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.     

Topological properties of the energy landscape of small peptides

The topology of the potential energy landscape (PEL) underlying the dynamics of a two dimensional off-lattice model for a heteropolymer is analyzed for different sequences of amino-acids. A statistical characterization of the metastable minima and first-order saddles of the PEL highlights structural differences in the landscape of good and bad folding sequences and provides insight on the chain dynamics during folding.     

Topological properties of the energy landscape of small peptides

In several works it has been shown that the interplay between short range and long range interactions, mimicking the hydrophobic effect, leads to the formation of the typical secondary structures in proteins, alpha-helices and beta-sheets. In this work we study in detail how the general properties of the energy landscape emerge in a model that presents both components. In this regard it proves useful a sort of perturbative approach. In our model many features of the energy landscape in absence of long range interaction can be determined analytically. The comparison between the energy landscape of this reduced model to that of the complete model gives interesting insight on the role of long range interactions.     

The free energy landscape of small molecule unbinding

The spontaneous dissociation of six small ligands from the active site of FKBP (the FK506 binding protein) is investigated by explicit water molecular dynamics simulations and network analysis. The ligands have between four (dimethylsulphoxide) and eleven (5-diethylamino-2-pentanone) non-hydrogen atoms, and an affinity for FKBP ranging from 20 to 0.2 mM. The conformations of the FKBP/ligand complex saved along multiple trajectories (50 runs at 310 K for each ligand) are grouped according to a set of intermolecular distances into nodes of a network, and the direct transitions between them are the links. The network analysis reveals that the bound state consists of several subbasins, i.e., binding modes characterized by distinct intermolecular hydrogen bonds and hydrophobic contacts. The dissociation kinetics show a simple (i.e., single-exponential) time dependence because the unbinding barrier is much higher than the barriers between subbasins in the bound state. The unbinding transition state is made up of heterogeneous positions and orientations of the ligand in the FKBP active site, which correspond to multiple pathways of dissociation. For the six small ligands of FKBP, the weaker the binding affinity the closer to the bound state (along the intermolecular distance) are the transition state structures, which is a new manifestation of Hammond behavior. Experimental approaches to the study of fragment binding to proteins have limitations in temporal and spatial resolution. Our network analysis of the unbinding simulations of small inhibitors from an enzyme paints a clear picture of the free energy landscape (both thermodynamics and kinetics) of ligand unbinding.     

Experimental comparison of energy landscape features of ubiquitin family proteins

Small ubiquitin-related modifiers (SUMO1 and SUMO2) are ubiquitin family proteins, structurally similar to ubiquitin, differing in terms of their amino acid sequence and functions. Therefore, they provide a great platform for investigating sequence-structure-stability-function relationship. Here, we used chemical denaturation in comparing the folding-unfolding pathways of the SUMO proteins with their structural homologue ubiquitin (UF45W-pseudo wild-type [WT] tryptophan variant) with structurally analogous tryptophan mutations (SUMO1 [S1F66W], SUMO2 [S2F62W]). Equilibrium denaturation studies report that ubiquitin is the most stable protein among the three. The observed denaturant-dependent folding rates of SUMOs are much lower than ubiquitin and primarily exhibit a two-state folding pathway unlike ubiquitin, which has a kinetic folding intermediate. We hypothesize that, as SUMO proteins start off as slow folders, they avoid stabilizing their folding intermediates and the presence of which might further slow-down their folding rates. The denaturant-dependent unfolding of ubiquitin is the fastest, followed by SUMO2, and slowest for SUMO1. However, the spontaneous unfolding rate constant is the lowest for ubiquitin (~40 times), and similar for SUMOs. This correlation between thermodynamic stability and kinetic stability is achieved by having different unfolding transition state positions with respect to the solvent-accessible surface area, as quantified by the Tanford β _u values: ubiquitin (0.42) > SUMO2 (0.20) > SUMO1 (0.16). The results presented here highlight the unique energy landscape features which help in optimizing the folding-unfolding rates within a structurally homologous protein family.     

