Folding funnels and conformational transitions via hinge-bending motions

In this article we focus on presenting a broad range of examples illustrating low-energy transitions via hinge-bending motions. The examples are divided according to the type of hinge-bending involved; namely, motions involving fragments of the protein chains, hinge-bending motions involving protein domains, and hinge-bending motions between the covalently unconnected subunits. We further make a distinction between allosterically and nonallosterically regulated proteins. These transitions are discussed within the general framework of folding and binding funnels. We propose that the conformers manifesting such swiveling motions are not the outcome of “induced fit” binding mechanism; instead, molecules exist in an ensemble of conformations that are in equilibrium in solution. These ensembles, which populate the bottoms of the funnels,a priori contain both the “open” and the “closed” conformational isomers. Furthermore, we argue that there are no fundamental differences among the physical principles behind the folding and binding funnels. Hence, there is no basic difference between funnels depicting ensembles of conformers of single molecules with fragment, or domain motions, as compared to subunits in multimeric quaternary structures, also showing such conformational transitions. The difference relates only to the size and complexity of the system. The larger the system, the more complex its corresponding fused funnel(s). In particular, funnels associated with allosterically regulated proteins are expected to be more complicated, because allostery is frequently involved with movements between subunits, and consequently is often observed in multichain and multimolecular complexes. This review centers on the critical role played by flexibility and conformational fluctuations in enzyme activity. Internal motions that extend over different time scales and with different amplitudes are known to be essential for the catalytic cycle. The conformational change observed in enzyme-substrate complexes as compared to the unbound enzyme state, and in particular the hinge-bending motions observed in enzymes with two domains, have a substantial effect on the enzymatic catalytic activity. The examples we review span the lipolytic enzymes that are particularly interesting, owing to their activation at the water-oil interface; an allosterically controlled dehydrogenase (lactate dehydrogenase); a DNA methyltransferase, with a covalently-bound intermediate; large-scale flexible loop motions in a glycolytic enzyme (TIM); domain motion in PGK, an enzyme which is essential in most cells, both for ATP generation in aerobes and for fermentation in anaerobes; adenylate kinase, showing large conformational changes, owing to their need to shield their catalytic centers from water; a calcium-binding protein (calmodulin), involved in a wide range of cellular calcium-dependent signaling; diphtheria toxin, whose large domain motion has been shown to yield “domain swapping” the hexameric glutamate dehydrogenase, which has been studied both in a thermophile and in a mesophile; an allosteric enzyme, showing subunit motion between the R and the T states (aspartate transcarbamoylase), and the historically well-studied lac represoor. Nonallosteric subunit transitions are also addressed with some examples (aspartate receptor andBamHI endonuclease). Hence, using this enzyme-catalysis-centered discussion, we address energy funnel landscapes of large-scale conformational transitions, rather than the faster, quasi-harmonic, thermal fluctuations.     

Folding and binding cascades: dynamic landscapes and population shifts

Whereas previously we have successfully utilized the folding funnels concept to rationalize binding mechanisms (Ma B, Kumar S, Tsai CJ, Nussinov R, 1999, Protein Eng 12:713-720) and to describe binding (Tsai CJ, Kumar S, Ma B, Nussinov R, 1999, Protein Sci 8:1181-1190), here we further extend the concept of folding funnels, illustrating its utility in explaining enzyme pathways, multimolecular associations, and allostery. This extension is based on the recognition that funnels are not stationary; rather, they are dynamic, depending on the physical or binding conditions (Tsai CJ, Ma B, Nussinov R, 1999, Proc Natl Acad Sci USA 96:9970-9972). Different binding states change the surrounding environment of proteins. The changed environment is in turn expressed in shifted energy landscapes, with different shapes and distributions of populations of conformers. Hence, the function of a protein and its properties are not only decided by the static folded three-dimensional structure; they are determined by the distribution of its conformational substates, and in particular, by the redistributions of the populations under different environments. That is, protein function derives from its dynamic energy landscape, caused by changes in its surroundings.     

Folding funnels and binding mechanisms.

