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.     

Deoxyribozymes with 2'-5' RNA ligase activity

In vitro selection was used to identify deoxyribozymes that ligate two RNA substrates. In the ligation reaction, a 2'-5' RNA phosphodiester linkage is created from a 2',3'-cyclic phosphate and a 5'-hydroxyl group. The new Mg(2+)-dependent deoxyribozymes provide 50-60% yield of ligated RNA in overnight incubations at pH 7.5 and 37 degrees C, and they afford 40-50% yield in 1 h at pH 9.0 and 37 degrees C. Various RNA substrate sequences may be joined by simple Watson-Crick covaration of the DNA binding arms that interact with the two RNA substrates. The current deoxyribozymes have some RNA substrate sequence requirements at the nucleotides immediately surrounding the ligation junction (either UAUA GGAA or UAUN GGAA, where the arrow denotes the ligation site and N equals any nucleotide). One of the new deoxyribozymes was used to prepare by ligation the Tetrahymena group I intron RNA P4-P6 domain, a representative structured RNA. Nondenaturing gel electrophoresis revealed that a 2'-5' linkage between nucleotides A233 and G234 of P4-P6 does not disrupt its Mg(2+)-dependent folding (DeltaDeltaG degrees ' < 0.2 kcal/mol). This demonstrates that a 2'-5' linkage does not necessarily interfere with structure in a folded RNA. Therefore, these non-native linkages may be acceptable in modified RNAs when structure/function relationships are investigated. Deoxyribozymes that ligate RNA should be particularly useful for preparing site-specifically modified RNAs for studies of RNA structure, folding, and catalysis.     

Tertiary interactions determine the accuracy of RNA folding

RNAs must fold into unique three-dimensional structures to function in the cell, but how each polynucleotide finds its native structure is not understood. To investigate whether the stability of the tertiary structure determines the speed and accuracy of RNA folding, docking of a tetraloop with its receptor in a bacterial group I ribozyme was perturbed by site-directed mutagenesis. Disruption of the tetraloop or its receptor destabilizes tertiary interactions throughout the ribozyme by 2-3 kcal/mol, demonstrating that tertiary interactions form cooperatively in the transition from a native-like intermediate to the native state. Nondenaturing PAGE and RNase T1 digestion showed that base pairs form less homogeneously in the mutant RNAs during the transition from the unfolded state to the intermediate. Thus, tertiary interactions between helices bias the ensemble of secondary structures toward native-like conformations. Time-resolved hydroxyl radical footprinting showed that the wild-type ribozyme folds completely within 5-20 ms. By contrast, only 40-60% of a tetraloop mutant ribozyme folds in 30-40 ms, with the remainder folding in 30-200 s via nonnative intermediates. Therefore, destabilization of tetraloop-receptor docking introduces an alternate folding pathway in the otherwise smooth energy landscape of the wild-type ribozyme. Our results show that stable tertiary structure increases the flux through folding pathways that lead directly and rapidly to the native structure.     

DNA constraints allow rational control of macromolecular conformation

We report that double-helical DNA constraints can be used to control the conformation of another molecule, RNA. When a covalently attached DNA constraint is structurally incompatible with the native Mg2+-dependent RNA conformation, RNA folding is disrupted, as revealed by nondenaturing gel electrophoresis and independently by chemical probing. Our approach is distinct from other efforts in DNA nanotechnology, which have prepared DNA objects by self-assembly, built static DNA lattices for assembly of other objects, and created nanomachines made solely of DNA. In contrast, our dynamic use of DNA to control the conformations of other macromolecules should have wide impact in nanotechnology applications ranging from materials science to biology.     

