A new analytical method for computing solvent-accessible surface area of macromolecules and its gradients

Protein-folding chaperones predict structure-function relationships and cancer risk in BRCA1 mutation carriers

Predicting the risk of cancer mutations is critical for early detection and prevention, but differences in allelic severity of human carriers confound risk predictions. Here, we elucidate protein folding as a cellular mechanism driving differences in mutation severity of tumor suppressor BRCA1. Using a high-throughput protein-protein interaction assay, we show that protein-folding chaperone binding patterns predict the pathogenicity of variants in the BRCA1 C-terminal (BRCT) domain. HSP70 selectively binds 94% of pathogenic BRCA1-BRCT variants, most of which engage HSP70 more than HSP90. Remarkably, the magnitude of HSP70 binding linearly correlates with loss of folding and function. We identify a prevalent class of human hypomorphic BRCA1 variants that bind moderately to chaperones and retain partial folding and function. Furthermore, chaperone binding signifies greater mutation penetrance and earlier cancer onset in the clinic. Our findings demonstrate the utility of chaperones as quantitative cellular biosensors of variant folding, phenotypic severity, and cancer risk.

Uncovering the structural stability of Magnaporthe oryzae effectors: a secretome-wide in silico analysis

Rice blast, caused by the ascomycete fungus Magnaporthe oryzae, is a deadly disease and a major threat to global food security. The pathogen secretes small proteinaceous effectors, virulence factors, inside the host to manipulate and perturb the host immune system, allowing the pathogen to colonize and establish a successful infection. While the molecular functions of several effectors are characterized, very little is known about the structural stability of these effectors. We analyzed a total of 554 small secretory proteins (SSPs) from the M. oryzae secretome to decipher key features of intrinsic disorder (ID) and the structural dynamics of the selected putative effectors through thorough and systematic in silico studies. Our results suggest that out of the total SSPs, 66% were predicted as effector proteins, released either into the apoplast or cytoplasm of the host cell. Of these, 68% were found to be intrinsically disordered effector proteins (IDEPs). Among the six distinct classes of disordered effectors, we observed peculiar relationships between the localization of several effectors in the apoplast or cytoplasm and the degree of disorder. We determined the degree of structural disorder and its impact on protein foldability across all the putative small secretory effector proteins from the blast pathogen, further validated by molecular dynamics simulation studies. This study provides definite clues toward unraveling the mystery behind the importance of structural distortions in effectors and their impact on plant-pathogen interactions. The study of these dynamical segments may help identify new effectors as well.Communicated by Ramaswamy H. Sarma.

Protein-Folding Chaperones Predict Structure-Function Relationships and Cancer Risk in BRCA1 Mutation Carriers

Identifying pathogenic mutations and predicting their impact on protein structure, function and phenotype remain major challenges in genome sciences. Protein-folding chaperones participate in structure-function relationships by facilitating the folding of protein variants encoded by mutant genes. Here, we utilize a high-throughput protein-protein interaction assay to test HSP70 and HSP90 chaperone interactions as predictors of pathogenicity for variants in the tumor suppressor BRCA1. Chaperones bind 77% of pathogenic BRCA1-BRCT variants, most of which engaged HSP70 more than HSP90. Remarkably, the magnitude of chaperone binding to variants is proportional to the degree of structural and phenotypic defect induced by BRCA1 mutation. Quantitative chaperone interactions identified BRCA1-BRCT separation-of-function variants and hypomorphic alleles missed by pathogenicity prediction algorithms. Furthermore, increased chaperone binding signified greater cancer risk in human BRCA1 carriers. Altogether, our study showcases the utility of chaperones as quantitative cellular biosensors of variant folding and phenotypic severity.

HIGHLIGHTS

Chaperones detect an abundance of pathogenic folding variants of BRCA1-BRCT.Degree of chaperone binding reflects severity of structural and phenotypic defect.Chaperones identify separation-of-function and hypomorphic variants. Chaperone interactions indicate penetrance and expressivity of BRCA1 alleles.

