The protein folding transition state: insights from kinetics and thermodynamics

We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4相似文献   

Protein structure and dynamics from single-molecule fluorescence resonance energy transfer

The pros and cons of single-molecule vs ensemble-averaged fluorescence resonance energy transfer (FRET) experiments, performed on proteins, are explored with the help of Langevin dynamics simulations. An off-lattice model of the polypeptide chain is employed, which gives rise to a well-defined native state and two-state folding kinetics. A detailed analysis of the distribution of the donor-acceptor distance is presented at different points along the denaturation curve, along with its dependence on the averaging time window. We show that unique information on the correlation between structure and dynamics, which can only be obtained from single-molecule experiments, is contained in the correlation between the donor-acceptor distance and its displacement. The latter is shown to provide useful information on the free energy landscape of the protein, which is complementary to that obtained from the distribution of donor-acceptor distances.     

Direct measurement of tertiary contact cooperativity in RNA folding

All structured biological macromolecules must overcome the thermodynamic folding problem to populate a unique functional state among a vast ensemble of unfolded and alternate conformations. The exploration of cooperativity in protein folding has helped reveal and distinguish the underlying mechanistic solutions to this folding problem. Analogous dissections of RNA tertiary stability remain elusive, however, despite the central biological importance of folded RNA molecules and the potential to reveal fundamental properties of structured macromolecules via comparisons of protein and RNA folding. We report a direct quantitative measure of tertiary contact cooperativity in a folded RNA. We precisely measured the stability of an independently folding P4-P6 domain from the Tetrahymena thermophila group I intron by single molecule fluorescence resonance energy transfer (smFRET). Using wild-type and mutant RNAs, we found that cooperativity between the two tertiary contacts enhances P4-P6 stability by 3.2 +/- 0.2 kcal/mol.     

NMR spectroscopic characterization of millisecond protein folding by transverse relaxation dispersion measurements

The cold shock protein CspB adopts its native and functional tertiary structure on the millisecond time scale. We employed transverse relaxation NMR methods, which allow a quantitative measurement of the cooperativity of this fast folding reaction on a residue basis. Thereby, chemical exchange contributions to the transverse relaxation rate (R(2)) were observed for every residue of CspB verifying the potential of this method to identify not only local dynamics but also to characterize global events. Toward this end, the homogeneity of the transition state of folding was probed by comparing Chevron plots (i.e., dependence of the apparent folding rate on the denaturant concentration) determined by stopped-flow fluorescence with Chevron plots of six residues acquired by R(2) dispersion experiments. The coinciding results obtained for probes at different locations in the three-dimensional structure of CspB indicate the ability and significance of transverse relaxation NMR to determine Chevron plots on a residue-by-residue basis providing detailed insights on the nature of the transition state of folding.     

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.     

Canonical and micro-canonical analysis of folding of trpzip2: An all-atom replica exchange Monte Carlo simulation study

The density of states of trpzip2, a β-hairpin peptide, has been explored at all-atom level. Replica exchange Monte Carlo method was used for sufficient sampling over a wide range of temperature. Micro-canonical analysis was performed to confirm that the phase transition behavior of this two-state folder is first-order-like. Canonical analysis of heat capacity suggests that hydrogen bonding interaction exerts a considerable positive influence on folding cooperativity, in contrast, hydrophobic interaction is insufficient for high degree of folding cooperativity. Furthermore, we explain physical nature of the folding process from free energy landscape perspective and extensively analyse hydrogen bonding and stacking energy.     

Nature of the cytochrome c molten globule

We have employed fluorescence energy transfer (FET) kinetics to probe unfolded and molten globule states of five dansyl (Dns) variants of Saccharomyces cerevisiae iso-1 cytochrome c. The covalently bound Fe(III) heme group quenches Dns fluorescence by energy transfer; measurements of FET kinetics yielded distributions of D-A distances (P(r)) for these states. The P(r) distributions and corresponding mean force potentials (U(r)) show that the cytochrome c molten globule is a highly structured state with a substantial number of native interactions. Wide P(r) distributions directly reflect the dynamic nature and conformational diversity of this molten globule. P(r) distributions for the "burst-phase" refolding intermediate suggest that the equilibrium cytochrome c molten globule is not a suitable model for early intermediates formed during protein refolding.     

