Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.     

Local secondary structure content predicts folding rates for simple,two-state proteins

Many single-domain proteins exhibit two-state folding kinetics, with folding rates that span more than six orders of magnitude. A quantity of much recent interest for such proteins is their contact order, the average separation in sequence between contacting residue pairs. Numerous studies have reached the surprising conclusion that contact order is well-correlated with the logarithm of the folding rate for these small, well-characterized molecules. Here, we investigate the physico-chemical basis for this finding by asking whether contact order is actually a composite number that measures the fraction of local secondary structure in the protein; viz. turns, helices, and hairpins. To pursue this question, we calculated the secondary structure content for 24 two-state proteins and obtained coefficients that predict their folding rates. The predicted rates correlate strongly with experimentally determined rates, comparable to the correlation with contact order. Further, these predicted folding rates are correlated strongly with contact order. Our results suggest that the folding rate of two-state proteins is a function of their local secondary structure content, consistent with the hierarchic model of protein folding. Accordingly, it should be possible to utilize secondary structure prediction methods to predict folding rates from sequence alone.     

Unification of the folding mechanisms of non-two-state and two-state proteins

We have collected the kinetic folding data for non-two-state and two-state globular proteins reported in the literature, and investigated the relationships between the folding kinetics and the native three-dimensional structure of these proteins. The rate constants of formation of both the intermediate and the native state of non-two-state folders were found to be significantly correlated with protein chain length and native backbone topology, which is represented by the absolute contact order and sequence-distant native pairs. The folding rate of two-state folders, which is known to be correlated with the native backbone topology, apparently does not correlate significantly with protein chain length. On the basis of a comparison of the folding rates of the non-two-state and two-state folders, it was found that they are similarly dependent on the parameters that reflect the native backbone topology. This suggests that the mechanisms behind non-two-state and two-state folding are essentially identical. The present results lead us to propose a unified mechanism of protein folding, in which folding occurs in a hierarchical manner, reflecting the hierarchy of the native three-dimensional structure, as embodied in the case of non-two-state folding with an accumulation of the intermediate. Apparently, two-state folding is merely a simplified version of hierarchical folding caused either by an alteration in the rate-limiting step of folding or by destabilization of the intermediate.     

ALASKA: A Mathematica package for two-state kinetic analysis of protein folding reactions

A Mathematica package (ALASKA) has been developed to simplify the measurement of protein folding kinetics by analysis of ¹H NMR lineshape analysis. This package reads NMR data in ASCII format and can simulate an aromatic ¹ NMR spectrum with or without lineshape broadening from chemical exchange. We describe the analysis of a urea denaturation series of a fast-folding protein, the G46A/G48A variant of monomeric repressor.     

Folding of a LysM domain: entropy-enthalpy compensation in the transition state of an ideal two-state folder

Protein-engineering methods (Φ-values) were used to investigate the folding transition state of a lysin motif (LysM) domain from Escherichia coli membrane-bound lytic murein transglycosylase D. This domain consists of just 48 structured residues in a symmetrical βααβ arrangement and is the smallest αβ protein yet investigated using these methods. An extensive mutational analysis revealed a highly robust folding pathway with no detectable transition state plasticity, indicating that LysM is an example of an ideal two-state folder. The pattern of Φ-values denotes a highly polarised transition state, with significant formation of the helices but no structure within the β-sheet. Remarkably, this transition state remains polarised after circularisation of the domain, and exhibits an identical Φ-value pattern; however, the interactions within the transition state are uniformly weaker in the circular variant. This observation is supported by results from an Eyring analysis of the folding rates of the two proteins. We propose that the folding pathway of LysM is dominated by enthalpic rather than entropic considerations, and suggest that the lower entropy cost of formation of the circular transition state is balanced, to some extent, by the lower enthalpy of contacts within this structure.     

