Temperature-dependent structural and functional features of a hyperthermostable enzyme using elastic neutron scattering

The dynamic behavior of an endoglucanase from the hyperthermophilic microorganism Pyrococcus furiosus was investigated using elastic neutron scattering. The temperature dependence of the atomic motions was correlated with conformational and functional characteristics of the enzyme. The onset of biological function at temperatures higher than approximately 25 degrees C (the hyperthermostable enzyme is essentially inactive at room temperature) was associated with a dynamical transition in the anharmonic motions domain. This transition from the nonactive to the enzymatically active conformation involved structurally similar conformational substates in the energy landscape. From the mean-square displacement of the protein atoms, the molecular flexibility and the effective force constants were calculated at different temperature zones. The results showed that the activity increases at higher temperatures where the intramolecular bonds are weakened and the overall rigidity of the protein is decreased. Further temperature increase resulted in significantly increased atomic fluctuations featuring heat denaturation of the protein.     

Coarse-grained biomolecular simulation with REACH: realistic extension algorithm via covariance Hessian

Coarse-graining of protein interactions provides a means of simulating large biological systems. Here, a coarse-graining method, REACH, is introduced, in which the force constants of a residue-scale elastic network model are calculated from the variance-covariance matrix obtained from atomistic molecular dynamics (MD) simulation. In test calculations, the C(alpha)-atoms variance-covariance matrices are calculated from the ensembles of 1-ns atomistic MD trajectories in monomeric and dimeric myoglobin, and used to derive coarse-grained force constants for the local and nonbonded interactions. Construction of analytical model functions of the distance-dependence of the interresidue force constants allows rapid calculation of the REACH normal modes. The model force constants from monomeric and dimeric myoglobin are found to be similar in magnitude to each other. The MD intra- and intermolecular mean-square fluctuations and the vibrational density of states are well reproduced by the residue-scale REACH normal modes without requiring rescaling of the force constant parameters. The temperature-dependence of the myoglobin REACH force constants reveals that the dynamical transition in protein internal fluctuations arises principally from softening of the elasticity in the nonlocal interactions. The REACH method is found to be a reliable way of determining spatiotemporal protein motion without the need for expensive computations of long atomistic MD simulations.     

Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.     

Enzyme activity below the dynamical transition at 220 K.

Enzyme activity requires the activation of anharmonic motions, such as jumps between potential energy wells. However, in general, the forms and time scales of the functionally important anharmonic dynamics coupled to motion along the reaction coordinate remain to be determined. In particular, the question arises whether the temperature-dependent dynamical transition from harmonic to anharmonic motion in proteins, which has been observed experimentally and using molecular dynamics simulation, involves the activation of motions required for enzyme function. Here we present parallel measurements of the activity and dynamics of a cryosolution of glutamate dehydrogenase as a function of temperature. The dynamical atomic fluctuations faster than approximately 100 ps were determined using neutron scattering. The results show that the enzyme remains active below the dynamical transition observed at approximately 220 K, i.e., at temperatures where no anharmonic motion is detected. Furthermore, the activity shows no significant deviation from Arrhenius behavior down to 190 K. The results indicate that the observed transition in the enzyme's dynamics is decoupled from the rate-limiting step along the reaction coordinate.     

Modulation of primary radical pair kinetics and energetics in photosystem II by the redox state of the quinone electron acceptor Q(A)