The shape-shifting quasispecies of RNA: one sequence, many functional folds

E Unus pluribum, or "Of One, Many", may be at the root of decoding the RNA sequence-structure-function relationship. RNAs embody the large majority of genes in higher eukaryotes and fold in a sequence-directed fashion into three-dimensional structures that perform functions conserved across all cellular life forms, ranging from regulating to executing gene expression. While it is the most important determinant of the RNA structure, the nucleotide sequence is generally not sufficient to specify a unique set of secondary and tertiary interactions due to the highly frustrated nature of RNA folding. This frustration results in folding heterogeneity, a common phenomenon wherein a chemically homogeneous population of RNA molecules folds into multiple stable structures. Often, these alternative conformations constitute misfolds, lacking the biological activity of the natively folded RNA. Intriguingly, a number of RNAs have recently been described as capable of adopting multiple distinct conformations that all perform, or contribute to, the same function. Characteristically, these conformations interconvert slowly on the experimental timescale, suggesting that they should be regarded as distinct native states. We discuss how rugged folding free energy landscapes give rise to multiple native states in the Tetrahymena Group I intron ribozyme, hairpin ribozyme, sarcin-ricin loop, ribosome, and an in vitro selected aptamer. We further describe the varying degrees to which folding heterogeneity impacts function in these RNAs, and compare and contrast this impact with that of heterogeneities found in protein folding. Embracing that one sequence can give rise to multiple native folds, we hypothesize that this phenomenon imparts adaptive advantages on any functionally evolving RNA quasispecies.     

Evidence for a thermodynamically distinct Mg2+ ion associated with formation of an RNA tertiary structure

A folding strategy adopted by some RNAs is to chelate cations in pockets or cavities, where the ions neutralize charge from solvent-inaccessible phosphate. Although such buried Mg(2+)-RNA chelates could be responsible for a significant fraction of the Mg(2+)-dependent stabilization free energy of some RNA tertiary structures, direct measurements have not been feasible because of the difficulty of finding conditions under which the free energy of Mg(2+) chelation is uncoupled from RNA folding and from unfavorable interactions with Mg(2+) ions in other environments. In a 58mer rRNA fragment, we have used a high-affinity thermophilic ribosomal protein to trap the RNA in a structure nearly identical to native; Mg(2+)- and protein-stabilized structures differ in the solvent exposure of a single nucleotide located at the chelation site. Under these conditions, titration of a high affinity chelation site takes place in a micromolar range of Mg(2+) concentration, and is partially resolved from the accumulation of Mg(2+) in the ion atmosphere. From these experiments, we estimate the total and site-specific Mg(2+)-RNA interaction free energies over the range of accessed Mg(2+) concentrations. At 0.1 mM Mg(2+) and 60 mM K(+), specific site binding contributes ～-3 kcal/mol of the total Mg(2+) interaction free energy of ～-13 kcal/mol from all sources; at higher Mg(2+) concentrations the site-binding contribution becomes a smaller proportion of the total (-4.5 vs -33 kcal/mol). Under approximately physiological ionic conditions, the specific binding site will be saturated but will provide only a fraction of the total free energy of Mg(2+)-RNA interactions.     

Determining the Mg2+ stoichiometry for folding an RNA metal ion core

The folding and catalytic function of RNA molecules depend on their interactions with divalent metal ions, such as magnesium. As with every molecular process, the most basic knowledge required for understanding the close relationship of an RNA with its metal ions is the stoichiometry of the interaction. Unfortunately, inventories of the numbers of divalent ions associated with unfolded and folded RNA states have been unattainable. A common approach has been to interpret Hill coefficients fit to folding equilibria as the number of metal ions bound upon folding. However, this approach is vitiated by the presence of diffusely associated divalent ions in a dynamic ion atmosphere and by the likelihood of multiple transitions along a folding pathway. We demonstrate that the use of molar concentrations of background monovalent salt can alleviate these complications. These simplifying solution conditions allow a precise determination of the stoichiometry of the magnesium ions involved in folding the metal ion core of the P4-P6 domain of the Tetrahymena group I ribozyme. Hill analysis of hydroxyl radical footprinting data suggests that the P4-P6 RNA core folds cooperatively upon the association of two metal ions. This unexpectedly small stoichiometry is strongly supported by counting magnesium ions associated with the P4-P6 RNA via fluorescence titration and atomic emission spectroscopy. By pinpointing the metal ion stoichiometry, these measurements provide a critical but previously missing step in the thermodynamic dissection of the coupling between metal ion binding and RNA folding.     