Relationships between the folding rate constant and the topological parameters of small two-state proteins based on general random walk model

In this paper, we propose an analytically tractable model of protein folding based on one-dimensional general random walk. A second-order differential equation for the mean folding time of a single protein is constructed which can be used to derive the observed relationship between the folding rate constant and the number of native contacts. The parameters appearing in the model can be determined by fitting the theoretical prediction to the experimental result. In addition, taking into account the fact that the number of native contacts is almost proportional to the relative contact order, we can also explain the observed relationship between the folding rate constant and the relative contact order.     

Experimental characterization of the folding kinetics of the notch ankyrin domain

Proteins constructed from linear arrays of tandem repeats provide a simplified architecture for understanding protein folding. Here, we examine the folding kinetics of the ankyrin repeat domain from the Drosophila Notch receptor, which consists of six folded ankyrin modules and a seventh partly disordered N-terminal ankyrin repeat sequence. Both the refolding and unfolding kinetics are best described as a sum of two exponential phases. The slow, minor refolding phase is limited by prolyl isomerization in the denatured state (D). The minor unfolding phase, which appears as a lag during fluorescence-detected unfolding, is consistent with an on-pathway intermediate (I). This intermediate, although not directly detected during refolding, is shown to be populated by interrupted refolding experiments. When plotted against urea, the rate constants for the major unfolding and refolding phases define a single non-linear v-shaped chevron, as does the minor unfolding phase. These two chevrons, along with unfolding amplitudes, are well-fitted by a sequential three-state model, which yields rate constants for the individual steps in folding and unfolding. Based on these fitted parameters, the D to I step is rate-limiting, and closely matches the major observed refolding phase at low denaturant concentrations. I appears to be midway between N and D in folding free energy and denaturant sensitivity, but has Trp fluorescence properties close to N. Although the Notch ankyrin domain has a simple architecture, folding is slow, with the limiting refolding rate constant as much as seven orders of magnitude smaller than expected from topological predictions.     

The folding mechanism of a two-domain protein: folding kinetics and domain docking of the gene-3 protein of phage fd

The gene-3 protein (G3P) of filamentous phages is essential for the infection of Escherichia coli. The carboxy-terminal domain anchors this protein in the phage coat, whereas the two amino-terminal domains N1 and N2 protrude from the phage surface. We analyzed the folding mechanism of the two-domain fragment N1-N2 of G3P (G3P(*)) and the interplay between folding and domain assembly. For this analysis, a variant of G3P(*) was used that contained four stabilizing mutations (IIHY-G3P(*)). The observed refolding kinetics extend from 10 ms to several hours. Domain N1 refolds very rapidly (with a time constant of 9.4 ms at 0.5 M guanidinium chloride, 25 degrees C) both as a part of IIHY-G3P(*) and as an isolated protein fragment. The refolding of domain N2 is slower and involves two reactions with time constants of seven seconds and 42 seconds. These folding reactions of the individual domains are followed by a very slow, spectroscopically silent docking process, which shows a time constant of 6200 seconds. This reaction was detected by a kinetic unfolding assay for native molecules. Before docking, N1 and N2 unfold fast and independently, after docking they unfold slowly in a correlated fashion. A high energy barrier is thus created by domain docking, which protects G3P kinetically against unfolding. The slow domain docking is possibly important for the infection of E.coli by the phage. Upon binding to the F pilus, the N2 domain separates from N1 and the binding site for TolA on domain N1 is exposed. Since domain reassembly is so slow, this binding site remains accessible until pilus retraction has brought N1 close to TolA on the bacterial surface.     

Relationship between stability of folding intermediates and amyloid formation for the yeast prion Ure2p: a quantitative analysis of the effects of pH and buffer system

