Rate of Intrachain Diffusion of Unfolded Cytochrome c

Copper(II) Binding to the Intrinsically Disordered C-Terminal Peptide of SARS-CoV-2 Virulence Factor Nsp1

The first encoded SARS-CoV-2 protein (Nsp1) binds to the human 40S ribosome and blocks synthesis of host proteins, thereby inhibiting critical elements of the innate immune response. The final 33 residues of the natively unstructured Nsp1 C-terminus adopt a helix-turn-helix geometry upon binding to the ribosome. We have characterized the fluctuating conformations of this peptide using circular dichroism spectroscopy along with measurements of tryptophan fluorescence and energy transfer. Tryptophan fluorescence decay kinetics reveal that copper(II) binds to the peptide at micromolar concentrations, and electron paramagnetic resonance spectroscopy indicates that the metal ion coordinates to the lone histidine residue.

N-Terminal Decarboxylation as a Probe for Intramolecular Contact Formation in γ-Glu-(Pro)n-Met Peptides

The kinetics of intramolecular-contact formation between remote functional groups in peptides with restricted conformational flexibility were examined using designed peptides with variable-length proline bridges. As probes for this motion, free radicals were produced using the ^•OH-induced oxidation at the C-terminal methionine residue of γ-Glu-(Pro)_n-Met peptides (n = 0-3). The progress of the radicals' motion along the proline bridges was monitored as the radicals underwent reactions along the peptides' backbones. Of particular interest was the reaction between the sulfur atom located in the side chain of the oxidized Met residue and the unprotonated amino group of the glutamic acid moiety. Interactions between them were probed by the radiation-chemical yields (expressed as G values) of the formation of C-centered, α-aminoalkyl radicals (αN) on the Glu residue. These radicals were monitored directly or via their reaction with p-nitroacetophenone (PNAP) to generate the optically detected PNAP^•- radical anions. The yields of these αN radicals were found to be linearly dependent on the number of Pro residues. A constant decrease by 0.09 μM J^-1 per spacing Pro residue of the radiation-chemical yields of G(αN) was observed. Previous reports support the conclusion that the αN radicals in these cases would have to result from (S∴N)⁺-bonded cyclic radical cations that arose as a result from direct contact between the ends of the peptides. Furthermore, by analogy with the rate constants for the formation of intramolecularly (S∴S)⁺-bonded radical cations in Met-(Pro)_n-Met peptides ( J. Phys. Chem. B 2016, 120, 9732), the rate constants for the formation of intramolecularly (S∴N)⁺-bonded radical cations are activated to the same extent for all of the γ-Glu-(Pro)_n-Met peptides. Thus, the continuous decrease of G(αN) with the number of Pro residues (from 0 to 3) suggests that the formation of a contact between the S-atom in the C-terminal Met residue and the N-atom of a deprotonated N-terminal amino group of Glu is controlled in peptides with 0 to 3 Pro residues by the relative diffusion of the S^•+ and unoxidized N-atom. The overall rate constants of cyclization to form the (S∴N)-bonded radical cations were estimated to be 3.8 × 10⁶, 1.8 × 10⁶, and 8.1 × 10⁵ s^-1 for peptides with n = 0, 1, and 2 Pro residues, respectively. If activation is the same for all of the peptides, then these rate constants are a direct indication for the end-to-end dynamics along the chain.

Protein folding from heterogeneous unfolded state revealed by time-resolved X-ray solution scattering

One of the most challenging tasks in biological science is to understand how a protein folds. In theoretical studies, the hypothesis adopting a funnel-like free-energy landscape has been recognized as a prominent scheme for explaining protein folding in views of both internal energy and conformational heterogeneity of a protein. Despite numerous experimental efforts, however, comprehensively studying protein folding with respect to its global conformational changes in conjunction with the heterogeneity has been elusive. Here we investigate the redox-coupled folding dynamics of equine heart cytochrome c (cyt-c) induced by external electron injection by using time-resolved X-ray solution scattering. A systematic kinetic analysis unveils a kinetic model for its folding with a stretched exponential behavior during the transition toward the folded state. With the aid of the ensemble optimization method combined with molecular dynamics simulations, we found that during the folding the heterogeneously populated ensemble of the unfolded state is converted to a narrowly populated ensemble of folded conformations. These observations obtained from the kinetic and the structural analyses of X-ray scattering data reveal that the folding dynamics of cyt-c accompanies many parallel pathways associated with the heterogeneously populated ensemble of unfolded conformations, resulting in the stretched exponential kinetics at room temperature. This finding provides direct evidence with a view to microscopic protein conformations that the cyt-c folding initiates from a highly heterogeneous unfolded state, passes through still diverse intermediate structures, and reaches structural homogeneity by arriving at the folded state.

Segmental Motions of Proteins under Non-native States Evaluated Using Quasielastic Neutron Scattering

Characterization of the dynamics of disordered polypeptide chains is required to elucidate the behavior of intrinsically disordered proteins and proteins under non-native states related to the folding process. Here we develop a method using quasielastic neutron scattering, combined with small-angle X-ray scattering and dynamic light scattering, to evaluate segmental motions of proteins as well as diffusion of the entire molecules and local side-chain motions. We apply this method to RNase A under the unfolded and molten-globule (MG) states. The diffusion coefficients arising from the segmental motions are evaluated and found to be different between the unfolded and MG states. The values obtained here are consistent with those obtained using the fluorescence-based techniques. These results demonstrate not only feasibility of this method but also usefulness to characterize the behavior of proteins under various disordered states.

X-ray snapshots reveal conformational influence on active site ligation during metalloprotein folding

Cytochrome c (cyt c) has long been utilized as a model system to study metalloprotein folding dynamics and the interplay between active site ligation and tertiary structure. However, recent reports regarding the weakness of the native Fe(ii)-S bond (Fe-Met80) call into question the role of the active site ligation in the protein folding process. In order to investigate the interplay between protein conformation and active site structures, we directly tracked the evolution of both during a photolysis-induced folding reaction using X-ray transient absorption spectroscopy and time-resolved X-ray solution scattering techniques. We observe an intermediate Fe-Met80 species appearing on ∼2 μs timescale, which should not be sustained without stabilization from the folded protein structure. We also observe the appearance of a new active site intermediate: a weakly interacting Fe-H2O state. As both intermediates require stabilization of weak metal-ligand interactions, we surmise the existence of a local structure within the unfolded protein that protects and limits the movement of the ligands, similar to the entatic state found in the native cyt c fold. Furthermore, we observe that in some of the unfolded ensemble, the local stabilizing structure is lost, leading to expansion of the unfolded protein structure and misligation to His26/His33 residues.

