Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments ( for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.

Protein folding kinetics exhibit an Arrhenius temperature dependence when corrected for the temperature dependence of protein stability

The anomalous temperature dependence of protein folding has received considerable attention. Here we show that the temperature dependence of the folding of protein L becomes extremely simple when the effects of temperature on protein stability are corrected for; the logarithm of the folding rate is a linear function of 1/T on constant stability contours in the temperature–denaturant plane. This convincingly demonstrates that the anomalous temperature dependence of folding derives from the temperature dependence of the interactions that stabilize proteins, rather than from the super Arrhenius temperature dependence predicted for the configurational diffusion constant on a rough energy landscape. However, because of the limited temperature range accessible to experiment, the results do not rule out models with higher order temperature dependences. The significance of the slope of the stability-corrected Arrhenius plots is discussed.

Limited internal friction in the rate-limiting step of a two-state protein folding reaction

Small, single-domain proteins typically fold via a compact transition-state ensemble in a process well fitted by a simple, two-state model. To characterize the rate-limiting conformational changes that underlie two-state folding, we have investigated experimentally the effects of changing solvent viscosity on the refolding of the IgG binding domain of protein L. In conjunction with numerical simulations, our results indicate that the rate-limiting conformational changes of the folding of this domain are strongly coupled to solvent viscosity and lack any significant “internal friction” arising from intrachain collisions. When compared with the previously determined solvent viscosity dependencies of other, more restricted conformational changes, our results suggest that the rate-limiting folding transition involves conformational fluctuations that displace considerable amounts of solvent. Reconciling evidence that the folding transition state ensemble is comprised of highly collapsed species with these and similar, previously reported results should provide a significant constraint for theoretical models of the folding process.

Denaturant-induced movement of the transition state of protein folding revealed by high-pressure stopped-flow measurements

The small all-β protein tendamistat folds and unfolds with two-state kinetics. We determined the volume changes associated with the folding process by performing kinetic and equilibrium measurements at variable pressure between 0.1 and 100 MPa (1 to 1,000 bar). GdmCl-induced equilibrium unfolding transitions reveal that the volume of the native state is increased by 41.4 ± 2.0 cm3/mol relative to the unfolded state. This value is virtually independent of denaturant concentration. The use of a high-pressure stopped-flow instrument enabled us to measure the activation volumes for the refolding (ΔVf0‡) and unfolding reaction (ΔVu0‡) over a broad range of GdmCl concentrations. The volume of the transition state is 60% native-like (ΔVf0‡ = 25.0 ± 1.2 cm3/mol) in the absence of denaturant, indicating partial solvent accessibility of the core residues. The volume of the transition state increases linearly with denaturant concentration and exceeds the volume of the native state above 6 M GdmCl. This result argues for a largely desolvated transition state with packing deficiencies at high denaturant concentrations and shows that the structure of the transition state depends strongly on the experimental conditions.

Magnesium-dependent folding of self-splicing RNA: Exploring the link between cooperativity, thermodynamics, and kinetics

Folding of the Tetrahymena self-splicing RNA into its active conformation involves a set of discrete intermediate states. The Mg2+-dependent equilibrium transition from the intermediates to the native structure is more cooperative than the formation of the intermediates from the unfolded states. We show that the degree of cooperativity is linked to the free energy of each transition and that the rate of the slow transition from the intermediates to the native state decreases exponentially with increasing Mg2+ concentration. Monovalent salts, which stabilize the folded RNA nonspecifically, induce states that fold in less than 30 s after Mg2+ is added to the RNA. A simple model is proposed that predicts the folding kinetics from the Mg2+-dependent change in the relative stabilities of the intermediate and native states.

The quorum-sensing transcriptional regulator TraR requires its cognate signaling ligand for protein folding, protease resistance, and dimerization

Complexes between the quorum-sensing regulator TraR and its inducing ligand autoinducer (AAI) are soluble in Escherichia coli, whereas apo-TraR is almost completely insoluble. Here we show that the lack of soluble TraR is due in large part to rapid proteolysis, inasmuch as apo-TraR accumulated to high levels in an E. coli strain deficient in Clp and Lon proteases. In pulse labeling experiments, AAI protected TraR against proteolysis only when it was added before the radiolabel. This observation indicates that TraR proteins can productively bind AAI only during their own synthesis on polysomes, whereas fully synthesized apo-TraR proteins are not functional AAI receptors. Purified apo-TraR was rapidly degraded by trypsin to oligopeptides, whereas TraR–AAI complexes were more resistant to trypsin and were cleaved at discrete interdomain linkers, indicating that TraR requires AAI to attain its mature tertiary structure. TraR–AAI complexes eluted from a gel filtration column as dimers and bound DNA as dimers. In contrast, apo-TraR was monomeric, and incubation with AAI under a variety of conditions did not cause dimerization. We conclude that AAI is critical for the folding of nascent TraR protein into its mature tertiary structure and that full-length apo-TraR cannot productively bind AAI and is consequently targeted for rapid proteolysis.