The dimeric yeast protein Ure2 shows prion-like behaviour in vivo and forms amyloid fibrils in vitro. A dimeric intermediate is populated transiently during refolding and is apparently stabilized at lower pH, conditions suggested to favour Ure2 fibril formation. Here we present a quantitative analysis of the effect of pH on the thermodynamic stability of Ure2 in Tris and phosphate buffers over a 100-fold protein concentration range. We find that equilibrium denaturation is best described by a three-state model via a dimeric intermediate, even under conditions where the transition appears two-state by multiple structural probes. The free energy for complete unfolding and dissociation of Ure2 is up to 50 kcal mol(-1). Of this, at least 20 kcal mol(-1) is contributed by inter-subunit interactions. Hence the native dimer and dimeric intermediate are significantly more stable than either of their monomeric counterparts. The previously observed kinetic unfolding intermediate is suggested to represent the dissociated native-like monomer. The native state is stabilized with respect to the dimeric intermediate at higher pH and in Tris buffer, without significantly affecting the dissociation equilibrium. The effects of pH, buffer, protein concentration and temperature on the kinetics of amyloid formation were quantified by monitoring thioflavin T fluorescence. The lag time decreases with increasing protein concentration and fibril formation shows pseudo-first order kinetics, consistent with a nucleated assembly mechanism. In Tris buffer the lag time is increased, suggesting that stabilization of the native state disfavours amyloid nucleation.     

Folding and unfolding mechanism of highly stable full-consensus ankyrin repeat proteins

Full-consensus designed ankyrin repeat proteins were designed with one to six identical repeats flanked by capping repeats. These proteins express well in Escherichia coli as soluble monomers. Compared to our previously described designed ankyrin repeat protein library, randomized positions have now been fixed according to sequence statistics and structural considerations. Their stability increases with length and is even higher than that of library members, and those with more than three internal repeats are resistant to denaturation by boiling or guanidine hydrochloride. Full denaturation requires their heating in 5 M guanidine hydrochloride. The folding and unfolding kinetics of the proteins with up to three internal repeats were analyzed, as the other proteins could not be denatured. Folding is monophasic, with a rate that is nearly identical for all proteins (∼ 400-800 s^− 1), indicating that essentially the same transition state must be crossed, possibly the folding of a single repeat. In contrast, the unfolding rate decreases by a factor of about 10⁴ with increasing repeat number, directly reflecting thermodynamic stability in these extraordinarily slow denaturation rates. The number of unfolding phases also increases with repeat number. We analyzed the folding thermodynamics and kinetics both by classical two-state and three-state cooperative models and by an Ising-like model, where repeats are considered as two-state folding units that can be stabilized by interacting with their folded nearest neighbors. This Ising model globally describes both equilibrium and kinetic data very well and allows for a detailed explanation of the ankyrin repeat protein folding mechanism.     

Destabilization of the Escherichia coli RNase H kinetic intermediate: switching between a two-state and three-state folding mechanism

Escherichia coli RNase H folds through a partially folded kinetic intermediate that mirrors a rarely populated, partially unfolded form detectable by native-state hydrogen exchange under equilibrium conditions. Residue 53 is at the interface of two helices known to be structured in this intermediate. Kinetic refolding studies on mutant proteins varying in size and hydrophobicity at residue 53 support a contribution of hydrophobicity to the stabilities of the kinetic intermediate and the transition state. Packing interactions also play a significant role in the stability of these two states, though they play a much larger role in the native-state stability. One dramatic mutation, I53D, results in the conversion from a three-state to a two-state folding mechanism, which is explained most easily through a simple destabilization of the kinetic intermediate such that it is no longer stable with respect to the unfolded state. These results demonstrate that interactions that stabilize an intermediate can accelerate folding if these same interactions are present in the transition state. Our results are consistent with a hierarchical model of folding, where the intermediate consists of native-like interactions, is on-pathway, and is productive for folding.     

Folding and assembly pathways of co-chaperonin proteins 10: Origin of bacterial thermostability

To compare folding/assembly processes of heptameric co-chaperonin proteins 10 (cpn10) from different species and search for the origin of thermostability in hyper-thermostable Aquifex aeolicus cpn10 (Aacpn10), we have studied two bacterial variants-Aacpn10 and Escherichia coli cpn10 (GroES)-and compared the results to data on Homo sapiens cpn10 (hmcpn10). Equilibrium denaturation of GroES by urea, guanidine hydrochloride (GuHCl) and temperature results in coupled heptamer-to-monomer transitions in all cases. This is similar to the behavior of Aacpn10 but differs from hmcpn10 denaturation in urea. Time-resolved experiments reveal that GroES unfolds before heptamer dissociation, whereas refolding/reassembly begins with folding of individual monomers; these assemble in a slower step. The sequential folding/assembly mechanism for GroES is rather similar to that observed for Aacpn10 but contradicts the parallel paths of hmcpn10. We reveal that Aacpn10's stability profile is shifted upwards, broadened, and also moved horizontally to higher temperatures, as compared to that of GroES.     

