Probing the transition state ensemble of a protein folding reaction by pressure-dependent NMR relaxation dispersion

The F61A/A90G mutant of a redesigned form of apocytochrome b562 folds by an apparent two-state mechanism. We have used the pressure dependence of 15N NMR relaxation dispersion rate profiles to study the changes in volumetric parameters that accompany the folding reaction of this protein at 45 degrees C. The experiments were performed under conditions where the folding/unfolding equilibrium could be studied at each pressure without addition of denaturants. The exquisite sensitivity of the methodology to small changes in folding/unfolding rates facilitated the use of relatively low-pressure values (between 1 and 270 bar) so that pressure-induced changes to the unfolded state ensemble could be minimized. A volume change for unfolding of -81 mL/mol is measured (at 1 bar), a factor of 1.4 larger (in absolute value) than the volume difference between the transition state ensemble (TSE) and the unfolded state. Notably, the changes in the free energy difference between folded and unfolded states and in the activation free energy for folding were not linear with pressure. Thus, the difference in the isothermal compressibility upon unfolding (-0.11 mL mol(-1) bar(-1)) and, for the first time, the compressibility of the TSE relative to the unfolded state (0.15 mL mol(-1) bar(-1)) could be calculated. The results argue for a TSE that is collapsed but loosely packed relative to the folded state and significantly hydrated, suggesting that the release of water occurs after the rate-limiting step in protein folding. The notion of a collapsed and hydrated TSE is consistent with expectations based on earlier temperature-dependent folding studies, showing that the barrier to folding at 45 degrees C is entropic (Choy, W. Y.; Zhou, Z.; Bai, Y.; Kay, L. E. J. Am. Chem. Soc. 2005, 127, 5066-5072).     

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.     

Effects of crowding and confinement on the structures of the transition state ensemble in proteins

Characterization of the structures of the transition state ensemble is a key step in describing the folding reaction. Using two variants of a coarse-grained model of the three-stranded beta-sheet WW domain and a fully automated progress variable clustering (PVC) algorithm, we have dissected the effect of macromolecular crowding and confinement on the changes in the transition state structures in comparison to bulk. Each amino acid is represented using a Calpha atom and a side chain. The distance between the Calpha atom and center of mass of the side chain is taken to be its effective van der Waals radius. For the bulk case, we predict using the PVC algorithm, which does not assume knowledge of the underlying folding reaction coordinate, that there are two classes of structures in the transition state ensemble (TSE). The structures in both of the classes are compact. The dominant cluster is more structured than the structures in the less populated class. In accord with bulk experiments, the residues in strands beta2 and beta3 and the interactions at the beta2-beta3 interface are structured. When only excluded volume interactions between the crowding particles and the WW domain are taken into account or when the protein is confined to an inert spherical pore, the overall structure of the TSE does not change dramatically. However, in this entropy dominated regime, the width of the TSE decreases and the structures become more oblate and less spherical as the volume fraction of crowding particle increases or when the pore radius decreases. It suggests that the shape changes, which are computed using the moment of inertia tensor, may represent the slow degrees of freedom during the folding process. When non-native interactions between side chains and interactions with the cavity of the pores are taken into account, the TSE becomes considerably broader. Although the topology in the transition has a fold similar to the native state, the structures are far more plastic than in the bulk. The TSE is sensitive to the size of the pore as well as interactions between the pore and the protein. The differences between the two cases (confinement in an inert pore and when pore-protein interactions are considered) arise due to the increased importance of enthalpic interactions in the transition state as the strength of the protein-pore interaction increases.     

Measuring pK(a) values in protein folding transition state ensembles by NMR spectroscopy

Protein folding kinetic data have been obtained for the marginally stable N-terminal SH3 domain of the Drosophila protein drk as a function of pH in order to investigate the electrostatic properties of Asp8 in the folding transition state ensemble. The slow exchange between folded and unfolded forms of the protein gives rise to separate NMR resonances for both folded and unfolded states at equilibrium. As a result, kinetic data can be derived from magnetization transfer between these two states without the need for denaturants. Using the fact that ionization of Asp8 dominates the electrostatic behavior of the protein between pH 2 and 3, along with pKa values for titrating groups in both folded and unfolded states that have been determined in a previous study, values of 2.9 +/- 0.1 and 3.3 +/- 0.2 are obtained for the pKa of Asp8 in the transition state for the wild-type protein and for a His7Ala mutant, respectively. The data are consistent with the partial formation in the transition state ensemble of an Asp8 side chain carboxylate-a Lys21 backbone amide interaction that represents a highly conserved contact in folded SH3 domains.     

