Parser for protein folding units

General patterns of protein structural organization have emerged from studies of hundreds of structures elucidated by X-ray crystallography and nuclear magnetic resonance. Structural units are commonly identified by visual inspection of molecular models using qualitative criteria. Here, we propose an algorithm for identification of structural units by objective, quantitative criteria based on atomic interactions. The underlying physical concept is maximal interactions within each unit and minimal interaction between units (domains). In a simple harmonic approximation, interdomain dynamics is determined by the strength of the interface and the distribution of masses. The most likely domain decomposition involves units with the most correlated motion, or largest interdomain fluctuation time. The decomposition of a convoluted 3-D structure is complicated by the possibility that the chain can cross over several times between units. Grouping the residues by solving an eigenvalue problem for the contact matrix reduces the problem to a one-dimensional search for all reasonable trial bisections. Recursive bisection yields a tree of putative folding units. Simple physical criteria are used to identify units that could exist by themselves. The units so defined closely correspond to crystallographers' notion of structural domains. The results are useful for the analysis of folding principles, for modular protein design and for protein engineering. © 1994 Wiley-Liss, Inc.     

Hydrophobic folding units at protein-protein interfaces: implications to protein folding and to protein-protein association.

A hydrophobic folding unit cutting algorithm, originally developed for dissecting single-chain proteins, has been applied to a dataset of dissimilar two-chain protein-protein interfaces. Rather than consider each individual chain separately, the two-chain complex has been treated as a single chain. The two-chain parsing results presented in this work show hydrophobicity to be a critical attribute of two-state versus three-state protein-protein complexes. The hydrophobic folding units at the interfaces of two-state complexes suggest that the cooperative nature of the two-chain protein folding is the outcome of the hydrophobic effect, similar to its being the driving force in a single-chain folding. In analogy to the protein-folding process, the two-chain, two-state model complex may correspond to the formation of compact, hydrophobic nuclei. On the other hand, the three-state model complex involves binding of already folded monomers, similar to the association of the hydrophobic folding units within a single chain. The similarity between folding entities in protein cores and in two-state protein-protein interfaces, despite the absence of some chain connectivities in the latter, indicates that chain linkage does not necessarily affect the native conformation. This further substantiates the notion that tertiary, non-local interactions play a critical role in protein folding. These compact, hydrophobic, two-chain folding units, derived from structurally dissimilar protein-protein interfaces, provide a rich set of data useful in investigations of the role played by chain connectivity and by tertiary interactions in studies of binding and of folding. Since they are composed of non-contiguous pieces of protein backbones, they may also aid in defining folding nuclei.     

Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.     

Automatic recognition of hydrophobic clusters and their correlation with protein folding units.

A method is described to objectively identify hydrophobic clusters in proteins of known structure. Clusters are found by examining a protein for compact groupings of side chains. Compact clusters contain seven or more residues, have an average of 65% hydrophobic residues, and usually occur in protein interiors. Although smaller clusters contain only side-chain moieties, larger clusters enclose significant portions of the peptide backbone in regular secondary structure. These clusters agree well with hydrophobic regions assigned by more intuitive methods and many larger clusters correlate with protein domains. These results are in striking contrast with the clustering algorithm of J. Heringa and P. Argos (1991, J Mol Biol 220:151-171). That method finds that clusters located on a protein's surface are not especially hydrophobic and average only 3-4 residues in size. Hydrophobic clusters can be correlated with experimental evidence on early folding intermediates. This correlation is optimized when clusters with less than nine hydrophobic residues are removed from the data set. This suggests that hydrophobic clusters are important in the folding process only if they have enough hydrophobic residues.     

From helix-coil transitions to protein folding

An evolution of procedures to simulate protein structure and folding pathways is described. From an initial focus on the helix-coil transition and on hydrogen-bonding and hydrophobic interactions, our original attempts to determine protein structure and folding pathways were based on an experimental approach. Experiments on the oxidative folding of reduced bovine pancreatic ribonuclease A (RNase A) led to a mechanism by which the molecule folded to the native structure by a minimum of four different pathways. The experiments with RNase A were followed by development of a molecular mechanics approach, first, making use of global optimization procedures and then with molecular dynamics (MD), evolving from an all-atom to a united-residue model. This hierarchical MD approach facilitated probing of the folding trajectory to longer time scales than with all-atom MD, and hence led to the determination of complete folding trajectories, thus far for a protein containing as many as 75 amino acid residues. With increasing refinement of the computational procedures, the computed results are coming closer to experimental observations, providing an understanding as to how physics directs the folding process.     

