Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

A polar, solvent-exposed residue can be essential for native protein structure

BACKGROUND: A large energy gap between the native state and the non-native folded states is required for folding into a unique three-dimensional structure. The features that define this energy gap are not well understood, but can be addressed using de novo protein design. Previously, alpha(2)D, a dimeric four-helix bundle, was designed and shown to adopt a native-like conformation. The high-resolution solution structure revealed that this protein adopted a bisecting U motif. Glu7, a solvent-exposed residue that adopts many conformations in solution, might be involved in defining the unique three-dimensional structure of alpha(2)D. RESULTS: A variety of hydrophobic and polar residues were substituted for Glu7 and the dynamic and thermodynamic properties of the resulting proteins were characterized by analytical ultracentrifugation, circular dichroism spectroscopy, and nuclear magnetic resonance spectroscopy. The majority of substitutions at this solvent-exposed position had little affect on the ability to fold into a dimeric four-helix bundle. The ability to adopt a unique conformation, however, was profoundly modulated by the residue at this position despite the similar free energies of folding of each variant. CONCLUSIONS: Although Glu7 is not involved directly in stabilizing the native state of alpha(2)D, it is involved indirectly in specifying the observed fold by modulating the energy gap between the native state and the non-native folded states. These results provide experimental support for hypothetical models arising from lattice simulations of protein folding, and underscore the importance of polar interfacial residues in defining the native conformations of proteins.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Im7 folding mechanism: misfolding on a path to the native state

Many proteins populate collapsed intermediate states during folding. In order to elucidate the nature and importance of these species, we have mapped the structure of the on-pathway intermediate of the four-helix protein, Im7, together with the conformational changes it undergoes as it folds to the native state. Kinetic data for 29 Im7 point mutants show that the intermediate contains three of the four helices found in the native structure, packed around a specific hydrophobic core. However, the intermediate contains many non-native interactions; as a result, hydrophobic interactions become disrupted in the rate-limiting transition state before the final helix docks onto the developing structure. The results of this study support a hierarchical mechanism of protein folding and explain why the misfolding of Im7 occurs. The data also demonstrate that non-native interactions can play a significant role in folding, even for small proteins with simple topologies.     

Understanding how small helical proteins fold: conformational dynamics of Im proteins relevant to their folding landscapes

Understanding the mechanism of folding of small proteins requires characterization of their starting unfolded states and any partially unfolded states populated during folding. Here, we review what is known from NMR about these states of Im7, a 4-helix bundle protein that folds via an on-pathway intermediate, and show that there is an alignment of non-native structure in urea-unfolded Im7 with the helices of native Im7 that is a consequence of hydrophobic helix-promoting residues also promoting cluster-formation in the unfolded protein. We suggest that this kind of alignment is present in other proteins and is relevant to how native state topology determines folding rates.     

A new computational model for protein folding based on atomic solvation.

A new model for calculating the solvation energy of proteins is developed and tested for its ability to identify the native conformation as the global energy minimum among a group of thousands of computationally generated compact non-native conformations for a series of globular proteins. In the model (called the WZS model), solvation preferences for a set of 17 chemically derived molecular fragments of the 20 amino acids are learned by a training algorithm based on maximizing the solvation energy difference between native and non-native conformations for a training set of proteins. The performance of the WZS model confirms the success of this learning approach; the WZS model misrecognizes (as more stable than native) only 7 of 8,200 non-native structures. Possible applications of this model to the prediction of protein structure from sequence are discussed.     

Switching two-state to three-state kinetics in the helical protein Im9 via the optimisation of stabilising non-native interactions by design

The four-helix protein Im7 folds through an on-pathway intermediate at pH 7.0 and 10 degrees C. By contrast, under these conditions there is no evidence for a populated intermediate in the folding of its more stable homologue, Im9, even in the presence of 0.4 M sodium sulphate. Previous studies using phi-value analysis have shown that the Im7 intermediate is misfolded, in that three of its four native helices are formed, but are docked in a non-native manner. Using knowledge of the structure of the intermediate of Im7, we have used rational design to stabilise an intermediate formed during the folding of Im9 by the introduction of specific stabilising interactions at positions known to stabilise the Im7 folding intermediate through non-native interactions. We show that the redesigned Im9 sequence folds with three-state kinetics at pH 7.0 and have used phi-value analysis to demonstrate that this species resembles the misfolded intermediate populated during Im7 folding. The redesigned Im9 sequence folds 20-fold faster than the wild-type protein under conditions in which folding is two-state. The data show that intermediate formation is an important feature of folding, even for small proteins such as Im9 for which these partially folded states do not become significantly populated. In addition, they show that the introduction of stabilising interactions can lead to rapid refolding, even when the contacts introduced are non-native.     

