Relative Folding Rates Research Articles

Structural Determinants of Misfolding in Multidomain Proteins.

Recent single molecule experiments, using either atomic force microscopy (AFM) or Förster resonance energy transfer (FRET) have shown that multidomain proteins containing tandem repeats may form stable misfolded structures. Topology-based simulation models have been used successfully to generate models for these structures with domain-swapped features, fully consistent with the available data. However, it is also known that some multidomain protein folds exhibit no evidence for misfolding, even when adjacent domains have identical sequences. Here we pose the question: what factors influence the propensity of a given fold to undergo domain-swapped misfolding? Using a coarse-grained simulation model, we can reproduce the known propensities of multidomain proteins to form domain-swapped misfolds, where data is available. Contrary to what might be naively expected based on the previously described misfolding mechanism, we find that the extent of misfolding is not determined by the relative folding rates or barrier heights for forming the domains present in the initial intermediates leading to folded or misfolded structures. Instead, it appears that the propensity is more closely related to the relative stability of the domains present in folded and misfolded intermediates. We show that these findings can be rationalized if the folded and misfolded domains are part of the same folding funnel, with commitment to one structure or the other occurring only at a relatively late stage of folding. Nonetheless, the results are still fully consistent with the kinetic models previously proposed to explain misfolding, with a specific interpretation of the observed rate coefficients. Finally, we investigate the relation between interdomain linker length and misfolding, and propose a simple alchemical model to predict the propensity for domain-swapped misfolding of multidomain proteins.

A Motion Planning Approach to Studying Molecular Motions

While structurally very different, protein and RNA molecules share an important attribute. The motions they undergo are strongly related to the function they perform. For example, many diseases such as Mad Cow disease or Alzheimer's disease are associated with protein misfolding and aggregation. Similarly, RNA folding velocity may regulate the plasmid copy number, and RNA folding kinetics can regulate gene expression at the translational level. Knowledge of the stability, folding, kinetics and detailed mechanics of the folding process may help provide insight into how proteins and RNAs fold. In this paper, we present an overview of our work with a computational method we have adapted from robotic motion planning to study molecular motions. We have val- idated against experimental data and have demonstrated that our method can capture biological results such as stochastic folding pathways, population kinetics of various conformations, and rela- tive folding rates. Thus, our method provides both a detailed view (e.g., individual pathways) and a global view (e.g., population kinetics, relative folding rates, and reaction coordinates) of energy land- scapes of both proteins and RNAs. We have validated these techniques by showing that we observe the same relative folding rates as shown in experiments for structurally similar protein molecules that exhibit different folding behaviors. Our analysis has also been able to predict the same relative gene expression rate for wild-type MS2 phage RNA and three of its mutants.

Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102-14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape-based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C-terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.

Structural parameters affecting the kinetics of RNA hairpin formation

There is little experimental knowledge on the sequence dependent rate of hairpin formation in RNA. We have therefore designed RNA sequences that can fold into either of two mutually exclusive hairpins and have determined the ratio of folding of the two conformations, using structure probing. This folding ratio reflects their respective folding rates. Changing one of the two loop sequences from a purine- to a pyrimidine-rich loop did increase its folding rate, which corresponds well with similar observations in DNA hairpins. However, neither changing one of the loops from a regular non-GNRA tetra-loop into a stable GNRA tetra-loop, nor increasing the loop size from 4 to 6 nt did affect the folding rate. The folding kinetics of these RNAs have also been simulated with the program ‘Kinfold’. These simulations were in agreement with the experimental results if the additional stabilization energies for stable tetra-loops were not taken into account. Despite the high stability of the stable tetra-loops, they apparently do not affect folding kinetics of these RNA hairpins. These results show that it is possible to experimentally determine relative folding rates of hairpins and to use these data to improve the computer-assisted simulation of the folding kinetics of stem–loop structures.

Dynamics, Energetics, and Structure in Protein Folding

For many decades, protein folding experimentalists have worked with no information about the time scales of relevant protein folding motions and without methods for estimating the height of folding barriers. Protein folding experiments have been interpreted using chemical models in which the folding process is characterized as a series of equilibria between two or more distinct states that interconvert with activated kinetics. Accordingly, the information to be extracted from experiments was circumscribed to apparent equilibrium constants and relative folding rates. Recent developments are changing this situation dramatically. The combination of fast-folding experiments with the development of analytical methods more closely connected to physical theory reveals that folding barriers in native conditions range from minimally high (approximately 14RT for the very slow folder AcP) to nonexistent. While slow-folding (i.e., > or = 1 ms) single-domain proteins are expected to fold in a two-state fashion, microsecond-folding proteins should exhibit complex behavior arising from crossing marginal or negligible folding barriers. This realization opens a realm of exciting opportunities for experimentalists. The free energy surface of a protein with a marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic factors from structural factors in folding. Kinetic experiments on these proteins provide the unique opportunity to measure folding dynamics directly. Furthermore, the complex distributions of time-dependent folding behaviors expected for these proteins might be accessible to single-molecule measurements. Here, we discuss some of these recent developments in protein folding, emphasizing aspects that can serve as a guide for experimentalists interested in exploiting this new avenue of research.