Time-resolved photovoltage measurements on destacked photosystem II membranes from spinach with the primary quinone electron acceptor Q(A) either singly or doubly reduced have been performed to monitor the time evolution of the primary radical pair P680(+)Pheo(-). The maximum transient concentration of the primary radical pair is about five times larger and its decay is about seven times slower with doubly reduced compared with singly reduced Q(A). The possible biological significance of these differences is discussed. On the basis of a simple reversible reaction scheme, the measured apparent rate constants and relative amplitudes allow determination of sets of molecular rate constants and energetic parameters for primary reactions in the reaction centers with doubly reduced Q(A) as well as with oxidized or singly reduced Q(A). The standard free energy difference DeltaG degrees between the charge-separated state P680(+)Pheo(-) and the equilibrated excited state (Chl(N)P680)* was found to be similar when Q(A) was oxidized or doubly reduced before the flash (approximately -50 meV). In contrast, single reduction of Q(A) led to a large change in DeltaG degrees (approximately +40 meV), demonstrating the importance of electrostatic interaction between the charge on Q(A) and the primary radical pair, and providing direct evidence that the doubly reduced Q(A) is an electrically neutral species, i.e., is doubly protonated. A comparison of the molecular rate constants shows that the rate of charge recombination is much more sensitive to the change in DeltaG degrees than the rate of primary charge separation.     

Probing protein mechanics: residue-level properties and their use in defining domains

It is becoming clear that, in addition to structural properties, the mechanical properties of proteins can play an important role in their biological activity. It nevertheless remains difficult to probe these properties experimentally. Whereas single-molecule experiments give access to overall mechanical behavior, notably the impact of end-to-end stretching, it is currently impossible to directly obtain data on more local properties. We propose a theoretical method for probing the mechanical properties of protein structures at the single-amino acid level. This approach can be applied to both all-atom and simplified protein representations. The probing leads to force constants for local deformations and to deformation vectors indicating the paths of least mechanical resistance. It also reveals the mechanical coupling that exists between residues. Results obtained for a variety of proteins show that the calculated force constants vary over a wide range. An analysis of the induced deformations provides information that is distinct from that obtained with measures of atomic fluctuations and is more easily linked to residue-level properties than normal mode analyses or dynamic trajectories. It is also shown that the mechanical information obtained by residue-level probing opens a new route for defining so-called dynamical domains within protein structures.     

Temperature derivative fluorescence spectroscopy as a tool to study dynamical changes in protein crystals

Motions through the energy landscape of proteins lead to biological function. At temperatures below a dynamical transition (150-250 K), some of these motions are arrested and the activity of some proteins ceases. Here, we introduce the technique of temperature-derivative fluorescence microspectrophotometry to investigate the dynamical behavior of single protein crystals. The observation of glass transitions in thin films of water/glycerol mixtures allowed us to demonstrate the potential of the technique. Then, protein crystals were investigated, after soaking the samples in a small amount of fluorescein. If the fluorophore resides within the crystal channels, temperature-dependent changes in solvent dynamics can be monitored. Alternatively, if the fluorophore binds to the protein, local dynamical transitions within the biomolecule can be probed directly. A clear dynamical transition was observed at 175 K in the active site of crystalline human butyrylcholinesterase. The results suggest that the dynamics of crystalline proteins is strongly dependent on solvent composition and confinement in the crystal channels. Beyond applications in the field of kinetic crystallography, the highly sensitive temperature-derivative fluorescence microspectrophotometry technique opens the way to many studies on the dynamics of biological nanosamples.     

Effect of the environment on the protein dynamical transition: a neutron scattering study

We performed an elastic neutron scattering investigation of the molecular dynamics of lysozyme solvated in glycerol, at different water contents h (grams of water/grams of lysozyme). The marked non-Gaussian behavior of the elastic intensity was studied in a wide experimental momentum transfer range, as a function of the temperature. The internal dynamics is well described in terms of the double-well jump model. At low temperature, the protein total mean square displacements exhibit an almost linear harmonic trend irrespective of the hydration level, whereas at the temperature T(d) a clear changeover toward an anharmonic regime marks a protein dynamical transition. The decrease of T(d) from approximately 238 K to approximately 195 K as a function of h is reminiscent of that found in the glass transition temperature of aqueous solutions of glycerol, thus suggesting that the protein internal dynamics as a whole is slave to the environment properties. Both T(d) and the total mean square displacements indicate that the protein flexibility strongly rises between 0.1 and 0.2h. This hydration-dependent dynamical activation, which is similar to that of hydrated lysozyme powders, is related to the specific interplay of the protein with the surrounding water and glycerol molecules.     

