Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Designing potential energy functions for protein folding.

By following a consistent line of physical reasoning, some fundamental understanding about the foldability of proteins has been achieved. In recent years, this has led to the development of a number of successful algorithms for optimizing potential energy functions for folding protein models. The differences between the folding mechanisms of simple, contact-based lattice proteins and more traditional, realistic protein models, however, still call for further development of the potentials in addition to the optimization approaches.     

The foldability landscape of model proteins

Molecular evolution may be considered as a walk in a multidimensional fitness landscape, where the fitness at each point is associated with features such as the function, stability, and survivability of these molecules. We present a simple model for the evolution of protein sequences on a landscape with a precisely defined fitness function. We use simple lattice models to represent protein structures, with the ability of a protein sequence to fold into the structure with lowest energy, quantified as the foldability, representing the fitness of the sequence. The foldability of the sequence is characterized based on the spin glass model of protein folding. We consider evolution as a walk in this foldability landscape and study the nature of the landscape and the resulting dynamics. Selective pressure is explicitly included in this model in the form of a minimum foldability requirement. We find that different native structures are not evenly distributed in interaction space, with similar structures and structures with similar optimal foldabilities clustered together. Evolving proteins marginally fulfill the selective criteria of foldability. As the selective pressure is increased, evolutionary trajectories become increasingly confined to “neutral networks,” where the sequence and the interactions can be significantly changed while a constant structure is maintained. © 1997 John Wiley & Sons, Inc. Biopoly 42: 427–438, 1997     

Identification of a key structural element for protein folding within beta-hairpin turns

Specific residues in a polypeptide may be key contributors to the stability and foldability of the unique native structure. Identification and prediction of such residues is, therefore, an important area of investigation in solving the protein folding problem. Atypical main-chain conformations can help identify strains within a folded protein, and by inference, positions where unique amino acids may have a naturally high frequency of occurrence due to favorable contributions to stability and folding. Non-Gly residues located near the left-handed alpha-helical region (L-alpha) of the Ramachandran plot are a potential indicator of structural strain. Although many investigators have studied mutations at such positions, no consistent energetic or kinetic contributions to stability or folding have been elucidated. Here we report a study of the effects of Gly, Ala and Asn substitutions found within the L-alpha region at a characteristic position in defined beta-hairpin turns within human acidic fibroblast growth factor, and demonstrate consistent effects upon stability and folding kinetics. The thermodynamic and kinetic data are compared to available data for similar mutations in other proteins, with excellent agreement. The results have identified that Gly at the i+3 position within a subset of beta-hairpin turns is a key contributor towards increasing the rate of folding to the native state of the polypeptide while leaving the rate of unfolding largely unchanged.     

Foldability, enzymatic activity, and interacting ability of barnase mutants obtained by permutation of secondary structure units

Barnase, a well-characterized ribonuclease, has been decomposed into six modules (M1-M6) or secondary structure units (S1-S6). We have studied the foldability and activity of the barnase mutants obtained by permutation of the four internal modules (M2-M5) or secondary structure units (S2-S5) to investigate whether permutation of these building blocks is a useful way to create foldable and/or functional proteins. In this study, we found that one of the secondary structure unit mutants was expressed in Escherichia coli only when His102 was substituted by alanine, which is a catalytic residue of wild-type barnase. This mutant (S2354H102A) had ordered conformations, which unfolded cooperatively during urea-induced unfolding experiments. S2354H102A interacted with other barnase mutants to show a distinct RNase activity, although its own activity was quite weak. This interaction was specific, because S2354H102A interacted with only barnase mutants having His 102 and certain orders of the secondary structure units giving a distinct RNase activity. These results suggest that secondary structure units permuted in barnase mutants maintain their intrinsic "interacting ability" that is used for the folding of wild-type barnase, and the units can form certain conformations that complement those of the appropriate counterparts. Seven of 23 secondary structure unit mutants and only 2 of 23 module mutants had RNase activity. On the basis of the results of analyses of foldability and RNase activity of the mutants performed in this and previous studies, we conclude that secondary structure units are more suitable than modules as building blocks to create novel foldable and/or functional proteins in the case of barnase.     

