A Survey of λ Repressor Fragments from Two-State to Downhill Folding

We survey the two-state to downhill folding transition by examining 20 λ_6-85^? mutants that cover a wide range of stabilities and folding rates. We investigated four new λ_6-85^? mutants designed to fold especially rapidly. Two were engineered using the core remodeling of Lim and Sauer, and two were engineered using Ferreiro et al.'s frustratometer. These proteins have probe-dependent melting temperatures as high as 80 °C and exhibit a fast molecular phase with the characteristic temperature dependence of the amplitude expected for downhill folding. The survey reveals a correlation between melting temperature and downhill folding previously observed for the β-sheet protein WW domain. A simple model explains this correlation and predicts the melting temperature at which downhill folding becomes possible. An X-ray crystal structure with a 1.64-Å resolution of a fast-folding mutant fragment shows regions of enhanced rigidity compared to the full wild-type protein.     

Recombination of S-peptide with S-protein during folding of ribonuclease S. I. Folding pathways of the slow-folding and fast-folding classes of unfolded S-protein.

The refolding kinetics of ribonuclease S have been measured by tyrosine absorbance, by tyrosine fluorescence emission, and by rapid binding of the specific inhibitor 2′CMP ² to folded RNAase S. The S-protein is first unfolded at pH 1.7 and then either mixed with S-peptide as refolding is initiated by a stopped-flow pH jump to pH 6.8, or the same results are obtained if S-protein and S-peptide are present together before refolding is initiated. The refolding kinetics of RNAase S have been measured as a function of temperature (10 to 40 °C) and of protein concentration (10 to 120 μm). The results are compared to the folding kinetics of S-protein alone and to earlier studies of RNAase A. A thermal folding transition of S-protein has been found below 30 °C at pH 1.7; its effects on the refolding kinetics are described in the following paper (Labhardt &; Baldwin, 1979).In this paper we characterize the refolding kinetics of unfolded S-protein, as it is found above 30 °C at pH 1.7, together with the kinetics of combination between S-peptide and S-protein during folding at pH 6.8. Two classes of unfolded S-protein molecules are found, fast-folding and slow-folding molecules, in a 20: 80 ratio. This is the same result as that found earlier for RNAase A; it is expected if the slow-folding molecules are produced by the slow cis-trans isomerization of proline residues after unfolding, since S-protein contains all four proline residues of RNAase A.The refolding kinetics of the fast-folding molecules show clearly that combination between S-peptide and S-protein occurs before folding of S-protein is complete. If combination occurred only after complete folding, then the kinetics of formation of RNAase S should be rather slow (5 s and 100 s at 30 °C) and nearly independent of protein concentration, as shown by separate measurements of the folding kinetics of S-protein, and of the combination between S-peptide and folded S-protein. The observed folding kinetics are faster than predicted by this model and also the folding rate increases strongly with protein concentration (apparent 1.6 order kinetics). The fact that RNAase S is formed more rapidly than S-protein alone is sufficient by itself to show that combination with S-peptide precedes complete folding of S-protein. Computer simulation of a simple, parallel-pathway scheme is able to reproduce the folding kinetics of the fast-folding molecules. All three probes give the same folding kinetics.These results exclude the model for protein folding in which the rate-limiting step is an initial diffusion of the polypeptide chain into a restricted range of three-dimensional configurations (“nueleation”) followed by rapid folding (“propagation”). If this model were valid, one would expect comparable rates of folding for RNAase A and for S-protein and one would also expect to find no populated folding intermediates, so that combination between S-peptide and S-protein should occur after folding is complete. Instead, RNAase A folds 60 times more rapidly than S-protein and also combination with S-peptide occurs before folding of S-protein is complete. The results demonstrate that the folding rate of S-protein increases after the formation, or stabilization, of an intermediate which results from combination with S-peptide. They support a sequential model for protein folding in which the rates of successive steps in folding depend on the stabilities of preceding intermediates.The refolding kinetics of the slow-folding molecules are complex. Two results demonstrate the presence of folding intermediates: (1) the three probes show different kinetic progress curves, and (2) the folding kinetics are concentration-dependent, in contrast to the results expected if complete folding of S-protein precedes combination with S-peptide. A faster phase of the slow-refolding reaction is detected both by tyrosine absorbance and fluorescence emission but not by 2′CMP binding, indicating that native RNAase S is not formed in this phase. Comparison of the kinetic progress curves measured by different probes is made with the use of the kinetic ratio test, which is defined here.     