The roughness of the protein energy landscape results in anomalous diffusion of the polypeptide backbone

Recombination of photolysed protein disulfide bonds confirms subdiffusional backbone motion and measures the roughness of the protein's energy landscape.

Kinetics of loop formation in worm-like chain polymers

A common theoretical approach to calculating reaction kinetics is to approximate a high-dimensional conformational search with a one-dimensional diffusion along an effective reaction coordinate. We employed Brownian dynamics simulations to test the validity of this approximation for loop formation kinetics in the worm-like chain polymer model. This model is often used to describe polymers that exhibit backbone stiffness beyond the monomer length scale. We find that one-dimensional diffusion models overestimate the looping time and do not predict the quantitatively correct dependence of looping time on chain length or capture radius. Our findings highlight the difficulty of describing high-dimensional polymers with simple kinetic theories.

Intrachain contact dynamics in unfolded cytochrome cb562

We have investigated intrachain contact dynamics in unfolded cytochrome cb562 by monitoring heme quenching of excited ruthenium photosensitizers covalently bound to residues along the polypeptide. Intrachain diffusion for chemically denatured proteins proceeds on the microsecond time scale with an upper limit of 0.1 μs. The rate constants exhibit a power-law dependence on the number of peptide bonds between the heme and Ru complex. The power-law exponent of -1.5 is consistent with theoretical models for freely jointed Gaussian chains, but its magnitude is smaller than that reported for several synthetic polypeptides. Contact formation within a stable loop was examined in a His63-heme ligated form of the protein under denaturing conditions. Loop formation accelerated contact kinetics for the Ru66 labeling site, owing to reduction in the length of the peptide separating redox sites. For other labeling sites within the stable loop, quenching rates were modestly reduced compared to the open chain polymer.

Conformational properties of polyglutamine sequences in guanidine hydrochloride solutions

Two sets of iso-1-cytochrome c variants have been prepared with N-terminal insertions of pure polyglutamine, i.e., PolyQ variants, or polyglutamine interrupted with lysine every sixth residue, i.e., Gln-rich variants. The polymer properties of these pure polyGln or Gln-rich sequences have been evaluated using equilibrium and kinetic His-heme loop formation methods for loop sizes ranging from 22 to 46 in 1.5, 3.0, and 6.0 M guanidine hydrochloride (GdnHCl). In 6.0 M GdnHCl, the scaling exponent, ν(3), for the pure polyGln sequences, is ~1.7--significantly less than ν(3) ≈ 2.15 for the Gln-rich sequences. The stability of the His-heme loops becomes progressively greater for the pure polyGln sequences relative to the Gln-rich sequences as GdnHCl concentration decreases from 6.0 to 1.5 M. Thus, the context of the sequence effects the polymer properties of Gln repeats even in denaturing concentrations of GdnHCl. Comparison of data for the Gln-rich variants with previous results for Gly-rich and Ala-rich variants shows that ν(3) ~ 2.2 for the Gln-rich, Gly-rich, and Ala-rich sequences in 6.0 M GdnHCl, whereas ν(3) remains unchanged at 3.0 M GdnHCl concentration for the Gln-rich and Ala-rich sequences but decreases to ~1.7 for the Gly-rich sequences. Thus, the polymer properties of Gln-rich and Ala-rich sequences are less sensitive to solvent quality in denaturing solutions of GdnHCl than Gly-rich sequences. Evaluation of Flory's characteristic ratio, C(n), for the Gln-rich and Ala-rich sequences relative to the Gly-rich sequences shows that Gln-rich sequences are stiffer than Ala-rich sequences at both 3.0 and 6.0 M GdnHCl.

Scaling properties of glycine-rich sequences in guanidine hydrochloride solutions

The intrinsic polymer properties of glycine-rich sequences are evaluated with a set of iso-1-cytochrome c variants with N-terminal inserts of the sequence (GGGGGK)(n) for n = 1-5. The thermodynamics and kinetics of His-heme loop formation are measured as a function of guanidine hydrochloride (GdnHCl) concentration for loop sizes ranging from 22 to 46 residues. The scaling exponent for loop formation, ν(3), evaluated using the Jacobson-Stockmayer equation is near 1.8, at 1.5 and 3.0 M GdnHCl, but it increases to 2.2 in 6.0 M GdnHCl. Previous work on a set of iso-1-cytochrome c variants with (AAAAAK)(n) inserts gave ν(3) = 2.2 for alanine-rich sequences in both 3.0 and 6.0 M GdnHCl. Chain stiffness was evaluated from the relative magnitude of Flory's characteristic ratio, C(n), for alanine-rich versus glycine-rich sequences. In 3.0 M GdnHCl, C(n)(Ala)/C(n)(Gly) is 1.6, decreasing to 1.3 in 6.0 M GdnHCl. The data suggest that solvent-backbone interactions dominate polypeptide conformational properties under good solvent conditions whereas side-chain-dependent properties are more important under poor solvent conditions. The results provide a direct experimental assessment in terms of polymer properties of the distinct roles of Gly versus Ala in the folding code.

Raising the speed limit for β-hairpin formation

Understanding the folding of the β-hairpin is a crucial step in studying how β-rich proteins fold. We have studied CLN025, an optimized ten residue synthetic peptide, which adopts a compact, well-structured β-hairpin conformation. Formation of the component β-sheet and β-turn structures of CLN025 was probed independently using a combination of equilibrium Fourier transform infrared spectroscopy and laser-induced temperature jump coupled with time-resolved infrared and fluorescence spectroscopies. We find that CLN025 is an ultrafast folder due to its small free energy barrier to folding and that it exceeds the predicted speed limit for β-hairpin formation by an order of magnitude. We also find that the folding mechanism cannot be described by a simple two-state model, but rather is a heterogeneous process involving two independent parallel processes. Formation of stabilizing cross-strand hydrophobic interactions and turn alignment occur competitively, with relaxation lifetimes of 82 ± 10 and 124 ± 10 ns, respectively, at the highest probed temperature. The ultrafast and heterogeneous folding kinetics observed for CLN025 provide evidence for folding on a nearly barrierless free energy landscape, and recalibrate the speed limit for the formation of a β-hairpin.

