Energy Landscape Of Proteins Research Articles

The ruggedness of protein–protein energy landscape and the cutoff for 1/r n potentials

Computational studies of the energetics of protein association are important for revealing the underlying fundamental principles and for designing better tools to model protein complexes. The interaction cutoff contribution to the ruggedness of protein-protein energy landscape is studied in terms of relative energy fluctuations for 1/r(n) potentials based on a simplistic model of a protein complex. This artificial ruggedness exists for short cutoffs and gradually disappears with the cutoff increase. The critical values of the cutoff were calculated for each of 11 popular power-type potentials with n=0/9, 12 and for two thresholds of 5% and 10%. The artificial ruggedness decreases to tolerable thresholds for cutoffs larger than the critical ones. The results showed that for both thresholds the critical cutoff is a non-monotonic function of the potential power n. The functions reach the maximum at n=3/4 and then decrease with the increase of the potential power. The difference between two cutoffs for 5% and 10% artificial ruggedness becomes negligible for potentials decreasing faster than 1/r(12). The analytical results obtained for the simple model of protein complexes agree with the analysis of artificial ruggedness in a dataset of 62 protein-protein complexes, with different parameterizations of soft Lennard-Jones potential and two types of protein representations: all-atom and coarse-grained. The results suggest that cutoffs larger than the critical ones can be recommended for protein-protein potentials.

Electrostatic effects on funneled landscapes and structural diversity in denatured protein ensembles

The denatured state of proteins is heterogeneous and susceptible to general hydrophobic and electrostatic forces, but to what extent does the funneled nature of protein energy landscapes play a role in the unfolded ensemble? We simulate the denatured ensemble of cytochrome c using a series of models. The models pinpoint the efficacy of incorporating energetic funnels toward the native state in contrast with models having no native structure-seeking tendency. These models also contain varying strengths of electrostatic effects and hydrophobic collapse. The simulations based on these models are compared with experimental distributions for the distances between a fluorescent donor and the heme acceptor that were extracted from time-resolved fluorescence energy transfer experiments on cytochrome c. Comparing simulations to detailed experimental data on several labeling sites allows us to quantify the dominant forces in denatured protein ensembles.

Calmodulin in Action

The ability to apply force to single molecules has allowed the controlled investigation of protein energy landscapes. However, limits in resolution have meant that studies have mainly been carried out at nonequilibrium, so that only unfolding and unbinding reactions could be investigated. Now Junker et al. (see the Perspective by Best and Hummer) have used a custom-built low-drift atomic force microscope to observe directly fluctuations of single calmodulin molecules under equilibrium conditions in the presence of Ca 2+ and target peptides. The results show how ligand binding modulates the folding dynamics of calmodulin. J. P. Junker, F. Ziegler, M. Rief, Ligand-dependent equilibrium fluctuations of single calmodulin molecules. Science 323 , 633–637 (2009). [Abstract][Full Text] R. B. Best, G. Hummer, Unfolding the secrets of calmodulin. Science 323 , 593–594 (2009). [Summary][Full Text]

Using Pressure Perturbation for Studying the Free Energy and Conformational Landscape of Proteins Upon Aggregation and Amyloid Formation

Pressure tuning in combination with calorimetric, spectroscopic and structural techniques (DSC, PPC, FTIR, SAXS, AFM) revealed new insights into the pre-aggregated regime as well as mechanistic details about concurrent aggregation pathways and the differential stability of insulin aggregates. A thorough thermodynamic approach has provided a coherent and precise description of changes of the partial specific volume, heat capacity, the coefficient of thermal expansion, as well as the adiabatic and isothermal compressibility of the protein upon unfolding and aggregation. This was only possible due to a novel application of ultrasound velocimetry and pressure perturbation calorimetry. Besides pressure, also solvational perturbations, accomplished by the addition of various salts and cosolvents such as glycerol, ethanol and TFE, have been explored. They exert pronounced and diversified effects on the unfolding, non-native assembly and fibril formation, which ultimately manifest in morphological variations of mature aggregates and fibrils (strains). The phenomenon of strains easily fits to a generalized protein energy landscape picture involving an alternative comb-shaped aggregation funnel. The pressure variable has also been explored to study more disease related amyloidogenic proteins, such as PrP and IAPP. Several examples will be given.