On predicting foldability of a protein from its sequence

Several properties of amino acid sequences corresponding to proteins that are known to fold are compared to those of randomly generated sequences and to sequences of intrinsically disordered proteins in order to find properties that distinguish folding sequences from the rest. The properties studied included helix and sheet propensities from secondary structure prediction, adjacency correlations, directionality correlations, as well as propensities of all possible triplets and quadruplets. Small differences between known folded and random sequences were observed for the adjacency and directional correlations, and significant differences were seen on the triplet and especially on the quadruplet propensities. Based on the differences in the adjacency, triplet or quadruplet propensities folding scores were defined and used to test the accuracy of foldability prediction based on these statistics. The best predictions were obtained from the quadruplet propensities.     

Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins

Recent experimental results suggest that the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble, at least for small, fast-folding proteins. To investigate the extent of the topological control of the folding process, we studied the folding of simplified models of five small globular proteins constructed using a Go-like potential to retain the information about the native structures but drastically reduce the energetic frustration and energetic heterogeneity among residue-residue native interactions. By comparing the structure of the transition state ensemble (experimentally determined by Phi-values) and of the intermediates with those obtained using our models, we show that these energetically unfrustrated models can reproduce the global experimentally known features of the transition state ensembles and "en-route" intermediates, at least for the analyzed proteins. This result clearly indicates that, as long as the protein sequence is sufficiently minimally frustrated, topology plays a central role in determining the folding mechanism.     

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.     

Protein Folding Requires Crowd Control in a Simulated Cell

Macromolecular crowding has a profound effect upon biochemical processes in the cell. We have computationally studied the effect of crowding upon protein folding for 12 small domains in a simulated cell using a coarse-grained protein model, which is based upon Langevin dynamics, designed to unify the often disjoint goals of protein folding simulation and structure prediction. The model can make predictions of native conformation with accuracy comparable with that of the best current template-free models. It is fast enough to enable a more extensive analysis of crowding than previously attempted, studying several proteins at many crowding levels and further random repetitions designed to more closely approximate the ensemble of conformations. We found that when crowding approaches 40% excluded volume, the maximum level found in the cell, proteins fold to fewer native-like states. Notably, when crowding is increased beyond this level, there is a sudden failure of protein folding: proteins fix upon a structure more quickly and become trapped in extended conformations. These results suggest that the ability of small protein domains to fold without the help of chaperones may be an important factor in limiting the degree of macromolecular crowding in the cell. Here, we discuss the possible implications regarding the relationship between protein expression level, protein size, chaperone activity and aggregation.     

A simple lattice model that exhibits a protein-like cooperative all-or-none folding transition

In a recent paper (D. Gront et al., Journal of Chemical Physics, Vol. 115, pp. 1569, 2001) we applied a simple combination of the Replica Exchange Monte Carlo and the Histogram methods in the computational studies of a simplified protein lattice model containing hydrophobic and polar units and sequence-dependent local stiffness. A well-defined, relatively complex Greek-key topology, ground (native) conformations was found; however, the cooperativity of the folding transition was very low. Here we describe a modified minimal model of the same Greek-key motif for which the folding transition is very cooperative and has all the features of the "all-or-none" transition typical of real globular proteins. It is demonstrated that the all-or-none transition arises from the interplay between local stiffness and properly defined tertiary interactions. The tertiary interactions are directional, mimicking the packing preferences seen in proteins. The model properties are compared with other minimal protein-like models, and we argue that the model presented here captures essential physics of protein folding (structurally well-defined protein-like native conformation and cooperative all-or-none folding transition).     

Contribution of the Conserved A16Leu to Insulin Foldability

Contributions of the evolutionarily conserved A16Leu and B17Leu to insulin foldability were characterized by evaluating folding properties of single-chain insulin analogs. The results showed A16Leu had much more significant effects on the foldability of insulin than B17Leu. Zhao-Jun Zhang and Lan Wu have equally contributed to this work.     