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 energy landscape and free energy excitations of cytochrome c

The covalently bound heme cofactor plays a dominant role in the folding of cytochrome c. Because of the complicated inorganic chemistry of the heme, some might consider the folding of cytochrome c to be a special case, following principles different from those used to describe the folding of proteins without cofactors. Recent investigations, however, demonstrate that common models describing folding for many proteins work well for cytochrome c when heme is explicitly introduced, generally providing results that agree with experimental observations. In this Account, we first discuss results from simple native structure-based models. These models include attractive interactions between nonadjacent residues only if they are present in the crystal structure at pH 7. Because attractive nonnative contacts are not included in native structure-based models, their energy landscapes can be described as "perfectly funneled". In other words, native structure-based models are energetically guided towards the native state and contain no energetic traps that would hinder folding. Energetic traps are denoted sources of "frustration", which cause specific transient intermediates to be populated. Native structure-based models do, however, include repulsion between residues due to excluded volume. Nonenergetic traps can therefore exist if the chain, which cannot cross over itself, must partially unfold so that folding can proceed. The ability of native structure-based models to capture this kind of motion is partly responsible for their successful predictions of folding pathways for many types of proteins. Models without frustration describe the sequence of folding events for cytochrome c well (as inferred from hydrogen-exchange experiments), thereby justifying their use as a starting point. At low pH, the experimentally observed folding sequence of cytochrome c deviates from that at pH 7 and from models with perfectly funneled energy landscapes. Here, alternate folding pathways are a result of "chemical frustration". This frustration arises because some regions of the protein are destabilized more than others due to the heterogeneous distribution of titratable residues that are protonated at low pH. Beginning with native structure-based terms, we construct more complex models by adding chemical frustration. These more complex models only modestly perturb the energy landscape, which remains, overall, well funneled. These perturbed models can accurately describe how alternative folding pathways are used at low pH. At alkaline pH, cytochrome c populates distinctly different structural ensembles. For instance, lysine residues are deprotonated and compete for the heme ligation site. The same models that can describe folding at low pH also predict well the structures and relative stabilities of intermediates populated at alkaline pH. The success of models based on funneled energy landscapes suggest that cytochrome c folding is driven primarily by native contacts. The presence of heme appears to add chemical complexity to the folding process, but it does not require fundamental modification of the general principles used to describe folding. Moreover, its added complexity provides a valuable means of probing the folding energy landscape in greater detail than is possible with simpler systems.

Importance of contact persistence in denatured state loop formation: kinetic insights into sequence effects on nucleation early in folding

Protein folding is dependent on the formation and persistence of simple loops early in folding. Ease of loop formation and persistence is believed to be dependent on the steric interactions of the residues involved in loop formation. We have previously investigated this factor in the denatured state of iso-1-cytochrome c using a five-amino-acid insert in front of a unique histidine in the N-terminal region of the protein. Previously, we reported that the apparent pK(a) values of loop formation for the most flexible (all Gly) and least flexible (all Ala) insert were, within error, the same. We evaluate whether this observation is due to differences in the persistence of loop contacts or due to effects of local sequence sterics and main-chain hydration on the persistence length of the chain. We also test whether sequence order affects loop formation. Here, we report kinetic results coupled to further mutagenesis of the insert to discern between these possibilities. We find that the amino acid-glycine versus alanine-next to the loop forming histidine has a dominant effect on loop kinetics and equilibria. A glycine in this position speeds loop breakage relative to alanine, resulting in less stable loops. At high percentage of Gly in the insert, rates of loop formation and breakage exactly compensate, leading to a leveling out in loop stability. Loop formation rates also increase with glycine content, inconsistent with poly-Gly segments being more extended than previously suspected due to main-chain hydration or local sterics. Unlike loop breakage rates, loop formation rates are insensitive to local sequence. Together, these observations suggest that contact persistence plays a more important role in defining the "folding code" than rates of loop formation.

A one-dimensional free energy surface does not account for two-probe folding kinetics of protein alpha(3)D

We present fluorescence-detected measurements of the temperature-jump relaxation kinetics of the designed three-helix bundle protein alpha(3)D taken under solvent conditions identical to previous infrared-detected kinetics. The fluorescence-detected rate is similar to the IR-detected rate only at the lowest temperature where we could measure it (326 K). The fluorescence-detected rate decreases by a factor of 3 over the 326-344 K temperature range, whereas the IR-detected rate remains nearly constant over the same range. To investigate this probe dependence, we tested an extensive set of physically reasonable one-dimensional (1D) free energy surfaces by Langevin dynamics simulation. The simulations included coordinate- and temperature-dependent roughness, diffusion coefficients, and IR/fluorescence spectroscopic signatures. None of these can reproduce the IR and fluorescence data simultaneously, forcing us to the conclusion that a 1D free energy surface cannot accurately describe the folding of alpha(3)D. This supports the hypothesis that alpha(3)D has a multidimensional free energy surface conducive to downhill folding at 326 K, and that it is already an incipient downhill folder with probe-dependent kinetics near its melting point.

Synchronous vs asynchronous chain motion in alpha-synuclein contact dynamics

alpha-Synuclein (alpha-syn) is an intrinsically unstructured 140-residue neuronal protein of uncertain function that is implicated in the etiology of Parkinson's disease. Tertiary contact formation rate constants in alpha-syn, determined from diffusion-limited electron-transfer kinetics measurements, are poorly approximated by simple random polymer theory. One source of the discrepancy between theory and experiment may be that interior-loop formation rates are not well approximated by end-to-end contact dynamics models. We have addressed this issue with Monte Carlo simulations to model asynchronous and synchronous motion of contacting sites in a random polymer. These simulations suggest that a dynamical drag effect may slow interior-loop formation rates by about a factor of 2 in comparison to end-to-end loops of comparable size. The additional deviations from random coil behavior in alpha-syn likely arise from clustering of hydrophobic residues in the disordered polypeptide.

Photolytic control and infrared probing of amide I mode in the dipeptide backbone-caged with the 4,5-dimethoxy-2-nitrobenzyl group

Alanine dipeptide analog 1 backbone-caged with a photolabile linker, 4,5-dimethoxy-2-nitrobenzyl (DmNb), was synthesized. UV-pulse-induced photochemical reaction of 1 was monitored by Fourier transform IR absorption spectroscopy under a steady-state condition or in a fast-scan mode. Upon photolysis of 1, the amide I band is changed from a doublet to a singlet with concomitant line shape changes of several IR bands. The change of the amide I band is directly associated with the photocleavage of the covalent N-C bond connecting the backbone amide of 2 to DmNb. Therefore, IR spectroscopy is useful for directly probing the photocleavage of backbone-caged peptide 1 and the concurrent release of native peptide 2. In contrast, UV-vis spectroscopy probing the irradiation-induced structural change of the 2-nitrobenzyl moiety itself may not provide a clue directly relevant to the photocleavage of such N-C bond. Time-resolved IR spectra recorded in a fast-scan mode after pulsed UV irradiation of 1 reveal that such photocleavage occurs at least faster than a few seconds of our instrumental time resolution.