Residue‐wise conformational stability of DLC8 dimer from native‐state hydrogen exchange

Dynein light chain (DLC8) is the smallest subunit of the dynein motor complex, which is known to act as a cargo adaptor in intracellular trafficking. The protein exists as a pure dimer at physiological pH and a completely folded monomer below pH 4. Here, we have determined the energy landscape of the dimeric protein using a combination of optical techniques and native-state hydrogen exchange of amide groups, the former giving the global features and the latter yielding the residue level details. The data indicated the presence of intermediates along the equilibrium unfolding transition. The hydrogen exchange data suggested that the molecule has differential stability in its various segments. We deduce from the free energy data that the antiparallel beta-sheets (beta4 and beta5) that form the hydrophobic core of the protein and the alpha2 helix, all of which are highly protected with regard to hydrogen exchange, contribute significantly to the initial step of the protein folding mechanism. Denaturant-dependent hydrogen exchange indicated further that some amides exchange via local fluctuations, whereas there are others which exchange via global unfolding events. Implications of these to cargo adaptability of the dimer are discussed.

Folding energy landscape and network dynamics of small globular proteins

The folding energy landscape of proteins has been suggested to be funnel-like with some degree of ruggedness on the slope. How complex the landscape, however, is still rather unclear. Many experiments for globular proteins suggested relative simplicity, whereas molecular simulations of shorter peptides implied more complexity. Here, by using complete conformational sampling of 2 globular proteins, protein G and src SH3 domain and 2 related random peptides, we investigated their energy landscapes, topological properties of folding networks, and folding dynamics. The projected energy surfaces of globular proteins were funneled in the vicinity of the native but also have other quite deep, accessible minima, whereas the randomized peptides have many local basins, including some leading to seriously misfolded forms. Dynamics in the denatured part of the network exhibited basin-hopping itinerancy among many conformations, whereas the protein reached relatively well-defined final stages that led to their native states. We also found that the folding network has the hierarchic nature characterized by the scale-free and the small-world properties.

The spectrum of biomolecular states and motions.

The universe of conformational substates of a protein molecule is huge. The complete energy landscape of proteins is, therefore, complex when studied at low temperature. Many experiments under physiological conditions commonly reveal a simpler spectrum of states. These states are individually ensembles of low temperature substates. That is, room temperature experiments probe the low free energy part of the spectrum of excitations. This paper describes how the complete landscape and the spectrum of these thermally excited motions can be related to each other. On funneled landscapes, partially folded ensembles of states are the most important excited states. Their properties and their free energy spectrum can often be predicted by native topology based models. Frustration, i.e., the conflict between inconsistent stabilizing interactions that have evolved for other purposes than optimizing folding, offers another mechanism for forming low free energy excitations. Frustration can be localized and quantified using energy landscape theory. Symmetry provides an obvious route to low free energy states in oligomeric systems, where simply repositioning parts of the molecule in ways quasi-equivalent to their relation in the native structure gives nearly degenerate energies.

Protein energy landscape roughness

The 'new view' of proteins sees protein reactions as parallel processes occurring along funnelled energy landscapes. These landscapes are generally not smooth, but are superimposed by hills and valleys of different heights and widths leading to roughness on the energy surface. In the present paper, we describe the origins of protein energy landscape roughness, measurements of its scale and its implications.

Navigating the Folding Energy Landscape of Green Fluorescent Protein

Navigating the Folding Energy Landscape of Green Fluorescent Protein

New method for deciphering free energy landscape of three-state proteins

We have developed a new simulation method to estimate the distance between the native state and the first transition state and the distance between the intermediate state and the second transition state of a protein which mechanically unfolds via intermediates. Assuming that the end-to-end extension DeltaR is a good reaction coordinate to describe the free energy landscape of proteins subjected to an external force, we define the midpoint extension DeltaR(*) between two transition states from either constant force or constant loading rate pulling simulations. In the former case, DeltaR(*) is defined as a middle point between two plateaus in the time-dependent curve of DeltaR, while, in the latter one, it is a middle point between two peaks in the force-extension curve. Having determined DeltaR(*), one can compute times needed to cross two transition state barriers starting from the native state. With the help of the Bell and microscopic kinetic theory, force dependencies of these unfolding times can be used to locate the intermediate state and to extract unfolding barriers. We have applied our method to the titin domain I27 and the fourth domain of Dictyostelium discoideum filamin (DDFLN4) and obtained reasonable agreement with experiments, using the C(alpha)-Go model.

Probing force-induced unfolding intermediates of a single staphylococcal nuclease molecule and the effect of ligand binding

Single-molecule manipulation techniques have given experimental access to unfolding intermediates of proteins that are inaccessible in conventional experiments. A detailed characterization of the intermediates is a challenging problem that provides new possibilities for directly probing the energy landscape of proteins. We investigated single-molecule mechanical unfolding of a small globular protein, staphylococcal nuclease (SNase), using atomic force microscopy. The unfolding trajectories of the protein displayed sub-molecular and stochastic behavior with typical lengths corresponding to the size of the unfolded substructures. Our results support the view that the single protein unfolds along multiple pathways as suggested in recent theoretical studies. Moreover, we found the drastic change, caused by the ligand and inhibitor bindings, in the mechanical unfolding dynamics.