DNA aptamer folding on gold nanoparticles: from colloid chemistry to biosensors

We have investigated the effect of the folding of DNA aptamers on the colloidal stability of gold nanoparticles (AuNPs) to which an aptamer is tethered. On the basis of the studies of two different aptamers (adenosine aptamer and K+ aptamer), we discovered a unique colloidal stabilization effect associated with aptamer folding: AuNPs to which folded aptamer structures are attached are more stable toward salt-induced aggregation than those tethered to unfolded aptamers. This colloidal stabilization effect is more significant when a DNA spacer was incorporated between AuNP and the aptamer or when lower aptamer surface graft densities were used. The conformation that aptamers adopt on the surface appears to be a key factor that determines the relative stability of different AuNPs. Dynamic light scattering experiments revealed that the sizes of AuNPs modified with folded aptamers were larger than those of AuNPs modified with unfolded (but largely collapsed) aptamers in salt solution. From both the electrostatic and steric stabilization points of view, the folded aptamers that are more extended from the surface have a higher stabilization effect on AuNP than the unfolded aptamers. On the basis of this unique phenomenon, colorimetric biosensors have been developed for the detection of adenosine, K+, adenosine deaminase, and its inhibitors. Moreover, distinct AuNP aggregation and redispersion stages can be readily operated by controlling aptamer folding and unfolding states with the addition of adenosine and adenosine deaminase.     

2'-mercaptonucleotide interference reveals regions of close packing within folded RNA molecules

The 2'-hydroxyl group makes essential contributions to RNA structure and function. As an approach to assess the ability of a mercapto group to serve as a functional analogue for the 2'-hydroxyl group, we synthesized 2'-mercaptonucleotides for use in nucleotide analogue interference mapping. To correlate the observed interference effects with tertiary structure, we used the independently folding DeltaC209 P4-P6 domain from the Tetrahymena group I intron. We generated populations of DeltaC209 P4-P6 molecules containing 2'-mercaptonucleotides located randomly throughout the domain and separated the folded molecules from the unfolded molecules by nondenaturing gel electrophoresis. Iodine-induced cleavage of the RNA molecules revealed the sites at which 2'-mercaptonucleotides interfere with folding. These interferences cluster in the most densely packed regions of the tertiary structure, occurring only at sites that lack the space and flexibility to accommodate a sulfur atom. Interference mapping with 2'-mercaptonucleotides therefore provides a method by which to identify structurally rigid and densely packed regions within folded RNA molecules.     

Estimating free-energy barrier heights for an ultrafast folding protein from calorimetric and kinetic data

Differential scanning calorimetry was used to measure the temperature dependence of the absolute heat capacity of the 35-residue subdomain of the villin headpiece, a protein that folds in 5 mus and is therefore assumed to have a small free-energy barrier separating folded and unfolded states. To obtain an estimate of the barrier height from the calorimetric data, two models, a variable-barrier model and an Ising-like model, were used to fit the heat capacity in excess of the folded state over the temperature range 15-125 degrees C. The variable-barrier model is based on an empirical mathematical form for the density of states, with four adjustable parameters and the enthalpy (H) as a reaction coordinate. The Ising-like model is based on the inter-residue contact map of the X-ray structure with exact enumeration of approximately 10(5) possible conformations, with two adjustable parameters in the partition function, and either the fraction of native contacts (Q) or the number of ordered residues (P) as reaction coordinates. The variable-barrier model provides an excellent fit to the data and yields a barrier height at the folding temperature ranging from 0.4 to 1.1 kcal mol(-1), while the Ising-like model provides a less good fit and yields barrier heights of 2.3 +/- 0.1 kcal mol(-1) and 2.1 +/- 0.1 kcal mol(-1) for the Q and P reaction coordinates, respectively. In both models, the barrier to folding increases with increasing temperature. Assuming a sufficiently large activation energy for diffusion on the free-energy surfaces, both models are consistent with the observation of a temperature-independent folding rate in previously published laser temperature-jump experiments. Analysis of this kinetic data, using an approximate form for the pre-exponential factor of Kramers theory and the 70 ns relaxation time for the fast phase that precedes the unfolding/refolding relaxation to determine the diffusion coefficient, results in a barrier height of 1.6 +/- 0.3 kcal mol-1 for an unspecified reaction coordinate. Although no independent test of the validity of the H, Q, or P reaction coordinates is given, the barrier-height estimates obtained with the three reaction coordinates are in quite good agreement with the value derived from a Kramers analysis of the kinetics that makes no assumptions about the reaction coordinate. However, the higher estimates obtained using Q or P appear more consistent with the finding of barrier-crossing kinetics of a villin mutant that folds in 700 ns, corresponding to a 1.3 kcal mol-1 reduction in the folding barrier relative to wild-type. All of the results suggest that the free-energy barrier to folding is sufficiently low that it should be possible to engineer this protein or find solution conditions that would eliminate the barrier to create the "downhill" folding scenario of Wolynes and Onuchic.     