Kinetics of interior loop formation in semiflexible chains

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison with the case are in excellent agreement with explicit Brownian dynamics simulations of wormlike chain (WLC) model. The interior looping times (tauIC) can be greatly altered in the cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then tauIC increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization (tauc) and interior looping (tauIC) times greatly increase at low ionic concentration. Because both tauc and tauIC are determined essentially by the effective persistence length [lp(R)] we computed lp(R) by varying the range of the repulsive interaction between the monomers. For short range interactions lp(R) nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.

Dissecting the Non-specific and Specific Components of the Initial Folding Reaction of Barstar by Multi-site FRET Measurements

Initial polypeptide chain collapse plays a major role in the development of subsequent structure during protein folding, but it has been difficult to elucidate the coupling between its cooperativity and specificity. To better understand this important aspect of protein folding, nine different intramolecular distances in the protein have been measured by fluorescence resonance energy transfer (FRET) in the product(s) of the initial, sub-millisecond collapse reaction during the folding of barstar, under different folding conditions. All nine distances contract in these initial folding products, when the denaturant concentration is reduced. Two of these distances were also measured in peptides corresponding to sequence segments 38-55 and 51-69 of the protein. Surprisingly, both distances do not contract in the peptides which remain fully unfolded when the denaturant concentration is reduced. This suggests that the contraction of at least some segments of the polypeptide chain may be facilitated only by contraction of other segments. In the case of the initial product of folding of the protein, the dependence on denaturant concentration of the relative change in each distance suggests that there are two components to the initial folding reaction. One is a nonspecific component, which appears to be driven by the change in denaturant concentration that is used to initiate refolding. This component corresponds to the collapse of completely unfolded protein (U) to unfolded protein in refolding conditions (U(C)). The extent of nonspecific collapse can be predicted by the response of completely unfolded protein to a change in denaturant concentration. All distances undergo such solvent-induced contraction, but each distance contracts to a different extent. There is also a specific component to initial sub-millisecond folding, in which some distances (but not all) contract more than that predicted by solvent-induced contraction. The observation that only some of the distances undergo contraction over and above solvent-induced contraction, suggest that this specific component is associated with the formation of a specific intermediate (I(E)). FRET efficiency and distance change differently for the different donor-acceptor pairs, with a change in denaturant concentration, indicating that the formation or dissolution of structure in U(C) and I(E) does not happen in a synchronized manner across different regions of the protein molecule. Also, all nine FRET efficiencies and intramolecular distances in the product(s) of sub-ms folding, change continuously with a change in denaturant concentration. Hence, it appears that the transitions from U to U(C) and to I(E) are gradual transformations, and not all-or-none structural transitions. Nevertheless, the product of these gradual transitions, I(E), possesses specific structure.

Conformational equilibration time of unfolded protein chains and the folding speed limit

The speed with which the conformers of unfolded protein chains interconvert is a fundamental question in the study of protein folding. Kinetic evidence is presented here for the time constant for interconversion of disparate unfolded chain conformations of a small globular protein, cytochrome c, in the presence of guanidine hydrochloride denaturant. The axial binding reactions of histidine and methionine residues with the Fe(II) heme cofactor were monitored with time-resolved magnetic circular dichroism spectroscopy after photodissociation of the CO complexes of unfolded protein obtained from horse and tuna and from several histidine mutants of the horse protein. A kinetic model fitting both the reaction rate constants and spectra of the intermediates was used to obtain a quantitative estimate of the conformational diffusion time. The latter parameter was approximated as a first-order time constant for exchange between conformational subensembles presenting either a methionine or a histidine residue to the heme iron for facile binding. The mean diffusional time constant of the wild type and variants was 3 +/- 2 mus, close to the folding "speed limit". The implications of the relatively rapid conformational equilibration time observed are discussed in terms of the energy landscape and classical pathway time regimes of folding, for which the conformational diffusion time can be considered a pivot point.

Nanosecond folding dynamics of a three-stranded beta-sheet

We studied conformational stability and folding kinetics of a three-stranded beta-sheet containing two rigid turns. Static infrared measurements indicate that this beta-sheet undergoes a broad but cooperative thermal unfolding transition with a midpoint at approximately 53 degrees C. Interestingly, time-resolved infrared experiments show that its relaxation kinetics in response to a temperature-jump (T-jump) occur on the nanosecond time scale (e.g., the relaxation time is approximately 140 ns at 35.0 degrees C), thereby suggesting that the conformational relaxation encounters only a small free energy barrier or even proceeds in a downhill manner. Further Langevin dynamics simulations suggest that the observed T-jump relaxation kinetics could be modeled by a conformational diffusion process along a single-well free energy profile, which allowed us to determine the effective diffusion constant and also the roughness of the folding energy landscape.

Alpha-synuclein tertiary contact dynamics

Tertiary contact formation rates in alpha-synuclein, an intrinsically disordered polypeptide implicated in Parkinson's disease, have been determined from measurements of diffusion-limited electron-transfer kinetics between triplet-excited tryptophan:3-nitrotyrosine pairs separated by 10, 12, 55, and 90 residues. Calculations based on a Markovian lattice model developed to describe intrachain diffusion dynamics for a disordered polypeptide give contact quenching rates for various loop sizes ranging from 6 to 48 that are in reasonable agreement with experimentally determined values for small loops (10-20 residues). Contrary to expectations, measured contact rates in alpha-synuclein do not continue to decrease as the loop size increases (>/=35 residues), and substantial deviations from calculated rates are found for the pairs W4-Y94, Y39-W94, and W4-Y136. The contact rates for these large loops indicate much shorter average donor-acceptor separations than expected for a random polymer.