Renormalization-group analysis of the R(I)-R(V) rotator phase transition

A model for coupled tilt angle and lattice distortion parameter is proposed to describe the R(I)-R(V) transition in n-alkane. The model is treated in the framework of a Landau mean-field theory and renormalization-group theory. The influence of gauche conformations and molecular flexibility on the R(I)-R(V) transition is discussed within the mean-field theory. The fluctuations on the R(I)-R(V) transition are discussed by the renormalization-group theory. Renormalization-group theory predicts that the R(I)-R(V) transition can be driven first order by fluctuations and becomes second order at a tricritical point. Available experimental data are consistent with our model.     

The native ensemble and folding of a protein molten-globule: functional consequence of downhill folding

The continually emerging functional significance of intrinsic disorder and conformational flexibility in proteins has challenged the long-standing dogma of a well-defined structure contributing to a specific function. Molten-globular states, a class of proteins with significant secondary-structure but a fluid hydrophobic core, is one such example. They have however been difficult to characterize due to the complexity of experimental data and lack of computational avenues. Here, we dissect the folding mechanism of the α-helical molten-globular protein NCBD from three fundamentally different approaches: statistical-mechanical variable barrier model, C(α)-based Gō-model and explicit water all-atom molecular dynamics (MD) simulations. We find that NCBD displays the characteristics of a one-state globally downhill folder but is significantly destabilized. Using simulation techniques, we generate a highly constrained but a heterogeneous native ensemble of the molten-globule for the first time that is consistent with experimental data including small angle X-ray scattering (SAXS), circular dichroism (CD), and nuclear magnetic resonance (NMR). The resulting native ensemble populates conformations reported in other bound-forms providing direct evidence to the mechanism of conformational selection for binding multiple partners in this domain. Importantly, our simulations reveal a connection between downhill folding and large conformational flexibility in this domain that has been evolutionarily selected and functionally exploited resulting in large binding promiscuity. Finally, the multimodel approach we employ here serves as a powerful methodology to study mechanisms and suggests that the thermodynamic features of molten-globules fall within the array of folding mechanisms available to small single-domain proteins.     

Bonding in ammonia borane: an analysis based on the natural orbitals for chemical valence and the extended transition state method (ETS-NOCV)

In the present study the natural orbitals for chemical valence (NOCVs) combined with the energy decomposition scheme (ETS) were used to characterize bonding in various clusters of ammonia borane (borazane): dimer D, trimer TR, tetramer TE, and the crystal based models: nonamer N and tetrakaidecamer TD. ETS-NOCV results have shown that shortening of the B-N bond (by ~0.1 ?) in ammonia borane crystal (as compared to isolated borazane molecule) is related to the enhancement of donation (by 6.5 kcal/mol) and electrostatic (by 11.3 kcal/mol) contributions. This, in turn, is caused solely by the electrostatic dipole-dipole interaction between ammonia borane units; dihydrogen bonding, BH···HN, formed between borazane units exhibits no direct impact on B-N bond contraction. On the other hand, formation of dihydrogen bonding appeared to be very important in the total stabilization of single borazane unit, namely, ETS-based data indicated that it leads to significant electronic stabilization ΔE(orb) = -17.5 kcal/mol, which is only slightly less important than the electrostatic term, ΔE(elstat) = -19.4 kcal/mol. Thus, both factors contribute to relatively high melting point of the borazane crystal. Deformation density contributions (Δρ(i)) obtained from NOCVs allowed to conclude that dihydrogen bonding is primarily based on outflow of electron density from B-H bonding orbitals to the empty σ*(N-H) (charge transfer component). Equally important is the covalent contribution resulting from the shift of the electron density from hydrogen atoms of both NH and BH groups to the interatomic regions of NH···HB. Quantitatively, averaged electronic strength of dihydrogen bond per one BH···HN link varies from 1.95 kcal/mol (for the crystal structure model, N), 2.47 kcal/mol (for trimer TR), through 2.65 kcal/mol (for tetramer TE), up to 3.95 kcal/mol (for dimer D).     