Prediction of the binding energy for small molecules,peptides and proteins

A fast and reliable evaluation of the binding energy from a single conformation of a molecular complex is an important practical task. Knowledge‐based scoring schemes may not be sufficiently general and transferable, while molecular dynamics or Monte Carlo calculations with explicit solvent are too computationally expensive for many applications. Recently, several empirical schemes using finite difference Poisson–Boltzmann electrostatics to predict energies for particular types of complexes were proposed. Here, an improved empirical binding energy function has been derived and validated on three different types of complexes: protein–small ligand, protein–peptide and protein–protein. The function uses the boundary element algorithm to evaluate the electrostatic solvation energy. We show that a single set of parameters can predict the relative binding energies of the heterogeneous validation set of complexes with 2.5 kcal/mol accuracy. We also demonstrate that global optimization of the ligand and of the flexible side‐chains of the receptor improves the accuracy of the evaluation. Copyright © 1999 John Wiley & Sons, Ltd.     

Using chimeric immunity proteins to explore the energy landscape for alpha-helical protein folding

To address the role of sequence in the folding of homologous proteins, the folding and unfolding kinetics of the all-helical bacterial immunity proteins Im2 and Im9 were characterised, together with six chimeric derivatives of these proteins. We show that both Im2 and Im9 fold rapidly (k(UN)(H(2)O)) approximately 2000 s(-1) at pH 7.0, 25 degrees C) in apparent two-state transitions, through rate-limiting transition states that are highly compact (beta(TS)0.93 and 0.96, respectively). Whilst the folding and unfolding properties of three of the chimeras (Im2 (1-44)(Im9), Im2 (1-64)(Im9 )and Im2 (25-44)(Im9)) are similar to their parental counterparts, in other chimeric proteins the introduced sequence variation results in altered kinetic behaviour. At low urea concentrations, Im2 (1-29)(Im9) and Im2 (56-64)(Im9) fold in two-state transitions via transition states that are significantly less compact (beta(TS) approximately 0.7) than those characterised for the other immunity proteins presented here. At higher urea concentrations, however, the rate-limiting transition state for these two chimeras switches or moves to a more compact species (beta(TS) approximately 0.9). Surprisingly, Im2 (30-64)(Im9) populates a highly collapsed species (beta(I)=0.87) in the dead-time (2.5 ms) of stopped flow measurements. These data indicate that whilst topology may place significant constraints on the folding process, specific inter-residue interactions, revealed here through multiple sequence changes, can modulate the ruggedness of the folding energy landscape.     

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.     

An analysis of non-bonded energy of proteins

Non-bonded energy of 16 proteins was calculated using the atomic co-ordinates obtained by X-ray crystallography. The curve of total energy against the number of atoms in proteins is approximately linear with a slight concaved shape. According to a linear equation to fit the curve, the extrapolated length of a polypeptide chain of a globular shape is expected to be 18 residues, which corresponds conceivably to an approximate size of nucleus for a folding of the polypeptide chain. Contributions from short-range and medium-range energies are always much greater than those from long-range energy for all the proteins and there seems to exist a change of each contribution in a range from 1200 to 1700 atoms. The energies with a lag less than four residues are a major part of the total energy and the contribution of energy from main-chain atoms is considerably higher than that from side-chain atoms. Side-chain atoms of a residue have a tendency to interact more strongly with main-chain atoms of N-terminal, than with those of C-terminal side of the residue, indicating asymmetry of the interaction in a protein. Amino acid residues in proteins may be divided into three groups by the order of strength of average energy. The first group exhibiting strong interaction consists mainly of hydrophobic amino acids and the third group consists of hydrophilic ones corresponding to the location in a protein molecule. Cys, val, leu and met are important for medium-range and long-range energies; gly and ala for medium-range energy; ile, trp, phe, tyr and arg for long-range energy. One simple application of the average energy of amino acid residues is illustrated to estimate local energy of a segment of nine residues given by a protein sequence. There is a good correlation between the curve computed by the average energy and the experimental curve for myoglobin.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

The energy landscape analysis of cancer mutations in protein kinases

The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.     

Prediction of thermophilic proteins using feature selection technique

The thermostability of proteins is particularly relevant for enzyme engineering. Developing a computational method to identify mesophilic proteins would be helpful for protein engineering and design. In this work, we developed support vector machine based method to predict thermophilic proteins using the information of amino acid distribution and selected amino acid pairs. A reliable benchmark dataset including 915 thermophilic proteins and 793 non-thermophilic proteins was constructed for training and testing the proposed models. Results showed that 93.8% thermophilic proteins and 92.7% non-thermophilic proteins could be correctly predicted by using jackknife cross-validation. High predictive successful rate exhibits that this model can be applied for designing stable proteins.     

