Rotamer strain as a determinant of protein structural specificity

We present direct evidence for a change in protein structural specificity due to hydrophobic core packing. High resolution structural analysis of a designed core variant of ubiquitin reveals that the protein is in slow exchange between two conformations. Examination of side-chain rotamers indicates that this dynamic response and the lower stability of the protein are coupled to greater strain and mobility in the core. The results suggest that manipulating the level of side-chain strain may be one way of fine tuning the stability and specificity of proteins.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Contact patterns between helices and strands of sheet define protein folding patterns

Comparing and classifying protein folding patterns allows organizing the known structures and enumerating possible protein structural patterns including those not yet observed. We capture the essence of protein folding patterns in a concise tableau representation based on the order and contact patterns of secondary structures: helices and strands of sheet. The tableaux are intelligible to both humans and computers. They provide a database, derived from the Protein Data Bank, mineable in studies of protein architecture. Using this database, we have: (i) determined statistical properties of secondary structure contacts in an unbiased set of protein domains from ASTRAL, (ii) observed that in 98% of cases, the tableau is a faithful representation of the folding pattern as classified in SCOP, (iii) demonstrated that to a large extent the local structure of proteins indicates their complete folding topology, and (iv) studied the use of the representation for fold identification.     

The osmophobic effect: natural selection of a thermodynamic force in protein folding

Intracellular organic osmolytes are present in certain organisms adapted to harsh environments and these osmolytes protect intracellular macromolecules against the denaturing environmental stress. In natural selection of organic osmolytes as protein stabilizers, it appears that the osmolyte property selected for is the unfavorable interaction between the osmolyte and the peptide backbone, a solvophobic thermodynamic force that we call the osmophobic effect. Because the peptide backbone is highly exposed to osmolyte in the denatured state, the osmophobic effect preferentially raises the free energy of the denatured state, shifting the equilibrium in favor of the native state. By focusing the solvophobic force on the denatured state, the native state is left free to function relatively unfettered by the presence of osmolyte. The osmophobic effect is a newly uncovered thermodynamic force in nature that complements the well-recognized hydrophobic interactions, hydrogen bonding, electrostatic and dispersion forces that drive protein folding. In organisms whose survival depends on the intracellular presence of osmolytes that can counteract denaturing stresses, the osmophobic effect is as fundamental to protein folding as these well-recognized forces.     

Morphogenesis of a protein: folding pathways and the energy landscape

Current knowledge on the reaction whereby a protein acquires its native three-dimensional structure was obtained by and large through characterization of the folding mechanism of simple systems. Given the multiplicity of amino acid sequences and unique folds, it is not so easy, however, to draw general rules by comparing folding pathways of different proteins. In fact, quantitative comparison may be jeopardized not only because of the vast repertoire of sequences but also in view of a multiplicity of structures of the native and denatured states. We have tackled the problem of the relationships between the sequence information and the folding pathway of a protein, using a combination of kinetics, protein engineering and computational methods, applied to relatively simple systems. Our strategy has been to investigate the folding mechanism determinants using two complementary approaches, i.e. (i) the study of members of the same family characterized by a common fold, but substantial differences in amino acid sequence, or (ii) heteromorphic pairs characterized by largely identical sequences but with different folds. We discuss some recent data on protein-folding mechanisms by presenting experiments on different members of the PDZ domain family and their circularly permuted variants. Characterization of the energetics and structures of intermediates and TSs (transition states), obtained by Φ-value analysis and restrained MD (molecular dynamics) simulations, provides a glimpse of the malleability of the dynamic states and of the role of the topology of the native states and of the denatured states in dictating folding and misfolding pathways.     

Direct observation of active protein folding using lock-in force spectroscopy

Direct observation of the folding of a single polypeptide chain can provide important information about the thermodynamic states populated along its folding pathway. In this study, we present a lock-in force-spectroscopy technique that improves resolution of atomic-force microscopy force spectroscopy to 400 fN. Using this technique we show that immunoglobulin domain 4 from Dictyostelium discoideum filamin (ddFLN4) refolds against forces of ∼4 pN. Our data show folding of this domain proceeds directly from an extended state and no thermodynamically distinct collapsed state of the polypeptide before folding is populated. Folding of ddFLN4 under load proceeds via an intermediate state. Three-state folding allows ddFLN4 to fold against significantly larger forces than would be possible for a mere two-state folder. We present a general model for protein folding kinetics under load that can predict refolding forces based on chain-length and zero force refolding rate.     

