Kinetics of cytochrome C folding: atomically detailed simulations

The vast range of time scales (from nanoseconds to seconds) during protein folding is a challenge for experiments and computations. To make concrete predictions on folding mechanisms, atomically detailed simulations of protein folding, using potentials derived from chemical physics principles, are desired. However, due to their computational complexity, straightforward molecular dynamics simulations of protein folding are impossible today. An alternative algorithm is used that makes it possible to compute approximate atomically detailed long time trajectories (the Stochastic Difference Equation in Length). This algorithm is used to compute 26 atomically detailed folding trajectories of cytochrome c (a millisecond process). The early collapse of the protein chain (with marginal formation of secondary structure), and the earlier formation of the N and C helices (compare to the 60's helix) are consistent with the experiment. The existence of an energy barrier upon entry to the molten globule is examined as well. In addition to (favorable) comparison to experiments, we show that non-native contacts drive the formation of the molten globule. In contrast to popular folding models, the non-native contacts do not form off-pathway kinetic traps in cytochrome c.     

Stable submolecular folding units in a non-compact form of cytochrome c.

Studies of structure, dynamics, and stability of cytochrome c (cyt c) at low pH in a non-compact pre-molten globule state indicate that the protein contains submolecular folding units that are independently stable. In high salt, acid cyt c (pD 2.2; where D is deuterium) is nearly as compact as the native form. Nuclear magnetic resonance (n.m.r.) line broadening typical of the molten globule form is seen, indicating loosened packing and increased mobility not only for side-chains but also for the main chain. As NaCl concentration is decreased below 0.05 M, cyt c expands due to the deshielding of electrostatic repulsions, attaining a linear extent perhaps double that of the native protein (viscosity, fluorescence). In the extended form, tertiary structural hydrogen bonds are largely broken (hydrogen exchange rate), some normally buried parts of the protein are exposed to water (fluorescence), and many of the native side-chain contacts must be lost. Nevertheless, almost all of the helical content is retained (circular dichroism). The helices involve the same amino acid residues that are helical in the native state (hydrogen exchange labeling monitored by 2-dimensional n.m.r.). The equilibrium constant for helix formation at 20 degrees C (0.02 M-NaCl, pD 2.2) is about 10 (hydrogen exchange rate), even though the individual helical segments when isolated have little or no structure. Additional experiments were done to check assumptions and calibrate parameters that underlie the hydrogen exchange analysis of protein folding. These results indicate that the native-like helical segments in the expanded non-globular form of cyt c exist as part of somewhat larger submolecular folding units that possess significant equilibrium stability. Results from equilibrium and kinetic studies of protein folding support the generality of this conclusion. This view is contrary to the two-state paradigm for equilibrium folding and inconsistent with the idea that side-chain packing constraints determine folding motifs. The result suggests an extension of the thermodynamic hypothesis for protein structure to kinetic folding processes, so that the amino acid code for equilibrium and kinetic folding may be the same, and also seems pertinent to the biological evolution of contemporary protein structures.     

Diffusion-collision model for the folding kinetics of myoglobin

The diffusion-collision model has been used to analyze the folding kinetics of myoglobin. The microdomains, which are the basic units that coalesce during the folding, are identified with the helices and the stabilizing contacts between helices are determined from the native structure. Both association and dissociation reactions are included and a range of stabilization parameters is investigated to determine the variation in overall rate and the relative contributions made by different intermediates during the folding process. In a comparison of folding to the native state and to the midpoint of the folding transition (i.e., 50% native protein at the completion of the reaction) significant differences in the contributing intermediates are found.     

Branching in the sequential folding pathway of cytochrome c

Previous results indicate that the folding pathways of cytochrome c and other proteins progressively build the target native protein in a predetermined stepwise manner by the sequential formation and association of native-like foldon units. The present work used native state hydrogen exchange methods to investigate a structural anomaly in cytochrome c results that suggested the concerted folding of two segments that have little structural relationship in the native protein. The results show that the two segments, an 18-residue omega loop and a 10-residue helix, are able to unfold and refold independently, which allows a branch point in the folding pathway. The pathway that emerges assembles native-like foldon units in a linear sequential manner when prior native-like structure can template a single subsequent foldon, and optional pathway branching is seen when prior structure is able to support the folding of two different foldons.     

