Energy Landscape Of Proteins Research Articles

Point Mutations in Membrane Proteins Reshape Energy Landscape and Populate Different Unfolding Pathways

Using single-molecule force spectroscopy, we investigated the effect of single point mutations on the energy landscape and unfolding pathways of the transmembrane protein bacteriorhodopsin. We show that the unfolding energy barriers in the energy landscape of the membrane protein followed a simple two-state behavior and represent a manifestation of many converging unfolding pathways. Although the unfolding pathways of wild-type and mutant bacteriorhodopsin did not change, indicating the presence of same ensemble of structural unfolding intermediates, the free energies of the rate-limiting transition states of the bacteriorhodopsin mutants decreased as the distance of those transition states to the folded intermediate states decreased. Thus, all mutants exhibited Hammond behavior and a change in the free energies of the intermediates along the unfolding reaction coordinate and, consequently, their relative occupancies. This is the first experimental proof showing that point mutations can reshape the free energy landscape of a membrane protein and force single proteins to populate certain unfolding pathways over others.

A hierarchy of timescales in protein dynamics is linked to enzyme catalysis

The synergy between structure and dynamics is essential to the function of biological macromolecules. Thermally driven dynamics on different timescales have been experimentally observed or simulated, and a direct link between micro- to milli-second domain motions and enzymatic function has been established. However, very little is understood about the connection of these functionally relevant, collective movements with local atomic fluctuations, which are much faster. Here we show that pico- to nano-second timescale atomic fluctuations in hinge regions of adenylate kinase facilitate the large-scale, slower lid motions that produce a catalytically competent state. The fast, local mobilities differ between a mesophilic and hyperthermophilic adenylate kinase, but are strikingly similar at temperatures at which enzymatic activity and free energy of folding are matched. The connection between different timescales and the corresponding amplitudes of motions in adenylate kinase and their linkage to catalytic function is likely to be a general characteristic of protein energy landscapes.

Probing Protein Fold Space with a Simplified Model

We probe the stability and near-native energy landscape of protein fold space using powerful conformational sampling methods together with simple reduced models and statistical potentials. Fold space is represented by a set of 280 protein domains spanning all topological classes and having a wide range of lengths (33–300 residues) amino acid composition and number of secondary structural elements. The degrees of freedom are taken as the loop torsion angles. This choice preserves the native secondary structure but allows the tertiary structure to change. The proteins are represented by three-point per residue, three-dimensional models with statistical potentials derived from a knowledge-based study of known protein structures. When this space is sampled by a combination of parallel tempering and equi-energy Monte Carlo, we find that the three-point model captures the known stability of protein native structures with stable energy basins that are near-native (all α: 4.77 Å, all β: 2.93 Å, α/β: 3.09 Å, α+β: 4.89 Å on average and within 6 Å for 71.41%, 92.85%, 94.29% and 64.28% for all-α, all-β, α/β and α+β, classes, respectively). Denatured structures also occur and these have interesting structural properties that shed light on the different landscape characteristics of α and β folds. We find that α/β proteins with alternating α and β segments (such as the β-barrel) are more stable than proteins in other fold classes.

Picosecond fluctuating protein energy landscape mapped by pressure–temperature molecular dynamics simulation

Microscopic statistical pressure fluctuations can, in principle, lead to corresponding fluctuations in the shape of a protein energy landscape. To examine this, nanosecond molecular dynamics simulations of lysozyme are performed covering a range of temperatures and pressures. The well known dynamical transition with temperature is found to be pressure-independent, indicating that the effective energy barriers separating conformational substates are not significantly influenced by pressure. In contrast, vibrations within substates stiffen with pressure, due to increased curvature of the local harmonic potential in which the atoms vibrate. The application of pressure is also shown to selectively increase the damping of the anharmonic, low-frequency collective modes in the protein, leaving the more local modes relatively unaffected. The critical damping frequency, i.e., the frequency at which energy is most efficiently dissipated, increases linearly with pressure. The results suggest that an invariant description of protein energy landscapes should be subsumed by a fluctuating picture and that this may have repercussions in, for example, mechanisms of energy dissipation accompanying functional, structural, and chemical relaxation.

Protein mechanical unfolding: A model with binary variables

A simple model, recently introduced as a generalization of the Wako-Saito; model of protein folding, is used to investigate the properties of widely studied molecules under external forces. The equilibrium properties of the model proteins, together with their energy landscape, are studied on the basis of the exact solution of the model. Afterwards, the kinetic response of the molecules to a force is considered, discussing both force clamp and dynamic loading protocols and showing that theoretical expectations are verified. The kinetic parameters characterizing the protein unfolding are evaluated by using computer simulations and agree nicely with experimental results, when these are available. Finally, the extended Jarzynski equality is exploited to investigate the possibility of reconstructing the free energy landscape of proteins with pulling experiments.