Coupling between Normal Modes Drives Protein Conformational Dynamics: Illustrations Using Allosteric Transitions in Myosin II

Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.     

Conformational dynamics of supramolecular protein assemblies

Supramolecular protein assemblies including molecular motors, cytoskeletal filaments, chaperones, and ribosomes play a central role in a broad array of cellular functions ranging from cell division and motility to RNA and protein synthesis and folding. Single-particle reconstructions of such assemblies have been growing rapidly in recent years, providing increasingly high resolution structural information under native conditions. While the static structure of these assemblies provides essential insight into their mechanism of biological function, their dynamical motions provide additional important information that cannot be inferred from structure alone. Here we present an unsupervised computational framework for the analysis of high molecular weight protein assemblies and use it to analyze the conformational dynamics of structures deposited in the Electron Microscopy Data Bank. Protein assemblies are modeled using a recently introduced coarse-grained modeling framework based on the finite element method, which is used to compute equilibrium thermal fluctuations, elastic strain energy distributions associated with specific conformational transitions, and dynamical correlations in distant molecular domains. Results are presented in detail for the ribosome-bound termination factor RF2 from Escherichia coli, the nuclear pore complex from Dictyostelium discoideum, and the chaperonin GroEL from E. coli. Elastic strain energy distributions reveal hinge-regions associated with specific conformational change pathways, and correlations in collective molecular motions reveal dynamical coupling between distant molecular domains that suggest new, as well as confirm existing, allosteric mechanisms. Results are publically available for use in further investigation and interpretation of biological function including cooperative transitions, allosteric communication, and molecular mechanics, as well as in further classification and refinement of electron microscopy based structures.     

Ionic-strength-dependent effects in protein folding: analysis of rate equilibrium free-energy relationships and their interpretation

The traditional approach to studying protein folding involves applying a perturbation, usually denaturant or mutation, and determining the effect upon the free energy of folding, DeltaG0, and the activation free energy, DeltaG(not equal). Data collected as a function of the perturbation can be used to construct rate equilibrium free-energy relationships, which report on the development of interactions in the transition state for folding. We examine the use of the ionic-strength-dependent rate equilibrium free-energy relationship in protein folding using the N-terminal domain of L9, a small alpha-beta protein, as a model system. Folding is two-state for the range of ionic strength examined, 0.045-1.52 M. The plot of DeltaG(not equal) versus DeltaG0 is linear (r2= 0.918), with a slope equal to 0.45. The relatively low value of the slope indicates that the ionic-strength-dependent interactions are modestly developed in the transition state. The slope is, however, greater than that of a plot of DeltaG(not equal) versus DeltaG0 constructed by varying pH, thus demonstrating directly that ionic-strength-dependent studies probe more than simple electrostatic interactions. Potential transition movement was probed by analysis of the denaturant, ionic strength cross-interaction parameters. The values are small but nonzero and positive, suggesting a small shift of the transition state toward the native state as the protein is destabilized, i.e., Hammond behavior. The complications that arise in the interpretation of ionic-strength-dependent rate equilibrium free-energy relationships are discussed, and it is concluded that the ionic-strength-dependent studies do not provide a reliable indicator of the role of electrostatic interactions. Complications include incomplete screening of electrostatic interactions, specific ion binding, Hofmeister effects, and the potential presence of electrostatic interactions in the denatured state ensemble.     

REACH coarse-grained biomolecular simulation: transferability between different protein structural classes