Statistical mechanics of protein folding with separable energy functions

We have initiated an entirely new approach to statistical mechanical models of strongly interacting systems where the configurational parameters and the potential energy function are both constructed so that the canonical partition function can be evaluated analytically. For a simplified model of proteins consisting of a single, fairly short polypeptide chain without cross-links, we can adjust the energy parameters to favor the experimentally determined native state of seven proteins having diverse types of folds. Then 497 test proteins are predicted to have stable native folds, even though they are also structurally diverse, and 480 of them have no significant sequence similarity to any of the training proteins.     

Proline residues in transmembrane alpha helices affect the folding of bacteriorhodopsin

Proline residues occur frequently in transmembrane alpha helices, which contrasts with their behaviour as helix-breakers in water-soluble proteins. The three membrane-embedded proline residues of bacteriorhodopsin have been replaced individually by alanine and glycine to give P50A, or P50G on helix B, P91A, or P91G on helix C, and P186A or P186G on helix F, and the effect on the protein folding kinetics has been investigated. The rate-limiting apoprotein folding step, which results in formation of a seven transmembrane, alpha helical state, was slower than wild-type protein for the Pro50 and Pro91 mutants, regardless of whether they were mutated to Ala or Gly. These proline residues give rise to several inter-helix contacts, which are therefore important in folding to the seven transmembrane helix state. No evidence for cis-trans isomerisations of the peptidyl prolyl bonds was found during this rate-limiting apoprotein folding step. Mutations of all three membrane-embedded proline residues affected the subsequent retinal binding and final folding to bacteriorhodopsin, suggesting that these proline residues contribute to formation of the retinal binding pocket within the helix bundle, again via helix/helix interactions. These results point to proline residues in transmembrane alpha helices being important in the folding of integral membrane proteins. The helix/helix interactions and hydrogen bonds that arise from the presence of proline residues in transmembrane alpha helices can affect the formation of transmembrane alpha helix bundles as well as cofactor binding pockets.     

Packing of transmembrane helices in bacteriorhodopsin folding: structure and thermodynamics

We propose a coarse-grained (CG) model to study the native structure and physical properties of helical membrane proteins (HMPs) using off-lattice computer simulations. Instead of considering sequence heterogeneity explicitly, we model its effect on the packing of helices by employing a mean packing parameter r(0), which is calculated from an all-atom (AA) model. Specifically, this CG model is applied to investigate the packing of helices in bacteriorhodopsin (BR), and predicts the seven helix bundle structure of BR with a root mean square deviation (RMSD) in coordinates of helix backbone atoms (N, C, C(alpha)) of 3.99 A from its crystal structure. This predicted structure is further refined in an AA model by Amber and the refined structure has a RMSD (in coordinates of helix backbone atoms) of 2.64 A. The predicted packing position, tilting angle, and orientation angle of each helix in the refined structure are consistent with experimental data and their physical origins can be well understood in our model. Our results show that a reasonably good structure of BR can be predicted by using such a dual-scale approach, provided that its secondary structure is known. Starting from a random initial configuration, the folded structure can be obtained in days using a regular desktop computer. Various thermodynamic properties of helix packing of BR are also investigated in this CG model.     

Folding-unfolding energy change of a simple sphere model protein and an energy landscape of the folding process

We have calculated the free energy of a spherical model of a protein or part of a protein generated in the way of protein folding. Two spherical models are examined; one is a homogeneous model consisting of only one residue type—hydrophobic. The other is a heterogeneous model consisting of two residue types—strong hydrophobic and weak hydrophobic. Both models show a folding transition state, and the latter model reproduces the trend of the experimental folded-unfolded energy change. The heterogeneous model suggests that in the folding process of a protein of more than 70 residues, a specific region of the protein folds first to form a stable region, then the other residues follow the folding process. The energy landscape of folding of a small protein is approximately a funnel model, whereas a flatter energy landscape is suggested for larger proteins of more than 55–70 residues. Proteins 33:408–416, 1998. © 1998 Wiley-Liss, Inc.     