Characterization of Intra-molecular Distances and Site-specific Dynamics in Chemically Unfolded Barstar: Evidence for Denaturant-dependent Non-random Structure

The structure and dynamics of the unfolded form of a protein are expected to play critical roles in determining folding pathways. In this study, the urea and guanidine hydrochloride (GdnHCl)-unfolded forms of the small protein barstar were explored by time-resolved fluorescence techniques. Barstar was labeled specifically with thionitrobenzoate (TNB), by coupling it to the thiol side-chain of a cysteine residue at one of the following positions on the sequence: 14, 25, 40, 42, 62, 82 and 89, in single cysteine-containing mutant proteins. Seven intra-molecular distances (R(DA)) under unfolding conditions were estimated from measurements of time-resolved fluorescence resonance energy transfer between the donor Trp53 and the non-fluorescent acceptor TNB coupled to one of the seven cysteine side-chains. The unfolded protein chain expands with an increase in the concentration of the denaturants. The extent of expansion was found to be non-uniform, with different intra-molecular distances expanding to different extents. In general, shorter distances were found to expand less when compared to longer spans. The extent of expansion was higher in the case of GdnHCl when compared to urea. A comparison of the measured values of R(DA) with those derived from a model based on excluded volume, revealed that while shorter spans showed good agreement, the experimental values of R(DA) of longer spans were smaller when compared to the theoretical values. Sequence-specific flexibility of the polypeptide was determined by time-resolved fluorescence anisotropy decay measurements on acrylodan or 1,5-IAEDANS labeled single cysteine-containing proteins under unfolding conditions. Rotational dynamics derived from these measurements indicated that the level of flexibility increased with increase in the concentration of denaturants and showed a graded increase towards the C-terminal end. Taken together, these results appear to indicate the presence of specific non-random coil structures and show that the deviation from random coil structure is different for the two denaturants.

Tertiary contact formation in alpha-synuclein probed by electron transfer

To explore tertiary contact formation in alpha-synuclein, a natively unfolded protein implicated in Parkinson's disease, we have measured the rates of reaction between a powerful electron donor, the tryptophan (W) triplet excited state, and an acceptor, 3-nitro-tyrosine (Y(NO2)) in six different variants, probing loop sizes between 15 and 132 residues. Electron transfer rates decrease with loop size with the fastest contact time of 140 ns for the N-terminal pair and the slowest of 1.2 mus for the N- to C-terminal pair. Diffusion coefficients ranging from approximately 2 x 10-6 to approximately 10-5 cm2 s-1 were extracted from simultaneous fits of the W to Y(NO2) electron (triplet excited state) and energy transfer (singlet excited state) kinetics.

Diffusion coefficients as a monitor of reaction kinetics of biological molecules

For revealing spectrally silent dynamics in chemical reactions, a new method, the time-dependent diffusion coefficient, is presented. Principles and typical examples of this method, in particular applications to biologically related reactions, are reviewed. The pulsed laser induced transient grating signal of the photo-decomposition reaction of caged ATP showed that the diffusion coefficient increases gradually with time reflecting the molecular size decrease by the dissociation. Hence, this rate should be a direct measurement of the photo-dissociation rate of ATP from the caged state. In an application to a protein folding reaction, the time-development of the diffusion coefficient was observed during the folding reaction. This time dependence was interpreted in terms of the intermolecular interaction change; i.e., conversion from the intermolecular hydrogen bonding to intramolecular one. It was found that the change of the hydrogen bonding network occurred by the two state manner in entire refolding process of cytochrome c. The unique feature of this time-dependent diffusion coefficient method is discussed.

The changing face of glucagon fibrillation: structural polymorphism and conformational imprinting

We have established a time-resolved fluorescence assay to study fibrillation of the 29 residue peptide hormone glucagon under a variety of different conditions in a high-throughput format. Fibrils formed at pH 2.5 differ in fibrillation kinetics, morphology, thioflavin T staining and FTIR/CD spectra depending on salts, glucagon concentration and fibrillation temperature. Apparent fibrillar stability correlates with spectral and kinetic properties; generally, fibrils formed under conditions favourable for rapid fibrillation (ambient temperatures, high glucagon concentration or high salt concentration) appear less thermostable than those formed under more challenging conditions (high temperatures, low glucagon or low salt concentrations). Properties of preformed fibrils used for seeding are inherited in a prion-like manner. Thus, we conclude that the structure of fibrils formed by glucagon is not the result of the global energy minimization, but rather kinetically controlled by solvent conditions and seed-imprinting. Fibrillar polymorphism, which is being reported for an increasing number of proteins, probably reflects that fibrils have not been under evolutionary constraints to retain a single active conformation. Our results highlight the complexity of the fibrillation mechanism of glucagon, since even subtle changes in fibrillation conditions can alter the type of fibrils formed, or result in formation of mixtures of several types of fibrils.

Kinetics of Loop Formation and Breakage in the Denatured State of Iso-1-cytochrome c

The earliest events in protein folding involve the formation of simple loops. Observing the rates of loop closure under denaturing conditions can provide direct insight into the relative probability and sequence determinants for formation of loops of different sizes. The persistence of these initial contacts is equally important for efficient folding, so measurement of rates of loop breakage under denaturing conditions is also essential. We have used stopped-flow and continuous-flow methods to measure the rates of histidine-heme loop formation and breakage in the denatured state of iso-1-cytochrome c (in the presence of 3 M guanidine HCl). The data indicate that the mechanism for forming loops is a two-step process, the first step being the deprotonation of the histidine, and the second step being the binding of the histidine to the heme. This mechanism makes it possible to extract both the rate constants of formation, k(f), and breakage, k(b), of loops from the pH dependence of the observed rate constant, k(obs). To determine the dependence of k(f) and k(b) on loop size, we have carried out kinetic measurements for seven single surface histidine variants of iso-1-cytochrome c. A scaling factor (the dependence of k(f) on log[loop size]) of approximately -1.8 is observed for loop formation, similar to that observed in other systems. The magnitude of k(b) varies from 30 s(-1) to 300 s(-1), indicating that the stability of different loops varies considerably. The implications of the kinetics of loop formation and breakage in the denatured state for the mechanism of protein folding are discussed.

Hydrogen bonding dynamics during protein folding of reduced cytochrome c: temperature and denaturant concentration dependence

Folding dynamics of reduced cytochrome c triggered by the laser-induced reduction method is investigated from a viewpoint of the intermolecular interaction change. Change of the diffusion coefficient of cytochrome c during the refolding process is traced in the time domain from the unfolded value to the native value continuously at various denaturant (guanidine hydrochloride (GdnHCl)) concentrations and temperatures. In the temperature range of 288 K-308 K and GdnHCl concentration range of 2.5 M-4.25 M, the diffusion change can be analyzed well by the two-state model consistently. It was found that the m(double dagger)-value and the activation energy of the transition state from the unfolded state for the hydrogen bonding network change are surprisingly similar to that for the local structural change around the heme group monitored by the fluorescence quenching experiment. This agreement suggests the existence of common or similar fundamental dynamics including water molecular movement to control the refolding dynamics. The nature of the transition state is discussed.