Role of pulling direction in understanding the energy landscape of proteins

Single-molecule force spectroscopy provide details of the underlying energy surfaces of proteins which are essential to the understanding of their unfolding process. Recently, it has been observed experimentally that by pulling proteins in different directions relative to their secondary structure, one can gain a better understanding of the shape of the energy landscape. We consider simple lattice models which are anisotropic in nature to study the response of a force in unfolding of a polymer. Our analytical solution of the model, supported by extensive numerical calculations, reveal that the force temperature diagrams are very different depending on the direction of the applied force. We find that either unzipping or shearing kind transitions dominate the dynamics of the unfolding process depending solely on the direction of the applied force.

High-throughput single-molecule force spectroscopy for membrane proteins

Atomic force microscopy-based single-molecule force spectroscopy (SMFS) is a powerfultool for studying the mechanical properties, intermolecular and intramolecularinteractions, unfolding pathways, and energy landscapes of membrane proteins. Onelimiting factor for the large-scale applicability of SMFS on membrane proteinsis its low efficiency in data acquisition. We have developed a semi-automatedhigh-throughput SMFS (HT-SMFS) procedure for efficient data acquisition. In addition, wepresent a coarse filter to efficiently extract protein unfolding events from large datasets. The HT-SMFS procedure and the coarse filter were validated using theproton pump bacteriorhodopsin (BR) from Halobacterium salinarum and theL-arginine/agmatine antiporter AdiC from the bacterium Escherichia coli. To screen formolecular interactions between AdiC and its substrates, we recorded data sets in theabsence and in the presence of L-arginine, D-arginine, and agmatine. Altogether∼400 000 force–distance curves were recorded. Application of coarse filtering to this wealth of data yielded six datasets with ∼200 (AdiC) and ∼400 (BR) force–distance spectra in each. Importantly, the raw data for most of these data setswere acquired in one to two days, opening new perspectives for HT-SMFS applications.

The Energy Landscapes of Repeat-Containing Proteins: Topology, Cooperativity, and the Folding Funnels of One-Dimensional Architectures

Repeat-proteins are made up of near repetitions of 20– to 40–amino acid stretches. These polypeptides usually fold up into non-globular, elongated architectures that are stabilized by the interactions within each repeat and those between adjacent repeats, but that lack contacts between residues distant in sequence. The inherent symmetries both in primary sequence and three-dimensional structure are reflected in a folding landscape that may be analyzed as a quasi–one-dimensional problem. We present a general description of repeat-protein energy landscapes based on a formal Ising-like treatment of the elementary interaction energetics in and between foldons, whose collective ensemble are treated as spin variables. The overall folding properties of a complete “domain” (the stability and cooperativity of the repeating array) can be derived from this microscopic description. The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (ΔGwater) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins. We show how the parameters for the “coarse-grained” description in terms of foldon spin variables can be extracted from more detailed folding simulations on perfectly funneled landscapes. To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions. Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are “poised” at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions.

From Valleys to Ridges: Exploring the Dynamic Energy Landscape of Single Membrane Proteins

Membrane proteins are involved in essential biological processes such as energy conversion, signal transduction, solute transport and secretion. All biological processes, also those involving membrane proteins, are steered by molecular interactions. Molecular interactions guide the folding and stability of membrane proteins, determine their assembly, switch their functional states or mediate signal transduction. The sequential steps of molecular interactions driving these processes can be described by dynamic energy landscapes. The conceptual energy landscape allows to follow the complex reaction pathways of membrane proteins while its modifications describe why and how pathways are changed. Single-molecule force spectroscopy (SMFS) detects, quantifies and locates interactions within and between membrane proteins. SMFS helps to determine how these interactions change with temperature, point mutations, oligomerization and the functional states of membrane proteins. Applied in different modes, SMFS explores the co-existence and population of reaction pathways in the energy landscape of the protein and thus reveals detailed insights into local mechanisms, determining its structural and functional relationships. Here we review how SMFS extracts the defining parameters of an energy landscape such as the barrier position, reaction kinetics and roughness with high precision.