Dissection of the ion-induced folding of the hammerhead ribozyme using 19F NMR

We have used 19F NMR to analyze the metal ion-induced folding of the hammerhead ribozyme by selective incorporation of 5fluorouridine. We have studied the chemical shift and linewidths of 19F resonances of 5-fluorouridine at the 4 and 7 positions in the ribozyme core as a function of added Mg2+. The data fit well to a simple two-state model whereby the formation of domain 1 is induced by the noncooperative binding of Mg2+ with an association constant in the range of 100 to 500 M−1, depending on the concentration of monovalent ions present. The results are in excellent agreement with data reporting on changes in the global shape of the ribozyme. However, the NMR experiments exploit reporters located in the center of the RNA sections undergoing the folding transitions, thereby allowing the assignment of specific nucleotides to the separate stages. The results define the folding pathway at high resolution and provide a time scale for the first transition in the millisecond range.

Effects of inefficient cleavage of the signal sequence of HIV-1 gp 120 on its association with calnexin, folding, and intracellular transport.

The HIV-1 envelope glycoprotein gp120 displays inefficient intracellular transport, which is caused by its retention in the endoplasmic reticulum. Coexpression in insect cells (Sf9) of HIV-1 gp120 with calnexin has shown that their interaction was modulated by the signal sequence of HIV-1 gp120. gp120, with its natural signal sequence, showed a prolonged association with calnexin with a t1/2 of greater than 20 min. Replacement of the natural signal sequence with the signal sequence from mellitin led to a decreased time of association of gp120 with calnexin (t1/2 < 10 min). These different times of calnexin association coincided both with the folding of gp120 as measured by the ability of bind CD4 and with endoplasmic reticulum to Golgi transport as analyzed by the acquisition of partial endoglycosidase H resistance. Using a monospecific antibody to the HIV-1 gp120 natural signal peptide, we showed that calnexin associated with N-glycosylated but uncleaved gp120. Only after dissociation from calnexin was gp120 cleaved, but very inefficiently. Only the small proportion of signal-cleaved gp120 molecules acquired transport competence and were secreted. This is the first report demonstrating the effect of the signal sequence on calnexin association.

Structure and function in rhodopsin: correct folding and misfolding in point mutants at and in proximity to the site of the retinitis pigmentosa mutation Leu-125-->Arg in the transmembrane helix C.

L125R is a mutation in the transmembrane helix C of rhodopsin that is associated with autosomal dominant retinitis pigmentosa. To probe the orientation of the helix and its packing in the transmembrane domain, we have prepared and studied the mutations E122R, I123R, A124R, S127R, L125F, and L125A at, and in proximity to, the above mutation site. Like L125R, the opsin expressed in COS-1 cells from E122R did not bind 11-cis-retinal, whereas those from I123R and S127R formed the rhodopsin chromophore partially. A124R opsin formed the rhodopsin chromophore (lambda max 495 nm) in the dark, but the metarhodopsin II formed on illumination decayed about 6.5 times faster than that of the wild type and was defective in transducin activation. The mutant opsins from L125F and L125A bound 11-cis-retinal only partially, and in both cases, the mixtures of the proteins produced were separated into retinal-binding and non-retinal-binding (misfolded) fractions. The purified mutant rhodopsin from L125F showed lambda max at 500 nm, whereas that from L125A showed lambda max at 503 nm. The mutant rhodopsin L125F showed abnormal bleaching behavior and both mutants on illumination showed destabilized metarhodopsin II species and reduced transducin activation. Because previous results have indicated that misfolding in rhodopsin is due to the formation of a disulfide bond other than the normal disulfide bond between Cys-110 and Cys-187 in the intradiscal domain, we conclude from the misfolding in mutants L125F and L125A that the folding in vivo in the transmembrane domain is coupled to that in the intradiscal domain.

Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications.