Universal transition state scaling relations for (de)hydrogenation over transition metals

We analyse the transition state energies for 249 hydrogenation/dehydrogenation reactions of atoms and simple molecules over close-packed and stepped surfaces and nanoparticles of transition metals using Density Functional Theory. Linear energy scaling relations are observed for the transition state structures leading to transition state scaling relations for all the investigated reactions. With a suitable choice of reference systems the transition state scaling relations form a universality class that can be approximated with one single linear relation describing the entire range of reactions over all types of surfaces and nanoclusters.     

A new method for rapid characterization of the folding pathways of multidisulfide-containing proteins

Oxidative folding is a composite process that consists of both the conformational folding to the native three-dimensional structure and the regeneration of the native disulfide bonds of a protein, frequently involving over 100 disulfide intermediate species. Understanding the oxidative folding pathways of a multiple-disulfide-containing protein is a very difficult task that often requires years of devoted research due to the high complexity of the process and the very similar features of the large number of intermediates. Here we developed a method for rapidly delineating the major features of the oxidative folding pathways of a protein. The method examines the temperature dependence of the oxidative folding rate of the protein in combination with reduction pulses. Reduction pulses expose the presence of structured intermediates along the pathways. The correlation between the regeneration rate at different temperatures and the stability of the structured intermediates reveals the role that the intermediates play in determining the pathway. The method was first tested with bovine pancreatic ribonuclease A whose folding pathways were defined earlier. Then, it was explored to discern some of the major features of the folding pathways of its homologue, frog Onconase. The results suggest that the stability of the three-dimensional structure of the native protein is a major determinant of the folding rate in oxidative folding.     

Experimental transition state for the B-chlorodiisopinocampheylborane (DIP-Cl) reduction

Asymmetric reductions of prochiral ketones are important transformations in the syntheses of natural products, pharmaceuticals, and fine chemicals. B-Chlorodiisopinocampheylborane (DIP-Cl), a stoichiometric reagent that is capable of reducing prochiral aralkyl ketones with high selectivity. Here, we utilize a recently developed ¹³C kinetic isotope effect (KIE) methodology to probe the symmetry breaking process inherent to this asymmetric reduction. Experimental KIEs and computed transition structures indicate significant roles for non-bonding interaction, specific directed orbital interactions, and hydrogen tunneling in this reaction.     

Synthetic nolanite Fe(2.5)V(1.5)V(5.6)O16 nanocrystals: a new room-temperature magnetic semiconductor with semiconductor-insulator transition

Nolanite Fe(2.5)V(1.5)V(5.6)O(16) nanocrystals have been successfully achieved by a facile solvothermal method for the first time. The magnetic semiconducting and semiconductor-insulator transition characters of the synthetic nolanite sample render it a promising candidate for the design of data storage devices and temperature-sensitive sensors.     

Flow injection analysis for oxidation state speciation of vanadium(IV) and vanadium(V) in natural water.

A sensitive and simultaneous spectrophotometric flow injection method for the determination of vanadium(IV) and vanadium(V) is proposed. The method is based on the effect of ligands such as 2,4,6-tris(2-pyridyl)-1,3,5-triazine (TPTZ) and diphosphate on the conditional redox potential of iron(III)/iron(II) system. A four-channel flow system is assembled. In this flow system, diluted hydrochloric acid (1.0 x 10(-2) mol dm(-3)) as a carrier for standard/sample, acetate buffer (pH 5.5) as a carrier for diphosphate solution, an equimolar mixed solution of iron(III) and iron(II) and a TPTZ solution are delivered, so that the baseline absorbance can be established by forming a constant amount of iron(II)-TPTZ complex (lambda(max) = 593 nm). Vanadium(IV) and/or vanadium(V) (400 microL) and diphosphate (200 microL) solutions are simultaneously introduced into the flow system; in this system the diphosphate solution passes through a delay coil. The potential of the iron(III)/iron(II) system increases in the presence of TPTZ, and therefore vanadium(IV) is easily oxidized by iron(III) to vanadium(V) to produce an iron(II)-TPTZ complex (a positive peak for vanadium(IV) appears). On the other hand, the potential of the redox system decreases in the presence of diphosphate, so that vanadium(V) can be easily reduced by iron(II) to vanadium(IV). In this case, the amount of iron(II) decreases according to the amount of vanadium(V). As a result, the produced iron(II)-TPTZ complex decreases (a negative peak for vanadium(V) appears). In this manner, two peaks for vanadium(IV) and vanadium(V) can be alternately obtained. The limits of detection (S/N = 3) are 1.98 x 10(-7) and 2.97 x 10(-7) mol dm(-3) for vanadium(IV) and vanadium(V), respectively. The method is applied to the simultaneous determination of vanadium(IV) and vanadium(V) in commercial bottled mineral water samples.     