Coarse graining of protein interactions provides a means of simulating large biological systems. The REACH (Realistic Extension Algorithm via Covariance Hessian) coarse-graining method, in which the force constants of a residue-scale elastic network model are calculated from the variance-covariance matrix obtained from atomistic molecular dynamics (MD) simulation, involves direct mapping between scales without the need for iterative optimization. Here, the transferability of the REACH force field is examined between protein molecules of different structural classes. As test cases, myoglobin (all α), plastocyanin (all β), and dihydrofolate reductase (α/β) are taken. The force constants derived are found to be closely similar in all three proteins. An MD version of REACH is presented, and low-temperature coarse-grained (CG) REACH MD simulations of the three proteins are compared with atomistic MD results. The mean-square fluctuations of the atomistic MD are well reproduced by the CGMD. Model functions for the CG interactions, derived by averaging over the three proteins, are also shown to produce fluctuations in good agreement with the atomistic MD. The results indicate that, similarly to the use of atomistic force fields, it is now possible to use a single, generic REACH force field for all protein studies, without having first to derive parameters from atomistic MD simulation for each individual system studied. The REACH method is thus likely to be a reliable way of determining spatiotemporal motion of a variety of proteins without the need for expensive computation of long atomistic MD simulations.     

Functions and Roles of Proteins: Diabetes as a Paradigm

Molecular and cellular biology has moved towards complete and accurate knowledge of how molecules behave in space and time. Protein is considered as the primary group of molecules responsible for mediating most physiological processes. Changes in the levels of proteins may lead to the altered function and are responsible for many diseases. This review provides a partial molecular explanation of biological force-ratio generation that may act to split protein into branches, and shows molecular functional divergence. Developing a non-reductionist theory of the cellular function in medicine is clearly not sufficient. Finding effective parameters of the models by characterizing molecular interactions becomes necessary. Protein interactivity and stability provides a basis for an integrated understanding of pathologies such diabetes. One example of how a mechanistic analysis of such physiological processes can be of value is the time-delay between mRNA and translation that can act as a fork allowing a slowdown in gene expression.     

Measuring the stability of partly folded proteins using TMAO

Standard methods for measuring free energy of protein unfolding by chemical denaturation require complete folding at low concentrations of denaturant so that a native baseline can be observed. Alternatively, proteins that are completely unfolded in the absence of denaturant can be folded by addition of the osmolyte trimethylamine N-oxide (TMAO), and the unfolding free energy can then be calculated through analysis of the refolding transition. However, neither chemical denaturation nor osmolyte-induced refolding alone is sufficient to yield accurate thermodynamic unfolding parameters for partly folded proteins, because neither method produces both native and denatured baselines in a single transition. Here we combine urea denaturation and TMAO stabilization as a means to bring about baseline-resolved structural transitions in partly folded proteins. For Barnase and the Notch ankyrin domain, which both show two-state equilibrium unfolding, we found that DeltaG degrees for unfolding depends linearly on TMAO concentration, and that the sensitivity of DeltaG degrees to urea (the m-value) is TMAO independent. This second observation confirms that urea and TMAO exert independent effects on stability over the range of cosolvent concentrations required to bring about baseline-resolved structural transitions. Thermodynamic parameters calculated using a global fit that assumes additive, linear dependence of DeltaG degrees on each cosolvent are similar to those obtained by standard urea-induced unfolding in the absence of TMAO. Finally, we demonstrate the applicability of this method to measurement of the free energy of unfolding of a partly folded protein, a fragment of the full-length Notch ankyrin domain.     

Fluorescence correlation spectroscopy: past, present, future

In recent years fluorescence correlation spectroscopy (FCS) has become a routine method for determining diffusion coefficients, chemical rate constants, molecular concentrations, fluorescence brightness, triplet state lifetimes, and other molecular parameters. FCS measures the spatial and temporal correlation of individual molecules with themselves and so provides a bridge between classical ensemble and contemporary single-molecule measurements. It also provides information on concentration and molecular number fluctuations for nonlinear reaction systems that complement single-molecule measurements. Typically implemented on a fluorescence microscope, FCS samples femtoliter volumes and so is especially useful for characterizing small dynamic systems such as biological cells. In addition to its practical utility, however, FCS provides a window on mesoscopic systems in which fluctuations from steady states not only provide the basis for the measurement but also can have important consequences for the behavior and evolution of the system. For example, a new and potentially interesting field for FCS studies could be the study of nonequilibrium steady states, especially in living cells.     

