MPa (1 kbar). It has attracted great interest in biophysical research because of its high activity under extreme conditions in the seabed. In this study, we use the quasielastic neutron scattering (QENS) technique to investigate the effects of pressure on the conformational flexibility and relaxation dynamics of IPPase over a wide temperature range. The β-relaxation dynamics of proteins was studied in the time ranges from 2 to 25 ps, and from 100 ps to 2 ns, using two spectrometers. Our results indicate that, under a pressure of 100 MPa, close to that of the native environment deep under the sea, IPPase displays much faster relaxation dynamics than a mesophilic model protein, hen egg white lysozyme (HEWL), at all measured temperatures, opposite to what we observed previously under ambient pressure. This contradictory observation provides evidence that the protein energy landscape is distorted by high pressure, which is significantly different for hyperthermophilic (IPPase) and mesophilic (HEWL) proteins. We further derive from our observations a schematic denaturation phase diagram together with energy landscapes for the two very different proteins, which can be used as a general picture to understand the dynamical properties of thermophilic proteins under pressure.

Stabilization of proteins in solid form

Immunogenicity of aggregated or otherwise degraded protein delivered from depots or other biopharmaceutical products is an increasing concern, and the ability to deliver stable, active protein is of central importance. We review characterization approaches for solid protein dosage forms with respect to metrics that are intended to be predictive of protein stability against aggregation and other degradation processes. Each of these approaches is ultimately motivated by hypothetical connections between protein stability and the material property being measured. We critically evaluate correlations between these properties and stability outcomes, and use these evaluations to revise the currently standing hypotheses. Based on this we provide simple physical principles that are necessary (and possibly sufficient) for generating solid delivery vehicles with stable protein loads. Essentially, proteins should be strongly coupled (typically through H-bonds) to the bulk regions of a phase-homogeneous matrix with suppressed β relaxation. We also provide a framework for reliable characterization of solid protein forms with respect to stability.

Thermal-induced force release in oxyhemoglobin

Oxygen is released to living tissues via conformational changes of hemoglobin from R-state (oxyhemoglobin) to T-state (desoxyhemoglobin). The detailed mechanism of this process is not yet fully understood. We have carried out micromechanical experiments on oxyhemoglobin crystals to determine the behavior of the Young’s modulus and the internal friction for temperatures between 20 °C and 70 °C. We have found that around 49 °C oxyhemoglobin crystal samples undergo a sudden and strong increase of their Young’s modulus, accompanied by a sudden decrease of the internal friction. This sudden mechanical change (and the ensuing force release) takes place in a partially unfolded state and precedes the full denaturation transition at higher temperatures. After this transformation, the hemoglobin crystals have the same mechanical properties as their initial state at room temperatures. We conjecture that it can be relevant for explaining the oxygen-releasing function of native oxyhemoglobin when the temperature is increased, e.g. due to active sport. The effect is specific for the quaternary structure of hemoglobin, and is absent for myoglobin with only one peptide sequence.

Thermodynamic properties of bulk and confined water

The thermodynamic response functions of water display anomalous behaviors. We study these anomalous behaviors in bulk and confined water. We use nuclear magnetic resonance (NMR) to examine the configurational specific heat and the transport parameters in both the thermal stable and the metastable supercooled phases. The data we obtain suggest that there is a behavior common to both phases: that the dynamics of water exhibit two singular temperatures belonging to the supercooled and the stable phase, respectively. One is the dynamic fragile-to-strong crossover temperature (T(L) ≃ 225 K). The second, T* ∼ 315 ± 5 K, is a special locus of the isothermal compressibility K(T)(T, P) and the thermal expansion coefficient α(P)(T, P) in the P-T plane. In the case of water confined inside a protein, we observe that these two temperatures mark, respectively, the onset of protein flexibility from its low temperature glass state (T(L)) and the onset of the unfolding process (T*).

You are lost without a map: Navigating the sea of protein structures

X-ray crystal structures propel biochemistry research like no other experimental method, since they answer many questions directly and inspire new hypotheses. Unfortunately, many users of crystallographic models mistake them for actual experimental data. Crystallographic models are interpretations, several steps removed from the experimental measurements, making it difficult for nonspecialists to assess the quality of the underlying data. Crystallographers mainly rely on "global" measures of data and model quality to build models. Robust validation procedures based on global measures now largely ensure that structures in the Protein Data Bank (PDB) are largely correct. However, global measures do not allow users of crystallographic models to judge the reliability of "local" features in a region of interest. Refinement of a model to fit into an electron density map requires interpretation of the data to produce a single "best" overall model. This process requires inclusion of most probable conformations in areas of poor density. Users who misunderstand this can be misled, especially in regions of the structure that are mobile, including active sites, surface residues, and especially ligands. This article aims to equip users of macromolecular models with tools to critically assess local model quality. Structure users should always check the agreement of the electron density map and the derived model in all areas of interest, even if the global statistics are good. We provide illustrated examples of interpreted electron density as a guide for those unaccustomed to viewing electron density.