Fast-Folding Pathways of the Thrombin-Binding Aptamer G-Quadruplex Revealed by a Markov State Model

G-quadruplex structures participate in many important cellular processes. For a better understanding of their functions, knowledge of the mechanism by which they fold into the functional native structures is necessary. In this work, we studied the folding process of the thrombin-binding aptamer G-quadruplex. Enabled by a computational paradigm that couples an advanced sampling method and a Markov state model, four folding intermediates were identified, including an antiparallel G-hairpin, two G-triplex structures, and a double-hairpin conformation. Likewise, a misfolded structure with a nonnative distribution of syn/anti guanines was also observed. Based on these states, a transition path analysis revealed three fast-folding pathways, along which the thrombin-binding aptamer would fold to the native state directly, with no evidence of potential nonnative competing conformations. The results also showed that the TGT-loop plays an important role in the folding process. The findings of this research may provide general insight about the folding of other G-quadruplex structures.     

Preorganized secondary structure as an important determinant of fast protein folding

The folding and unfolding kinetics of the B-domain of staphylococcal protein A, a small three-helix bundle protein, were probed by NMR. The lineshape of a single histidine resonance was fit as a function of denaturant to give folding and unfolding rate constants. The B-domain folds extremely rapidly in a two-state manner, with a folding rate constant of 120,000 s-1, making it one of the fastest-folding proteins known. Diffusion-collision theory predicts folding and unfolding rate constants that are in good agreement with the experimental values. The apparent rate constant as a function of denaturant ('chevron plot') is predicted within an order of magnitude. Our results are consistent with a model whereby fast-folding proteins utilize a diffusion-collision mechanism, with the preorganization of one or more elements of secondary structure in the unfolded protein.     

Computational design and experimental testing of the fastest-folding β-sheet protein

One of the most important and elusive goals of molecular biology is the formulation of a detailed, atomic-level understanding of the process of protein folding. Fast-folding proteins with low free-energy barriers have proved to be particularly productive objects of investigation in this context, but the design of fast-folding proteins was previously driven largely by experiment. Dramatic advances in the attainable length of molecular dynamics simulations have allowed us to characterize in atomic-level detail the folding mechanism of the fast-folding all-β WW domain FiP35. In the work reported here, we applied the biophysical insights gained from these studies to computationally design an even faster-folding variant of FiP35 containing only naturally occurring amino acids. The increased stability and high folding rate predicted by our simulations were subsequently validated by temperature-jump experiments. The experimentally measured folding time was 4.3 μs at 80 °C—about three times faster than the fastest previously known protein with β-sheet content and in good agreement with our prediction. These results provide a compelling demonstration of the potential utility of very long molecular dynamics simulations in redesigning proteins well beyond their evolved stability and folding speed.     

The evolutionary landscape of functional model proteins.

To study the distinct influences of structure and function on evolution, we propose a minimalist model for proteins with binding pockets, called functional model proteins, based on a shifted-HP model on a two-dimensional square lattice. These model proteins are not maximally compact and contain an empty lattice site surrounded by at least three nearest neighbors, thus providing a binding pocket. Functional model proteins possess a unique native state, cooperative folding and tolerance to mutation. Due to the explicit functionality in these models (by design), we have been able to explore their fitness or evolutionary landscapes, as characterized by the size and distribution of homologous families and by the complexity of the inter-relatedness of the functional model proteins. Mindful that these minimalist models are highly idealized and two-dimensional, functional model proteins should nevertheless provide a useful means for exploring the constraints of maintaining structure and function on the evolution of proteins.     