Calculation of the free energy and cooperativity of protein folding

Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design.     

Cooperative folding in a multi-domain protein

Most protein domains are found in multi-domain proteins, yet most studies of protein folding have concentrated on small, single-domain proteins or on isolated domains from larger proteins. Spectrin domains are small (106 amino acid residues), independently folding domains consisting of three long alpha-helices. They are found in multi-domain proteins with a number of spectrin domains in tandem array. Structural studies have shown that in these arrays the last helix of one domain forms a continuous helix with the first helix of the following domain. It has been demonstrated that a number of spectrin domains are stabilised by their neighbours. Here we investigate the molecular basis for cooperativity between adjacent spectrin domains 16 and 17 from chicken brain alpha-spectrin (R16 and R17). We show that whereas the proteins unfold as a single cooperative unit at 25 degrees C, cooperativity is lost at higher temperatures and in the presence of stabilising salts. Mutations in the linker region also cause the cooperativity to be lost. However, the cooperativity does not rely on specific interactions in the linker region alone. Most mutations in the R17 domain cause a decrease in cooperativity, whereas proteins with mutations in the R16 domain still fold cooperatively. We propose a mechanism for this behaviour.     

Non-linear rate-equilibrium free energy relationships and Hammond behavior in protein folding

Non-linear rate-equilibrium relationships upon mutation or changes in solvent conditions are frequently observed in protein folding reactions and are usually interpreted in terms of Hammond behavior. Here we first give a general overview over the concept of transition state movements in chemical reactions and discuss its application to protein folding. We then show examples for genuine Hammond behavior and for apparent transition state movements caused by other effects like changes in the rate-limiting step of the folding reaction or ground state effects, i.e. structural changes in either the native state or the unfolded state. These examples show that apparent transition state movements can easily be mistaken for Hammond behavior. We describe experimental tests using self- and cross-interaction parameters to distinguish between structural changes in a single transition state following Hammond behavior and apparent transition state movements caused by other effects.     

Fluctuations of primary ubiquitin folding intermediates in a force clamp

Folding experiments of single ubiquitin molecules under force clamp using an atomic force microscope revealed a dynamic long-lived intermediate with nanometer scale end-to-end distance fluctuations along an unexpectedly complex folding pathway. To examine the nature of this intermediate at the atomic level as well as the driving forces that give rise to the observed fluctuations, we performed molecular dynamics refolding simulations of unfolded ubiquitin under constant force. After an initial fast collapse, we find a highly dynamic, broad ensemble of conformations with partial and continuously changing secondary structure and side chain interactions. This ensemble resembles a molten-globule-like state, similar in nature to the previously described non-native state of ubiquitin in solution, but stretched by the external force. The scale of the end-to-end distance fluctuations derived from the simulations compares well with experiment. Transient formation of unspecific and metastable hydrophobic clusters along the chain are found to give rise to the observed end-to-end distance fluctuations. These distinct collapses, interpreted as folding attempts, imply an upper limit for the folding attempt frequency of approximately 10 ns. Our results suggest possible relations between force-induced unfolding and temperature or chemically induced denaturation.     

The role of protein homochirality in shaping the energy landscape of folding

The homochirality, or isotacticity, of the natural amino acids facilitates the formation of regular secondary structures such as alpha-helices and beta-sheets. However, many examples exist in nature where novel polypeptide topologies use both l- and d-amino acids. In this study, we explore how stereochemistry of the polypeptide backbone influences basic properties such as compactness and the size of fold space by simulating both lattice and all-atom polypeptide chains. We formulate a rectangular lattice chain model in both two and three dimensions, where monomers are chiral, having the effect of restricting local conformation. Syndiotactic chains with alternating chirality of adjacent monomers have a very large ensemble of accessible conformations characterized predominantly by extended structures. Isotactic chains on the other hand, have far fewer possible conformations and a significant fraction of these are compact. Syndiotactic chains are often unable to access maximally compact states available to their isotactic counterparts of the same length. Similar features are observed in all-atom models of isotactic versus syndiotactic polyalanine. Our results suggest that protein isotacticity has evolved to increase the enthalpy of chain collapse by facilitating compact helical states and to reduce the entropic cost of folding by restricting the size of the unfolded ensemble of competing states.     