An efficient algorithm calculating common solvent accessible volume

The solvent accessible surface area and the solvent accessible volume are measurements commonly used in implicit solvent models to include the effect of forces exerted by solvents on the protein surfaces (or the atoms on protein surfaces). The two measurements have limitations in describing interactions between proteins (or proteins’ atoms) mediated/bridged by solvents. This is because describing the interactions between proteins should be able to capture the chain of protein-solvent-protein interactions while the solvent accessible surface area or the solvent accessible volume can capture only protein-solvent interactions. If we represent the solvent as a continuous medium, we can consider an atom of a protein can effectively interact with the solvent within a certain distance from its surface (or its own solvent-interacting sphere). In this case, the protein-solvent-protein interactions can be measured by the amount of solvent interacting with two proteins’ atoms at the same time (or the volume shared by the two atoms’ solvent-interacting spheres excluding the volumes occupied by proteins’ atoms). We call the shared volume as the common solvent accessible volume (CSAV); there has been no method developed to determine the CSAV. In this work, we propose a new sweep-line-based method that efficiently calculates the common solvent accessible volume. The performance and accuracy of the proposed sweep-line-based method are compared with those of the naïve voxel-based method. The proposed method takes log-linear time to the number of atoms involved in a CSAV calculation and linear time to the resolution. Our results, tested with 52 protein structures of various sizes, show that the proposed sweep-line-based method is superior to the voxel-based method in both computational efficiency and accuracy.

Temperature and Guanidine Hydrochloride Effects on the Folding Thermodynamics of WW Domain and Variants

We used simulations based on an all-atom Go model to calculate the folding temperatures (T_fs) and free energies (ΔGs) of two variants of the WW domain, which is a small all-β-sheet protein. The results, without adjusting any parameter, are in good agreement with experiments, thus validating the simulations. We then used the molecular transfer model to predict the changes in the ΔGs and T_fs as the guanidine hydrochloride concentration is varied. The predictions can be readily tested in experiments.

Generalizing Continuum Solvation in Crystal to Nonaqueous Solvents: Implementation, Parametrization, and Application to Molecules and Surfaces

We present an extension of a generalized finite-difference Poisson-Boltzmann (FDPB) continuum solvation model based on a self-consistent reaction field treatment to nonaqueous solvents. Implementation and reparametrization of the cavitation, dispersion, and structural (CDS) effects nonelectrostatic model are presented in CRYSTAL, with applications to both finite and infinite periodic systems. For neutral finite systems, computed errors with respect to available experimental data on free energies of solvation of 2523 solutes in 91 solvents, as well as 144 transfer energies from water to 14 organic solvents are on par with the reference SM12 solvation model for which the CDS parameters have been developed. Calculations performed on a TiO₂ anatase surface and compared to VASPsol data revealed an overall very good agreement of computed solvation energies, surface energies, as well as band structure changes upon solvation in three different solvents, validating the general applicability of the reparametrized FDPB approach to neutral nonperiodic and periodic solutes in aqueous and nonaqueous solvents. For ionic species, while the reparametrized CDS model led to large errors on free energies of solvation of anions, addition of a corrective term based on Abraham's acidity of the solvent significantly improved the accuracy of the proposed continuum solvation model, leading to errors on aqueous pK_a of a test set of 83 solutes divided by a factor of 4 compared to the reference solvation model based on density (SMD). Overall, therefore, these encouraging results demonstrate that the generalized FDPB continuum solvation model can be applied to a broad range of solutes in various solvents, ranging from finite neutral or charged solutes to extended periodic surfaces.