A comparison of the folding kinetics of a small,artificially selected DNA aptamer with those of equivalently simple naturally occurring proteins

The folding of larger proteins generally differs from the folding of similarly large nucleic acids in the number and stability of the intermediates involved. To date, however, no similar comparison has been made between the folding of smaller proteins, which typically fold without well-populated intermediates, and the folding of small, simple nucleic acids. In response, in this study, we compare the folding of a 38-base DNA aptamer with the folding of a set of equivalently simple proteins. We find that, as is true for the large majority of simple, single domain proteins, the aptamer folds through a concerted, millisecond-scale process lacking well-populated intermediates. Perhaps surprisingly, the observed folding rate falls within error of a previously described relationship between the folding kinetics of single-domain proteins and their native state topology. Likewise, similarly to single-domain proteins, the aptamer exhibits a relatively low urea-derived Tanford β, suggesting that its folding transition state is modestly ordered. In contrast to this, however, and in contrast to the behavior of proteins, ϕ-value analysis suggests that the aptamer''s folding transition state is highly ordered, a discrepancy that presumably reflects the markedly more important role that secondary structure formation plays in the folding of nucleic acids. This difference notwithstanding, the similarities that we observe between the two-state folding of single-domain proteins and the two-state folding of this similarly simple DNA presumably reflect properties that are universal in the folding of all sufficiently cooperative heteropolymers irrespective of their chemical details.     

Evolutionary computer programming of protein folding and structure predictions

In order to understand the mechanism of protein folding and to assist the rational de-novo design of fast-folding, non-aggregating and stable artificial enzymes it is very helpful to be able to simulate protein folding reactions and to predict the structures of proteins and other biomacromolecules. Here, we use a method of computer programming called "evolutionary computer programming" in which a program evolves depending on the evolutionary pressure exerted on the program. In the case of the presented application of this method on a computer program for folding simulations, the evolutionary pressure exerted was towards faster finding deep minima in the energy landscape of protein folding. Already after 20 evolution steps, the evolved program was able to find deep minima in the energy landscape more than 10 times faster than the original program prior to the evolution process.     

An Overlapping Region between the Two Terminal Folding Units of the Outer Surface Protein A (OspA) Controls Its Folding Behavior

Although many naturally occurring proteins consist of multiple domains, most studies on protein folding to date deal with single-domain proteins or isolated domains of multi-domain proteins. Studies of multi-domain protein folding are required for further advancing our understanding of protein folding mechanisms. Borrelia outer surface protein A (OspA) is a β-rich two-domain protein, in which two globular domains are connected by a rigid and stable single-layer β-sheet. Thus, OspA is particularly suited as a model system for studying the interplays of domains in protein folding. Here, we studied the equilibria and kinetics of the urea-induced folding–unfolding reactions of OspA probed with tryptophan fluorescence and ultraviolet circular dichroism. Global analysis of the experimental data revealed compelling lines of evidence for accumulation of an on-pathway intermediate during kinetic refolding and for the identity between the kinetic intermediate and a previously described equilibrium unfolding intermediate. The results suggest that the intermediate has the fully native structure in the N-terminal domain and the single layer β-sheet, with the C-terminal domain still unfolded. The observation of the productive on-pathway folding intermediate clearly indicates substantial interactions between the two domains mediated by the single-layer β-sheet. We propose that a rigid and stable intervening region between two domains creates an overlap between two folding units and can energetically couple their folding reactions.     

Fuzzy-oil-drop hydrophobic force field--a model to represent late-stage folding (in silico) of lysozyme

A model of hydrophobic collapse (in silico), which is generally considered to be the driving force for protein folding, is presented in this work. The model introduces the external field in the form of a fuzzy-oil-drop assumed to represent the environment. The drop is expressed in the form of a three-dimensional Gauss function. The usual probability value is assumed to represent the hydrophobicity distribution in the three-dimensional space of the virtual environment. The differences between this idealized hydrophobicity distribution and the one represented by the folded polypeptide chain is the parameter to be minimized in the structure optimization procedure. The size of fuzzy-oil-drop is critical for the folding process. A strong correlation between protein length and the dimension of the native and early-stage molecular form was found on the basis of single-domain proteins analysis. A previously presented early-stage folding (in silico) model was used to create the starting structure for the procedure of late-stage folding of lysozyme. The results of simulation were found to be promising, although additional improvements for the formation of beta-structure and disulfide bonds as well as the participation of natural ligand in folding process seem to be necessary.     