Dynamics of protein folding and cofactor binding monitored by single-molecule force spectroscopy

Many proteins in living cells require cofactors to carry out their biological functions. To reach their functional states, these proteins need to fold into their unique three-dimensional structures in the presence of their cofactors. Two processes, folding of the protein and binding of cofactors, intermingle with each other, making the direct elucidation of the folding mechanism of proteins in the presence of cofactors challenging. Here we use single-molecule atomic force microscopy to directly monitor the folding and cofactor binding dynamics of an engineered metal-binding protein G6-53 at the single-molecule level. Using the mechanical stability of different conformers of G6-53 as sensitive probes, we directly identified different G6-53 conformers (unfolded, apo- and Ni²⁺-bound) populated along the folding pathway of G6-53 in the presence of its cofactor Ni²⁺. By carrying out single-molecule atomic force microscopy refolding experiments, we monitored kinetic evolution processes of these different conformers. Our results suggested that the majority of G6-53 folds through a binding-after-folding mechanism, whereas a small fraction follows a binding-before-folding pathway. Our study opens an avenue to utilizing force spectroscopy techniques to probe the folding dynamics of proteins in the presence of cofactors at the single-molecule level, and we anticipated that this method can be used to study a wide variety of proteins requiring cofactors for their function.     

Calculation of mutational free energy changes in transition states for protein folding

Recent advances in experimental and computational methods have made it possible to determine with considerable accuracy the structures whose formation is rate limiting for the folding of some small proteins-the transition state ensemble, or TSE. We present a method to analyze and validate all-atom models of such structures. The method is based on the comparison of experimental data with the computation of the change in free energy of the TSE resulting from specific mutations. Each mutation is modeled individually in all members of an ensemble of transition state structures using a method originally developed to predict mutational changes in the stability of native proteins. We first apply this method to six proteins for which we have determined the TSEs with a technique that uses experimental mutational data (Phi-values) as restraints in the structure determination and find a highly significant correlation between the calculated free energy changes and those derived from experimental kinetic data. We then use the procedure to analyze transition state structures determined by molecular dynamics simulations of unfolding, again finding a high correlation. Finally, we use the method to estimate changes in folding rates of several hydrophobic core mutants of Fyn SH3. Taken together, these results show that the procedure developed here is a tool of general validity for analyzing, assessing, and improving the quality of the structures of transition states for protein folding.     

Probing the energy landscape of protein folding/unfolding transition states

Previous molecular dynamics (MD) simulations of the thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided atomic-resolution models of the transition state ensemble that is well supported by experimental studies. Here, we use simulations to further investigate the energy landscape around the transition state region. Nine structures within approximately 35 ps and 3 A C(alpha) RMSD of the transition state ensemble identified in a previous 498 K thermal denaturation simulation were quenched under the quasi-native conditions of 335 K and neutral pH. All of the structures underwent hydrophobically driven collapse in response to the drop in temperature. Structures less denatured than the transition state became structurally more native-like, while structures that were more denatured than the transition state tended to show additional loss of native structure. The structures in the immediate region of the transition state fluctuated between becoming more and less native-like. All of the starting structures had the same native-like topology and were quite similar (within 3.5 A C(alpha) RMSD). That the structures all shared native-like topology, yet diverged into either more or less native-like structures depending on which side of the transition state they occupied on the unfolding trajectory, indicates that topology alone does not dictate protein folding. Instead, our results suggest that a detailed interplay of packing interactions and interactions with water determine whether a partially denatured protein will become more native-like under refolding conditions.