Analytical calculation of the solvent-accessible surface area and its nuclear gradients by stereographic projection: A general approach for molecules, polymers, nanotubes, helices, and surfaces

In this article, we explore an alternative to the analytical Gauss-Bonnet approach for computing the solvent-accessible surface area (SASA) and its nuclear gradients. These two key quantities are required to evaluate the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models. We extend a previously proposed analytical approach for finite systems based on the stereographic projection technique to infinite periodic systems such as polymers, nanotubes, helices, or surfaces and detail its implementation in the Crystal code. We provide the full derivation of the SASA nuclear gradients, and introduce an iterative perturbation scheme of the atomic coordinates to stabilize the gradients calculation for certain difficult symmetric systems. An excellent agreement of computed SASA with reference analytical values is found for finite systems, while the SASA size-extensivity is verified for infinite periodic systems. In addition, correctness of the analytical gradients is confirmed by the excellent agreement obtained with numerical gradients and by the translational invariance achieved, both for finite and infinite periodic systems. Overall therefore, the stereographic projection approach appears as a general, simple, and efficient technique to compute the key quantities required for the calculation of the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models applicable to both finite and infinite periodic systems.

Dipole-dipole interactions between tryptophan side chains and hydration water molecules dominate the observed dynamic stokes shift of lysozyme

The fluorescence intensity of tryptophan residues in hen egg-white lysozyme was measured up to 500 ps after the excitation by irradiation pulses at 290 nm. From the time-dependent variation of fluorescence intensity in a wavelength range of 320-370 nm, the energy relaxation in the dynamic Stokes shift was reconstructed as the temporal variation in wavenumber of the estimated fluorescence maximum. The relaxation was approximated by two exponential curves with decay constants of 1.2 and 26.7 ps. To interpret the relaxation, a molecular dynamics simulation of 75 ns was conducted for lysozyme immersed in a water box. From the simulation, the energy relaxation in the electrostatic interactions of each tryptophan residue was evaluated by using a scheme derived from the linear response theory. Dipole-dipole interactions between each of the Trp62 and Trp123 residues and hydration water molecules displayed an energy relaxation similar to that experimentally observed regarding time constants and magnitudes. The side chains of these residues were partly or fully exposed to the solvent. In addition, by inspecting the variation in dipole moments of the hydration water molecules around lysozyme, it was suggested that the observed relaxation could be attributed to the orientational relaxation of hydration water molecules participating in the hydrogen-bond network formed around each of the two tryptophan residues.

RiSLnet: Rapid identification of smart mutant libraries using protein structure network. Application to thermal stability enhancement

A key point of protein stability engineering is to identify specific target residues whose mutations can stabilize the protein structure without negatively affecting the function or activity of the protein. Here, we propose a method called RiSLnet (Rapid identification of Smart mutant Library using residue network) to identify such residues by combining network analysis for protein residue interactions, identification of conserved residues, and evaluation of relative solvent accessibility. To validate its performance, the method was applied to four proteins, that is, T4 lysozyme, ribonuclease H, barnase, and cold shock protein B. Our method predicted beneficial mutations in thermal stability with ~62% average accuracy when the thermal stability of the mutants was compared with the ones in the Protherm database. It was further applied to lysine decarboxylase (CadA) to experimentally confirm its accuracy and effectiveness. RiSLnet identified mutations increasing the thermal stability of CadA with the accuracy of ~60% and significantly reduced the number of candidate residues (~99%) for mutation. Finally, combinatorial mutations designed by RiSLnet and in silico saturation mutagenesis yielded a thermally stable triple mutant with the half-life (T _1/2 ) of 114.9 min at 58°C, which is approximately twofold higher than that of the wild-type.

Changes in hydration structure are necessary for collective motions of a multi-domain protein

Conformational motions of proteins are necessary for their functions. To date, experimental studies measuring conformational fluctuations of a whole protein structure have revealed that water molecules hydrating proteins are necessary to induce protein functional motions. However, the underlying microscopic mechanism behind such regulation remains unsolved. To clarify the mechanism, multi-domain proteins are good targets because it is obvious that water molecules between domains play an important role in domain motions. Here, we show how changes in hydration structure microscopically correlate with large-amplitude motions of a multi-domain protein, through molecular dynamics simulation supported by structural analyses and biochemical experiments. We first identified collective domain motions of the protein, which open/close an active-site cleft between domains. The analyses on changes in hydration structure revealed that changes in local hydration in the depth of the cleft are necessary for the domain motion and vice versa. In particular, ‘wetting’/‘drying’ at a hydrophobic pocket and ‘adsorption’/‘dissociation’ of a few water molecules at a hydrophilic crevice in the cleft were induced by dynamic rearrangements of hydrogen-bond networks, and worked as a switch for the domain motions. Our results microscopically demonstrated the importance of hydrogen-bond networks of water molecules in understanding energy landscapes of protein motions.