Time-dependent communication between multiple amino acids during protein folding

Cooperativity is considered to be a key organizing principle behind biomolecular assembly, recognition and folding. However, it has remained very challenging to quantitatively characterize how cooperative processes occur on a concerted, multiple-interaction basis. Here, we address how and when the folding process is cooperative on a molecular scale. To this end, we analyze multipoint time-correlation functions probing time-dependent communication between multiple amino acids, which were computed from long folding simulation trajectories. We find that the simultaneous multiple amino-acid contact formation, which is absent in the unfolded state, starts to develop only upon entering the folding transition path. Interestingly, the transition state, whose presence is connected to the macrostate cooperative behavior known as the two-state folding, can be identified as the state in which the amino-acid cooperativity is maximal. Thus, our work not only provides a new mechanistic view on how protein folding proceeds on a multiple-interaction basis, but also offers a conceptually novel characterization of the folding transition state and the molecular origin of the phenomenological cooperative folding behavior. Moreover, the multipoint correlation function approach adopted here is general and can be used to expand the understanding of cooperative processes in complex chemical and biomolecular systems.

Cooperativity in contact formation among multiple amino acids starts to develop upon entering the folding transition path and attains a maximum at the folding transition state, providing the molecular origin of the two-state folding behavior.     

UV-resonance raman thermal unfolding study of Trp-cage shows that it is not a simple two-state miniprotein

Trp-cage, a synthetic 20 residue polypeptide, is proposed to be an ultrafast folding synthetic miniprotein which utilizes tertiary contacts to define its native conformation. We utilized UV resonance Raman spectroscopy (UVRS) with 204 and 229 nm excitation to follow its thermal melting. Our results indicate that Trp-cage melting is complex, and it is not a simple two-state process. Using 204 nm excitation we probe the peptide secondary structure and find the Trp-cage's alpha-helix shows a broad melting curve where on average four alpha-helical amide bonds melt upon a temperature increase from 4 to 70 degrees C. Using 229 nm excitation we probe the environment of the Trp side chain and find that its immediate environment becomes more compact as the temperature is increased from 4 to 20 degrees C; however, further temperature increases lead to exposure of the Trp to water. The chi(2) angle of the Trp side chain remains invariant throughout the entire temperature range. Previous kinetic results indicated a single-exponential decay in the 4-70 degrees C temperature range, suggesting that Trp-cage behaves as a two-state folder. However, this miniprotein does not show clear two-state behavior in our steady-state studies. Rather it shows a continuous distribution of steady-state spectral parameters. Only the alpha-helix melting curve even hints of a cooperative transition. Possibly, the previous kinetic results monitor only a small region of the Trp-cage which locally appears two-state. This would then argue for spatially decoupled folding even for this small peptide.     

Dimers of dipyrrometheneboron difluoride (BODIPY) with light spectroscopic applications in chemistry and biology.

A ground-state dimer (denoted D(I)) exhibiting a strong absorption maximum at 477 nm (epsilon = 97 000 M(-1)cm(-1)) can form between adjacent BODIPY groups attached to mutant forms of the protein, plasminogen activator inhibitor type 1 (PAI-1). No fluorescence from excited D(I) was detected. A locally high concentration of BODIPY groups was also achieved by doping lipid phases (micelles, vesicles) with BODIPY-labeled lipids. In addition to an absorption band located at about 480 nm, a new weak absorption band is also observed at ca. 570 nm. Both bands are ascribed to the formation of BODIPY dimers of different conformation (D(I) and D(II)). Contrary to D(I) in PAI-1, the D(II) aggregates absorbing at 570 nm are emitting light observed as a broad band centered at about 630 nm. The integrated absorption band of D(I) is about twice that of the monomer, which is compatible with exciton coupling within a dimer. The F?rster radius of electronic energy transfer between a BODIPY excited monomer and the ground-state dimer (D(I)()) is 57 +/- 2 A. A simple model of exciton coupling suggests that in D(I) two BODIPY groups are stacked on top of each other in a sandwich-like configuration with parallel electronic transition dipoles. For D(II) the model suggests that the S(0) --> S(1) transition dipoles are colinear. An explanation for the previously reported (J. Am. Chem. Soc. 1994, 116, 7801) exceptional light spectroscopic properties of BODIPY is also presented. These are ascribed to the extraordinary electric properties of the BODIPY chromophore. First, changes of the permanent electric dipole moment (Delta(mu) approximately -0.05 D) and polarizability (-26 x 10(-40) C m(2) V(-1)) between the ground and the first excited states are small. Second, the S(0) <--> S(1) electronic transition dipole moments are perpendicular to Delta(mu).     