Electrostatics of nucleic acid folding under conformational constraint

RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Protonation/deprotonation effects on the stability of the Trp-cage miniprotein

The Trp-cage miniprotein is a 20 amino acid peptide that exhibits many of the properties of globular proteins. In this protein, the hydrophobic core is formed by a buried Trp side chain. The folded state is stabilized by an ion pair between aspartic acid and an arginine side chain. The effect of protonating the aspartic acid on the Trp-cage miniprotein folding/unfolding equilibrium is studied by explicit solvent molecular dynamics simulations of the protein in the charged and protonated Asp9 states. Unbiased Replica Exchange Molecular Dynamics (REMD) simulations, spanning a wide temperature range, are carried out to the microsecond time scale, using the AMBER99SB forcefield in explicit TIP3P water. The protein structural ensembles are studied in terms of various order parameters that differentiate the folded and unfolded states. We observe that in the folded state the root mean square distance (rmsd) from the backbone of the NMR structure shows two highly populated basins close to the native state with peaks at 0.06 nm and 0.16 nm, which are consistent with previous simulations using the same forcefield. The fraction of folded replicas shows a drastic decrease because of the absence of the salt bridge. However, significant populations of conformations with the arginine side chain exposed to the solvent, but within the folded basin, are found. This shows the possibility to reach the folded state without formation of the ion pair. We also characterize changes in the unfolded state. The equilibrium populations of the folded and unfolded states are used to characterize the thermodynamics of the system. We find that the change in free energy difference due to the protonation of the Asp amino acid is 3 kJ mol(-1) at 297 K, favoring the charged state, and resulting in ΔpK(1) = 0.5 units for Asp9. We also study the differences in the unfolded state ensembles for the two charge states and find significant changes at low temperature, where the protonated Asp side chain makes multiple hydrogen bonds to the protein backbone.     

Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations

Globally RNA folding occurs in multiple stages involving chain compaction and subsequent rearrangement by a number of parallel routes to the folded state. However, the sequence-dependent details of the folding pathways and the link between collapse and folding are poorly understood. To obtain a comprehensive picture of the thermodynamics and folding kinetics we used molecular simulations of coarse-grained model of a pseudoknot found in the conserved core domain of the human telomerase (hTR) by varying both temperature (T) and ion concentration (C). The phase diagram in the [T,C] plane shows that the boundary separating the folded and unfolded state for the finite 47-nucleotide system is relatively sharp, implying that from a thermodynamic perspective hTR behaves as an apparent two-state system. However, the folding kinetics following single C-jump or T-quench is complicated, involving multiple channels to the native state. Although globally folding kinetics triggered by T-quench and C-jump are similar, the kinetics of chain compaction are vastly different, which reflects the role of initial conditions in directing folding and collapse. Remarkably, even after substantial reduction in the overall size of hTR, the ensemble of compact conformations are far from being nativelike, suggesting that the search for the folded state occurs among the ensemble of low-energy fluidlike globules. The rate of unfolding, which occurs in a single step, is faster upon C-decrease compared to a jump in temperature. To identify "hidden" states that are visited during the folding process we performed simulations by periodically interrupting the approach to the folded state by lowering C. These simulations show that hTR reaches the folded state through a small number of connected clusters that are repeatedly visited during the pulse sequence in which the folding or unfolding is interrupted. The results from interrupted folding simulations, which are in accord with non-equilibrium single-molecule folding of a large ribozyme, show that multiple probes are needed to reveal the invisible states that are sampled by RNA as it folds. Although we have illustrated the complexity of RNA folding using hTR as a case study, general arguments and qualitative comparisons to time-resolved scattering experiments on Azoarcus group I ribozyme and single-molecule non-equilibrium periodic ion-jump experiments establish the generality of our findings.     