A thermodynamic molecular switch in biological systems: ribonuclease S' fragment complementation reactions

It is well known that essentially all biological systems function over a very narrow temperature range. Most typical macromolecular interactions show DeltaH degrees (T) positive (unfavorable) and a positive DeltaS degrees (T) (favorable) at low temperature, because of a positive (DeltaCp degrees /T). Because DeltaG degrees (T) for biological systems shows a complicated behavior, wherein DeltaG degrees (T) changes from positive to negative, then reaches a negative value of maximum magnitude (favorable), and finally becomes positive as temperature increases, it is clear that a deeper-lying thermodynamic explanation is required. This communication demonstrates that the critical factor is a temperature-dependent DeltaCp degrees (T) (heat capacity change) of reaction that is positive at low temperature but switches to a negative value at a temperature well below the ambient range. Thus the thermodynamic molecular switch determines the behavior patterns of the Gibbs free energy change and hence a change in the equilibrium constant, K(eq), and/or spontaneity. The subsequent, mathematically predictable changes in DeltaH degrees (T), DeltaS degrees (T), DeltaW degrees (T), and DeltaG degrees (T) give rise to the classically observed behavior patterns in biological reactivity, as may be seen in ribonuclease S' fragment complementation reactions.     

Instantaneous Normal Modes and the Protein Glass Transition

In the instantaneous normal mode method, normal mode analysis is performed at instantaneous configurations of a condensed-phase system, leading to modes with negative eigenvalues. These negative modes provide a means of characterizing local anharmonicities of the potential energy surface. Here, we apply instantaneous normal mode to analyze temperature-dependent diffusive dynamics in molecular dynamics simulations of a small protein (a scorpion toxin). Those characteristics of the negative modes are determined that correlate with the dynamical (or glass) transition behavior of the protein, as manifested as an increase in the gradient with T of the average atomic mean-square displacement at ∼220 K. The number of negative eigenvalues shows no transition with temperature. Further, although filtering the negative modes to retain only those with eigenvectors corresponding to double-well potentials does reveal a transition in the hydration water, again, no transition in the protein is seen. However, additional filtering of the protein double-well modes, so as to retain only those that, on energy minimization, escape to different regions of configurational space, finally leads to clear protein dynamical transition behavior. Partial minimization of instantaneous configurations is also found to remove nondiffusive imaginary modes. In summary, examination of the form of negative instantaneous normal modes is shown to furnish a physical picture of local diffusive dynamics accompanying the protein glass transition.     

Mean and variance of the Gibbs free energy of oligonucleotides in the nearest neighbor model under varying conditions

MOTIVATION: In order to assess the stability of DNA-DNA hybridizations-for example during PCR primer design or oligonucleotide selection for microarrays-one needs to predict the change in Gibbs free energy DeltaG during hybridization. The nearest neighbor model provides a good compromise between accuracy and computational simplicity for this task. To determine optimal combinations of reaction parameters (temperature, salt concentration, oligonucleotide length and GC-content), one would like to understand how DeltaG depends on all of these parameters simultaneously. RESULTS: We derive analytic results about the distribution of nearest neighbor DeltaG values for a Bernoulli random sequence model (specified by oligonucleotide length and average GC-content) under given experimental conditions. We find that the distribution of DeltaG values is approximately Gaussian and provide exact formulas for expectation and variance.     

Imaging molecular interactions in living cells by FRET microscopy

F?rster resonance energy transfer (FRET) is applied extensively in all fields of biological research and technology, generally as a 'nanoruler' with a dynamic range corresponding to the intramolecular and intermolecular distances characterizing the molecular structures that regulate cellular function. The complex underlying network of interactions reflects elementary reactions operating under strict spatio-temporal control: binding, conformational transition, covalent modification and transport. FRET imaging provides information about all these molecular processes with high specificity and sensitivity via probes expressed by or introduced from the external medium into the cell, tissue or organism. Current approaches and developments in the field are discussed with emphasis on formalism, probes and technical implementation.     

Vibrational Dynamics of Icosahedrally Symmetric Biomolecular Assemblies Compared with Predictions Based on Continuum Elasticity

Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses.