Evolutionary potentials: structure specific knowledge-based potentials exploiting the evolutionary record of sequence homologs

We introduce a new type of knowledge-based potentials for protein structure prediction, called 'evolutionary potentials', which are derived using a single experimental protein structure and all three-dimensional models of its homologous sequences. The new potentials have been benchmarked against other knowledge-based potentials, resulting in a significant increase in accuracy for model assessment. In contrast to standard knowledge-based potentials, we propose that evolutionary potentials capture key determinants of thermodynamic stability and specific sequence constraints required for fast folding.     

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.     

Multistep denaturation of Borrelia burgdorferi OspA, a protein containing a single-layer beta-sheet

Outer surface protein A (OspA) from the Lyme disease spirochete, Borrelia burgdorferi, is a dumbbell-shaped protein in which two globular domains are connected by a three-stranded beta-sheet segment that is solvent-exposed on both faces. Previous studies showed that the whole protein, including the single-layer beta-sheet, is highly rigid. To elucidate the folding mechanism and the role of the central beta-sheet in the formation of the rigid molecule, we investigated the equilibrium thermal denaturation reaction of OspA. We applied differential scanning calorimetry, heteronuclear NMR spectroscopy, and solution small-angle X-ray scattering (SAXS) to characterize the reaction in detail. All three techniques revealed that OspA denatures in two separable cooperative transitions. NMR measurements on OspA specifically 15N-labeled at Lys residues identified the locations of the two folding units and revealed that the C-terminal segment is less stable than the remaining N-terminal segment. The boundary between the two folding units is located within the central beta-sheet. The interconversion among the three folding states (fully folded, C-terminus unfolded, and fully denatured) is slow relative to chemical shift differences (<24 Hz), indicating that there are significant kinetic barriers in the denaturation reactions. SAXS measurements determined the radius of gyration of the native protein to be 25.0 +/- 0.3 A, which increases to 34.4 +/- 1.0 A in the first transition, and then to 56.1 +/- 1.6 A in the second transition. Thus, the intermediate state, in which the C-terminal folding unit is already denatured, is still compact. These results provide a basis for elucidating the folding mechanism of OspA.     

The nucleation of monomeric parallel beta-sheet-like structures and their self-assembly in aqueous solution

The aromatic diacid residue 4,6-dibenzofuranbispropionic acid (1) was designed to nucleate a parallel beta-sheet-like structure in small peptides in aqueous solution via a hydrogen-bonded hydrophobic cluster. Even though a 14-membered ring hydrogen bond necessary for parallel beta-sheet formation is favored in simple amides composed of 1, this hydrogen bonding interaction does not appear to be sufficient to nucleate parallel beta-sheet formation in the absence of hydrophobic clustering between the dibenzofuran portion of 1 and the hydrophobic side chains of the flanking alpha-amino acids. The subsequence --hydrophobic residue-1-hydrophobic residue-- is required for folding in the context of a nucleated two-stranded parallel beta-sheet structure. In all cases where the peptidomimetics can fold into two diastereomeric parallel beta-sheet structures having different hydrogen bonding networks, these conformations appear to exchange rapidly. The majority of the parallel beta-sheet structures evaluated herein undergo linked intramolecular folding and self-assembly, affording a fibrillar beta-sheet quaternary structure. To unlink folding and assembly, asymmetric parallel beta-sheet structures incorporating N-methylated alpha-amino acid residues have been synthesized using a new solid phase approach. Residue 1 facilitates the folding of several peptides described within affording a monomeric parallel beta-sheet-like structure in aqueous solution, as ascertained by a variety of spectroscopic and biophysical methods, increasing our understanding of parallel beta-sheet structure.     

Reversible unfolding of beta-sheets in membranes: a calorimetric study

The hexapeptide acetyl-Trp-Leu(5) (AcWL(5)) has the remarkable ability to assemble reversibly and spontaneously into beta-sheets on lipid membranes as a result of monomer partitioning followed by cooperative assembly. This system provides a unique opportunity to study the thermodynamics of protein folding in membranes, which we have done using isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC). The results, which may represent the first example of reversible thermal unfolding of peptides in membranes, help to define the contribution of hydrogen bonding to the extreme thermal stability of membrane proteins. ITC revealed that the enthalpy change for partitioning of monomeric, unstructured AcWL(5) from water into membranes was zero within experimental error over the temperature range of 5 degrees C to 75 degrees C. DSC showed that the beta-sheet aggregates underwent a reversible, endothermic, and very asymmetric thermal transition with a concentration-dependent transition temperature (T(m)) in the range of 60 degrees C to 80 degrees C. A numerical model of nucleation and growth-dependent assembly of oligomeric beta-sheets, proposed earlier to describe beta-sheet formation in membranes, recreated remarkably well the unusual shape and concentration-dependence of the transition peaks. The enthalpy for thermal unfolding of AcWL(5) beta-sheets in the membrane was found to be about 8(+/-1)kcal mol(-1), or about 1.3(+/-0.2)kcal mol(-1) per residue.     

Mutational analysis of the folding transition state of the C-terminal domain of ribosomal protein L9: a protein with an unusual beta-sheet topology

The C-terminal domain of ribosomal protein L9 (CTL9) is a 92-residue alpha-beta protein which contains an unusual three-stranded mixed parallel and antiparallel beta-sheet. The protein folds in a two-state fashion, and the folding rate is slow. It is thought that the slow folding may be caused by the necessity of forming this unusual beta-sheet architecture in the transition state for folding. This hypothesis makes CTL9 an interesting target for folding studies. The transition state for the folding of CTL9 was characterized by phi-value analysis. The folding of a set of hydrophobic core mutants was analyzed together with a set of truncation mutants. The results revealed a few positions with high phi-values (> or = 0.5), notably, V131, L133, H134, V137, and L141. All of these residues were found in the beta-hairpin region, indicating that the formation of this structure is likely to be the rate-limiting step in the folding of CTL9. One face of the beta-hairpin docks against the N-terminal helix. Analysis of truncation mutants of this helix confirmed its importance in folding. Mutations at other sites in the protein gave small phi-values, despite the fact that some of them had major effects on stability. The analysis indicates that formation of the antiparallel hairpin is critical and its interactions with the first helix are also important. Thus, the slow folding is not a consequence of the need to fully form the unusual three-stranded beta-sheet in the transition state. Analysis of the urea dependence of the folding rates indicates that mutations modulate the unfolded state. The folding of CTL9 is broadly consistent with the nucleation-condensation model of protein folding.     

Thermodynamic and kinetic exploration of the energy landscape of Borrelia burgdorferi OspA by native-state hydrogen exchange

We report a native-state hydrogen-exchange (HX) method to simultaneously obtain both thermodynamic and kinetic information on the formation of multiple excited states in a folding energy landscape. Our method exploits the inherent dispersion and pH dependence of the intrinsic HX rates to cover both the EX2 (thermodynamic) and EX1 (kinetic) regimes. At each concentration of denaturant, HX measurements are performed over a range of pH values. Using this strategy, we dissected Borrelia burgdorferi OspA, a predominantly beta-sheet protein containing a unique single-layer beta-sheet, into five cooperative units and postulated excited states predominantly responsible for HX. More importantly, we determined the interconversion rates between these excited states and the native state. The use of both thermodynamic and kinetic information from native-state HX enabled us to construct a folding landscape of this 28kDa protein, including local minima and maxima, and to discriminate on-pathway and off-pathway intermediates. This method, which we term EX2/EX1 HX, should be a powerful tool for characterizing the complex folding mechanisms exhibited by the majority of proteins.     

Equilibrium folding and stability of myotrophin: a model ankyrin repeat protein

Proteins containing stretches of repeating amino acid sequences are prevalent throughout nature, yet little is known about the general folding and assembly mechanisms of these systems. Here we propose myotrophin as a model system to study the folding of ankyrin repeat proteins. Myotrophin is folded over a large pH range and is soluble at high concentrations. Thermal and urea denaturation studies show that the protein displays cooperative two-state folding properties despite its modular nature. Taken together with previous studies on other ankyrin repeat proteins, our data suggest that the two-state folding pathway may be characteristic of ankyrin repeat proteins and other integrated alpha-helical repeat proteins in general.     

In vitro folding and assembly of the Escherichia coli ATP-binding cassette transporter, BtuCD

Studies on membrane protein folding have focused on monomeric α-helical proteins and a major challenge is to extend this work to larger oligomeric membrane proteins. Here, we study the Escherichia coli (E. coli) ATP-binding cassette (ABC) transporter that imports vitamin B(12) (the BtuCD protein) and use it as a model system for investigating the folding and assembly of a tetrameric membrane protein complex. Our work takes advantage of the modular organization of BtuCD, which consists of two transmembrane protein subunits, BtuC, and two cytoplasmically located nucleotide-binding protein subunits, BtuD. We show that the BtuCD transporter can be re-assembled from both prefolded and partly unfolded, urea denatured BtuC and BtuD subunits. The in vitro re-assembly leads to a BtuCD complex with the correct, native, BtuC and BtuD subunit stoichiometry. The highest rates of ATP hydrolysis were achieved for BtuCD re-assembled from partly unfolded subunits. This supports the idea of cooperative folding and assembly of the constituent protein subunits of the BtuCD transporter. BtuCD folding also provides an opportunity to investigate how a protein that contains both membrane-bound and aqueous subunits coordinates the folding requirements of the hydrophobic and hydrophilic subunits.     

Explicit-chain model of native-state hydrogen exchange: implications for event ordering and cooperativity in protein folding

Native-state hydrogen exchange experiments on several proteins have revealed partially unfolded conformations with diverse stabilities. These equilibrium observations have been used to support kinetic arguments that folding proceeds via a sequential "pathway." This interpretative logic is evaluated here by analyzing the relationship between thermodynamic behavior and folding kinetics in a class of simplified lattice protein models. The chain models studied have varying degrees of cooperative interplay (coupling) between local helical conformational preference and favorable nonlocal interactions. When model cooperativity is high, as native conditions are weakened, "isotherms" of free energy of exchange for residues belonging to the same helix merge together before global unfolding. The point of merger depends on the model energetic favorability of the helix. This trend is similar to the corresponding experimental observations. Kinetically, we find that the ordering of helix formation in the very last stage of native core assembly tends to follow the stabilities of their converged isotherms. In a majority (but not all) of folding trajectories, the final assembly of helices that are thermodynamically more stable against exchange precedes that of helices that are less stable against exchange. These model features are in partial agreement with common experimental interpretations. However, the model results also underscore the ensemble nature of the folding process: the kinetics of helix formation is not a discrete, strictly "all-or-none" process as that envisioned by certain non-explicit-chain models. Helices generally undergo many cycles of partial formation and dissolution before their conformations are fixed in the final assembly stage of folding, a kinetic stage that takes up only approximately 2% of the average folding time in the present model; and the ordering of the helices' final assembly in some trajectories can be different from the dominant ordering stipulated by the exchange isotherms.     

A pairwise residue contact area-based mean force potential for discrimination of native protein structure

Background  

Considering energy function to detect a correct protein fold from incorrect ones is very important for protein structure prediction and protein folding. Knowledge-based mean force potentials are certainly the most popular type of interaction function for protein threading. They are derived from statistical analyses of interacting groups in experimentally determined protein structures. These potentials are developed at the atom or the amino acid level. Based on orientation dependent contact area, a new type of knowledge-based mean force potential has been developed.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

Importance of secondary structural specificity determinants in protein folding: insertion of a native beta-sheet sequence into an alpha-helical coiled-coil

To examine how a short secondary structural element derived from a native protein folds when in a different protein environment, we inserted an 11-residue beta-sheet segment (cassette) from human immunoglobulin fold, Fab new, into an alpha-helical coiled-coil host protein (cassette holder). This de novo design protein model, the structural cassette mutagenesis (SCM) model, allows us to study protein folding principles involving both short- and long-range interactions that affect secondary structure stability and conformation. In this study, we address whether the insertion of this beta-sheet cassette into the alpha-helical coiled-coil protein would result in conformational change nucleated by the long-range tertiary stabilization of the coiled-coil, therefore overriding the local propensity of the cassette to form beta-sheet, observed in its native immunoglobulin fold. The results showed that not only did the nucleating helices of the coiled-coil on either end of the cassette fail to nucleate the beta-sheet cassette to fold with an alpha-helical conformation, but also the entire chimeric protein became a random coil. We identified two determinants in this cassette that prevented coiled-coil formation: (1) a tandem dipeptide NN motif at the N-terminal of the beta-sheet cassette, and (2) the hydrophilic Ser residue, which would be buried in the hydrophobic core if the coiled-coil structure were to fold. By amino acid substitution of these helix disruptive residues, that is, either the replacement of the NN motif with high helical propensity Ala residues or the substitution of Ser with Leu to enhance hydrophobicity, we were able to convert the random coil chimeric protein into a fully folded alpha-helical coiled-coil. We hypothesized that this NN motif is a "secondary structural specificity determinant" which is very selective for one type of secondary structure and may prevent neighboring residues from adopting an alternate protein fold. These sequences with secondary structural specificity determinants have very strong local propensity to fold into a specific secondary structure and may affect overall protein folding by acting as a folding initiation site.     

Influence of protein structure databases on the predictive power of statistical pair potentials

A long standing goal in protein structure studies is the development of reliable energy functions that can be used both to verify protein models derived from experimental constraints as well as for theoretical protein folding and inverse folding computer experiments. In that respect, knowledge-based statistical pair potentials have attracted considerable interests recently mainly because they include the essential features of protein structures as well as solvent effects at a low computing cost. However, the basis on which statistical potentials are derived have been questioned. In this paper, we investigate statistical pair potentials derived from protein three-dimensional structures, addressing in particular questions related to the form of these potentials, as well as to the content of the database from which they are derived. We have shown that statistical pair potentials depend on the size of the proteins included in the database, and that this dependence can be reduced by considering only pairs of residue close in space (i.e., with a cutoff of 8 Å). We have shown also that statistical potentials carry a memory of the quality of the database in terms of the amount and diversity of secondary structure it contains. We find, for example, that potentials derived from a database containing α-proteins will only perform best on α-proteins in fold recognition computer experiments. We believe that this is an overall weakness of these potentials, which must be kept in mind when constructing a database. Proteins 31:139–149, 1998. © 1998 Wiley-Liss, Inc.     

Structural elements regulating amyloidogenesis: a cholinesterase model system

Polymerization into amyloid fibrils is a crucial step in the pathogenesis of neurodegenerative syndromes. Amyloid assembly is governed by properties of the sequence backbone and specific side-chain interactions, since fibrils from unrelated sequences possess similar structures and morphologies. Therefore, characterization of the structural determinants driving amyloid aggregation is of fundamental importance. We investigated the forces involved in the amyloid assembly of a model peptide derived from the oligomerization domain of acetylcholinesterase (AChE), AChE(586-599), through the effect of single point mutations on beta-sheet propensity, conformation, fibrilization, surfactant activity, oligomerization and fibril morphology. AChE(586-599) was chosen due to its fibrilization tractability and AChE involvement in Alzheimer's disease. The results revealed how specific regions and residues can control AChE(586-599) assembly. Hydrophobic and/or aromatic residues were crucial for maintaining a high beta-strand propensity, for the conformational transition to beta-sheet, and for the first stage of aggregation. We also demonstrated that positively charged side-chains might be involved in electrostatic interactions, which could control the transition to beta-sheet, the oligomerization and assembly stability. Further interactions were also found to participate in the assembly. We showed that some residues were important for AChE(586-599) surfactant activity and that amyloid assembly might preferentially occur at an air-water interface. Consistently with the experimental observations and assembly models for other amyloid systems, we propose a model for AChE(586-599) assembly in which a steric-zipper formed through specific interactions (hydrophobic, electrostatic, cation-pi, SH-aromatic, metal chelation and polar-polar) would maintain the beta-sheets together. We also propose that the stacking between the strands in the beta-sheets along the fiber axis could be stabilized through pi-pi interactions and metal chelation. The dissection of the specific molecular recognition driving AChE(586-599) amyloid assembly has provided further knowledge on such poorly understood and complicated process, which could be applied to protein folding and the targeting of amyloid diseases.     

A novel side-chain orientation dependent potential derived from random-walk reference state for protein fold selection and structure prediction

Background

An accurate potential function is essential to attack protein folding and structure prediction problems. The key to developing efficient knowledge-based potential functions is to design reference states that can appropriately counteract generic interactions. The reference states of many knowledge-based distance-dependent atomic potential functions were derived from non-interacting particles such as ideal gas, however, which ignored the inherent sequence connectivity and entropic elasticity of proteins.

Methodology

We developed a new pair-wise distance-dependent, atomic statistical potential function (RW), using an ideal random-walk chain as reference state, which was optimized on CASP models and then benchmarked on nine structural decoy sets. Second, we incorporated a new side-chain orientation-dependent energy term into RW (RWplus) and found that the side-chain packing orientation specificity can further improve the decoy recognition ability of the statistical potential.

Significance

RW and RWplus demonstrate a significantly better ability than the best performing pair-wise distance-dependent atomic potential functions in both native and near-native model selections. It has higher energy-RMSD and energy-TM-score correlations compared with other potentials of the same type in real-life structure assembly decoys. When benchmarked with a comprehensive list of publicly available potentials, RW and RWplus shows comparable performance to the state-of-the-art scoring functions, including those combining terms from multiple resources. These data demonstrate the usefulness of random-walk chain as reference states which correctly account for sequence connectivity and entropic elasticity of proteins. It shows potential usefulness in structure recognition and protein folding simulations. The RW and RWplus potentials, as well as the newly generated I-TASSER decoys, are freely available in http://zhanglab.ccmb.med.umich.edu/RW.     

Distributions of beta sheets in proteins with application to structure prediction

We recently developed the Rosetta algorithm for ab initio protein structure prediction, which generates protein structures from fragment libraries using simulated annealing. The scoring function in this algorithm favors the assembly of strands into sheets. However, it does not discriminate between different sheet motifs. After generating many structures using Rosetta, we found that the folding algorithm predominantly generates very local structures. We surveyed the distribution of beta-sheet motifs with two edge strands (open sheets) in a large set of non-homologous proteins. We investigated how much of that distribution can be accounted for by rules previously published in the literature, and developed a filter and a scoring method that enables us to improve protein structure prediction for beta-sheet proteins. Proteins 2002;48:85-97.     

Prediction of protein structure by simulating coarse-grained folding pathways: a preliminary report

A set of software tools designed to study protein structure and kinetics has been developed. The core of these tools is a program called Folding Machine (FM) which is able to generate low resolution folding pathways using modest computational resources. The FM is based on a coarse-grained kinetic ab initio Monte-Carlo sampler that can optionally use information extracted from secondary structure prediction servers or from fragment libraries of local structure. The model underpinning this algorithm contains two novel elements: (a) the conformational space is discretized using the Ramachandran basins defined in the local phi-psi energy maps; and (b) the solvent is treated implicitly by rescaling the pairwise terms of the non-bonded energy function according to the local solvent environments. The purpose of this hybrid ab initio/knowledge-based approach is threefold: to cover the long time scales of folding, to generate useful 3-dimensional models of protein structures, and to gain insight on the protein folding kinetics. Even though the algorithm is not yet fully developed, it has been used in a recent blind test of protein structure prediction (CASP5). The FM generated models within 6 A backbone rmsd for fragments of about 60-70 residues of alpha-helical proteins. For a CASP5 target that turned out to be natively unfolded, the trajectory obtained for this sequence uniquely failed to converge. Also, a new measure to evaluate structure predictions is presented and used along the standard CASP assessment methods. Finally, recent improvements in the prediction of beta-sheet structures are briefly described.