The long-held views on lock-and-key versus induced fit in binding arose from the notion that a protein exists in a single, most stable conformation, dictated by its sequence. However, in solution proteins exist in a range of conformations, which may be described by statistical mechanical laws and their populations follow statistical distributions. Upon binding, the equilibrium will shift in favor of the bound conformation from the ensemble of conformations around the bottom of the folding funnel. Hence here we extend the implications and the usefulness of the folding funnel concept to explain fundamental binding mechanisms.     

Transient, highly populated, building blocks folding model

Protein folding is a hierarchical event, in which transiently formed local structural elements assemble to yield the native conformation. In principle, multiple paths glide down the energy landscape, but, in practice, only a few of the paths are highly traveled. Here, the literature is reviewed in this light, and, particularly, a hierarchical, building block protein-folding model is presented, putting it in the context of a broad range of experimental and theoretical results published over the past few years. The model is based on two premises: First, although the local building block elements may be unstable, they nevertheless have higher population times than all alternate conformations; and, second, protein folding progresses through a combinatorial assembly of these elements. Through the binding of the most favorable building block conformers, there is a redistribution of the conformers in solution, propagating the protein-folding reaction. We describe the algorithm, and illustrate its usefulness, then we focus on its utility in assigning simple vs complex folding pathways, on chaperonin-assisted folding, on its relevance to domain-swapping processes, and on its relevance and relationship to disconnectivity graphs and tree diagrams. Considering protein folding as initiating from local transient structural elements is consistent with available experimental and theoretical results. Here, we have shown that, early in the folding process, sequential interactions are likely to take place, even if the final native fold is a complex, nonsequential one. Such a route is favorable kinetically and entropically. Through the construction of anatomy trees, the model enables derivation of the major folding pathways and their bumps, and qualitatively explains the kinetics of protein folding.     

Structure and function of ciliated peritoneal funnels in the toad kidney (Bufo marinus)

Scanning electron microscopy revealed 600-800 ciliated peritoneal funnels opening onto the ventral surface of each kidney in Bufo marinus. The size and configuration of funnel apertures vary greatly, but individuals course beneath the kidney surface before opening into peritubular blood vessels. Injections of India ink into the peritoneal cavity demonstrate that cilia lining the peritoneal funnels create a current carrying peritoneal fluid into the renal vasculature. Clearance of fluid by the funnels was dependent on pressure in the peritubular vessels, and was increased by arginine vasotocin. Ciliated peritoneal funnels may provide an important route for return of lymphatic fluid from the peritoneal cavity to the vasculature.     

154 Protein folding and binding funnels: a common driving force and a common mechanism

Under the free energy landscape theory, both the protein-folding and protein–ligand binding processes are driven by the decrease in total Gibbs free energy of the protein-solvent or protein–ligand-solvent system, which involves the non-complementary changes between the entropy and enthalpy, ultimately leading to a global free energy minimization of these thermodynamic systems (Ji & Liu, 2011; Liu et al., 2012; Yang, Ji & Liu, 2012). In the case of protein folding, the lowering of the system free energy coupled with the gradual reduction in conformational degree of freedom of the folding intermediates determines that the shape of the free energy landscape for protein folding must be funnel-like (Dill & Chan, 1997), rather than non-funneled shapes (Ben-Naim, 2012). In the funnel-like free energy landscape, protein folding can be viewed as going down the hill via multiple parallel routes from a vast majority of individual non-native states on surface outside the funnel to the native states located around the bottom of the funnel. The first stage of folding, i.e. the rapid hydrophobic collapse process, is driven by the solvent entropy maximization. Concretely, the water molecules squeeze and sequestrate the hydrophobic amino acid side chains within the interior of the folding intermediates while exposing the polar and electrostatically charged side chains on the intermediate surface so as to minimize the solvent-accessible surface area of the solute and thus, the minimal contacts between the folding intermediates and the water molecules. This will maximize the entropy of the solvent, thus contributing substantially to lowering of the system free energy due to an absolute advantage of the solvent in both quantity and mass (Yang, Ji & Liu, 2012). The resulting molten globule states (Ohgushi & Wada, 1983), within which a few transient secondary structural components and tertiary contacts have been formed but many native contacts or close residue–residue interactions has yet to form, need to be further sculptured into the native states. This is a relatively slow “bottleneck” process because the competitive interactions between protein residues within the folding intermediates and between residues and water molecules may repeat many rounds to accumulate a large enough number of stable noncovalent bonds capable of counteracting the conformational entropy loss of the intermediates, thus putting this bottleneck stage under the enthalpy control (i.e. negative enthalpy change), contributing further to the lowering of the system free energy. Although the protein–ligand association occurs around the rugged bottom of the free energy landscape, the exclusion of water from the binding interfaces and the formation of noncovalent bonds between the two partners can still lower the system free energy. In conjunction with the loss of the rotational and translational degrees of freedom of the two partners as well as the loss of the conformational entropy of the protein, these processes could merge, downwards expand, and further narrow the free energy wells within which the protein–ligand binding process takes place, thereby making them look like a funnel, which we term the binding funnel. In this funnel, the free energy downhill process follows a similar paradigm to the protein-folding process. For example, if the initial collisions/contacts occur between the properly complementary interfaces of the protein and ligand, a large amount of water molecules (which usually form a water network around the solute surface) will be displaced to suit the need for maximizing the solvent entropy. This process is similar to that of the hydrophobic collapse during protein folding, resulting in a loosely associated protein–ligand complex that needs also to be further adapted into a tight complex, i.e. the second step which is mainly driven by the negative enthalpy change through intermolecular competitive interactions to gradually accumulate the noncovalent bonds and ultimately, to stabilize the complex at a tightly bound state. Taken together, we conclude that whether in the protein-folding or in the protein–ligand binding process, both the entropy-driven first step and the enthalpy-driven second step contribute to the lowering of the system free energy, resulting in the funnel-like folding or binding free energy landscape.     