Role of the Cys 2-Cys 10 disulfide bond for the structure, stability, and folding kinetics of ribonuclease T1.

The Cys 2-Cys 10 disulfide bond in ribonuclease T1 was broken by substituting Cys 2 and Cys 10 by Ser and Asn, respectively, as present in ribonuclease F1. This C2S/C10N variant resembles the wild-type protein in structure and in catalytic activity. Minor structural changes were observed by 2-dimensional NMR in the local environment of the substituted amino acids only. The thermodynamic stability of ribonuclease T1 is strongly reduced by breaking the Cys 2-Cys 10 bond, and the free energy of denaturation is decreased by about 10 kJ/mol. The folding mechanism is not affected, and the trans to cis isomerizations of Pro 39 and Pro 55 are still the rate-limiting steps of the folding process. The differences in the time courses of unfolding and refolding are correlated with the decrease in stability: the folding kinetics of the wild-type protein and the C2S/C10N variant become indistinguishable when they are compared under conditions of identical stability. Apparently, the Cys 2-Cys 10 disulfide bond is important for the stability but not for the folding mechanism of ribonuclease T1. The breaking of this bond has the same effect on stability and folding kinetics as adding 1 M guanidinium chloride to the wild-type protein.     

Cystic Fibrosis: Channel, Catalytic, and Folding Properties of the CFTR Protein

The identification and characterization of the CFTR gene and protein have provided not only a major impetus to the dissection of the molecular pathophysiology of cystic fibrosis (CF) but also a new perspective on the structure and function of the large supeifamily of membrane transport proteins to which it belongs. While the mechanism of the active vectorial translocation of many hydrophobic substrates by several of these transporters remains nearly as perplexing as it has for several decades, considerable insight has been gained into the control of the bi-directional permeation of chloride ions through a single CFTR channel by the phosphorylation of the R-domain and ATP interactions at the two nucleotide binding domains. However, details of these catalytic and allosteric mechanisms remain to be elucidated and await the replacement of two-dimensional conceptualizations with three dimensional structure information. Secondary and tertiary structure determination is required both for the understanding of the mechanism of action of the molecule and to enable a more complete appreciation of the misfolding and misprocessing of mutant CFTR molecules. This is the primary cause of the disease in the majority of the patients and hence understanding the details of the cotranslational interactions with multiple molecular chaperones, the ubiquitin-proteasome pathway and other components of the quality control machinery at the endoplasmic reticulum could provide a basis for the development of new therapeutic interventions.     

ATP-dependent translocation of proteins along single-stranded DNA: models and methods of analysis of pre-steady state kinetics

Processive DNA helicases are able to translocate along single-stranded DNA (ssDNA) with biased directionality in a nucleoside triphosphate-dependent reaction, although translocation is not generally sufficient for helicase activity. An understanding of the mechanism of protein translocation along ssDNA requires pre-steady state transient kinetic experiments. Although ensemble experimental approaches have been developed recently for the study of translocation of proteins along DNA, quantitative analysis of the complete time-courses from these experiments, which is needed to obtain quantitative estimates of translocation kinetic parameters (rate constants, processivity, step sizes and ATP coupling) has been lacking. We discuss three ensemble transient kinetic experiments that can be used to study protein translocation along ssDNA, along with the advantages and limitations of each approach. We further describe methods to analyze the complete kinetic time-courses obtained from such experiments performed with a series of ssDNA lengths under "single-round" conditions (i.e. in the absence of re-binding of dissociated protein to DNA). These analysis methods utilize a sequential "n-step" model for protein translocation along ssDNA and enable quantitative determinations of the rate constant, processivity and step size for translocation through global non-linear least-squares fitting of the full time-courses.     