The paradoxical behavior of a highly structured misfolded intermediate in RNA folding

Like many structured RNAs, the Tetrahymena group I ribozyme is prone to misfolding. Here we probe a long-lived misfolded species, referred to as M, and uncover paradoxical aspects of its structure and folding. Previous work indicated that a non-native local secondary structure, termed alt P3, led to formation of M during folding in vitro. Surprisingly, hydroxyl radical footprinting, fluorescence measurements with site-specifically incorporated 2-aminopurine, and functional assays indicate that the native P3, not alt P3, is present in the M state. The paradoxical behavior of alt P3 presumably arises because alt P3 biases folding toward M, but, after commitment to this folding pathway and before formation of M, alt P3 is replaced by P3. Further, structural and functional probes demonstrate that the misfolded ribozyme contains extensive native structure, with only local differences between the two states, and the misfolded structure even possesses partial catalytic activity. Despite the similarity of these structures, re-folding of M to the native state is very slow and is strongly accelerated by urea, Na+, and increased temperature and strongly impeded by Mg2+ and the presence of native peripheral contacts. The paradoxical observations of extensive native structure within the misfolded species but slow conversion of this species to the native state are readily reconciled by a model in which the misfolded state is a topological isomer of the native state, and computational results support the feasibility of this model. We speculate that the complex topology of RNA secondary structures and the inherent rigidity of RNA helices render kinetic traps due to topological isomers considerably more common for RNA than for proteins.     

Exploring the cytochrome c folding mechanism: cytochrome c552 from thermus thermophilus folds through an on-pathway intermediate

Understanding the role of partially folded intermediate states in the folding mechanism of a protein is a crucial yet very difficult problem. We exploited a kinetic approach to demonstrate that a transient intermediate of a thermostable member of the widely studied cytochrome c family (cytochrome c552 from Thermus thermophilus) is indeed on-pathway. This is the first clear indication of an obligatory intermediate in the folding mechanism of a cytochrome c. The fluorescence properties of this intermediate demonstrate that the relative position of the heme and of the only tryptophan residue cannot correspond to their native orientation. Based on an analysis of the three-dimensional structure of cytochrome c552, we propose an interpretation of the data which explains the residual fluorescence of the intermediate and is consistent with the established role played by some conserved interhelical interactions in the folding of other members of this family. A limited set of topologically conserved contacts may guide the folding of evolutionary distant cytochromes c through the same partially structured state, which, however, can play different kinetic roles, acting either as an intermediate or a transition state.     

Early events in protein folding: Is there something more than hydrophobic burst?

The presence of native contacts in the denatured state of many proteins suggests that elements of the biologically active structure of these molecules are formed during the initial stage of the folding process. The rapidity with which these events take place makes it difficult to study them in vitro, but, by the same token, suitable for studies in silico. With the help of all-atom, explicit solvent, molecular dynamics simulations we have followed in time, starting from elongated structureless conformations, the early events in the folding of src-SH3 domain and of proteins G, L, and CI2. It is observed that within the first 50 ns two important events take place, essentially independent of each other: hydrophobic collapse and formation of a few selected native contacts. The same contacts are also found in simulations carried out in the presence of guanidinium chloride in order to reproduce the conditions used to characterize experimentally the denatured state and testify to the fact that these contacts are to be considered a resilient characterizing property of the denaturated state.     

Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. II. Alpha-helical motifs

Dynamic Monte Carlo simulations of the folding pathways of alpha-helical protein motifs have been undertaken in the context of a diamond lattice model of globular proteins. The first question addressed in the nature of the assembly process of an alpha-helical hairpin. While the hairpin could, in principle, be formed via the diffusion-collision-adhesion of isolated performed helices, this is not the dominant mechanism of assembly found in the simulations. Rather, the helices that form native hairpins are constructed on-site, with folding initiating at or near the turn in almost all cases. Next, the folding/unfolding pathways of four-helix bundles having tight bends and one and two long loops in the native state are explored. Once again, an on-site construction mechanism of folding obtains, with a hairpin forming first, followed by the formation of a three-helix bundle, and finally the fourth helix of the native bundle assembles. Unfolding is essentially the reverse of folding. A simplified analytic theory is developed that reproduces the equilibrium folding transitions obtained from the simulations remarkably well and, for the dominant folding pathway, correctly identifies the intermediates seen in the simulations. The analytic theory provides the free energy along the reaction co-ordinate and identifies the transition state for all three motifs as being quite close to the native state, with three of the four helices assembled, and approximately one turn of the fourth helix in place. The transition state is separated from the native conformation by a free-energy barrier of mainly energetic origin and from the denatured state by a barrier of mainly entropic origin. The general features of the folding pathway seen in all variants of the model four-helix bundles are similar to those observed in the folding of beta-barrel, Greek key proteins; this suggests that many of the qualitative aspects of folding are invariant to the particular native state topology and secondary structure.     

Computer simulations of membrane protein folding: structure and dynamics

A lattice model of membrane proteins with a composite energy function is proposed to study their folding dynamics and native structures using Monte Carlo simulations. This model successfully predicts the seven helix bundle structure of sensory rhodopsin I by practicing a three-stage folding. Folding dynamics of a transmembrane segment into a helix is further investigated by varying the cooperativity in the formation of alpha helices for both random folding and assisted folding. The chain length dependence of the folding time of a hydrophobic segment to a helical state is studied for both free and anchored chains. An unusual length dependence in the folding time of anchored chains is observed.     

The structure of cytochrome b562 from Escherichia coli at 2.5 A resolution.

The structure of cytochrome b562 from Escherichia coli has been determined at 2.5 A resolution by x-ray diffraction methods. Protein phases were computed by the single isomorphous replacement method with anomalous scattering measurements from the native and uranyl acetate-substituted crystals. The electron density was averaged about the noncrystallographic 2-fold axis relating 2 molecules in the triclinic unit cell. The protein consists of four nearly parallel alpha helices and represents a new class of cytochrome structure. The heme group is inserted between the helices near one end of the molecule with one heme face partially exposed to solvent. The two heme ligands are histidine and methionine. The 2 phenylalanines are packed internally near the heme group, and the 2 tyrosines are on the surface, also near the heme group. The folding of the protein resembles that of hemerythrin and tobacco mosaic virus protein and shows a different topology from that of cytochrome b5, cytochrome c, or the globins.     

Non-native interactions play an effective role in protein folding dynamics

Systematic Monte Carlo simulations of simple lattice models show that the final stage of protein folding is an ordered process where native contacts get locked (i.e., the residues come into contact and remain in contact for the duration of the folding process) in a well‐defined order. The detailed study of the folding dynamics of protein‐like sequences designed as to exhibit different contact energy distributions, as well as different degrees of sequence optimization (i.e., participation of non‐native interactions in the folding process), reveals significant differences in the corresponding locking scenarios—the collection of native contacts and their average locking times, which are largely ascribable to the dynamics of non‐native contacts. Furthermore, strong evidence for a positive role played by non‐native contacts at an early folding stage was also found. Interestingly, for topologically simple target structures, a positive interplay between native and non‐native contacts is observed also toward the end of the folding process, suggesting that non‐native contacts may indeed affect the overall folding process. For target models exhibiting clear two‐state kinetics, the relation between the nucleation mechanism of folding and the locking scenario is investigated. Our results suggest that the stabilization of the folding transition state can be achieved through the establishment of a very small network of native contacts that are the first to lock during the folding process.     

Folding mechanism of Pseudomonas aeruginosa cytochrome c551: role of electrostatic interactions on the hydrophobic collapse and transition state properties.