Assessing the energy landscape of CAPRI targets by FunHunt

RosettaDock has repeatedly created high-resolution structures of protein complexes in the CAPRI experiment, thanks to the explicit modeling of conformational changes of the monomers at the side chain level. These models can be selected based on their energy. During the search for the lowest-energy model, RosettaDock samples a deep funnel around the native orientation, but additional funnels may appear in the energy landscape, especially in cases where backbone conformational changes occur upon binding. We have previously developed FunHunt, a Support Vector Machine-based classifier that distinguishes the energy funnels around the native orientation from other funnels in the energy landscape. Here we assess the ability of FunHunt to help in model selection in the CAPRI experiment. For all of 12 recent CAPRI targets, FunHunt clearly identifies a near-native funnel in comparison to the funnel around the lowest energy model identified by the RosettaDock global search protocol. FunHunt is also able to choose a near-native orientation among models submitted by predictor groups, demonstrating its general applicability for model selection. This suggests that FunHunt will be a valuable tool in coming CAPRI rounds for the selection of models, and for the definition of regions that need further refinement with restricted backbone flexibility.     

Structured disorder and conformational selection

Traditionally, molecular disorder has been viewed as local or global instability. Molecules or regions displaying disorder have been considered inherently unstructured. The term has been routinely applied to cases for which no atomic coordinates can be derived from crystallized molecules. Yet, even when it appears that the molecules are disordered, prevailing conformations exist, with population times higher than those of all alternate conformations. Disordered molecules are the outcome of rugged energy landscapes away from the native state around the bottom of the funnel. Ruggedness has a biological function, creating a distribution of structured conformers that bind via conformational selection, driving association and multimolecular complex formation, whether chain-linked in folding or unlinked in binding. We classify disordered molecules into two types. The first type possesses a hydrophobic core. Here, even if the native conformation is unstable, it still has a large enough population time, enabling its experimental detection. In the second type, no such hydrophobic core exists. Hence, the native conformations of molecules belonging to this category have shorter population times, hindering their experimental detection. Although there is a continuum of distribution of hydrophobic cores in proteins, an empirical, statistically based hydrophobicity function may be used as a guideline for distinguishing the two disordered molecule types. Furthermore, the two types relate to steps in the protein folding reaction. With respect to protein design, this leads us to propose that engineering-optimized specific electrostatic interactions to avoid electrostatic repulsion would reduce the type I disordered state, driving the molten globule (MG) --> native (N) state. In contrast, for overcoming the type II disordered state, in addition to specific interactions, a stronger hydrophobic core is also indicated, leading to the denatured --> MG --> N state.     