Prediction of folding pathway and kinetics among plant hemoglobins using an average distance map method

Computational methods, such as the ADM (average distance map) method, have been developed to predict folding of homologous proteins. In this work we used the ADM method to predict the folding pathway and kinetics among selected plant nonsymbiotic (nsHb), symbiotic (Lb), and truncated (tHb) hemoglobins (Hbs). Results predicted that (1) folding of plant Hbs occurs throughout the formation of compact folding modules mostly formed by helices A, B, and C, and E, F, G, and H (folding modules A/C and E/H, respectively), and (2) primitive (moss) nsHbs fold in the C-->N direction, evolved (monocot and dicot) nsHbs fold either in the C-->N or N-->C direction, and Lbs and plant tHbs fold in the C-->N direction. We also predicted relative folding rates of plant Hbs from qualitative analyses of the stability of subdomains and classified plant Hbs into fast and moderate folding. ADM analysis of nsHbs predicted that prehelix A plays a role during folding of the N-terminal domain of Ceratodon nsHb, and that CD-loop plays a role in folding of primitive (Physcomitrella and Ceratodon) but not evolved nsHbs. Modeling of the rice Hb1 A/C and E/H modules showed that module E/H overlaps to the Mycobacterium tuberculosis HbO two-on-two folding. This observation suggests that module E/H is an ancient tertiary structure in plant Hbs.

The Protein Folding Transition State: What Are φ-Values Really Telling Us?

Protein engineering-based studies of the folding transition state have accelerated significantly in the last decade, and more than a half dozen proteins have been subjected to extensive Phi-value analysis. A general picture is emerging from these studies of a transition state in which the large majority of experimentally characterized side chains participate in relatively homogeneous and energetically weak interactions playing only a relatively small role in defining relative folding rates.

Peptide models of four possible insulin folding intermediates with two disulfides.

The single-chain insulin (PIP) can spontaneously fold into native structure through preferred kinetic intermediates. During refolding, pairing of the first disulfide A20-B19 is highly specific, whereas pairing of the second disulfide is likely random because two two-disulfide intermediates have been trapped. To get more details of pairing property of the second disulfide, four model peptides of possible folding intermediates with two disulfides were prepared by protein engineering, and their properties were analyzed. The four model peptides were named [A20-B19, A7-B7]PIP, [A20-B19, A6-B7]PIP, [A20-B19, A6-A11]PIP, and [A20-B19, A7-A11]PIP according to their remaining disulfides. The four model peptides all adopt partially folded structure with moderate conformational differences. In redox buffer, the disulfides of the model peptides are more easily reduced than those of the wild-type PIP. During in vitro refolding, the reduced model peptides share similar relative folding rates but different folding yields: The refolding efficiency of the reduced [A20-B19, A7-A11]PIP is about threefold lower than that of the other three peptides. The present results indicate that the folding intermediates corresponding to the present model peptides all adopt partially folded conformation, and can be formed during PIP refolding, but the chance of forming the intermediate with disulfide [A20-B19, A7-A11] is much lower than that of forming the other three intermediates.

Cooperativity, Smooth Energy Landscapes and the Origins of Topology-dependent Protein Folding Rates

The relative folding rates of simple, single-domain proteins, proteins whose folding energy landscapes are smooth, are highly dispersed and strongly correlated with native-state topology. In contrast, the relative folding rates of small, Gō-potential lattice polymers, which also exhibit smooth energy landscapes, are poorly dispersed and insignificantly correlated with native-state topology. Here, we investigate this discrepancy in light of a recent, quantitative theory of two-state folding kinetics, the topomer search model. This model stipulates that the topology-dependence of two-state folding rates is a direct consequence of the extraordinarily cooperative equilibrium folding of simple proteins. We demonstrate that traditional Gō polymers lack the extreme cooperativity that characterizes the folding of naturally occurring, two-state proteins and confirm that the folding rates of a diverse set of Gō 27-mers are poorly dispersed and effectively uncorrelated with native state topology. Upon modestly increasing the cooperativity of the Gō-potential, however, significantly increased dispersion and strongly topology-dependent kinetics are observed. These results support previous arguments that the cooperative folding of simple, single-domain proteins gives rise to their topology-dependent folding rates. We speculate that this cooperativity, and thus, indirectly, the topology–rate relationship, may have arisen in order to generate the smooth energetic landscapes upon which rapid folding can occur.