A model study of protein nascent chain and cotranslational folding using hydrophobic-polar residues

To study protein nascent chain folding during biosynthesis, we investigate the folding behavior of models of hydrophobic and polar (HP) chains at growing length using both two-dimensional square lattice model and an optimized three-dimensional 4-state discrete off-lattice model. After enumerating all possible sequences and conformations of HP heteropolymers up to length N = 18 and N = 15 in two and three-dimensional space, respectively, we examine changes in adopted structure, stability, and tolerance to single point mutation as the nascent chain grows. In both models, we find that stable model proteins have fewer folded nascent chains during growth, and often will only fold after reaching full length. For the few occasions where partial chains of stable proteins fold, these partial conformations on average are very similar to the corresponding parts of the final conformations at full length. Conversely, we find that sequences with fewer stable nascent chains and sequences with native-like folded nascent chains are more stable. In addition, these stable sequences in general can have many more point mutations and still fold into the same conformation as the wild type sequence. Our results suggest that stable proteins are less likely to be trapped in metastable conformations during biosynthesis, and are more resistant to point-mutations. Our results also imply that less stable proteins will require the assistance of chaperone and other factors during nascent chain folding. Taken together with other reported studies, it seems that cotranslational folding may not be a general mechanism of in vivo protein folding for small proteins, and in vitro folding studies are still relevant for understanding how proteins fold biologically.     

Computational simulation of the statistical properties of unfolded proteins

A simple Monte Carlo method was used to generate ensembles of simulated polypeptide conformations that are restricted only by steric repulsion. The models used for these simulations were based on the sequences of four real proteins, ranging in size from 26 to 268 amino acid residues, and included all non-hydrogen atoms. Two sets of calculations were performed, one that included only intra-residue steric repulsion terms and those between adjacent residues, and one that included repulsion terms between all possible atom pairs, so as to explicitly account for the excluded volume effect. Excluded volume was found to increase the average radius of gyration of the chains by 20-40%, with the expansion factor increasing with chain length. Contrary to recent suggestions, however, the excluded volume effect did not greatly restrict the distribution of dihedral angles or favor native-like topologies. The average dimensions of the ensembles calculated with excluded volume were consistent with those measured experimentally for unfolded proteins of similar sizes under denaturing conditions, without introducing any adjustable scaling factor. The simulations also reproduced experimentally determined effective concentrations for the formation of disulfide bonds in reduced and unfolded proteins. The statistically generated ensembles included significant numbers of conformations that were nearly as compact as the corresponding native proteins, as well as many that were as accessible to solvent as a fully extended chain. On the other hand, conformations with as much buried surface area as the native proteins were very rare, as were highly extended conformations. These results suggest that the overall properties of unfolded proteins can be usefully described by a random coil model and that an unfolded polypeptide can undergo significant collapse while losing only a relatively small fraction of its conformational entropy.     

Optimal local propensities for model proteins

Lattice models of proteins were used to examine the role of local propensities in stabilizing the native state of a protein, using techniques drawn from spin-glass theory to characterize the free-energy landscapes. In the strong evolutionary limit, optimal conditions for folding are achieved when the contributions from local interactions to the stability of the native state is small. Further increasing the local interactions rapidly decreases the foldability. © 1995 Wiley-Liss, Inc.     

Non-random-coil behavior as a consequence of extensive PPII structure in the denatured state

Unfolded proteins may contain a native or nonnative residual structure, which has important implications for the thermodynamics and kinetics of folding, as well as for misfolding and aggregation diseases. However, it has been universally accepted that residual structure should not affect the global size scaling of the denatured chain, which obeys the statistics of random coil polymers. Here we use a single-molecule optical technique—fluorescence correlation spectroscopy—to probe the denatured state of a set of repeat proteins containing an increasing number of identical domains, from 2 to 20. The availability of this set allows us to obtain the scaling law for the unfolded state of these proteins, which turns out to be unusually compact, strongly deviating from random coil statistics. The origin of this unexpected behavior is traced to the presence of an extensive nonnative polyproline II helical structure, which we localize to specific segments of the polypeptide chain. We show that the experimentally observed effects of polyproline II on the size scaling of the denatured state can be well-described by simple polymer models. Our findings suggest a hitherto unforeseen potential of nonnative structure to induce significant compaction of denatured proteins, significantly affecting folding pathways and kinetics.     