On the energy components governing molecular recognition in the framework of continuum approaches

Molecular recognition is a process that brings together several biological macromolecules to form a complex and one of the most important characteristics of the process is the binding free energy. Various approaches exist to model the binding free energy, provided the knowledge of the 3D structures of bound and unbound molecules. Among them, continuum approaches are quite appealing due to their computational efficiency while at the same time providing predictions with reasonable accuracy. Here we review recent developments in the field emphasizing on the importance of adopting adequate description of physical processes taking place upon the binding. In particular, we focus on the efforts aiming at capturing some of the atomistic details of the binding phenomena into the continuum framework. When possible, the energy components are reviewed independently of each other. However, it is pointed out that rigorous approaches should consider all energy contributions on the same footage. The two major schemes for utilizing the individual energy components to predict binding affinity are outlined as well.

TRIFORCE: Tessellated Semianalytical Solvent Exposed Surface Areas and Derivatives

We present a new approach to the calculation of solvent-accessible surface areas of molecules with potential application to surface area based methods for determination of solvation free energies. As in traditional analytical and statistical approaches, this new algorithm, called TRIFORCE, reports both component areas and derivatives as a function of the atomic coordinates and radii. Unique to TRIFORCE are the rapid and scalable approaches for the determination of sphere intersection points and numerical estimation of the surface areas, derivatives, and other properties that can be associated with the surface area facets. The algorithm performs a special tessellation and semianalytical integration that uses a precomputed look-up table. This provides a simple way to balance numerical accuracy and memory usage. TRIFORCE calculates derivatives in the same manner, enabling application in force-dependent activities such as molecular geometry minimization. TRIFORCE is available free of charge for academic purposes as both a C++ library, which can be directly interfaced to existing molecular simulation packages, and a web-accessible application.

Propensity to form amyloid fibrils is encoded as excitations in the free energy landscape of monomeric proteins

Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation-prone (N(⁎)) states, which are rarely populated under force free native conditions but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration ([C]), mechanical force (f), and temperature exhibit an apparent two-state behavior, without revealing the presence of the elusive N(⁎) states. Interestingly, the phase boundaries separating the folded and unfolded states at all [C] and f fall on a master curve, which can be quantitatively described using an analogy to superconductors in a magnetic field. The free energy profiles as a function of the molecular extension (R), which are accessible in pulling experiments, (R), reveal the presence of a native-like N(⁎) with a disordered solvent-exposed amino-terminal β-strand. The structure of the N(⁎) state is identical with that found in Fyn SH3 by NMR dispersion experiments. We show that the timescale for fibril formation can be estimated from the population of the N(⁎) state, determined by the free energy gap separating the native structure and the N(⁎) state, a finding that can be used to assess fibril forming tendencies of proteins. The structures of the N(⁎) state are used to show that oligomer formation and likely route to fibrils occur by a domain-swap mechanism in SH3 domain.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Collapse kinetics and chevron plots from simulations of denaturant-dependent folding of globular proteins