Conformational polymorphism of wild-type and mutant prion proteins: Energy landscape analysis

Conformational transitions are thought to be the prime mechanism of prion diseases. In this study, the energy landscapes of a wild-type prion protein (PrP) and the D178N and E200K mutant proteins were mapped, enabling the characterization of the normal isoforms (PrP(C)) and partially unfolded isoforms (PrP(PU)) of the three prion protein analogs. It was found that the three energy landscapes differ in three respects: (i) the relative stability of the PrP(C) and the PrP(PU) states, (ii) the transition pathways from PrP(C) to PrP(PU), and (iii) the relative stability of the three helices in the PrP(C) state. In particular, it was found that although helix 1 (residues 144-156) is the most stable helix in wild-type PrP, its stability is dramatically reduced by both mutations. This destabilization is due to changes in the charge distribution that affects the internal salt bridges responsible for the greater stability of this helix in wild-type PrP. Although both mutations result in similar destabilization of helix 1, they a have different effect on the overall stability of PrP(C) and of PrP(PU) isoforms and on structural properties. The destabilization of helix 1 by mutations provides additional evidences to the role of this helix in the pathogenic transition from the PrP(C) to the pathogenic isoform PrP(SC).     

Movement distances and density estimation of small mammals using the spool-and-line technique

Edge effect is an inherent problem when using trapping grids to estimate density of small mammals, resulting in a sampling area larger than the area of the grid. Distances between captures of individuals are used to estimateA(W), the effective sampling area of a trapping grid, but grid size sets a limit for the largest detectable distance. The spool-and-line technique is proposed here as a new method to estimateA(W). Movement distances based on the spool-and-line technique were compared to similar movement distances based on capture-recapture of three species of marsupials of the Atlantic Forest of Brazil. Distances based on the two methods were uncorrelated, and only ln-transformed distances based on the spool-and-line were normally distributed. The maximum distance moved (MaxD) estimated by the spool-and-line was chosen as the more accurate and practical distance to estimate edge effect. Estimates of the effective sampling area and densities for the common opossumDidelphis aurita (Wied-Neuwied, 1826), were compared using MaxD based on spool-and-line (MaxDs p o o l ) , capture-recapture (MaxD_cap), and also the distance between traps (DT). MaxD_spool reflected more accurately density variation between seasons. Movement distances of small mammals based on the spool-and-line technique permit more accurate estimates of density and its dynamics.     

Deciphering the energy landscape of the interaction uranyl-DCP with antibodies using dynamic force spectroscopy

Previous studies on molecular recognition of uranyl-DCP (dicarboxy-phenanthroline chelator) compound by two distinct monoclonal antibodies (Mabs U04S and U08S) clearly showed the presence of a biphasic shape in Bell-Evans’ plots and an accentuated difference in slopes at the high loading rates. To further explore the basis in the slope difference, we have performed complementary experiments using antibody PHE03S, raised against uranyl-DCP but, presenting a strong cross-reactivity toward the DCP chelator. This work allowed us to obtain a reallocation of the respective contributions of the metal ion itself and that of the chelator. Results led us to propose a 2D schematic model representing two energy barriers observed in the systems Mabs U04S- and U08S-[UO₂-DCP] where the outer barrier characterizes the interaction between UO₂ and Mab whereas the inner barrier characterizes the interaction between DCP and Mab. Using dynamic force spectroscopy, it is thus possible to dissect molecular interactions during the unbinding between proteins and ligands.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.     

The energy landscape of modular repeat proteins: topology determines folding mechanism in the ankyrin family

Proteins consisting of repeating amino acid motifs are abundant in all kingdoms of life, especially in higher eukaryotes. Repeat-containing proteins self-organize into elongated non-globular structures. Do the same general underlying principles that dictate the folding of globular domains apply also to these extended topologies? Using a simplified structure-based model capturing a perfectly funneled energy landscape, we surveyed the predicted mechanism of folding for ankyrin repeat containing proteins. The ankyrin family is one of the most extensively studied classes of non-globular folds. The model based only on native contacts reproduces most of the experimental observations on the folding of these proteins, including a folding mechanism that is reminiscent of a nucleation propagation growth. The confluence of simulation and experimental results suggests that the folding of non-globular proteins is accurately described by a funneled energy landscape, in which topology plays a determinant role in the folding mechanism.