Thermodynamics and kinetics of protein folding: an evolutionary perspective

This article appeals to an evolutionary model which postulates that primordial proteins were described by small polypeptide chains which (i) lack disulfide bridges, and (ii) display slow folding rates with multi-state kinetics, to determine relations between structural properties of proteins and their folding kinetics. We parameterize the energy landscape of proteins in terms of thermodynamic activation variables. The model studies evolutionary changes in these thermodynamic parameters, and we invoke relations between these activation variables and structural properties of the protein to predict the following correspondence between protein structure and folding kinetics. 1. Proteins with inter- and intra-chain disulfide bridges: large variability in both folding rates and stability of intermediates, multi-state kinetics. 2. Proteins which lack inter and intra-chain disulfide bridges. 2.1 Single-domain chains: fast folding rates; unstable intermediates; two-state kinetics. 2.2 Multi-domain monomers: intermediate rates; metastable intermediates; multi-state kinetics. 2.3 Multi-domain oligomers: slow rates; metastable intermediates; multi-state kinetics. The evolutionary model thus provides a kinetic characterization of one important subfamily of proteins which we describe by the following properties: Folding dynamics of single-domain proteins which lack disulfide bridges are described by two-state kinetics. Folding rate of this class of proteins is positively correlated with the thermodynamic stability of the folded state.     

Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model.

We use a simple off-lattice Langevin model of protein folding to characterize the folding and unfolding of a fast-folding, 46 residue three-helix bundle. Under conditions at which the C-terminal helix is 30 % stable, we observe a clear three-state folding mechanism. In the on-pathway intermediate state, the middle and C-terminal helices are folded and in contact with each other, while the N-terminal region remains disordered. Nevertheless, under these conditions this intermediate is thermodynamically unstable relative to its unfolded state. The first and highest folding barrier corresponds to the organization of the hinge between the middle and C-terminal helices. A subsequent major barrier corresponds to the organization of the hinge between the middle and N-terminal helices. Hyperstabilizing the hinge regions leads to twice the folding rate that is obtained from hyperstabilizing the helices, even though much fewer contacts are involved in hinge hyperstabilization than in helix hyperstabilization. Unfolding follows single-exponential kinetics, even at temperatures only slightly above the folding transition temperature.     

Toward resolution of ambiguity for the unfolded state

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA.     

Hairpins participating in folding of human telomeric sequence quadruplexes studied by standard and T-REMD simulations

DNA G-hairpins are potential key structures participating in folding of human telomeric guanine quadruplexes (GQ). We examined their properties by standard MD simulations starting from the folded state and long T-REMD starting from the unfolded state, accumulating ∼130 μs of atomistic simulations. Antiparallel G-hairpins should spontaneously form in all stages of the folding to support lateral and diagonal loops, with sub-μs scale rearrangements between them. We found no clear predisposition for direct folding into specific GQ topologies with specific syn/anti patterns. Our key prediction stemming from the T-REMD is that an ideal unfolded ensemble of the full GQ sequence populates all 4096 syn/anti combinations of its four G-stretches. The simulations can propose idealized folding pathways but we explain that such few-state pathways may be misleading. In the context of the available experimental data, the simulations strongly suggest that the GQ folding could be best understood by the kinetic partitioning mechanism with a set of deep competing minima on the folding landscape, with only a small fraction of molecules directly folding to the native fold. The landscape should further include non-specific collapse processes where the molecules move via diffusion and consecutive random rare transitions, which could, e.g. structure the propeller loops.     