Quantitative description of how proteins fold under experimental conditions remains a challenging problem. Experiments often use urea and guanidinium chloride to study folding whereas the natural variable in simulations is temperature. To bridge the gap, we use the molecular transfer model that combines measured denaturant-dependent transfer free energies for the peptide group and amino acid residues, and a coarse-grained C(α)-side chain model for polypeptide chains to simulate the folding of src SH(3) domain. Stability of the native state decreases linearly as [C] (the concentration of guanidinium chloride) increases with the slope, m, that is in excellent agreement with experiments. Remarkably, the calculated folding rate at [C] = 0 is only 16-fold larger than the measured value. Most importantly ln k(obs) (k(obs) is the sum of folding and unfolding rates) as a function of [C] has the characteristic V (chevron) shape. In every folding trajectory, the times for reaching the native state, interactions stabilizing all the substructures, and global collapse coincide. The value of (m(f) is the slope of the folding arm of the chevron plot) is identical to the fraction of buried solvent accessible surface area in the structures of the transition state ensemble. In the dominant transition state, which does not vary significantly at low [C], the core of the protein and certain loops are structured. Besides solving the long-standing problem of computing the chevron plot, our work lays the foundation for incorporating denaturant effects in a physically transparent manner either in all-atom or coarse-grained simulations.

ASPDock: protein-protein docking algorithm using atomic solvation parameters model

Background

Atomic Solvation Parameters (ASP) model has been proven to be a very successful method of calculating the binding free energy of protein complexes. This suggests that incorporating it into docking algorithms should improve the accuracy of prediction. In this paper we propose an FFT-based algorithm to calculate ASP scores of protein complexes and develop an ASP-based protein-protein docking method (ASPDock).

Results

The ASPDock is first tested on the 21 complexes whose binding free energies have been determined experimentally. The results show that the calculated ASP scores have stronger correlation (r ≈ 0.69) with the binding free energies than the pure shape complementarity scores (r ≈ 0.48). The ASPDock is further tested on a large dataset, the benchmark 3.0, which contain 124 complexes and also shows better performance than pure shape complementarity method in docking prediction. Comparisons with other state-of-the-art docking algorithms showed that ASP score indeed gives higher success rate than the pure shape complementarity score of FTDock but lower success rate than Zdock3.0. We also developed a softly restricting method to add the information of predicted binding sites into our docking algorithm. The ASP-based docking method performed well in CAPRI rounds 18 and 19.

Conclusions

ASP may be more accurate and physical than the pure shape complementarity in describing the feature of protein docking.

Studying submicrosecond protein folding kinetics using a photolabile caging strategy and time-resolved photoacoustic calorimetry

Kinetic measurement of protein folding is limited by the method used to trigger folding. Traditional methods, such as stopped flow, have a long mixing dead time and cannot be used to monitor fast folding processes. Here, we report a compound, 4-(bromomethyl)-6,7-dimethoxycoumarin, that can be used as a "photolabile cage" to study the early stages of protein folding. The folding process of a protein, RD1, including kinetics, enthalpy, and volume change, was studied by the combined use of a phototriggered caging strategy and time-resolved photoacoustic calorimetry. The cage caused unfolding of the photolabile protein, and then a pulse UV laser (∼10(-9) s) was used to break the cage, leaving the protein free to refold and allowing the resolving of two folding events on a nanosecond time scale. This strategy is especially good for monitoring fast folding proteins that cannot be studied by traditional methods.

Investigation of the molecular surface area and volume: Defined and calculated by the molecular face theory

Based on the molecular face (MF) theory, the molecular face surface area (MFSA) and molecular face volume (MFV) are defined. For a variety of organic molecules and several inorganic molecules, the MFSA and MFV have been studied and calculated in terms of an algorithm of our own via the Matlab package. The MFV shows a very good linear relationship with the experimentally measured critical molar volume. It is also found that the MFSA and MFV have significant linear correlations with those of the commonly used hard-sphere model and the electron density isosurface.