Influence of the native topology on the folding barrier for small proteins

The possibility of downhill instead of two-state folding for proteins has been a very controversial topic which arose from recent experimental studies. From the theoretical side, this question has also been accomplished in different ways. Given the experimental observation that a relationship exists between the native structure topology of a protein and the kinetic and thermodynamic properties of its folding process, Gō-type potentials are an appropriate way to approach this problem. In this work, we employ an interaction potential from this family to get a better insight on the topological characteristics of the native state that may somehow determine the presence of a thermodynamic barrier in the folding pathway. The results presented here show that, indeed, the native topology of a small protein has a great influence on its folding behavior, mostly depending on the proportion of local and long range contacts the protein has in its native structure. Furthermore, when all the interactions present contribute in a balanced way, the transition results to be cooperative. Otherwise, the tendency to a downhill folding behavior increases.     

Protein folding kinetics: barrier effects in chemical and thermal denaturation experiments

Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.     

The protein folding transition-state ensemble from a Gō-like model

Characterizing the structure of transition states (TS) is a first step towards understanding two-state protein folding mechanisms. However, a direct experimental characterization of these states is challenging and indirect information derived from protein engineering methodologies (?-value analysis) is often difficult to interpret. We present here a theoretical study on the nature of the transition state ensemble for three representative proteins covering the major structural classes using a mean-field C(α)-based Gō-model. We identify that transition state ensembles are dominated by local contacts, indicating that most non-local contacts form only upon crossing the macroscopic folding free energy barrier. We demonstrate that the mean ?-value corresponds to the fraction of stabilization energy gained at the barrier-top in two-state-like systems, and that it depends monotonically on the stability conditions. Furthermore, we show that there is a fundamental connection between small destabilization and large ?-values that in turn depends on the location of the mutated residue in the structure. These results that are in agreement with the recent empirical findings highlight the importance of local energetics in determining folding mechanisms.     

The temperature-induced denaturation of small globular proteins as a first-order phase transition of ‘crystal molecules’

A general feature of temperature-induced reversible denaturation of small globular proteins is its all-or-none character. This strong cooperativity leads to think that protein molecules, possessing only two accessible thermodynamic states, the native and the denatured one, resemble ‘crystal molecules’ that melt at raising temperature. An analysis, grounded on mean field theory, allows to conclude that the two-state transition is a first-order phase transition. The implication of this conclusion are briefly discussed.     

Identification of intermediate species in protein-folding by quantitative analysis of amplitudes in time-domain fluorescence spectroscopy

In protein-folding studies it is often required to differentiate a system with only two-states, namely the native (N) and unfolded (U) forms of the protein present at any condition of the solvent, from a situation wherein intermediate state(s) could also be present. This differentiation of a two-state from a multi-state structural transition is non-trivial when studied by the several steady-state spectroscopic methods that are popular in protein-folding studies. In contrast to the steady-state methods, time-resolved fluorescence has the capability to reveal the presence of heterogeneity of structural forms due to the ‘fingerprint’ nature of fluorescence lifetimes of various forms. In this work, we establish this method by quantitative analysis of amplitudes associated with fluorescence lifetimes in multiexponential decays. First, we show that we can estimate, accurately, the relative population of species from two-component mixtures of non-interacting molecules such as fluorescent dyes, peptides and proteins. Subsequently, we demonstrate, by analysing the amplitudes of fluorescence lifetimes which are controlled by fluorescence resonance energy transfer (FRET), that the equilibrium folding-unfolding transition of the small single-domain protein barstar is not a two-step process.     