Rerouting the Folding Pathway of the Notch Ankyrin Domain by Reshaping the Energy Landscape

The modular nature of repeat proteins has made them a successful target for protein design. Ankyrin repeat, TPR, and leucine rich repeat domains that have been designed solely on consensus information have been shown to have higher thermostability than their biological counterparts. We have previously shown that we can reshape the energy landscape of a repeat protein by adding multiple C-terminal consensus ankyrin repeats to the five N-terminal repeats of the Notch ankyrin domain. Here we explore how the folding mechanism responds to reshaping of the energy landscape. We have used analogous substitutions of a conserved alanine with glycine in each repeat to determine the distribution of structure in the transition state ensembles of constructs containing one (Nank1-5C1) and two consensus (Nank1-5C2) ankyrin repeats. Whereas folding of the wild-type Notch ankyrin domain is slowed by substitutions in its central repeats, (1) folding of Nank1-5C1 and Nank1-5C2 is slowed by substitutions in the C-terminal repeats. Thus, the addition of C-terminal stabilizing repeats shifts the transition state ensemble toward the C-terminal repeats, rerouting the folding pathway of the ankyrin repeat domain. These findings indicate that, for the Notch ankyrin domain, folding pathways are selected based on local energetics.

Manipulating and Detecting a Protein's Energy Landscape

We have developed a novel method to explore the single molecule behavior of proteins in the low force regime of the laser tweezers. Individual protein molecules are tethered between two polystyrene beads using two dsDNA molecules, which are in turn attached to the protein through unique engineered cysteine residues. One bead is held by suction on the tip of a pipette while the other is held in the optical trap. The force and distance between the beads is varied by moving the bead on the pipette relative to the bead in the trap. The DNA handles can be attached to any exposed cysteine residues, allowing a variety of pulling geometries to be used to investigate the anisotropy of the protein energy landscape. The low spring of laser tweezers enabled us to directly monitor low force refolding events and fluctuations between different molecular structures at quasi‐equilibrium conditions. Data exploring the behavior of different protein protein topologies, different pulling geometries and the relationship to bulk solution studies of the energy landscape will be presented.

Vertebrate Membrane Proteins: Structure, Function, and Insights from Biophysical Approaches

Membrane proteins are key targets for pharmacological intervention because they are vital for cellular function. Here, we analyze recent progress made in the understanding of the structure and function of membrane proteins with a focus on rhodopsin and development of atomic force microscopy techniques to study biological membranes. Membrane proteins are compartmentalized to carry out extra- and intracellular processes. Biological membranes are densely populated with membrane proteins that occupy approximately 50% of their volume. In most cases membranes contain lipid rafts, protein patches, or paracrystalline formations that lack the higher-order symmetry that would allow them to be characterized by diffraction methods. Despite many technical difficulties, several crystal structures of membrane proteins that illustrate their internal structural organization have been determined. Moreover, high-resolution atomic force microscopy, near-field scanning optical microscopy, and other lower resolution techniques have been used to investigate these structures. Single-molecule force spectroscopy tracks interactions that stabilize membrane proteins and those that switch their functional state; this spectroscopy can be applied to locate a ligand-binding site. Recent development of this technique also reveals the energy landscape of a membrane protein, defining its folding, reaction pathways, and kinetics. Future development and application of novel approaches during the coming years should provide even greater insights to the understanding of biological membrane organization and function.

Mapping the Energy Landscape of Repeat Proteins using NMR-detected Hydrogen Exchange

Repeat proteins contain tandem arrays of a simple structural motif. In contrast to globular proteins, repeat proteins are stabilized only by interactions between residues that are relatively close together in the sequence, with no ”long-range” interactions. Our work focuses on the tetratricopeptide repeat (TPR), a 34 amino acid helix-turn-helix motif found in tandem arrays in many natural proteins. Earlier, we reported the design and characterization of a series of consensus TPR (CTPR) proteins, which are built as arrays of multiple tandem copies of a 34 amino acid consensus sequence. Here, we present the results of extensive hydrogen exchange (HX) studies of the folding–unfolding behavior of two CTPR proteins (CTPR2 and CTPR3). We used HX to detect and characterize partially folded species that are populated at low frequency in the nominally folded state. We show that for both proteins the equilibrium folding–unfolding transition is non-two-state, but sequential, with the outermost helices showing a significantly higher probability than inner helices of being unfolded. We show that the experimentally observed unfolding behavior is consistent with the predictions of a simple Ising model, in which individual helices are treated as ”spin-equivalents”. The results that we present have general implications for our understanding of the thermodynamic properties of repeat proteins.

Hidden structure in protein energy landscapes

Inherent structure theory is used to discover strong connections between simple characteristics of protein structure and the energy landscape of a Gō model. The potential energies and vibrational free energies of inherent structures are highly correlated, and both reflect simple measures of networks of native contacts. These connections have important consequences for models of protein dynamics and thermodynamics.