Generating triangulated macromolecular surfaces by Euclidean Distance Transform

Macromolecular surfaces are fundamental representations of their three-dimensional geometric shape. Accurate calculation of protein surfaces is of critical importance in the protein structural and functional studies including ligand-protein docking and virtual screening. In contrast to analytical or parametric representation of macromolecular surfaces, triangulated mesh surfaces have been proved to be easy to describe, visualize and manipulate by computer programs. Here, we develop a new algorithm of EDTSurf for generating three major macromolecular surfaces of van der Waals surface, solvent-accessible surface and molecular surface, using the technique of fast Euclidean Distance Transform (EDT). The triangulated surfaces are constructed directly from volumetric solids by a Vertex-Connected Marching Cube algorithm that forms triangles from grid points. Compared to the analytical result, the relative error of the surface calculations by EDTSurf is <2–4% depending on the grid resolution, which is 1.5–4 times lower than the methods in the literature; and yet, the algorithm is faster and costs less computer memory than the comparative methods. The improvements in both accuracy and speed of the macromolecular surface determination should make EDTSurf a useful tool for the detailed study of protein docking and structure predictions. Both source code and the executable program of EDTSurf are freely available at http://zhang.bioinformatics.ku.edu/EDTSurf.

Joint neighbors approximation of macromolecular solvent accessible surface area

A new method for approximate analytical calculations of solvent accessible surface area (SASA) for arbitrary molecules and their gradients with respect to their atomic coordinates was developed. This method is based on the recursive procedure of pairwise joining of neighboring atoms. Unlike other available methods of approximate SASA calculations, the method has no empirical parameters, and therefore can be used with comparable accuracy in calculations of SASA in folded and unfolded conformations of macromolecules of any chemical nature. As shown by tests with globular proteins in folded conformations, average errors in absolute atomic surface area is around 1 A2, while for unfolded protein conformations it varies from 1.65 to 1.87 A2. Computational times of the method are comparable with those by GETAREA, one of the fastest exact analytical methods available today.

Systematic study of the boundary composition in Poisson Boltzmann calculations

We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but our results are also of interest to finite difference techniques of Poisson Boltzmann calculations. At first, we identify the critical size of the geometrical elements for discretizing the boundary, and thus the necessary resolution required to establish numerical convergence. In the following two steps we perform reference calculations on a set of dipeptides in different conformations using the Polarizable Continuum Model and a high-level Density Functional as well as a high-quality basis set. Afterwards, we propose a mechanism for defining appropriate boundary geometries. Finally, we compare the classic Poisson Boltzmann description with the Quantum Chemical description, and aim at finding appropriate fitting parameters to get a close match to the reference data. Surprisingly, when using default AMBER partial charges and the rigorous geometric parameters derived in the initial two stages, no scaling of the partial charges is necessary and the best fit against the reference set is obtained automatically.

A contact energy function considering residue hydrophobic environment and its application in protein fold recognition

The three-dimensional (3D) structure prediction of proteins is an important task in bioinformatics. Finding energy functions that can better represent residue-residue and residue-solvent interactions is a crucial way to improve the prediction accuracy. The widely used contact energy functions mostly only consider the contact frequency between different types of residues; however, we find that the contact frequency also relates to the residue hydrophobic environment. Accordingly, we present an improved contact energy function to integrate the two factors, which can reflect the influence of hydrophobic interaction on the stabilization of protein 3D structure more effectively. Furthermore, a fold recognition (threading) approach based on this energy function is developed. The testing results obtained with 20 randomly selected proteins demonstrate that, compared with common contact energy functions, the proposed energy function can improve the accuracy of the fold template prediction from 20% to 50%, and can also improve the accuracy of the sequence-template alignment from 35% to 65%.

Folding of the protein domain hbSBD

The folding of the alpha-helix domain hbSBD of the mammalian mitochondrial branched-chain alpha-ketoacid dehydrogenase complex is studied by the circular dichroism technique in absence of urea. Thermal denaturation is used to evaluate various thermodynamic parameters defining the equilibrium unfolding, which is well described by the two-state model with the folding temperature T(F) = 317.8 +/- 1.95 K and the enthalpy change DeltaH(G) = 19.67 +/- 2.67 kcal/mol. The folding is also studied numerically using the off-lattice coarse-grained Go model and the Langevin dynamics. The obtained results, including the population of the native basin, the free-energy landscape as a function of the number of native contacts, and the folding kinetics, also suggest that the hbSBD domain is a two-state folder. These results are consistent with the biological function of hbSBD in branched-chain alpha-ketoacid dehydrogenase.