Changes of protein stiffness during folding detect protein folding intermediates

Single-molecule force-quench atomic force microscopy (FQ-AFM) is used to detect folding intermediates of a simple protein by detecting changes of molecular stiffness of the protein during its folding process. Those stiffness changes are obtained from shape and peaks of an autocorrelation of fluctuations in end-to-end length of the folding molecule. The results are supported by predictions of the equipartition theorem and agree with existing Langevin dynamics simulations of a simplified model of a protein folding. In the light of the Langevin simulations the experimental data probe an ensemble of random-coiled collapsed states of the protein, which are present both in the force-quench and thermal-quench folding pathways.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

Zinc-dependent protein folding

Studies of classic zinc-finger peptides over the past 15 years have offered insights into the coupled processes of metal binding and protein folding. Within the past two years, this insight has been used to increase our understanding of the importance of first and second shell contributions (i.e. contributions from direct and indirect metal ligands) to metal binding and protein-folding stability, and led to advances in de novo protein design and protein redesign.     

Ribosome-DnaK interactions in relation to protein folding

Bacterial ribosomes or their 50S subunit can refold many unfolded proteins. The folding activity resides in domain V of 23S RNA of the 50S subunit. Here we show that ribosomes can also refold a denatured chaperone, DnaK, in vitro, and the activity may apply in the folding of nascent DnaK polypeptides in vivo. The chaperone was unusual as the native protein associated with the 50S subunit stably with a 1:1 stoichiometry in vitro. The binding site of the native protein appears to be different from the domain V of 23S RNA, the region with which denatured proteins interact. The DnaK binding influenced the protein folding activity of domain V modestly. Conversely, denatured protein binding to domain V led to dissociation of the native chaperone from the 50S subunit. DnaK thus appears to depend on ribosomes for its own folding, and upon folding, can rebind to ribosome to modulate its general protein folding activity.     

Hydrogen exchange methods to study protein folding

The measurement of amino acid-resolved hydrogen exchange (HX) has provided the most detailed information so far available on the structure and properties of protein folding intermediates. Direct HX measurements can define the structure of tenuous molten globule forms that are generally inaccessible to the usual crystallographic and NMR methods (C. Redfield review in this issue). HX pulse labeling methods can specify the structure, stability and kinetics of folding intermediates that exist for less than 1 s during kinetic folding. Native state HX methods can detect and characterize folding intermediates that exist as infinitesimally populated high energy excited state forms under native conditions. The results obtained in these ways suggest principles that appear to explain the properties of partially folded intermediates and how they are organized into folding pathways. The application of these methods is detailed here.     

Cotranslational protein folding

The review analyzes the research concerning the folding of proteins in the course of their synthesis on ribosomes. The experimental data obtained for various proteins using various methods give grounds for concluding that a nascent protein largely acquires its spatial structure while still attached to the ribosome, and final folding into the biologically active conformation takes place as soon as the completed protein is released therefrom. Cotranslational folding is characteristic of both bacterial and eukaryotic cells, and appears to be the universal and the most evolutionarily ancient mechanism.     

Pro-sequence-assisted protein folding

Many proteins, including proteases and growth factors, are synthesized as precursors in the form of prepro-proteins. Whereas the pre-sequences usually act as signal peptides for transport, the pro-sequences of an increasing number of these proteins have been found to be essential for the correct folding of their associated proteins. In contrast to the action of molecular chaperones, pro-sequences appear to catalyse the protein-folding reaction directly. The similarity between the pro-sequence-assisted folding mechanisms of different proteases supports the hypothesis that a common folding mechanism has developed through convergent evolution. Further, the frequent requirement of the pro-sequences for both folding and intracellular transport or secretion suggests that these two functionalities are intimately related.     

Membrane protein folding

Investigating the in vitro refolding of proteins that naturally reside in biological membranes is a notoriously difficult task. Biophysical studies on model systems are beginning to provide a sound physical basis for membrane protein folding that should help to alleviate this problem. Highlights of these studies include insights into the interaction of transmembrane alpha helices, as well as into the important role that membrane lipids play in folding.     

Theory of protein folding

Protein folding should be complex. Proteins organize themselves into specific three-dimensional structures, through a myriad of conformational changes. The classical view of protein folding describes this process as a nearly sequential series of discrete intermediates. In contrast, the energy landscape theory of folding considers folding as the progressive organization of an ensemble of partially folded structures through which the protein passes on its way to the natively folded structure. As a result of evolution, proteins have a rugged funnel-like landscape biased toward the native structure. Connecting theory and simulations of minimalist models with experiments has completely revolutionized our understanding of the underlying mechanisms that control protein folding.     

Mechanisms of protein folding

Understanding the mechanism by which a polypeptide chain folds into its native structure is a central problem of modern biophysics. The collaborative efforts of experimental and theoretical studies recently raised the tantalizing possibility to define a unifying mechanism for protein folding. In this review we summarize some of these intriguing advances and analyze them together with a discussion on the new findings concerning the so-called downhill folding.     

Complexity of protein folding

It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two-and three-dimensional mathematical model describing the folding process as a free energy minimization problems is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard (“conditionally intractable”). Some of the possible ramifications of this results are speculated upon.