Ultrafast events in the folding of ferrocytochrome c

Laser flash photolysis and stopped-flow methods have been used to study the dynamic events in the micro- to millisecond time bin in the refolding of horse ferrocytochrome c in the full range of guanidine hydrochloride concentration at pH 12.8 (+/-0.1), 22 degrees C. Under the absolute refolding condition, the earliest relaxation time of the unfolded protein chain is less than 1 micros. The chain then undergoes diffusive dynamics-mediated contraction and expansion, in which intrapolypeptide ligands make transient contacts with the heme iron, giving rise to two distinct kinetic phases of approximately 0.4 and approximately 3 micros. Under moderate to absolute refolding conditions, the rates of these processes show little dependence on the denaturant concentration, indicating the absence of structural element in the incipient or the relaxed state. Chain expansion and contraction events continue until the polypeptide finds a stable and supportive transition state. The crossing of this transition barrier, which rate-limits the folding of alkaline ferrocytochrome c, is characterized by a stopped-flow measured time constant of approximately 3 ms in aqueous solvent. Observed kinetics thus implicate no submillisecond folding structure. The folding kinetics is effectively two state in which the unfolded polypeptide first relaxes to an unstructured chain and then crosses over a late rate-limiting barrier to achieve the native conformation. The experimentally observed rates as a function of guanidine hydrochloride concentration have been simulated by numerically calculated microscopic rates of a simple kinetic model that captures the essential features of folding.

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.

Correspondence between anomalous m- and DeltaCp-values in protein folding

Proteins folding according to a classical two-state system characteristically show V-shaped chevron plots. We have previously interpreted the symmetrically curved chevron plot of the protein U1A as denaturant-dependent movements in the position of the transition state ensemble (TSE). S6, a structural analog of U1A, shows a classical V-shaped chevron plot indicative of straightforward two-state kinetics, but the mutant LA30 has a curved unfolding limb, which is most consistent with TSE mobility. The kinetic m-values (derivatives of the rate constants with respect to denaturant concentration) in themselves depend on denaturant concentration. To obtain complementary information about putative mobile TSEs, we have carried out a thermodynamic analysis of the three proteins, based on data for refolding and unfolding over the range 10 degrees C to 70 degrees C. The data at all temperatures can be fitted to two-state model systems. Importantly, for all three proteins the activation heat capacities are, within error, identical to the heat capacities measured in independent experiments under equilibrium conditions. Although the equilibrium heat capacities are essentially invariant with regard to denaturant concentration, the activation heat capacities, similar to the structurally equivalent kinetic m-values, show marked denaturant dependence. Furthermore, the values of beta++ at different denaturant concentrations measured by m-values and by heat capacity values are very similar. These observations are consistent with significant transition state movements within the framework of two-state folding. The basis for TSE movement appears to be enthalpic rather than entropic, suggesting that the binding energy of denaturant-protein interactions is a major determinant of the response of energy landscape contours to changing environments.

Kinetics of intermolecular interaction during protein folding of reduced cytochrome c

Kinetics of intermolecular interaction between reduced cytochrome c (Cyt c) protein and solvent during the protein-refolding process is studied by monitoring the time dependence of apparent diffusion coefficient (D) using the pulsed-laser-induced transient grating technique. The refolding was triggered by photoinduced reduction of unfolded Fe(III) Cyt c in 3.5 M guanidine hydrochloride (GdnHCl) solution and the change in the diffusion coefficient was monitored in time domain. The relationship between D and the protein conformations under equilibrium condition were investigated at various GdnHCl concentrations using a photolabeling reagent. The time dependence of the observed transient grating signal was analyzed using these data and two models: a continuous change model of the intermolecular interaction and a two-state model. It was found that the TG signals in various time ranges can be consistently reproduced well by the two-state model. The dynamics of D is expressed well by a single exponential function with a rate constant of 22 +/- 7 s(-1) in a whole time range. The folding process of Cyt c is discussed based on these observations.

Primary and secondary structure dependence of peptide flexibility assessed by fluorescence-based measurement of end-to-end collision rates

The intrachain fluorescence quenching of the fluorophore 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) is measured in short peptide fragments, namely the two strands and the turn of the N-terminal beta-hairpin of ubiquitin. The investigated peptides adopt a random-coil conformation in aqueous solution according to CD and NMR experiments. The combination of quenchers with different quenching efficiencies, namely tryptophan and tyrosine, allows the extrapolation of the rate constants for end-to-end collision rates as well as the dissociation of the end-to-end encounter complex. The measured activation energies for fluorescence quenching demonstrate that the end-to-end collision process in peptides is partially controlled by internal friction within the backbone, while measurements in solvents of different viscosities (H2O, D2O, and 7.0 M guanidinium chloride) suggest that solvent friction is an additional important factor in determining the collision rate. The extrapolated end-to-end collision rates, which are only slightly larger than the experimental rates for the DBO/Trp probe/quencher system, provide a measure of the conformational flexibility of the peptide backbone. The chain flexibility is found to be strongly dependent on the type of secondary structure that the peptides represent. The collision rates for peptides derived from the beta-strand motifs (ca. 1 x 10(7) s(-1)) are ca. 4 times slower than that derived from the beta-turn. The results provide further support for the hypothesis that chain flexibility is an important factor in the preorganization of protein fragments during protein folding. Mutations to the beta-turn peptide show that subtle sequence changes strongly affect the flexibility of peptides as well. The protonation and charge status of the peptides, however, are shown to have no significant effect on the flexibility of the investigated peptides. The meaning and definition of end-to-end collision rates in the context of protein folding are critically discussed.

The kinetics of conformational fluctuations in an unfolded protein measured by fluorescence methods

The simplest dynamic model for an unfolded protein is a statistical coil that continually undergoes substantial conformational fluctuations. A growing number of studies indicate that the unfolded protein is not a simple random coil but rather forms transient structures. We have directly measured the rate of conformational fluctuations of unfolded intestinal fatty acid binding protein (131 aa, 15 kDa) by using fluorescence self-quenching in combination with fluorescence correlation spectroscopy. The conformational fluctuations in this state have an apparent relaxation time, tauR, of 1.6 microsec in 3 M guanidine-HCl at pH 7 and 20 degrees C. The value of tauR increases with increasing solution viscosity, suggesting a diffusive process. In the molten globule state at pH 2, tauR is 2.5 microsec, increasing further with the formation of salt-induced secondary structure. These measurements, which should be widely applicable to other systems, can provide important information about the still incompletely understood conformational properties of unfolded proteins and the mechanism of protein folding.