Experimental support for the foldability–function tradeoff hypothesis: Segregation of the folding nucleus and functional regions in fibroblast growth factor‐1

The acquisition of function is often associated with destabilizing mutations, giving rise to the stability–function tradeoff hypothesis. To test whether function is also accommodated at the expense of foldability, fibroblast growth factor‐1 (FGF‐1) was subjected to a comprehensive φ‐value analysis at each of the 11 turn regions. FGF‐1, a β‐trefoil fold, represents an excellent model system with which to evaluate the influence of function on foldability: because of its threefold symmetric structure, analysis of FGF‐1 allows for direct comparisons between symmetry‐related regions of the protein that are associated with function to those that are not; thus, a structural basis for regions of foldability can potentially be identified. The resulting φ‐value distribution of FGF‐1 is highly polarized, with the majority of positions described as either folded‐like or denatured‐like in the folding transition state. Regions important for folding are shown to be asymmetrically distributed within the protein architecture; furthermore, regions associated with function (i.e., heparin‐binding affinity and receptor‐binding affinity) are localized to regions of the protein that fold after barrier crossing (late in the folding pathway). These results provide experimental support for the foldability–function tradeoff hypothesis in the evolution of FGF‐1. Notably, the results identify the potential for folding redundancy in symmetric protein architecture with important implications for protein evolution and design.     

Universality classes in folding times of proteins

Molecular dynamics simulations in simplified models allow one to study the scaling properties of folding times for many proteins together under a controlled setting. We consider three variants of the Go models with different contact potentials and demonstrate scaling described by power laws and no correlation with the relative contact order parameter. We demonstrate existence of at least three kinetic universality classes that are correlated with the types of structure: the alpha-, alpha-beta-, and beta- proteins have the scaling exponents of approximately 1.7, 2.5, and 3.2, respectively. The three classes merge into one when the contact range is truncated at a reasonable value. We elucidate the role of the potential associated with the chirality of a protein.     

An RNA foldability metric; implications for the design of rapidly foldable RNA sequences

Evidence is presented suggesting, for the first time, that the protein foldability metric σ = (T_θ − T_f) / T_θ, where T_θ and T_f are, respectively, the collapse and folding transition temperatures, could be used also to measure the foldability of RNA sequences. These results provide further evidence of similarities between the folding energy landscapes of proteins and RNA. The importance of σ is discussed in the context of the in silico design of rapidly foldable RNA sequences.     

Time-resolved small-angle X-ray scattering investigation of the folding dynamics of heme oxygenase: implication of the scaling relationship for the submillisecond intermediates of protein folding

Polypeptide collapse is generally observed as the initial folding dynamics of proteins with more than 100 residues, and is suggested to be caused by the coil-globule transition explained by Flory's theory of polymers. To support the suggestion by establishing a scaling behavior between radius of gyration (Rg) and chain length for the initial folding intermediates, the folding dynamics of heme oxygenase (HO) was characterized by time-resolved, small-angle X-ray scattering. HO is a highly helical protein without disulfide bridges, and is the largest protein (263 residues) characterized by the method. The folding process of HO was found to contain a transient oligomerization; however, the conformation within 10 ms was demonstrated to be monomeric and to possess Rg of 26.1(+/-1.1) A. Together with the corresponding data for proteins with different chain lengths, the seven Rg values demonstrated the scaling relationship to chain length with a scaling exponent of 0.35+/-0.11, which is close to the theoretical value of 1/3 predicted for globules in solutions where monomer-monomer interactions are favored over monomer-solvent interactions (poor solvent). The finding indicated that the initial folding dynamics of proteins bears the signature of the coil-globule transition, and offers a clue to explain the folding mechanisms of proteins with different chain lengths.     

Protein design at the interface of the pre-biotic and biotic worlds

"Proteogenesis" (the origin of proteins) is a likely key event in the unsolved problem of biogenesis (the origin of life). The raw material for the very first proteins comprised the available amino acids produced and accumulated upon the early earth via abiotic chemical and physical processes. A broad consensus is emerging that this pre-biotic set likely comprised Ala, Asp, Glu, Gly, Ile, Leu, Pro, Ser, Thr, and Val. A key question in proteogenesis is whether such abiotically-produced amino acids comprise a "foldable" set. Current knowledge of protein folding identifies properties of complexity, secondary structure propensity, hydrophobic-hydrophilic patterning, core-packing potential, among others, as necessary elements of foldability. None of these requirements excludes the pre-biotic set of amino acids from being a foldable set. Moreover, nucleophile and metal ion/mineral binding capabilities also appear present in the pre-biotic set. Properties of the pre-biotic set, however, likely restrict foldability to the acidophilic/halophilic environment.