Gold nanoparticle based NSET for monitoring Mg2+ dependent RNA folding

Understanding the mechanism of how RNA molecules fold into their native structures are vital to their functional properties. Here we report for the first time that gold nanoparticle based NSET can be used for probing the transition states of an RNA unfolding reaction. Our result shows that time-dependent NSET can clearly distinguish structural transitions between unfolded to folded states. Our experimental observation point out that NSET can be used for the design of an optical based molecular ruler to track RNA folding transition states at distances more than double the distances achievable using traditional dipole-dipole Coulombic energy transfer based methods.     

Diffusive dynamics on multidimensional rough free energy surfaces

The dynamics of processes relevant to chemistry and biophysics on rough free energy landscapes is investigated using a recently developed algorithm to solve the Smoluchowski equation. Two different processes are considered: ligand rebinding in MbCO and protein folding. For the rebinding dynamics of carbon monoxide (CO) to native myoglobin (Mb) from locations around the active site, the two-dimensional free energy surface (FES) is constructed using extensive molecular dynamics simulations. The surface describes the minima in the A state (bound MbCO), CO in the distal pocket and in the Xe4 pocket, and the transitions between these states and allows to study the diffusion of CO in detail. For the folding dynamics of protein G, a previously determined two-dimensional FES was available. To follow the diffusive dynamics on these rough free energy surfaces, the Smoluchowski equation is solved using the recently developed hierarchical discrete approximation method. From the relaxation of the initial nonequilibrium distribution, experimentally accessible quantities such as the rebinding time for CO or the folding time for protein G can be calculated. It is found that the free energy barrier for CO in the Xe4 pocket and in the distal pocket (B state) closer to the heme iron is approximately 6 kcal/mol which is considerably larger than the inner barrier which separates the bound state and the B state. For the folding of protein G, a barrier of approximately 10 kcal/mol between the unfolded and the folded state is consistent with folding times of the order of milliseconds.     

Phenylene Ethynylene‐Tethered Perylene Bisimide Folda‐Dimer and Folda‐Trimer: Investigations on Folding Features in Ground and Excited States

In this work, we have elucidated in detail the folding properties of two perylene bisimide (PBI) foldamers composed of two and three PBI units, respectively, attached to a phenylene ethynylene backbone. The folding behaviors of these new PBI folda‐dimer and trimer have been studied by solvent‐dependent UV/Vis absorption and 1D and 2D NMR spectroscopy, revealing facile folding of both systems in tetrahydrofuran (THF). In CHCl₃ the dimer exists in extended (unfolded) conformation, whereas partially folded conformations are observed in the trimer. Temperature‐dependent ¹H NMR spectroscopic studies in [D₈]THF revealed intramolecular dynamic processes for both PBI foldamers due to, on the one hand, hindered rotation around C?N imide bonds and, on the other hand, backbone flapping; the latter process being energetically more demanding as it was observed only at elevated temperature. The structural features of folded conformations of the dimer and trimer have been elucidated by different 2D‐NMR spectroscopy (e.g., ROESY and DOSY) in [D₈]THF. The energetics of folding processes for the PBI dimer and trimer have been assessed by calculations applying various methods, particularly the semiempirical PM6‐DH2 and the more sophisticated B97D approach, in which relevant dispersion corrections are included. These calculations corroborate the results of NMR spectroscopic studies. Folding features in the excited states of these PBI foldamers have been characterized by using time‐resolved fluorescence and transient absorption spectroscopy in THF and CHCl₃, exhibiting similar solvent‐dependent behavior as observed for the ground state. Interestingly, photoinduced electron transfer (PET) process from electron‐donating backbone to electron‐deficient PBI core for extended, but not for folded, conformations was observed, which can be explained by a fast relaxation of excited PBI stacks in the folded conformation into fluorescent excimer states.     