Small, single-module proteins that fold in a single cooperative step may be paradigms for understanding early events in protein-folding pathways generally. Recent experimental studies of the 64-residue chymotrypsin inhibitor 2 (CI2) support a nucleation mechanism for folding, as do some computer stimulations. CI2 has a nucleation site that develops only in the transition state for folding. The nucleus is composed of a set of adjacent residues (an alpha-helix), stabilized by long-range interactions that are formed as the rest of the protein collapses around it. A simple analysis of the optimization of the rate of protein folding predicts that rates are highest when the denatured state has little residual structure under physiological conditions and no intermediates accumulate. This implies that any potential nucleation site that is composed mainly of adjacent residues should be just weakly populated in the denatured state and become structured only in a high-energy intermediate or transition state when it is stabilized by interactions elsewhere in the protein. Hierarchical mechanisms of folding in which stable elements of structure accrete are unfavorable. The nucleation-condensation mechanism of CI2 fulfills the criteria for fast folding. On the other hand, stable intermediates do form in the folding of more complex proteins, and this may be an unavoidable consequence of increasing size and nucleation at more than one site.

Toward an outline of the topography of a realistic protein-folding funnel.

Experimental information on the structure and dynamics of molten globules gives estimates for the energy landscape's characteristics for folding highly helical proteins, when supplemented by a theory of the helix-coil transition in collapsed heteropolymers. A law of corresponding states relating simulations on small lattice models to real proteins possessing many more degrees of freedom results. This correspondence reveals parallels between "minimalist" lattice results and recent experimental results for the degree of native character of the folding transition state and molten globule and also pinpoints the needs of further experiments.

Disulfide folding pathways of cystine knot proteins: Tying the knot within the circular backbone of the cyclotides

The plant cyclotides are a fascinating family of circular proteins that contain a cyclic cystine knot motif. The knotted topology and cyclic nature of the cyclotides pose interesting questions about folding mechanisms and how the knotted arrangement of disulfide bonds is formed. In the current study we have examined the oxidative refolding and reductive unfolding of the prototypic cyclotide, kalata B1. A stable two-disulfide intermediate accumulated during oxidative refolding but not in reductive unfolding. Mass spectrometry and NMR spectroscopy were used to show that the intermediate contained a native-like structure with two native disulfide bonds topologically similar to the intermediate isolated for the related cystine knot protein EETI-II (LeNguyen, D., Heitz, A., Chiche, L., El Hajji, M., and Castro B. (1993) Protein Sci. 2, 165-174). However, the folding intermediate observed for kalata B1 is not the immediate precursor of the three-disulfide native peptide and does not accumulate in the reductive unfolding process, in contrast to the intermediate observed for EETI-II. These alternative pathways of linear and cyclic cystine knot proteins appear to be related to the constraints imposed by the cyclic backbone of kalata B1 and the different ring size of the cystine knot. The three-dimensional structure of a synthetic version of the two-disulfide intermediate of kalata B1 in which Ala residues replace the reduced Cys residues provides a structural insight into why the two-disulfide intermediate is a kinetic trap on the folding pathway.

Diversity in the disulfide folding pathways of cystine knot peptides

The plant cyclotides are a fascinating family of circular proteins that contain a cyclic cystine knot motif (CCK). This unique family was discovered only recently but contains over 50 known sequences to date. Various biological activities are associated with these peptides including antimicrobial and insecticidal activity. The knotted topology and cyclic nature of the cyclotides; poses interesting questions about the folding mechanisms and how the knotted arrangement of disulfide bonds is formed. Some studies have been performed on related inhibitor cystine knot (ICK) containing peptides, but little is known about the folding mechanisms of CCK molecules. We have examined the oxidative refolding and reductive unfolding of the prototypic member of the cyclotide family, kalata B1. Analysis of the rates of formation of the intermediates along the reductive unfolding pathway highlights the stability conferred by the cystine knot motif. Significant differences are observed between the folding of kalata B1 and an acyclic cystine knot protein, EETI-II, suggesting that the circular backbone has a significant influence in directing the folding pathway.

Oxidative folding of the cystine knot motif in cyclotide proteins

The cyclotides are a large family of plant proteins that have a cyclic backbone and a knotted arrangement of three conserved disulfide bonds. Despite the apparent complexity of their cystine knot motif it is possible to efficiently fold these proteins, as exemplified by oxidative folding studies on the prototypic cyclotide, kalata B1. This mini-review reports on the current understanding of the folding process in cyclotides. The synthesis and folding of these molecules paves the way for their application as stable molecular templates.

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.