Folding simulations of small proteins

Understanding how a protein folds is a long-standing challenge in modern science. We have used an optimized atomistic model (united-residue force field) to simulate folding of small proteins of various structures: HP-36 (alpha protein), protein A (beta), 1fsd (alpha+beta), and betanova (beta). Extensive Monte Carlo folding simulations (ten independent runs with 10(9) Monte Carlo steps at a temperature) starting from non-native conformations are carried out for each protein. In all cases, proteins fold into their native-like conformations at appropriate temperatures, and glassy transitions occur at low temperatures. To investigate early folding trajectories, 200 independent runs with 10(6) Monte Carlo steps are also performed at a fixed temperature for a protein. There are a variety of possible pathways during non-equilibrium early processes (fast process, approximately 10(4) Monte Carlo steps). Finally, these pathways converge to the point unique for each protein. The convergence point of the early folding pathways can be determined only by direct folding simulations. The free energy surface, an equilibrium thermodynamic property, dictates the rest of the folding (slow process, approximately 10(8) Monte Carlo steps).     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Identification of native protein folds amongst a large number of incorrect models. The calculation of low energy conformations from potentials of mean force

We present an approach that is able to detect native folds amongst a large number of non-native conformations. The method is based on the compilation of potentials of mean force of the interactions of the C beta atoms of all amino acid pairs from a database of known three-dimensional protein structures. These potentials are used to calculate the conformational energy of amino acid sequences in a number of different folds. For a substantial number of proteins we find that the conformational energy of the native state is lowest amongst the alternatives. Exceptions are proteins containing large prosthetic groups, Fe-S clusters or polypeptide chains that do not adopt globular folds. We discuss briefly potential applications in various fields of protein structural research.     

Amino Acid Insertion Reveals a Necessary Three-Helical Intermediate in the Folding Pathway of the Colicin E7 Immunity Protein Im7

The small (87-residue) α-helical protein Im7 (an inhibitor protein for colicin E7 that provides immunity to cells producing colicin E7) folds via a three-state mechanism involving an on-pathway intermediate. This kinetic intermediate contains three of four native helices that are oriented in a non-native manner so as to minimise exposed hydrophobic surface area at this point in folding. The short (6-residue) helix III has been shown to be unstructured in the intermediate ensemble and does not dock onto the developing hydrophobic core until after the rate-limiting transition state has been traversed. After helix III has docked, it adopts an α-helical secondary structure, and the side chains of residues within this region provide contacts that are crucial to native-state stability. In order to probe further the role of helix III in the folding mechanism of Im7, we created a variant that contains an eight-amino-acid polyalanine-like helix stabilised by a Glu-Arg salt bridge and an Asn-Pro-Gly capping motif, juxtaposed C-terminal to the natural 6-residue helix III. The effect of this insertion on the structure of the native protein and its folding mechanism were studied using NMR and ?-value analysis, respectively. The results reveal a robust native structure that is not perturbed by the presence of the extended helix III. Mutational analysis performed to probe the folding mechanism of the redesigned protein revealed a conserved mechanism involving the canonical three-helical intermediate. The results suggest that folding via a three-helical species stabilised by both native and non-native interactions is an essential feature of Im7 folding, independent of the helical propensity of helix III.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

Statistical mechanics of protein folding by cluster distance geometry

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.     

Wild type, mutant protein unfolding and phase transition detected by single-nanopore recording

Understanding protein folding remains a challenge. A difficulty is to investigate experimentally all the conformations in the energy landscape. Only single molecule methods, fluorescence and force spectroscopy, allow observing individual molecules along their folding pathway. Here we observe that single-nanopore recording can be used as a new single molecule method to explore the unfolding transition and to examine the conformational space of native or variant proteins. We show that we can distinguish unfolded states from partially folded ones with the aerolysin pore. The unfolding transition curves of the destabilized variant are shifted toward the lower values of the denaturant agent compared to the wild type protein. The dynamics of the partially unfolded wild type protein follows a first-order transition. The denaturation curve obtained with the aerolysin pore is similar to that obtained with the α-hemolysin pore. The nanopore geometry or net charge does not influence the folding transition but changes the dynamics.     

Using scores derived from statistical coupling analysis to distinguish correct and incorrect folds in de-novo protein structure prediction

Distinguishing native from non-native folds remains a challenging problem for protein structure prediction. We describe a method, SCA-distance scoring, based on results from statistical coupling analysis which discriminates between native and non-native folds produced by a de novo protein structure prediction method for four out of five test proteins. The method is particularly good at discriminating non-native folds which are close in RMSD to the true fold but contain a change in an internal structural element. SCA-distance scoring is a useful addition to the tools available for distinguishing native from non-native folds in protein structure prediction.     

Blind Test of Physics-Based Prediction of Protein Structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.     