Probing the complete folding trajectory of a DNA hairpin using dual beam fluorescence fluctuation spectroscopy

The conformational fluctuations of dye-quencher labeled DNA hairpin molecules in aqueous solution were investigated using dual probe beam fluorescence fluctuation spectroscopy. The measurements revealed the flow and diffusion times of the DNA molecules through two spatially offset optical probe regions, the absolute and relative concentrations of each conformational substate of the DNA, and the kinetics of the DNA hairpin folding and unfolding reactions in the 1 micros to 10 ms time range. A DNA hairpin containing a 21-nucleotide polythymine loop and a 4-base pair stem exhibited double exponential relaxation kinetics, with time constants of 84 and 393 micros. This confirms that folding and melting of the DNA hairpin structure is not a two state process but proceeds by way of metastable intermediate states. The fast time constant corresponds to formation and unfolding of an intermediate, and the slow time constant is due to formation and disruption of the fully base-paired stem. This is consistent with a previous study of a similar DNA hairpin with a 5-base pair stem, in which the fast reaction was attributed to the fluctuations of an intermediate DNA conformation [J. Am. Chem. Soc. 2006, 128, 1240-1249]. In that case, reactions involving the native conformation could not be observed directly due to the limited observation time range of the fluorescence correlation spectroscopy experiment. The intermediate states of the DNA hairpins are suggested to be due to a collapsed ensemble of folded hairpins containing various partially folded or misfolded conformations.     

Constrained proper sampling of conformations of transition state ensemble of protein folding

Characterizing the conformations of protein in the transition state ensemble (TSE) is important for studying protein folding. A promising approach pioneered by Vendruscolo et al. [Nature (London) 409, 641 (2001)] to study TSE is to generate conformations that satisfy all constraints imposed by the experimentally measured φ values that provide information about the native likeness of the transition states. Fai?sca et al. [J. Chem. Phys. 129, 095108 (2008)] generated conformations of TSE based on the criterion that, starting from a TS conformation, the probabilities of folding and unfolding are about equal through Markov Chain Monte Carlo (MCMC) simulations. In this study, we use the technique of constrained sequential Monte Carlo method [Lin et al., J. Chem. Phys. 129, 094101 (2008); Zhang et al. Proteins 66, 61 (2007)] to generate TSE conformations of acylphosphatase of 98 residues that satisfy the φ-value constraints, as well as the criterion that each conformation has a folding probability of 0.5 by Monte Carlo simulations. We adopt a two stage process and first generate 5000 contact maps satisfying the φ-value constraints. Each contact map is then used to generate 1000 properly weighted conformations. After clustering similar conformations, we obtain a set of properly weighted samples of 4185 candidate clusters. Representative conformation of each of these cluster is then selected and 50 runs of Markov chain Monte Carlo (MCMC) simulation are carried using a regrowth move set. We then select a subset of 1501 conformations that have equal probabilities to fold and to unfold as the set of TSE. These 1501 samples characterize well the distribution of transition state ensemble conformations of acylphosphatase. Compared with previous studies, our approach can access much wider conformational space and can objectively generate conformations that satisfy the φ-value constraints and the criterion of 0.5 folding probability without bias. In contrast to previous studies, our results show that transition state conformations are very diverse and are far from nativelike when measured in cartesian root-mean-square deviation (cRMSD): the average cRMSD between TSE conformations and the native structure is 9.4 A? for this short protein, instead of 6 A? reported in previous studies. In addition, we found that the average fraction of native contacts in the TSE is 0.37, with enrichment in native-like β-sheets and a shortage of long range contacts, suggesting such contacts form at a later stage of folding. We further calculate the first passage time of folding of TSE conformations through calculation of physical time associated with the regrowth moves in MCMC simulation through mapping such moves to a Markovian state model, whose transition time was obtained by Langevin dynamics simulations. Our results indicate that despite the large structural diversity of the TSE, they are characterized by similar folding time. Our approach is general and can be used to study TSE in other macromolecules.