Disulfide bonds and protein folding

The applications of disulfide-bond chemistry to studies of protein folding, structure, and stability are reviewed and illustrated with bovine pancreatic ribonuclease A (RNase A). After surveying the general properties and advantages of disulfide-bond studies, we illustrate the mechanism of reductive unfolding with RNase A, and discuss its application to probing structural fluctuations in folded proteins. The oxidative folding of RNase A is then described, focusing on the role of structure formation in the regeneration of the native disulfide bonds. The development of structure and conformational order in the disulfide intermediates during oxidative folding is characterized. Partially folded disulfide species are not observed, indicating that disulfide-coupled folding is highly cooperative. Contrary to the predictions of "rugged funnel" models of protein folding, misfolded disulfide species are also not observed despite the potentially stabilizing effect of many nonnative disulfide bonds. The mechanism of regenerating the native disulfide bonds suggests an analogous scenario for conformational folding. Finally, engineered covalent cross-links may be used to assay for the association of protein segments in the folding transition state, as illustrated with RNase A.     

Protein folding mechanisms and the multidimensional folding funnel

An important idea that emerges from the energy landscape theory of protein folding is that subtle global features of the protein landscape can profoundly affect the apparent mechanism of folding. The relationship between various characteristic temperatures in the phase diagrams and landmarks in the folding funnel at fixed temperatures can be used to classify different folding behaviors. The one-dimensional picture of a folding funnel classifies folding kinetics into four basic scenarios, depending on the relative location of the thermodynamic barrier and the glass transition as a function of a single-order parameter. However, the folding mechanism may not always be quantitatively described by a single-order parameter. Several other order parameters, such as degree of secondary structure formation, collapse and topological order, are needed to establish the connection between minimalist models and proteins in the laboratory. In this article we describe a simple multidimensional funnel based on two-order parameters that measure the degree of collapse and topological order. The appearance of several different “mechanisms” is illustrated by analyzing lattice models with different potentials and sequences with different degrees of design. In most cases, the two-dimensional analysis leads to a classification of mechanisms totally in keeping with the one-dimensional scheme, but a topologically distinct scenario of fast folding with traps also emerges. The nature of traps depends on the relative location of the glass transition surface and the thermodynamic barrier in the multidimensional funnel. Proteins 32:136–158, 1998. © 1998 Wiley-Liss, Inc.     

Disparate degrees of hypervariable loop flexibility control T-cell receptor cross-reactivity, specificity, and binding mechanism

αβ T-cell receptors (TCRs) recognize multiple antigenic peptides bound and presented by major histocompatibility complex molecules. TCR cross-reactivity has been attributed in part to the flexibility of TCR complementarity-determining region (CDR) loops, yet there have been limited direct studies of loop dynamics to determine the extent of its role. Here we studied the flexibility of the binding loops of the αβ TCR A6 using crystallographic, spectroscopic, and computational methods. A significant role for flexibility in binding and cross-reactivity was indicated only for the CDR3α and CDR3β hypervariable loops. Examination of the energy landscapes of these two loops indicated that CDR3β possesses a broad, smooth energy landscape, leading to rapid sampling in the free TCR of a range of conformations compatible with different ligands. The landscape for CDR3α is more rugged, resulting in more limited conformational sampling that leads to specificity for a reduced set of peptides as well as the major histocompatibility complex protein. In addition to informing on the mechanisms of cross-reactivity and specificity, the energy landscapes of the two loops indicate a complex mechanism for TCR binding, incorporating elements of both conformational selection and induced fit in a manner that blends features of popular models for TCR recognition.     

Distinguishing between sequential and nonsequentially folded proteins: implications for folding and misfolding.