The role of water in protein's behavior: The two dynamical crossovers studied by NMR and FTIR techniques

The role the solvent plays in determining the biological activity of proteins is of primary importance. Water is the solvent of life and proteins need at least a water monolayer covering their surface in order to become biologically active. We study how the properties of water and the effect of its coupling with the hydrophilic moieties of proteins govern the regime of protein activity. In particular we follow, by means of Fourier Transform Infrared spectroscopy, the thermal evolution of the amide vibrational modes of hydrated lysozyme in the temperature interval 180 K < T < 350 K. In such a way we are able to observe the thermal limit of biological activity characterizing hydrated lysozyme. Finally we focus on the region of lysozyme thermal denaturation by following the evolution of the proton Nuclear Magnetic Resonance (NMR) spectra for 298 K < T < 366 K with the High-Resolution Magic Angle Spinning probe. Our data suggest that the hydrogen bond coupling between hydration water and protein hydrophilic groups is crucial in triggering the main mechanisms that define the enzymatic activity of proteins.

Specificity and affinity quantification of flexible recognition from underlying energy landscape topography

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.

Flexibility in biomolecular recognition is crucial for the function. Flexibility often leads to moderate binding affinity but high binding specificity, challenging the conventional wisdom that high specificity is guaranteed by high affinity. Currently, understanding of the relationship between affinity and specificity in flexible biomolecular recognition is still obscure, even in a qualitative way. By exploring the intrinsic biomolecular recognition energy landscapes, we provided a novel way to quantify the thermodynamic intrinsic specificity by energy landscape topography and kinetic specificity by association rate. We show quantitatively that flexibility decreases binding affinity while increases binding specificity, and the relative changes in affinity and specificity are strongly correlated with the degree of flexibility. Our results show that more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Importantly, we demonstrated that flexibility modulates affinity and specificity through the underlying energy landscape. Our study establishes the quantitative relationship among flexibility, affinity and specificity, bridging the gap between theory and experiments.

The glassy state of crambin and the THz time scale protein-solvent fluctuations possibly related to protein function

BACKGROUND

THz experiments have been used to characterize the picosecond time scale fluctuations taking place in the model, globular protein crambin.

RESULTS

Using both hydration and temperature as an experimental parameter, we have identified collective fluctuations (<= 200 cm(-1)) in the protein. Observation of the protein dynamics in the THz spectrum from both below and above the glass transition temperature (Tg) has provided unique insight into the microscopic interactions and modes that permit the solvent to effectively couple to the protein thermal fluctuations.

CONCLUSIONS

Our findings suggest that the solvent dynamics on the picosecond time scale not only contribute to protein flexibility but may also delineate the types of fluctuations that are able to form within the protein structure.

Hydrophobic actuation of a DNA origami bilayer structure

Amphiphilic compounds have a strong tendency to form aggregates in aqueous solutions. It is shown that such aggregation can be utilized to fold cholesterol-modified, single-layered DNA origami structures into sandwich-like bilayer structures, which hide the cholesterol modifications in their interior. The DNA bilayer structures unfold after addition of the surfactant Tween 80, and also in the presence of lipid bilayer membranes, with opening kinetics well described by stretched exponentials. It is also demonstrated that by combination with an appropriate lock and key mechanism, hydrophobic actuation of DNA sandwiches can be made conditional on the presence of an additional molecular input such as a specific DNA sequence.

Does a dry protein undergo a glass transition?

Bovine serum albumin (BSA) with extremely low hydration level 0.04, which is usually defined as dry, has been investigated in the temperature range between 200 and 340 K by incoherent inelastic neutron scattering using the neutron time-of-flight spectrometer FOCUS (PSI, Switzerland). Anomalous temperature behavior has been revealed for relaxational and low-frequency vibrational dynamics of BSA in the vicinity of 250 K. The mean-square atomic displacement has been shown to exhibit a change in the slope of temperature dependence near the same temperature. The presented results point out that the glass-like transition occurs in the dry protein.

Rare-event trajectory ensemble analysis reveals metastable dynamical phases in lattice proteins

We explore the dynamical large deviations of a lattice heteropolymer model of a protein by means of path sampling of trajectories. We uncover the existence of nonequilibrium dynamical phase transitions in ensembles of trajectories between active and inactive dynamical phases, whose nature depends on the properties of the interaction potential. We consider three potentials: two heterogeneous interaction potentials and a homogeneous Gō potential. When preserving the full heterogeneity of interactions due to a given amino acid sequence, either in a fully interacting model or in a native contacts interacting model (heterogeneous Gō model), the observed dynamic transitions occur between equilibrium highly native states and highly native but kinetically trapped states. A native activity is defined that allows us to distinguish these dynamic phases. In contrast, for the homogeneous Gō model, where all native interaction energies are uniform and the amino acid sequence plays no role, the dynamical transition is a direct consequence of the static bistability between the unfolded and the native state. In the two heterogeneous interaction models the native-active and native-inactive states, despite their thermodynamic similarity, have widely varying dynamical properties, and the transition between them occurs even in lattice proteins whose sequences are designed to make them optimal folders.