Specific non-native hydrophobic interactions in a hidden folding intermediate: implications for protein folding

Structures of intermediates and transition states in protein folding are usually characterized by amide hydrogen exchange and protein engineering methods and interpreted on the basis of the assumption that they have native-like conformations. We were able to stabilize and determine the high-resolution structure of a partially unfolded intermediate that exists after the rate-limiting step of a four-helix bundle protein, Rd-apocyt b(562), by multidimensional NMR methods. The intermediate has partial native-like secondary structure and backbone topology, consistent with our earlier native state hydrogen exchange results. However, non-native hydrophobic interactions exist throughout the structure. These and other results in the literature suggest that non-native hydrophobic interactions may occur generally in partially folded states. This can alter the interpretation of mutational protein engineering results in terms of native-like side chain interactions. In addition, since the intermediate exists after the rate-limiting step and Rd-apocyt b(562) folds very rapidly (k(f) approximately 10(4) s(-1)), these results suggest that non-native hydrophobic interactions, in the absence of topological misfolding, are repaired too rapidly to slow folding and cause the accumulation of folding intermediates. More generally, these results illustrate an approach for determining the high-resolution structure of folding intermediates.     

Discrimination of native loop conformations in membrane proteins: decoy library design and evaluation of effective energy scoring functions

The recent determination of crystal structures for several important membrane proteins opens the way for comparative modeling of their membrane-spanning regions. However, the ability to predict correctly the structures of loop regions, which may be critical, for example, in ligand binding, remains a considerable challenge. To meet this challenge, accurate scoring methods have to discriminate between candidate conformations of an unknown loop structure. Some success in loop prediction has been reported for globular proteins; however, the proximity of membrane protein loops to the lipid bilayer casts doubt on the applicability of the same scoring methods to this problem. In this work, we develop "decoy libraries" of non-native folds generated, using the structures of two membrane proteins, with molecular dynamics and Monte Carlo techniques over a range of temperatures. We introduce a new approach for decoy library generation by constructing a flat distribution of conformations covering a wide range of Calpha-root-mean-square deviation (RMSD) from the native structure; this removes possible bias in subsequent scoring stages. We then score these decoy conformations with effective energy functions, using increasingly more cpu-intensive implicit solvent models, including (1) simple Coulombic electrostatics with constant or distance-dependent dielectrics; (2) atomic solvation parameters; (3) the effective energy function (EEF1) of Lazaridis and Karplus; (4) generalized Born/Analytical Continuum Solvent; and (5) finite-difference Poisson-Boltzmann energy functions. We show that distinction of native-like membrane protein loops may be achieved using effective energies with the assumption of a homogenous environment; thus, the absence of the adjacent lipid bilayer does not affect the scoring ability. In particular, the Analytical Continuum Solvent and finite-difference Poisson-Boltzmann energy functions are seen to be the most powerful scoring functions. Interestingly, the use of the uncharged states of ionizable sidechains is shown to aid prediction, particularly for the simplest energy functions.     

Differential effects of ribosomal proteins and Mg2+ ions on a conformational switch during 30S ribosome 5′-domain assembly

Ribosomal protein S4 nucleates assembly of the 30S ribosome 5′ and central domains, which is crucial for the survival of cells. Protein S4 changes the structure of its 16S rRNA binding site, passing through a non-native intermediate complex before forming native S4-rRNA contacts. Ensemble FRET was used to measure the thermodynamic stability of non-native and native S4 complexes in the presence of Mg²⁺ ions and other 5′-domain proteins. Equilibrium titrations of Cy3-labeled 5′-domain RNA with Cy5-labeled protein S4 showed that Mg²⁺ ions preferentially stabilize the native S4-rRNA complex. In contrast, ribosomal proteins S20 and S16 act by destabilizing the non-native S4-rRNA complex. The full cooperative switch to the native complex requires S4, S16, and S20 and is achieved to a lesser degree by S4 and S16. The resulting thermodynamic model for assembly of the 30S body illustrates how ribosomal proteins selectively bias the equilibrium between alternative rRNA conformations, increasing the cooperativity of rRNA folding beyond what can be achieved by Mg²⁺ ions alone.     

Calcium as a Crucial Cofactor for Low Density Lipoprotein Receptor Folding in the Endoplasmic Reticulum

The family of low density lipoprotein (LDL) receptors mediate uptake of a plethora of ligands from the circulation and couple this to signaling, thereby performing a crucial role in physiological processes including embryonic development, cancer development, homeostasis of lipoproteins, viral infection, and neuronal plasticity. Structural integrity of individual ectodomain modules in these receptors depends on calcium, and we showed before that the LDL receptor folds its modules late after synthesis via intermediates with abundant non-native disulfide bonds and structure. Using a radioactive pulse-chase approach, we here show that for proper LDL receptor folding, calcium had to be present from the very early start of folding, which suggests at least some native, essential coordination of calcium ions at the still largely non-native folding phase. As long as the protein was in the endoplasmic reticulum (ER), its folding was reversible, which changed only upon both proper incorporation of calcium and exit from the ER. Coevolution of protein folding with the high calcium concentration in the ER may be the basis for the need for this cation throughout the folding process even though calcium is only stably integrated in native repeats at a later stage.