A minimal proteinlike lattice model: an alpha-helix motif

A simple protein model of a four-helix bundle motif on a face-centered cubic lattice has been studied. Total energy of a conformation includes attractive interactions between hydrophobic residues, repulsive interactions between hydrophobic and polar residues, and a potential that favors helical turns. Using replica exchange Monte Carlo simulations we have estimated a set of parameters for which the native structure is a global minimum of conformational energy. Then we have shown that all the above types of interactions are necessary to guarantee the cooperativity of folding transition and to satisfy the thermodynamic hypothesis.     

Solvent Effects on Excited-State Relaxation Dynamics of Paddle-Wheel BODIPY-Hexaoxatriphenylene Conjugates: Insights from Non-adiabatic Dynamics Simulations

Understanding the excited state dynamics of donor-acceptor (D-A) complexes is of fundamental importance both experimentally and theoretically. Herein, we have first explored the photoinduced dynamics of a recently synthesized paddle-wheel BODIPY-hexaoxatriphenylene (BODIPY is the abbreviation for BF\begin{document}$ _2 $\end{document}-chelated dipyrromethenes) conjugates D-A complexes with the combination of both electronic structure calculations and non-adiabatic dynamics simulations. On the basis of computational results, we concluded that the BODIPY-hexaoxatriphenylene (BH) conjugates will be promoted to the local excited (LE) states of the BODIPY fragments upon excitation, which is followed by the ultrafast exciton transfer from LE state to charge transfer (CT). Instead of the photoinduced electron transfer process proposed in previous experimental work, such a exciton transfer process is accompanied with the photoinduced hole transfer from BODIPY to hexaoxatriphenylene. Additionally, solvent effects are found to play an important role in the photoinduced dynamics. Specifically, the hole transfer dynamics is accelerated by the acetonitrile solvent, which can be ascribed to significant influences of the solvents on the charge transfer states, i.e. the energy gaps between LE and CT excitons are reduced greatly and the non-adiabatic couplings are increased in the meantime. Our present work not only provides valuable insights into the underlying photoinduced mechanism of BH, but also can be helpful for the future design of novel donor-acceptor conjugates with better optoelectronic performance.     

Fluorescence and REMPI spectroscopy of jet-cooled isolated 2-phenylindene in the S1 state

We investigated the spectroscopy of the first excited singlet electronic state S1 of 2-phenylindene using both fluorescence excitation spectroscopy and resonantly enhanced multiphoton ionization spectroscopy. Moreover, we investigated the dynamics of the S1 state by determining state-selective fluorescence lifetimes up to an excess energy of approximately 3400 cm(-1). Ab initio calculations were performed on the torsional potential energy curve and the equilibrium and transition state geometries and normal-mode frequencies of the first excited singlet state S1 on the CIS level of theory. Numerous vibronic transitions were assigned, especially those involving the torsional normal mode. The torsional potentials of the ground and first excited electronic states were simulated by matching the observed and calculated torsional frequency spacings in a least-squares fitting procedure. The simulated S1 potential showed very good agreement with the ab initio potential calculated on the CIS/6-31G(d,p) level of theory. TDDFT energy corrections improved the match with the simulated S(1) torsional potential. The latter calculation yielded a torsional barrier of V2 = 6708 cm(-1), and the simulation a barrier of V2 = 6245 cm(-1). Ground-state normal-mode frequencies were calculated on the B3LYP/6-31G(d,p) level of theory, which were used to interpret the infrared spectrum, the FDS spectrum of the transition and hot bands of the FES spectrum. The fluorescence intensities of the nu49 overtone progression could reasonably be reproduced by considering the geometry changes upon electronic excitation predicted by the ab initio calculations. On the basis of the torsional potential calculations, it could be ruled out that the uniform excess energy dependence of the fluorescence lifetimes is linked to the torsional barrier in the excited state. The rotational band contour simulation of the transition yielded rotational constants in close agreement to the ab initio values for both electronic states. Rotational coherence signals were obtained by polarization-analyzed, time-resolved measurements of the fluorescence decay of the transition. The simulation of these signals yielded corroborating evidence as to the quality of the ab initio calculated rotational constants of both states. The origin of the anomalous intensity discrepancy between the fluorescence excitation spectrum and the REMPI spectrum is discussed.