Boson peak as a probe of quantum effects in a glassy state of biomolecules: the case of L-cysteine

Some physical properties of hydrated biomolecules, e.g., the occurrence of a boson peak, have been recognized to resemble those of glassy states. The present work shows that quantum fluctuations play a fundamental role in describing the glassy state of biomolecules, particularly at lower hydration levels. There is a linear relationship between the quantumness and the slope of the temperature dependence of the boson peak frequency, which is used to classify the extent of quantum contributions to the glassy state of glasses in general. Lastly, we demonstrate that the boson peak two-band spectral structure that is observed in some cases can be directly linked to the anisotropy of the elastic properties of the material. The amino acid L-cysteine is studied in detail. The findings are compared with previously reported data for other macromolecules.

Quantifying the topography of the intrinsic energy landscape of flexible biomolecular recognition

Biomolecular functions are determined by their interactions with other molecules. Biomolecular recognition is often flexible and associated with large conformational changes involving both binding and folding. However, the global and physical understanding for the process is still challenging. Here, we quantified the intrinsic energy landscapes of flexible biomolecular recognition in terms of binding-folding dynamics for 15 homodimers by exploring the underlying density of states, using a structure-based model both with and without considering energetic roughness. By quantifying three individual effective intrinsic energy landscapes (one for interfacial binding, two for monomeric folding), the association mechanisms for flexible recognition of 15 homodimers can be classified into two-state cooperative "coupled binding-folding" and three-state noncooperative "folding prior to binding" scenarios. We found that the association mechanism of flexible biomolecular recognition relies on the interplay between the underlying effective intrinsic binding and folding energy landscapes. By quantifying the whole global intrinsic binding-folding energy landscapes, we found strong correlations between the landscape topography measure Λ (dimensionless ratio of energy gap versus roughness modulated by the configurational entropy) and the ratio of the thermodynamic stable temperature versus trapping temperature, as well as between Λ and binding kinetics. Therefore, the global energy landscape topography determines the binding-folding thermodynamics and kinetics, crucial for the feasibility and efficiency of realizing biomolecular function. We also found "U-shape" temperature-dependent kinetic behavior and a dynamical cross-over temperature for dividing exponential and nonexponential kinetics for two-state homodimers. Our study provides a unique way to bridge the gap between theory and experiments.

Photophysical and ligand binding studies of metalloporphyrins bearing hydrophilic distal superstructure

UV-vis absorption and emission studies on zinc and iron porphyrin complexes bearing H-bonding distal superstructures have been performed in two different organic solvents- tetrahydrofuran (THF) (coordinating) and dichloromethane (DCM) (non-coordinating). Quantum yields and lifetimes have been measured for these complexes which are in good agreement with the other reported metalloporphyrins. Binding affinities with anionic ligands such as N3- , CN- , S-2 , F- were monitored for these two complexes in aqueous media and the respective binding constant values were calculated. The Zn complex shows more selectivity towards cyanide while the Fe complex shows more selectivity towards azide.

Secondary structural analysis of proteins based on (13)C chemical shift assignments in unresolved solid-state NMR spectra enhanced by fragmented structure database

Magic-angle-spinning solid-state (13)C NMR spectroscopy is useful for structural analysis of non-crystalline proteins. However, the signal assignments and structural analysis are often hampered by the signal overlaps primarily due to minor structural heterogeneities, especially for uniformly-(13)C,(15)N labeled samples. To overcome this problem, we present a method for assigning (13)C chemical shifts and secondary structures from unresolved two-dimensional (13)C-(13)C MAS NMR spectra by spectral fitting, named reconstruction of spectra using protein local structures (RESPLS). The spectral fitting was conducted using databases of protein fragmented structures related to (13)C(α), (13)C(β), and (13)C' chemical shifts and cross-peak intensities. The experimental (13)C-(13)C inter- and intra-residue correlation spectra of uniformly isotope-labeled ubiquitin in the lyophilized state had a few broad peaks. The fitting analysis for these spectra provided sequence-specific C(α), C(β), and C' chemical shifts with an accuracy of about 1.5 ppm, which enabled the assignment of the secondary structures with an accuracy of 79 %. The structural heterogeneity of the lyophilized ubiquitin is revealed from the results. Test of RESPLS analysis for simulated spectra of five different types of proteins indicated that the method allowed the secondary structure determination with accuracy of about 80 % for the 50-200 residue proteins. These results demonstrate that the RESPLS approach expands the applicability of the NMR to non-crystalline proteins exhibiting unresolved (13)C NMR spectra, such as lyophilized proteins, amyloids, membrane proteins and proteins in living cells.

Sensing proteins through nanopores: fundamental to applications

Proteins subjected to an electric field and forced to pass through a nanopore induce blockades of ionic current that depend on the protein and nanopore characteristics and interactions between them. Recent advances in the analysis of these blockades have highlighted a variety of phenomena that can be used to study protein translocation and protein folding, to probe single-molecule catalytic reactions in order to obtain kinetic and thermodynamic information, and to detect protein-antibody complexes, proteins with DNA and RNA aptamers, and protein-pore interactions. Nanopore design is now well controlled, allowing the development of future biotechnologies and medicine applications.