On prediction of folding nuclei in globular proteins

The approach described in this paper on the prediction of folding nuclei in globular proteins with known three dimensional structures is based on a search of the lowest saddle points through the barrier separating the unfolded state from the native structure on the free-energy landscape of protein chain. This search is performed by a dynamic programming method. Comparison of theoretical results with experimental data on the folding nuclei of two dozen of proteins shows that our model provides good phi value predictions for proteins whose structures have been determined by X-ray analysis, with a less limited success for proteins whose structures have been determined by NMR techniques only. Consideration of a full ensemble of transition states results in more successful prediction than consideration of only the transition states with the minimal free energy. In conclusion we have predicted the localization of folding nuclei for three dimensional protein structures for which kinetics of folding is studied now but the localization of folding nuclei is still unknown.     

Fuzzy-Oil-Drop Hydrophobic Force Field—A Model to Represent Late-stage Folding (In Silico) of Lysozyme

Abstract

A model of hydrophobic collapse (in silico), which is generally considered to be the driving force for protein folding, is presented in this work. The model introduces the external field in the form of a fuzzy-oil-drop assumed to represent the environment. The drop is expressed in the form of a three-dimensional Gauss function. The usual probability value is assumed to represent the hydrophobicity distribution in the three-dimensional space of the virtual environment. The differences between this idealized hydrophobicity distribution and the one represented by the folded polypeptide chain is the parameter to be minimized in the structure optimization procedure. The size of fuzzy-oil-drop is critical for the folding process. A strong correlation between protein length and the dimension of the native and early-stage molecular form was found on the basis of single-domain proteins analysis. A previously presented early-stage folding (in silico) model was used to create the starting structure for the procedure of late-stage folding of lysozyme. The results of simulation were found to be promising, although additional improvements for the formation of β-structure and disulfide bonds as well as the participation of natural ligand in folding process seem to be necessary.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation

A statistical-mechanical model (a noninteracting local structure model) of folding and unfolding transition in globular proteins is described and a formulation is given to calculate the partition function. The process of transition is discussed in this model within the framework of equilibrium statistical mechanics. In order to clarify the range of applicability of such an approach, the characteristics of the folding and unfolding transition in globular proteins are analyzed from the statistical-physical point of view. A theoretical advantage is pointed out in studying folding and unfolding processes taking place as conformational fluctuations in individual protein molecules under macroscopic equilibrium at the melting temperature. In this case, paths of folding and unfolding are shown to be identical in the statistical sense. A key to the noninteracting local structure model lies in the concept of local structures and the assumption of the absence of interactions between local structures. A local structure is defined as a continuous section of the chain which takes the same or similar local conformation as in the native conformation. The assumption of the absence of inter-actions between local structures endows the model with the remarkable character that its partition function can be calculated exactly; thereby the equilibrium population of various conformations along the folding and unfolding paths can be discussed only by a knowledge of the folded native conformation.     

Dynamic association of trigger factor with protein substrates.

Trigger factor is a ribosome-bound folding helper, which, apparently, combines two functions, chaperoning of nascent proteins and catalyzing prolyl isomerization in their folding. Immediate chaperone binding at the ribosome might interfere with rapid protein folding reactions, and we find that trigger factor indeed retards the in vitro folding of a protein with native prolyl isomers. The kinetic analysis of trigger factor binding to a refolding protein reveals that the adverse effects of trigger factor on conformational folding are minimized by rapid binding and release. The complex between trigger factor and a substrate protein is thus very short-lived, and fast-folding proteins can escape efficiently from an accidental interaction with trigger factor. Protein chains with incorrect prolyl isomers cannot complete folding and therefore can rebind for further rounds of catalysis. Unlike DnaK, trigger factor interacts with substrate proteins in a nucleotide-independent binding reaction, which seems to be optimized for high catalytic activity rather than for chaperone function. The synthetic lethality, observed when the genes for both DnaK and trigger factor are disrupted, might result from an indirect linkage. In the absence of trigger factor, folding is retarded and more aggregates form, which can neither be prevented nor disposed of when DnaK is lacking as well.