We describe here an algorithm for distinguishing sequential from nonsequentially folding proteins. Several experiments have recently suggested that most of the proteins that are synthesized in the eukaryotic cell may fold sequentially. This proposed folding mechanism in vivo is particularly advantageous to the organism. In the absence of chaperones, the probability that a sequentially folding protein will misfold is reduced significantly. The problem we address here is devising a procedure that would differentiate between the two types of folding patterns. Footprints of sequential folding may be found in structures where consecutive fragments of the chain interact with each other. In such cases, the folding complexity may be viewed as being lower. On the other hand, higher folding complexity suggests that at least a portion of the polypeptide backbone folds back upon itself to form three-dimensional (3D) interactions with noncontiguous portion(s) of the chain. Hence, we look at the mechanism of folding of the molecule via analysis of its complexity, that is, through the 3D interactions formed by contiguous segments on the polypeptide chain. To computationally splice the structure into consecutively interacting fragments, we either cut it into compact hydrophobic folding units or into a set of hypothetical, transient, highly populated, contiguous fragments ("building blocks" of the structure). In sequential folding, successive building blocks interact with each other from the amino to the carboxy terminus of the polypeptide chain. Consequently, the results of the parsing differentiate between sequentially vs. nonsequentially folded chains. The automated assessment of the folding complexity provides insight into both the likelihood of misfolding and the kinetic folding rate of the given protein. In terms of the funnel free energy landscape theory, a protein that truly follows the mechanism of sequential folding, in principle, encounters smoother free energy barriers. A simple sequentially folded protein should, therefore, be less error prone and fold faster than a protein with a complex folding pattern.     

PABMB Lecture. Protein dynamics, folding and misfolding: from basic physical chemistry to human conformational diseases.

Proteins exhibit a variety of motions ranging from amino acid side-chain rotations to the motions of large domains. Recognition of their conformational flexibility has led to the view that protein molecules undergo fast dynamic interconversion between different conformational substates. This proposal has received support from a wide variety of experimental techniques and from computer simulations of protein dynamics. More recently, studies of the subunit dissociation of oligomeric proteins induced by hydrostatic pressure have shown that the characteristic times for subunit exchange between oligomers and for interconversion between different conformations may be rather slow (hours or days). In such cases, proteins cannot be treated as an ensemble of rapidly interconverting conformational substates, but rather as a persistently heterogeneous population of different long-lived conformers. This is reminiscent of the deterministic behavior exhibited by macroscopic bodies, and may have important implications for our understanding of protein folding and biological functions. Here, we propose that the deterministic behavior of proteins may be closely related to the genesis of conformational diseases, a class of pathological conditions that includes transmissible spongiform encephalopathies, Alzheimer's disease and other amyloidosis.     

Fluctuations between stabilizing and destabilizing electrostatic contributions of ion pairs in conformers of the c-Myc-Max leucine zipper

In solution proteins often exhibit backbone and side-chain flexibility. Yet electrostatic interactions in proteins are sensitive to motions. Hence, here we study the contribution of ion pairs toward protein stability in a range of conformers which sample the conformational space in solution. Specifically, we focus on the electrostatic contributions of ion pairs to the stability of each of the conformers in the NMR ensemble of the c-Myc-Max leucine zipper and to their average energy minimized structure. We compute the electrostatic contributions of inter- and intra-helical ion pairs and of an ion pair network. We find that the electrostatic contributions vary considerably among the 40 NMR conformers. Each ion pair, and the network, fluctuates between being stabilizing and being destabilizing. This fluctation reflects the variability in the location of the ion pairing residues and in the geometric orientation of these residues, both with respect to each other and with respect to other charged groups in the rest of the protein. Ion pair interactions in the c-Myc-Max leucine zipper in solution depend on the protein conformer which is analyzed. Hence, the overall stabilizing (or destabilizing) contribution of an ion pair is conformer population-dependent. This study indicates that free energy calculations performed using the continuum electrostatics methodology are sensitive to protein conformational details.     

Entropic barriers, transition states, funnels, and exponential protein folding kinetics: a simple model

This paper presents an analytically tractable model that captures the most elementary aspect of the protein folding problem, namely that both the energy and the entropy decrease as a protein folds. In this model, the system diffuses within a sphere in the presence of an attractive spherically symmetric potential. The native state is represented by a small sphere in the center, and the remaining space is identified with unfolded states. The folding temperature, the time-dependence of the populations, and the relaxation rate are calculated, and the folding dynamics is analyzed for both golf-course and funnel-like energy landscapes. This simple model allows us to illustrate a surprising number of concepts including entropic barriers, transition states, funnels, and the origin of single exponential relaxation kinetics.     

Protein folding: matching theory and experiment.