Interaction cutoff effect on ruggedness of protein–protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.

Effects of Serine-to-Cysteine Mutations on β-Lactamase Folding

B. licheniformis exo-small β-lactamase (ESBL) has two nonsequential domains and a complex architecture. We replaced ESBL serine residues 126 and 265 with cysteine to probe the conformation of buried regions in each domain. Spectroscopic, hydrodynamic, and chemical methods revealed that the mutations do not alter the native fold but distinctly change stability (S-126C > wild-type > S-126/265C > S-265C ESBL) and the features of partially folded states. The observed wild-type ESBL equilibrium intermediate has decreased fluorescence but full secondary structure. S-126C ESBL intermediate has the fluorescence of the unfolded state, no thiol reactivity, and partial secondary structure. S-265C and S-126/265C ESBL populate intermediate states unfolded by fluorescence and thiol reactivity but with full secondary structure. Mass analysis of S-126/265C ESBL in the partially folded state proved that both thiol groups become exposed simultaneously. None of the intermediates is compatible with sequential domain unfolding. Molecular dynamics simulation suggests that the stabilizing effect of the S-126C substitution is due to optimization of van der Waals interactions and packing. On the other hand, destabilization induced by the S-265C mutation results from alteration of the hydrogen-bond network. The results illustrate the large impact that seemingly conservative serine-to-cysteine changes can have on the energy landscape of proteins.

Sampling of states for estimating the folding funnel entropy and energy landscape of a model alpha-helical hairpin peptide

Protein folding times are many orders of magnitude shorter than would occur if the peptide chain randomly sampled possible configurations, which implies that protein folding is a directed process. The detailed shape of protein's energy landscape determines the rate and reliability of folding to the native state, but the large number of structural degrees of freedom generates an energy landscape that is hard to visualize because of its high dimensionality. A commonly used picture is that of an energy funnel leading from high energy random coil state down to the low energy native state. As lattice computer models of protein dynamics become more realistic, the number of possible configurations becomes too large to count directly. Statistical mechanic and thermodynamic approaches allow us to count states in an approximate manner to quantify the entropy and energy of the energy landscape within a folding funnel for an alpha-helical protein. We also discuss the problems that arise in attempting to count the huge number of individual states of the random coil at the top of the funnel.

Energetics of the Native Energy Landscape of a Two-Domain Calcium Sensor Protein: Distinct Folding Features of the Two Domains

The protein folding energy landscape allows a thorough understanding of the protein folding problem which in turn helps in understanding various aspects of biological functions. Characterizing the cooperative unfolding units and the intermediates along the folding funnel of a protein is a challenging task. In this paper, we investigated the native energy landscape of EhCaBP, a calcium sensor, belonging to the same EF-hand superfamily as calmodulin. EhCaBP is a two-domain EF-hand protein consisting of two EF-hands in each domain and binding to four Ca2+ cations. Native-state hydrogen exchange (HX) was used to assess the folding features of the landscape and also to throw light on the structure-folding function paradigm of calcium sensor proteins. HX measurements under the EX2 regime provided the thermodynamic information about the protein folding events under native conditions. HX studies revealed that the unfolding of EhCaBP is not a two-state process. Instead, it proceeds through cooperative units. The C-terminal domain exhibits less denaturant dependence than the N-terminal domain, suggesting that the former is dominated by local fluctuations. It is interesting to note that the N- and C-terminal domains of EhCaBP have distinct folding features. In fact, these observed differences can regulate the domain-dependent target recognition of two-domain Ca2+ sensor proteins.

Cooperative propagation of local stability changes from low‐stability and high‐stability regions in a SH3 domain

Site-directed mutagenesis has been used to produce local stability changes at two regions of the binding site surface of the alpha-spectrin SH3 domain (Spc-SH3) differing in their intrinsic stability. Mutations were made at residue 56, located at the solvent-exposed side of the short 3(10) helix, and at residue 21 in the tip of the flexible RT-loop. NMR chemical-shift analysis and X-ray crystallography indicated negligible changes produced by the mutations in the native structure limited to subtle rearrangements near the mutated residue and at flexible loops. Additionally, mutations do not alter importantly the SH3 binding site structure, although produce significant changes in its affinity for a proline-rich decapeptide. The changes in global stability measured by differential scanning calorimetry are consistent the local energy changes predicted by theoretical models, with the most significant effects observed for the Ala-Gly mutations. Propagation of the local stability changes throughout the domain structure has been studied at a per-residue level of resolution by NMR-detected amide hydrogen-deuterium exchange (HX). Stability propagation is remarkably efficient in this small domain, apparently due to its intrinsically low stability. Nevertheless, the HX-core of the domain is not fully cooperative, indicating the existence of co-operative subunits within the core, which is markedly polarized. An equilibrium phi-analysis of the changes in the apparent Gibbs energies of HX per residue produced by the mutations has allowed us to characterize structurally the conformational states leading to HX. Some of these states resemble notably the folding transition state of the Spc-SH3 domain, suggesting a great potential of this approach to explore the folding energy landscape of proteins. An energy perturbation propagates more effectively from a flexible region to the core than in the opposite direction, because the former affects a broader region of the energy landscape than the latter. This might be of importance in understanding the special thermodynamic signature of the SH3-peptide interaction and the relevance of the dual character of SH3 binding sites.