We report on the folding kinetics of the small 82 residue cytochrome c551from Pseudomonas aeruginosa. The presence of two Trp residues (Trp56 and Trp77) allows the monitoring of fluorescence quenching on refolding in two different regions of the protein. A single His residue (the iron-coordinating His16) permits the study of refolding in the absence of miscoordination events. After identification of the kinetic traps (Pro isomerization and aggregation of denatured protein), overall refolding kinetics is described by two processes: (i) a burstphase collapse (faster than milliseconds) which we show to be a global event leading to a state whose compactness depends on the overall net charge; at the isoeletric pH (4.7), it is maximally compact, while above and below it is more expanded; and (ii) an exponential phase (in the millisecond time range) leading to the native protein via a transition state(s) possibly involving the formation of a specific salt bridge between Lys10 and Glu70, at the contact between the N and C-terminal helices. Comparison with the widely studied horse cytochrome c allows the discussion of similarities and differences in the folding of two proteins which have the same "fold" despite a very low degree of sequence homology (<30 %).     

Concordant exploration of the kinetics of RNA folding from global and local perspectives

Time-resolved small-angle X-ray scattering (SAXS) with millisecond time-resolution reveals two discrete phases of global compaction upon Mg2+-mediated folding of the Tetrahymena thermophila ribozyme. Electrostatic relaxation of the RNA occurs rapidly and dominates the first phase of compaction during which the observed radius of gyration (R(g)) decreases from 75 angstroms to 55 angstroms. A further decrease in R(g) to 45 angstroms occurs in a well-defined second phase. An analysis of mutant ribozymes shows that the latter phase depends upon the formation of long-range tertiary contacts within the P4-P6 domain of the ribozyme; disruption of the three remaining long-range contacts linking the peripheral helices has no effect on the 55-45 angstroms compaction transition. A better understanding of the role of specific tertiary contacts in compaction was obtained by concordant time-resolved hydroxyl radical (OH) analyses that report local changes in the solvent accessibility of the RNA backbone. Comparison of the global and local measures of folding shows that formation of a subset of native tertiary contacts (i.e. those defining the ribozyme core) can occur within a highly compact ensemble whose R(g) is close to that of the fully folded ribozyme. Analyses of additional ribozyme mutants and reaction conditions establish the generality of the rapid formation of a partially collapsed state with little to no detectable tertiary structure. These studies directly link global RNA compaction with formation of tertiary structure as the molecule acquires its biologically active structure, and underscore the strong dependence on salt of both local and global measures of folding kinetics.     

Monovalent ion-mediated folding of the Tetrahymena thermophila ribozyme

The time-course of monovalent cation-induced folding of the L-21 Sca1 Tetrahymena thermophila ribozyme and a selected mutant was quantitatively followed using synchrotron X-ray (.OH) footprinting. Initiating folding by increasing the concentration of either Na+ or K+ to 1.5M from an initial condition of approximately 0.008 M Na+ at 42 degrees C resulted in the complete formation of tertiary contacts within the P5abc subdomain and between the peripheral helices within the dead time of our measurements (k>50 s(-1)). These results contrast with folding rates of 2-0.2 s(-1) previously observed for formation of these contacts in 10mM Mg2+ from the same initial condition. Thus, the initial formation of native tertiary contacts is inhibited by divalent but not monovalent cations. The native contacts within the catalytic core form without a detectable burst phase at rates of 0.4-1.0 s(-1) in a manner reminiscent of the Mg2+-dependent folding behavior, although tenfold faster. The tertiary interactions stabilizing the catalytic core interaction with P4-P6 and P2.1, as well as one of the protections internal for the P4-P6 domain, display progress curves with appreciable burst amplitudes and a phase comparable in rate to that of the catalytic core. That the slow folding of the ribozyme's core is a consequence of the alt-P3 secondary structure is shown by the 100% burst phase amplitudes that are observed for folding of the U273A mutant ribozyme within which the native secondary structure (P3) is strengthened. Thus, formation of a misfolded intermediate(s) resulting from the alt-P3 secondary structure is independent of ion valency while the rate at which the respective intermediates are resolved is sensitive to ion valency. The overall portrait painted by these results is that ion valency differentially affects steps in the folding process and that folding in monovalent ion alone for the U273A mutant Tetrahymena ribozyme is fast and direct.     