Many faces of the unfolded state: conformational heterogeneity in denatured yeast cytochrome C

We have measured fluorescence energy-transfer (FET) kinetics from a dansyl fluorophore (Dns) introduced by derivatization of a Cys side-chain to the Fe(III) heme covalently attached to unfolded yeast iso-1 cytochrome c (cyt). To gain a global picture of the unfolded state, we examined variants with the fluorophore attached on three different helices (K4C, E66C, K99C) and in three different loops (H39C, D50C, L85C). Analysis of the FET kinetics data gave distributions of distances between the fluorescent donor and acceptor; these distributions demonstrate that the guanidine hydrochloride (GuHCl)-denatured polypeptide ensemble is not a simple random coil. Although misligation imposes some constraints, it is not the only source of structural complexity in the unfolded protein. Our FET kinetics data reveal a high degree of heterogeneity in the unfolded ensemble of cytochrome c. We detect relatively large populations of compact structures in unfolded Dns(C50)cyt, Dns(C39)cyt, and Dns(C66)cyt. These structures likely play a role in forming a hydrophobic core during the folding process.

The folding of spectrin domains II: phi-value analysis of R16

Studies on the folding of helical proteins have shown a wide range of different mechanisms and highlighted the importance of helical propensity as a factor in determining folding mechanism. Here, we contribute to this interesting field with the protein engineering phi-value analysis of the 16th domain of chicken brain alpha-spectrin, R16. The fortuitous curvature seen in the unfolding arm of the chevron plot allows us to investigate both early and late events in folding. R16 is the first two-state helical protein for which this has been possible.

Internal friction controls the speed of protein folding from a compact configuration

Several studies have found millisecond protein folding reactions to be controlled by the viscosity of the solvent: Reducing the viscosity allows folding to accelerate. In the limit of very low solvent viscosity, however, one expects a different behavior. Internal interactions, occurring within the solvent-excluded interior of a compact molecule, should impose a solvent-independent upper limit to folding speed once the bulk diffusional motions become sufficiently rapid. Why has this not been observed? We have studied the effect of solvent viscosity on the folding of cytochrome c from a highly compact, late-stage intermediate configuration. Although the folding rate accelerates as the viscosity declines, it tends toward a finite limiting value approximately 10(5) s(-1) as the viscosity tends toward zero. This limiting rate is independent of the cosolutes used to adjust solvent friction. Therefore, interactions within the interior of a compact denatured polypeptide can limit the folding rate, but the limiting time scale is very fast. It is only observable when the solvent-controlled stages of folding are exceedingly rapid or else absent. Interestingly, we find a very strong temperature dependence in these "internal friction"-controlled dynamics, indicating a large energy scale for the interactions that govern reconfiguration within compact, near-native states of a protein.

Zinc-porphyrin Solvation in Folded and Unfolded States of Zn-cytochrome c

After a brief review of the use of photochemical triggers and heme metal substitution to probe the folding dynamics of cytochrome c, we present new results on the photophysics and photochemistry of folded and unfolded states of the zinc-substituted protein (Zn-cyt c). Our measurements of Zn-cyt c triplet state decay kinetics reveal a systematic isotope effect on lifetimes: the decay in the folded protein (tau(H)2(O) approximately 10 ms) is only modestly affected by isotopically substituted buffers (k(H)2(O)/k(D)2(O) = 1.2), whereas a reduced triplet lifetime (approximately 1.3 ms) and greater isotope effect (1.4) were found for the chemically denatured, fully unfolded protein. The shortest lifetime (0.1-0.4 ms) and greatest isotope effect (1.5) were found for a fully exposed model compound, zinc-substituted N-acetyl-microperoxidase-8 (ZnAcMP8), implying that the unfolded protein provides some protection to the Zn-porphyrin group even under fully denaturing conditions. Further evidence for partial structure in unfolded Zn-cyt c comes from bimolecular quenching experiments using Ru(NH(3))(6)(3+) as an external Zn-porphyrin triplet state quencher. In the presence of quencher, partially unfolded protein at midpoint guanidinium chloride (GdmCl) and urea concentrations exhibits biphasic triplet decay kinetics, a fast component corresponding to an extended, solvent-exposed state (6.6 x 10(8) M(-1) s(-1) in GdmCl, 6.3 x 10(8) M(-1) s(-1) in urea) and a slow component attributable to a compact, relatively solvent-inaccessible, state (5.9 x 10(7) M(-1) s(-1) in GdmCl, 8.6 x 10(6) M(-1) s(-1) in urea). The variation in Zn-porphyrin solvation for the compact states in the two denaturants reveals that the cofactor in the partially unfolded protein is better protected in urea solutions.

Thermodynamics of heat activation of single capsaicin ion channels VR1

Temperature affects functions of all ion channels, but few of them can be gated directly. The vanilloid receptor VR1 provides one exception. As a pain receptor, it is activated by heat >42 degrees C in addition to other noxious stimuli, e.g. acids and vanilloids. Although it is understood how ligand- and voltage-gated channels might detect their stimuli, little is known on how heat could be sensed and activate a channel. In this study, we characterized the heat-induced single-channel activity of VR1, in an attempt to localize the temperature-dependent components involved in the activation of the channel. At <42 degrees C, openings were few and brief. Raising the ambient temperature rapidly increased the frequency of openings. Despite the large temperature coefficient of the apparent activity (Q(10) approximately 27), the unitary current, the open dwell-times, and the intraburst closures were all only weakly temperature dependent (Q(10) < 2). Instead, heat had a localized effect on the reduction of long closures between bursts (Q(10) approximately 7) and the elongation of burst durations (Q(10) approximately 32). Both membrane lipids and solution ionic strength affected the temperature threshold of the activation, but neither diminished the response. The thermodynamic basis of heat activation is discussed, to elucidate what makes a thermal-sensitive channel unique.