Novel characteristics of persistent spectral hole-burning and hole-filling in Photosystem II core complexes

We report spectral hole-burning as well as spontaneous and photo-induced hole-filling in Photosystem II (PSII) core complexes. A comparison is made between measurements on initially dark-adapted PSII cores in which the plastoquinone Q A is either neutral or photo-reduced to Q A - by illumination at 1.7 K, with samples where Q A is reduced by either 260 K illumination or chemical treatment. The latter preparations have the advantage of exhibiting minimal change in Q A - with either time or illumination at 1.7 K. This stability allowed us to investigate the association of rapid hole-filling reported for PSII core complexes with the spontaneous re-oxidation of Q A - , which occurs in dark-adapted samples after 1.7 K illumination. We find that spontaneous hole-filling also occurs in PSII with stable Q A - configurations. In either class of sample, spontaneous hole-filling occurs at significantly greater rates than for ‘normal’ two level system hole-burning processes in chlorophyll-protein antenna complexes. It is suggested that the rapid spontaneous hole-filling is associated with protein relaxation within the energy landscape of the PSII core proteins. This landscape may also be involved in influencing other processes such as low-temperature Q A reduction and re-oxidation. Shallow holes burnt in Q A samples exhibit a narrow ( ∼ 2 cm - 1 ) photoproduct on the low energy side of the hole. Subsequent illumination of holes burnt at 690 nm with 705 nm light induces strong hole-filling. These results are discussed with respect to charge and excitation energy transfer processes in PSII cores.

2P107 タンパク質フォールディングのエネルギー地形とネットワーク : マルチカノニカル・フラグメントアセンブリシミュレーション(蛋白質(物性(安定性、折れ畳みなど)),口頭発表,第45回日本生物物理学会年会)

2P107 タンパク質フォールディングのエネルギー地形とネットワーク : マルチカノニカル・フラグメントアセンブリシミュレーション(蛋白質(物性(安定性、折れ畳みなど)),口頭発表,第45回日本生物物理学会年会)

The effects of cosolutes on protein dynamics: The reversal of denaturant‐induced protein fluctuations by trimethylamine N‐oxide

The protein stabilizing effects of the small molecule osmolyte, trimethylamine N-oxide, against chemical denaturant was investigated by NMR spin-relaxation measurements and model-free analysis. In the presence of 0.7 M guanidine hydrochloride increased picosecond-nanosecond dynamics are observed in the protein ribonuclease A. These increased fluctuations occur throughout the protein, but the most significant increases in flexibility occur at positions believed to be the first to unfold. Addition of 0.35 M trimethylamine N-oxide to this destabilized form of ribonuclease results in significant rigidification of the protein backbone as assessed by (1)H-(15)N order parameters. Statistically, these order parameters are the same as those measured in native ribonuclease indicating that TMAO reduces the amplitude of backbone fluctuations in a destabilized protein. These data suggest that TMAO restricts the bond vector motions on the protein energy landscape to resemble those motions that occur in the native protein and points to a relation between stability and dynamics in this enzyme.

Curvature of the Energy Landscape and Folding of Model Proteins

We study the geometric properties of the energy landscape of coarse-grained, off-lattice models of polymers by endowing the configuration space with a suitable metric, depending on the potential energy function, such that the dynamical trajectories are the geodesics of the metric. Using numerical simulations, we show that the fluctuations of the curvature clearly mark the folding transition, and that this quantity allows to distinguish between polymers having a proteinlike behavior (i.e., that fold to a unique configuration) and polymers which undergo a hydrophobic collapse but do not have a folding transition. These geometrical properties are defined by the potential energy without requiring any prior knowledge of the native configuration.