Computer simulations of protein folding by targeted molecular dynamics

We have performed 128 folding and 45 unfolding molecular dynamics runs of chymotrypsin inhibitor 2 (CI2) with an implicit solvation model for a total simulation time of 0.4 microseconds. Folding requires that the three-dimensional structure of the native state is known. It was simulated at 300 K by supplementing the force field with a harmonic restraint which acts on the root-mean-square deviation and allows to decrease the distance to the target conformation. High temperature and/or the harmonic restraint were used to induce unfolding. Of the 62 folding simulations started from random conformations, 31 reached the native structure, while the success rate was 83% for the 66 trajectories which began from conformations unfolded by high-temperature dynamics. A funnel-like energy landscape is observed for unfolding at 475 K, while the unfolding runs at 300 K and 375 K as well as most of the folding trajectories have an almost flat energy landscape for conformations with less than about 50% of native contacts formed. The sequence of events, i.e., secondary and tertiary structure formation, is similar in all folding and unfolding simulations, despite the diversity of the pathways. Previous unfolding simulations of CI2 performed with different force fields showed a similar sequence of events. These results suggest that the topology of the native state plays an important role in the folding process.     

Structural description of acid-denatured cytochrome c by hydrogen exchange and 2D NMR

Hydrogen exchange and two-dimensional nuclear magnetic resonance (2D NMR) techniques were used to characterize the structure of oxidized horse cytochrome c at acid pH and high ionic strength. Under these conditions, cytochrome c is known to assume a globular conformation (A state) with properties resembling those of the molten globule state described for other proteins. In order to measure the rate of hydrogen-deuterium exchange for individual backbone amide protons in the A state, samples of oxidized cytochrome c were incubated at 20 degrees C in D2O buffer (pD 2.2, 1.5 M NaCl) for time periods ranging from 2 min to 500 h. The exchange reaction was then quenched by transferring the protein to native conditions (pD 5.3). The extent of exchange for 44 amide protons trapped in the refolded protein was measured by 2D NMR spectroscopy. The results show that this approach can provide detailed information on H-bonded secondary and tertiary structure in partially folded equilibrium forms of a protein. All of the slowly exchanging amide protons in the three major helices of native cytochrome c are strongly protected from exchange at acid pH, indicating that the A state contains native-like elements of helical secondary structure. By contrast, a number of amide protons involved in irregular tertiary H-bonds of the native structure (Gly37, Arg38, Gln42, Ile57, Lys79, and Met80) are only marginally protected in the A state, indicating that these H-bonds are unstable or absent. The H-exchange results suggest that the major helices of cytochrome c and their common hydrophobic domain are largely preserved in the globular acidic form while the loop region of the native structure is flexible and partly disordered.     

RNA tertiary interactions mediate native collapse of a bacterial group I ribozyme

Large RNAs collapse into compact intermediates in the presence of counterions before folding to the native state. We previously found that collapse of a bacterial group I ribozyme correlates with the formation of helices within the ribozyme core, but occurs at Mg2+ concentrations too low to support stable tertiary structure and catalytic activity. Here, using small-angle X-ray scattering, we show that Mg2+-induced collapse is a cooperative folding transition that can be fit by a two-state model. The Mg2+ dependence of collapse is similar to the Mg2+ dependence of helix assembly measured by partial ribonuclease T1 digestion and of an unfolding transition measured by UV hypochromicity. The correspondence between multiple probes of RNA structure further supports a two-state model. A mutation that disrupts tertiary contacts between the L9 tetraloop and its helical receptor destabilized the compact state by 0.8 kcal/mol, while mutations in the central triplex were less destabilizing. These results show that native tertiary interactions stabilize the compact folding intermediates under conditions in which the RNA backbone remains accessible to solvent.     

Partially formed native tertiary interactions in the A-state of cytochrome c.