Equilibrium collapse and the kinetic 'foldability' of proteins.

An important element of protein folding theory has been the identification of equilibrium parameters that might uniquely distinguish rapidly folding polypeptide sequences from those that fold slowly. One such parameter, termed sigma, is a dimensionless, equilibrium measure of the coincidence of chain compaction and folding that is predicted to be an important determinant of relative folding kinetics. To test this prediction and improve our understanding of the putative relationship between nonspecific compaction of the unfolded state and protein folding kinetics, we have used small-angle X-ray scattering and circular dichroism spectroscopy to measure the sigma of five well-characterized proteins. Consistent with theoretical predictions, we find that near-perfect coincidence of the unfolded state contraction and folding (sigma approximately 0) is associated with the rapid kinetics of these naturally occurring proteins. We do not, however, observe any significant correlation between sigma and either the relative folding rates of these proteins or the presence or absence of well-populated kinetic intermediates. Thus, while sigma approximately 0 may be a necessary condition to ensure rapid folding, differences in sigma do not account for the wide range of rates and mechanisms with which naturally occurring proteins fold.

On the Relationship Between Protein Stability and Folding Kinetics: A Comparative Study of the N-terminal Domains of RNase HI, E. coli and Bacillus stearothermophilus L9

There is currently a great deal of interest in proteins that fold in a single highly cooperative step. Particular attention has been focused on elucidating the factors that govern folding rates of simple proteins. Recently, the topology of the native state has been proposed to be the most important determinant of their folding rates. Here we report a comparative study of the folding of three topologically equivalent proteins that adapt a particularly simple α/β fold. The folding kinetics of the N-terminal domain of RNase HI and the N-terminal domain of the ribosomal protein L9 from Escherichia coli (eNTL9) were compared to the previously characterized N-terminal domain of L9 from Bacillus stearothermophilus (bNTL9). This 6.2kDa protein, which is one of simplest examples of the ABCαD motif, folds via a two-state mechanism on the millisecond to submillisecond time scale. The RNase HI domain and bNTL9 have very similar tertiary structures but there is little similarity in primary sequence. bNTL9 and eNTL9 share the same biological function and a similar primary sequence but differ significantly in stability. Fluorescence-detected stopped-flow experiments showed that the three proteins fold in a two-state fashion. The folding rates in the absence of denaturant were found to be very different, ranging form 21s−1 to 790s−1 at 10°C. The diverse folding rates appear to reflect large differences in the stability of the proteins. When compared at an isostability point, the folding rates converged to a similar value and there is a strong linear correlation between the log of the folding rate and stability for this set of proteins. These observations are consistent with the idea that stability can play an important role in dictating relative folding rates among topologically equivalent proteins.

The folding kinetics and thermodynamics of the Fyn-SH3 domain.

The equilibrium unfolding and the kinetic folding and unfolding of the 67 residue Fyn-SH3 domain have been investigated. Equilibrium unfolding experiments indicate that, despite the lack of both disulfide bonds and prosthetic groups, Fyn-SH3 is relatively stable with a free energy of folding of -6.0 +/- 0.6 kcal mol-1 at 20 degrees C. Kinetic experiments indicate that the domain refolds in a rapid two-state manner without significant population of intermediates (k = 94.3 s-1 in H2O at 20 degrees C). Despite the presence of two proline residues, the refolding of the domain is monophasic, and no significant proline isomerization-like refolding phase is observed. This can be attributed to an extremely low level of the incorrect (cis) isomer of the structurally important Pro134 residue in the protein denatured in 8 M guanidine hydrochloride. Analysis of the temperature and guanidine hydrochloride dependence of the folding rate suggests that the folding transition state of this protein is relatively well organized. A comparison with the refolding kinetics and thermodynamics of other homologous SH3 domains indicates that these exhibit an equivalent degree of transition state organization. This potentially arises from conservation of key features of the transition state conformation despite sometimes relatively low overall sequence identity. Such a comparison further suggests that relative thermodynamic stability is an important factor in determining the relative folding rates of natural proteins with a common fold, but that specific details of the amino acid sequence can also play a significant role in individual cases.