Multiple probes reveal a native-like intermediate during low-temperature refolding of ubiquitin

We investigate the refolding of ubiquitin Phe45Trp/Ile61Ala (Ub(*)I61A) in a low-temperature, high-viscosity buffer, where folding is slowed so that apparent two-state and three-state mechanisms are readily distinguishable. Ub(*)I61A forms a compact ensemble rapidly (as judged from stopped-flow, small-angle X-ray scattering) with a secondary structure signature similar to that of the native state (as judged from stopped-flow circular dichroism from 215 nm to 250 nm), but the fluorescence signature still resembles the guanidinium-denatured state. The compact ensemble forms over a range of solvent and temperature conditions. The native fluorescence signature, which requires the tryptophan residue to be packed tightly, is acquired at least 500 times more slowly. Molecular dynamics simulations at 495 K show no contraction of the backbone in ethylene glycol buffer compared to pure aqueous buffer, and no significant effect on the local backbone structure of the unfolded protein. Only at higher simulation temperature does a backbone contraction appear. Thus, it appears unlikely that the aqueous ethylene glycol buffer fundamentally changes the folding mechanism of ubiquitin. We suggest that ubiquitin forms a compact ensemble with native-like secondary structure, but without tight packing, long before the native state.

A limiting speed for protein folding at low solvent viscosity

Because protein folding dynamics are heavily overdamped, Kramers theory predicts the rate of folding to scale inversely with the reaction friction, which is usually interpreted to mean the solvent viscosity. This does not mean, however, that the speed of folding can increase without limit as solvent viscosity decreases. We show that, in a sufficiently fast-folding protein, the folding speed approaches a finite limit at low solvent viscosity, indicating a reaction controlled by internal friction.

Kinetics of end-to-end collision in short single-stranded nucleic acids

A novel fluorescence-based method, which entails contact quenching of the long-lived fluorescent state of 2,3-diazabicyclo[2.2.2]-oct-2-ene (DBO), was employed to measure the kinetics of end-to-end collision in short single-stranded oligodeoxyribonucleotides of the type 5'-DBO-(X)n-dG with X = dA, dC, dT, or dU and n = 2 or 4. The fluorophore was covalently attached to the 5' end and dG was introduced as an efficient intrinsic quencher at the 3' terminus. The end-to-end collision rates, which can be directly related to the efficiency of intramolecular fluorescence quenching, ranged from 0.1 to 9.0 x 10(6) s(-1). They were strongly dependent on the strand length, the base sequence, as well as the temperature. Oligonucleotides containing dA in the backbone displayed much slower collision rates and significantly higher positive activation energies than strands composed of pyrimidine bases, suggesting a higher intrinsic rigidity of oligoadenylate. Comparison of the measured collision rates in short single-stranded oligodeoxyribonucleotides with the previously reported kinetics of hairpin formation indicates that the intramolecular collision is significantly faster than the nucleation step of hairpin closing. This is consistent with the configurational diffusion model suggested by Ansari et al. (Ansari, A.; Kuznetsov, S. V.; Shen, Y. Proc.Natl. Acad. Sci. USA 2001, 98, 7771-7776), in which the formation of misfolded loops is thought to slow hairpin formation.

Cytochrome c folding dynamics

Understanding how denatured polypeptides self-assemble into correctly folded native protein structures is one of the grand challenges of 21st century science. Cytochrome c refolding has been exhaustively studied with a vast array of triggers and spectroscopic probes. Within the past year, atomically detailed dynamics simulations of this process have appeared as well. This wealth of data provides insights into the conformations and dynamics of diverse parts of the polypeptide at many stages in the refolding reaction. The combination of innovative experiments and powerful computational methods promises to produce a model that reconciles many disparate observations of cytochrome c folding.

Protein dynamics and the immunological evolution of molecular recognition

While it is accepted that protein flexibility plays a role in protein folding, catalysis, and molecular recognition, few techniques are capable of the rigorous measurement of protein motions required to quantify flexibility. Three-pulse photon echo shift spectroscopy can be used to measure the time scale of protein motions, and we have used this technique, along with steady-state spectroscopy and binding and structural data, to examine the immunological evolution of protein flexibility in an anti-fluorescein antibody. Two light chain somatic mutations increase affinity for fluorescein by 12-fold but also significantly affect flexibility. Specifically, a rigidification of the protein is seen in each of three observable motions; two slower motions undergo decreased amplitudes of displacement, by 3- and 20-fold, respectively, in response to an applied force, and the distribution associated with the amplitude of a faster motion is narrowed upon somatic mutation. The somatic mutations appear to rigidify the antibody-fluorescein complex by more strongly anchoring fluorescein to the protein and by more tightly packing the complex. The data demonstrate that in addition to affinity, antibody dynamics are systematically manipulated during affinity maturation, and they imply that the evolution of protein flexibility may be a central component of the immune response. The results also reflect the type of protein rigidification that may be important for other biological interactions, such as protein-protein, protein-ligand or protein-drug, and enzyme-substrate recognition.

Polymer Models of Protein Stability, Folding, and Interactions

The unfolded state and flexible linkers in the folded structure play essential roles in protein stability and folding and protein-protein interactions. Intrinsic to these roles is the fact that unfolded proteins and flexible linkers sample many different conformations. Polymer models may capture this and complement experiments in elucidating the contributions of the unfolded state and flexible linkers. Here I review what can be predicted from these models and how well these predictions match experiments. For example, Gaussian chain models give quantitatively reasonable predictions of the effects of residual charge-charge interactions in the unfolded state and qualitatively reasonable results for the effects of spatial confinement and macromolecular crowding on protein stability. A wormlike chain model has met with success in quantifying the effects of flexible linkers in binding affinity enhancement and in regulatory switches. In future developments, more realistic models may emerge from molecular dynamics simulations, and these models will guide experiments to advance our understanding of the unfolded state and flexible linkers.

Intramolecular singlet–singlet energy transfer in antenna-substituted azoalkanes

Two novel azoalkane bichromophores and related model compounds have been synthesised and photophysically characterised. Dimethylphenylsiloxy (DPSO) or dimethylnaphthylsiloxy (DNSO) serve as aromatic donor groups (antenna) and the azoalkane 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) as the acceptor. The UV spectral window of DBO (250-300 nm) allows selective excitation of the donor. Intramolecular singlet-singlet energy transfer to DBO is highly efficient and proceeds with quantum yields of 0.76 with DPSO and 0.99 with DNSO. The photophysical and spectral properties of the bichromophoric systems suggest that energy transfer occurs through diffusional approach of the donor and acceptor within a van der Waals contact at which the exchange mechanism is presumed to dominate. Furthermore, akin to the behaviour of electron-transfer systems in the Marcus inverted region, a rate of energy transfer 2.5 times slower was observed for the system with the more favourable energetics, i.e. singlet-singlet energy transfer from DPSO proceeded slower than from DNSO, although the process is more exergonic for DPSO (-142 kJ mol(-1) for DPSO versus-67 kJ mol(-1) for DNSO).