Pressure-Jump-Induced Kinetics Reveals a Hydration Dependent Folding/Unfolding Mechanism of Ribonuclease A

Pressure-jump ( p-jump)-induced relaxation kinetics was used to explore the energy landscape of protein folding/unfolding of Y115W, a fluorescent variant of ribonuclease A. Pressure-jumps of 40 MPa amplitude (5 ms dead-time) were conducted both to higher (unfolding) and to lower (folding) pressure, in the range from 100 to 500 MPa, between 30 and 50°C. Significant deviations from the expected symmetrical protein relaxation kinetics were observed. Whereas downward p-jumps resulted always in single exponential kinetics, the kinetics induced by upward p-jumps were biphasic in the low pressure range and monophasic at higher pressures. The relative amplitude of the slow phase decreased as a function of both pressure and temperature. At 50°C, only the fast phase remained. These results can be interpreted within the framework of a two-dimensional energy surface containing a pressure- and temperature-dependent barrier between two unfolded states differing in the isomeric state of the Asn-113–Pro-114 bond. Analysis of the activation volume of the fast kinetic phase revealed a temperature-dependent shift of the unfolding transition state to a larger volume. The observed compensation of this effect by glycerol offers an explanation for its protein stabilizing effect.

Exploring the relationship between funneled energy landscapes and two‐state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

Multiple routes lead to the native state in the energy landscape of the β-trefoil family

In general, the energy landscapes of real proteins are sufficiently well designed that the depths of local energetic minima are small compared with the global bias of the native state. Because of the funneled nature of energy landscapes, models that lack energetic frustration have been able to capture the main structural features of the transition states and intermediates found in experimental studies of both small and large proteins. In this study we ask: Are the experimental differences in folding mechanisms among members of a particular structural family due to local topological constraints that deviate from the tertiary fold common to the family? The beta-trefoil structural family members IL-1beta, hisactophilin, and acidic/basic FGFs were chosen to address this question. It has been observed that the topological landscape of the beta-trefoils allows for the population of diverse, geometrically disconnected routes that provide energetically similar but structurally distinct ways for this family to fold. Small changes in topology or energetics can alter the preferred route. Taken together, these results indicate that the global fold of the beta-trefoil family determines the energy landscape but that the routes accessed on that landscape might differ as a result of functional requirements of the individual family members.

Diversity in free energy landscape and folding pathway of proteins with the same native topology

To elucidate the role of relative stability of subdomains in folding processes of multi-domain proteins, we have studied a free-energy landscape of c-type lysozyme by Monte Carlo simulations using a realistic lattice model with a Gō-like interaction. By varying the relative interaction strength of two subdomains as a parameter, we obtained a variety of the free-energy landscapes. Experimentally-observed diversity in folding processes of c-type lysozymes can then be described by this Gō-like model with only one variable parameter. The result demonstrates that folding of multi-domain proteins can be understood in the framework of the energy landscape theory.

Mapping the Energy Landscape of Biomolecules Using Single Molecule Force Correlation Spectroscopy: Theory and Applications

We present, to our knowledge, a new theory that takes internal dynamics of proteins into account to describe forced-unfolding and force-quench refolding in single molecule experiments. In the current experimental setup (using either atomic force microscopy or laser optical tweezers) the distribution of unfolding times, P( t), is measured by applying a constant stretching force f S from which the apparent f S-dependent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy to map the parameters of the energy landscape of proteins. In force correlation spectroscopy, the joint distribution P( T, t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant f S separated by release periods T during which the force is quenched to f Q < f S. During the release period, the protein can collapse to a manifold of compact states or refold. We show that P( T, t) at various f S and f Q values can be used to resolve the kinetics of unfolding as well as formation of native contacts. We also present methods to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P( T, t). The theory and a wormlike chain model for the unfolded states allows us to obtain the persistence length l p and the f Q-dependent relaxation time, giving us an estimate of collapse timescale at the single molecular level, in the coil states of the polypeptide chain. Thus, a more complete description of landscape of protein native interactions can be mapped out if unfolding time data are collected at several values of f S and f Q. We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein ( S1) with β-sheet architecture for several values of f S, T, and f Q = 0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.

Dynamic Distance Disorder in Proteins Is Caused by Trapping

Dynamic disorder in proteins, as demonstrated by variations in single-molecule electron transfer rates, is investigated by molecular dynamics simulations. The potential of mean force for the fluctuating donor-acceptor distance is calculated for the NAD(P)H:flavin oxidoreductase (Fre) complex with flavin adenine dinucleotide (FAD) and is found to be in agreement with that estimated from electron transfer experiments. The calculated autocorrelation function of the distance fluctuations has a simple exponential behavior at low temperatures and stretched exponential behavior at higher temperatures on femtosecond to nanosecond time scales. This indicates that the calculated dynamic disorder arises from a wide range of trapping times in potential wells on the protein energy landscape and suggests a corresponding origin for the stretched exponential behavior observed experimentally on longer time scales.