Nitrogen atom transfer from iron(IV) nitrido complexes: a dual-nature transition state for atom transfer

The mechanism of nitrogen atom transfer from four-coordinate tris(carbene)borate iron(IV) nitrido complexes to phosphines and phosphites has been investigated. In the absence of limiting steric effects, the rate of nitrogen atom transfer to phosphines increases with decreasing phosphine σ-basicity. This trend has been quantified by a Hammett study with para-substituted triarylphosphines, and is contrary to the expectations of an electrophilic nitrido ligand. On the basis of electronic structure calculations, a dual-nature transition state for nitrogen atom transfer is proposed, in which a key interaction involves the transfer of electron density from the nitrido highest occupied molecular orbital (HOMO) to the phosphine lowest unoccupied molecular orbital (LUMO). Compared to analogous atom transfer reactions from a 5d metal, these results show how the electronic plasticity of a 3d metal results in rapid atom transfer from pseudotetrahedral late metal complexes.     

Relationships between unfolded configurations of proteins and dynamics of folding to the native state

We compare folding trajectories of chymotrypsin inhibitor (CI2) using a dynamic Monte Carlo scheme with Go-type potentials. The model considers the four backbone atoms of each residue and a sphere centered around C^β the diameter of which is chosen according to the type of the side group. Bond lengths and bond angles are kept fixed. Folding trajectories are obtained by giving random increments to the φ and ψ torsion angles with some bias toward the native state. Excluded volume effects are considered. Two sets of 20 trajectories are obtained, with different initial configurations. The first set is generated from random initial configurations. The initial configurations of the second set are generated according to knowledge-based neighbor dependent torsion probabilities derived from triplets in the Protein Data Bank. Compared to chains with randomly generated initial configurations, those generated with neighbor-dependent probabilities (i) fold faster, (ii) have better defined secondary structure elements, and (iii) have less number of non-native contacts during folding. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3667–3678, 2006     

Adsorption-spectroscopic method for multielement analysis: Determination of Cr(VI), V(V), Ni(II), and Cu(II) from one sample using a two-layer adsorbent

The possibility of preconcentrating vanadium, chromium, copper, and nickel by the simultaneous adsorption in a flow-through mode on a two-layer adsorbent and the determination of metal ions by diffuse reflectance spectroscopy was studied. The adsorbent was made of a polyacrylonitrile fiber, one layer of which was filled with an AV-17 anion exchanger (PANV-AV-17), while another layer, with a KU-2 cation exchanger (PANV-KU-2). The procedure was based on the simultaneous preconcentration of vanadium and chromium on the first disk and nickel and copper on the second disk, by pumping the analyzed solution through both disks in a flow-through cell. Then, vanadium was determined on the disk of PANV-AV-17 with 8-hydroxyquinoline-5-sulfonic acid in 0.1 M HCl; next, chromium was determined with 1,5-diphenylcarbazide; the complex of vanadium was decomposed by 0.5 M H₂SO₄ and ascorbic acid. In the PANV-KU-2 disk, nickel was determined with dimethylglyoxime and then copper was analyzed with sodium diethyldithiocarbamate; the complex of nickel was decomposed with 1 M HCl. The selectivity factors were determined. A procedure was developed for the dynamic adsorption-spectroscopic determination of the following elements present simultaneously (μg/mL): V, 0.01–0.05; Cr, 0.002–0.015; Ni, 0.02–0.10; and Cu, 0.02–0.15. The results of analysis of model solutions are presented for different component ratios, RSD < 20%.     

Fast method of XANES data collection suitable for oxidation state mapping

XANES has been recently used for the determination of oxidation states of actinides in environmental samples. To obtain reliable results, however, a sufficiently long counting time at every probing energy and a large number of experimental points per XANES spectrum are required, due to the complex mathematical model used to fit the measured spectrum. This makes micro-mapping difficult, since the time required for data collection becomes unacceptably long. A simplified model for data collection and evaluation is presented. Its effectiveness has been tested by measuring the distribution of Pu oxidation states in a “hot” particle coming from a nuclear weapon test site.