Considerable insight into protein structure, stability, and folding has been obtained from studies of non-native states. We have studied the extent of native tertiary contacts in one such molecule, the A-state of yeast iso-1-ferricytochrome c. Previously, we showed that the interface between the N and C-terminal helices is completely formed in the A-state. Here, we focus on interactions essential for forming the heme pocket of eukaryotic cytochromes c. To determine the extent of these interactions, we used saturation mutagenesis at the evolutionarily invariant residue leucine 68, and measured the free energy of denaturation for the native states and the A-states of functional variants. We show that, unlike the interaction between the terminal helices, the native interactions between the 60s helix and the rest of the protein are not completely formed in the A-state.     

Manifestations of native topology in the denatured state ensemble of Rhodopseudomonas palustris cytochrome c'

To provide insight into the role of local sequence in the nonrandom coil behavior of the denatured state, we have extended our measurements of histidine-heme loop formation equilibria for cytochrome c' to 6 M guanidine hydrochloride. We observe that there is some reduction in the scatter about the best fit line of loop stability versus loop size data in 6 M versus 3 M guanidine hydrochloride, but the scatter is not eliminated. The scaling exponent, ν(3), of 2.5 ± 0.2 is also similar to that found previously in 3 M guanidine hydrochloride (2.6 ± 0.3). Rates of histidine-heme loop breakage in the denatured state of cytochrome c' show that some histidine-heme loops are significantly more persistent than others at both 3 and 6 M guanidine hydrochloride. Rates of histidine-heme loop formation more closely approximate random coil behavior. This observation indicates that heterogeneity in the denatured state ensemble results mainly from contact persistence. When mapped onto the structure of cytochrome c', the histidine-heme loops with slow breakage rates coincide with chain reversals between helices 1 and 2 and between helices 2 and 3. Molecular dynamics simulations of the unfolding of cytochrome c' at 498 K show that these reverse turns persist in the unfolded state. Thus, these portions of the primary structure of cytochrome c' set up the topology of cytochrome c' in the denatured state, predisposing the protein to fold efficiently to its native structure.     

The folding kinetics of the SDS-induced molten globule form of reduced cytochrome c

The folding of reduced cytochrome c (redcyt c) is increasingly being recognized as undergoing a mechanism that deviates from a two-state process. In previous far-UV TRORD studies of redcyt c folding, a rapidly forming intermediate was attributed to the appearance of a molten-globule-like (MG) state [Chen, E., Goldbeck, R. A., and Kliger, D. S. (2003) J. Phys. Chem. A 107, 8149-8155]. A slow folding phase (>1 ms) was identified with the formation of native (N) secondary structure from that MG form. Here, using 0.65 mM SDS to induce the MG state in oxidized cytochrome c, folding of redcyt c was triggered with fast photoreduction and probed from early microseconds to milliseconds using far-UV TRORD spectroscopy. The kinetics of the reaction are described with a time constant of 50 +/- 16 ms, which corresponds to 1 +/- 0.6 ms upon extrapolation of the data to zero SDS concentration. The latter folding time is about 5 times faster than the calculated GuHCl-free time constant of 5.5 +/- 1.4 ms for slow-phase folding obtained in our previous study. This ratio of rates would be consistent with a scenario in which 20-30% MG that is suggested to form in the fast phase of redcyt c folding in GuHCl is an obligatory intermediate. The native state forms from this obligatory intermediate with an observed rate, k(f) = fk(G-->N) where f is the fractional population of MG and k(G-->N) is the microscopic rate for MG --> N. Calculation and comparison of the m(#)/m values show agreement within the uncertainties between the SDS ( approximately 0.5) and GuHCl ( approximately 0.3) based redcyt c folding experiments, suggesting that the two experiments report on comparable intermediates. The m values were obtained from far-UV CD SDS titration experiments, from which calculated thermodynamic parameters allowed estimation of the reduction potential for the MG state to be approximately 155 mV (-15 kJ/mol) vs NHE which, like the reduction potential for the native state, is more favorable than that for the unfolded protein.