The impact of folding funnels and folding simulations on the way experimentalists interpret results is examined. The image of the transition state has changed from a unique species that has a strained configuration, with a correspondingly high free energy, to a more ordinary folding intermediate, whose balance between limited conformational entropy and stabilizing contacts places it at the top of the free energy barrier. Evidence for a broad transition barrier comes from studies showing that mutations can change the position of the barrier. The main controversial issue now is whether populated folding intermediates are productive on-pathway intermediates or dead-end traps. Direct experimental evidence is needed. Theories suggesting that populated intermediates are trapped in a glasslike state are usually based on mechanisms which imply that trapping would only be extremely short-lived (e.g., nanoseconds) in water at 25 degrees C. There seems to be little experimental evidence for long-lived trapping in monomers, if folding aggregates are excluded. On the other hand, there is good evidence for kinetic trapping in dimers. alpha-Helix formation is currently the fastest known process in protein folding, and incipient helices are present at the start of folding. Fast helix formation has the effect of narrowing drastically the choice of folding routes. Thus helix formation can direct folding. It changes the folding metaphor from pouring liquid down a folding funnel to a train leaving a switchyard with only a few choices of exit tracks.     

Mutational analysis of the BPTI folding pathway: I. Effects of aromatic-->leucine substitutions on the distribution of folding intermediates.

The roles of aromatic residues in determining the folding pathway of bovine pancreatic trypsin inhibitor (BPTI) were analyzed mutationally by examining the distribution of disulfide-bonded intermediates that accumulated during the refolding of protein variants in which tyrosine or phenylalanine residues were individually replaced with leucine. The eight substitutions examined all caused significant changes in the intermediate distribution. In some cases, the major effect was to decrease the accumulation of intermediates containing two of the three disulfides found in the native protein, without affecting the distribution of earlier intermediates. Other substitutions, however, led to much more random distributions of the intermediates containing only one disulfide. These results indicate that the individual residues making up the hydrophobic core of the native protein make clearly distinguishable contributions to conformation and stability early in folding: The early distribution of intermediates does not appear to be determined by a general hydrophobic collapse. The effects of the substitutions were generally consistent with the structures of the major intermediates determined by NMR studies of analogs, confirming that the distribution of disulfide-bonded species is determined by stabilizing interactions within the ordered regions of the intermediates. The plasticity of the BPTI folding pathway implied by these results can be described using conformational funnels to illustrate the degree to which conformational entropy is lost at different stages in the folding of the wild-type and mutant proteins.     

Activity-stability relationships in extremophilic enzymes

Psychrophilic, mesophilic, and thermophilic alpha-amylases have been studied as regards their conformational stability, heat inactivation, irreversible unfolding, activation parameters of the reaction, properties of the enzyme in complex with a transition state analog, and structural permeability. These data allowed us to propose an energy landscape for a family of extremophilic enzymes based on the folding funnel model, integrating the main differences in conformational energy, cooperativity of protein unfolding, and temperature dependence of the activity. In particular, the shape of the funnel bottom, which depicts the stability of the native state ensemble, also accounts for the thermodynamic parameters of activation that characterize these extremophilic enzymes, therefore providing a rational basis for stability-activity relationships in protein adaptation to extreme temperatures.     

Folding of the SAM-I riboswitch: A tale with a twist

Riboswitches are ligand-dependent RNA genetic regulators that control gene expression by altering their structures. The elucidation of riboswitch conformational changes before and after ligand recognition is crucial to understand how riboswitches can achieve high ligand binding affinity and discrimination against cellular analogs. The detailed characterization of riboswitch folding pathways suggest that they may use their intrinsic conformational dynamics to sample a large array of structures, some of which being nearly identical to ligand-bound molecules. Some of these structural conformers can be "captured" upon ligand binding, which is crucial for the outcome of gene regulation. Recent studies about the SAM-I riboswitch have revealed unexpected and previously unknown RNA folding mechanisms. For instance, the observed helical twist of the P1 stem upon ligand binding to the SAM-I aptamer adds a new element in the repertoire of RNA strategies for recognition of small metabolites. From an RNA folding perspective, these findings also strongly indicate that the SAM-I riboswitch could achieve ligand recognition by using an optimized combination of conformational capture and induced-fit approaches, a feature that may be shared by other RNA regulatory sequences.