Foldon, the natural trimerization domain of T4 fibritin, dissociates into a monomeric A-state form containing a stable beta-hairpin: atomic details of trimer dissociation and local beta-hairpin stability from residual dipolar couplings

The C-terminal domain of T4 fibritin (foldon) is obligatory for the formation of the fibritin trimer structure and can be used as an artificial trimerization domain. Its native structure consists of a trimeric beta-hairpin propeller. At low pH, the foldon trimer disintegrates into a monomeric (A-state) form that has similar properties as that of an early intermediate of the trimer folding pathway. The formation of this A-state monomer from the trimer, its structure, thermodynamic stability, equilibrium association and folding dynamics have been characterized to atomic detail by modern high-resolution NMR techniques. The foldon A-state monomer forms a beta-hairpin with intact and stable H-bonds that is similar to the monomer in the foldon trimer, but lacks a defined structure in its N and C-terminal parts. Its thermodynamic stability in pure water is comparable to designed hairpins stabilized in alcohol/water mixtures. Details of the thermal unfolding of the foldon A-state have been characterized by chemical shifts and residual dipolar couplings (RDCs) detected in inert, mechanically stretched polyacrylamide gels. At the onset of the thermal transition, uniform relative changes in RDC values indicate a uniform decrease of local N-HN and Calpha-Halpha order parameters for the hairpin strand residues. In contrast, near-turn residues show particular thermal stability in RDC values and hence in local order parameters. This coincides with increased transition temperatures of the beta-turn residues observed by chemical shifts. At high temperatures, the RDCs converge to non-zero average values consistent with predictions from random chain polymer models. Residue-specific deviations above the unfolding transition reveal the persistence of residual order around proline residues, large hydrophobic residues and at the beta-turn.     

Functional display of proteins, mutant proteins, fragments of proteins and peptides on the surface of filamentous (bacterio) phages: A review

Cytoplasmic expression of complex eukaryotic proteins inEscherichia coli usually yields inactive protein preparations. In some cases, (part) of the biological activity can be recovered by rather inefficient denaturation-renaturation procedures. Recently, novel concepts have been developed for the expression of fully functional eukaryotic proteins inE. coli. Essential to the success of these procedures is the transport of such proteins across the inner membrane to the periplasmic space, allowing proper folding and the establishment of disulfide bonding. Subsequently, fully functional proteins can be exposed on the surface of filamentous (bacterio)phages, provided a system is employed that consists of a cloning vector (e.g. the phagemid pComb3, Barbas et al., 1991) that generates phage particles in the presence of a helper phage. The main advantage of surface display of recombinant proteins is to facilitate the screening of very large numbers of different molecules by simple selection methods (panning). In addition, periplasmic expression yields relatively large quantities (e.g. 1 mg l^–1 of culture) soluble protein. In this review, the principle aspects of this novel expression system based on the phagemid pComb3 will be discussed. Two examples for functional periplasmic expression of human proteins inE. coli will be presented, namely i) the antigen-binding moiety (Fab fragment) of human immunoglobulins (IgGs) and ii) the human plasminogen activator inhibitor 1, an essential regulator of the plasminogen activation system. Finally, perspectives for the application of this system to express mutant proteins, fragments of proteins and peptides are indicated.Abbreviations Ap^R ampicillin resistance - cfu colony forming unit(s) - cpIII gene III-encoded coat protein of M13 - cpVIII gene VIII-encoded coat protein of M13 - ER endoplasmic reticulum - Fab fragment of Ig containing light chain, variable region and first constant region of heavy chain - Fd variable region and first constant region of the heavy chain - Fv fragment containing variable regions of heavy and light chain - Ig immunoglobulin - Km^R kanamycin resistance - kb kilobase or 1000 basepairs - PAI-1 plasminogen activator inhibitor 1 - t-PA tissue-type plasminogen activator - u-PA urokinase-type plasminogen activator