Time-resolved Small-angle X-ray Scattering Investigation of the Folding Dynamics of Heme Oxygenase: Implication of the Scaling Relationship for the Submillisecond Intermediates of Protein Folding

NMR and Single-Molecule FRET Insights into Fast Protein Motions and Their Relation to Function

Proteins often undergo large-scale conformational transitions, in which secondary and tertiary structure elements (loops, helices, and domains) change their structures or their positions with respect to each other. Simple considerations suggest that such dynamics should be relatively fast, but the functional cycles of many proteins are often relatively slow. Sophisticated experimental methods are starting to tackle this dichotomy and shed light on the contribution of large-scale conformational dynamics to protein function. In this review, we focus on the contribution of single-molecule Förster resonance energy transfer and nuclear magnetic resonance (NMR) spectroscopies to the study of conformational dynamics. We briefly describe the state of the art in each of these techniques and then point out their similarities and differences, as well as the relative strengths and weaknesses of each. Several case studies, in which the connection between fast conformational dynamics and slower function has been demonstrated, are then introduced and discussed. These examples include both enzymes and large protein machines, some of which have been studied by both NMR and fluorescence spectroscopies.

An innovative data processing method for studying nanoparticle formation in droplet microfluidics using X-rays scattering

X-ray scattering techniques provide a powerful means of characterizing the formation of nanoparticles in solution. Coupling these techniques to segmented-flow microfluidic devices that offer well-defined environments gives access to in situ time-resolved analysis, excellent reproducibility, and eliminates potential radiation damage. However, analysis of the resulting datasets can be extremely time-consuming, where these comprise frames corresponding to the droplets alone, the continuous phase alone, and to both at their interface. We here describe a robust, low-cost, and versatile droplet microfluidics device and use it to study the formation of magnetite nanoparticles with simultaneous synchrotron SAXS and WAXS. Lateral outlet capillaries facilitate the X-ray analysis and reaction times of between a few seconds and minutes can be accommodated. A two-step data processing method is then described that exploits the unique WAXS signatures of the droplets, continuous phase, and interfacial region to identify the frames corresponding to the droplets. These are then sorted, and the background scattering is subtracted using an automated frame-by-frame approach, allowing the signal from the nanoparticles to be isolated from the raw data. Modeling these data gives quantitative information about the evolution of the sizes and structures of the nanoparticles, in agreement with TEM observations. This versatile platform can be readily employed to study a wide range of dynamic processes in heterogeneous systems.

Bundling Process of Citrulline Polypeptides upon UCST-Type Phase Separation

Ureido-modified poly(l-citrulline) (l-ornithine-co-l-citrulline denoted by PlOC) shows UCST-type phase separation behavior even under physiologically relevant conditions, which forms an α-helix structure above its phase separation temperature (T_p) but transforms into a solid-like aggregation composed of regular hexagonal packed cylinders below the T_p. This morphological transformation is characteristic of the phase separation behavior, but the mechanism behind it has remained incompletely understood. Here, we studied the phase separation behavior using small-angle X-ray scattering (SAXS) measurements. To analyze the SAXS data, we employed the modified unified model proposed previously, which decomposes the scattering profile into each structural element, such as the α-helices and their aggregation formed via hydrogen-bonding interactions between the ureido groups. The aggregation level is dependent on the temperature (T) and grouped into three classes: (1) mass-fractal aggregation composed of the α-helix (T > T_p), (2) spherical aggregation composed of the hexagonal packed cylinder (T < T_p), and (3) micro-order agglomeration formed by mutual fusion of the spherical aggregation, which appears as a solid-like aggregation. The SAXS analysis suggested that the transformation from the dispersed state as the α-helix to the agglomeration containing hierarchical structures occurs in a stepwise manner when the temperature falls below the T_p, which might also be transition behavior similar to the process of protein folding through folding intermediates.

Conformational Properties Relevant to the Amyloidogenicity of β2-Microglobulin Analyzed Using Pressure- and Salt-Dependent Chemical Shift Data

β₂-Microglobulin (β₂m) is associated with dialysis-related amyloidosis. In vitro experiments have shown that β₂m forms amyloid fibrils at acidic pHs in the presence of moderate concentrations of salt. Previous studies suggested that acid-denatured β₂m has a hydrophobic residual structure, and the exposure of the hydrophobic residues enhances the association with seeds or other β₂m monomers. However, the nature of the residual structure relevant to its amyloidogenicity remains to be investigated. To understand the structural properties of acid-denatured β₂m and the role of salt, we investigated pressure- and salt concentration-dependent conformational changes by nuclear magnetic resonance spectroscopy and other methods. Here, pressure was utilized to characterize the conformers existing in a conformational equilibrium at ambient pressure. The obtained pressure- and salt concentration-dependent chemical shift data were simultaneously subjected to principal component analysis to characterize individual conformational change events. Unexpectedly, the addition of salt induced an expansion of the β₂m molecule, which likely resulted from the exclusion of the N-terminal region from the hydrophobic cluster region. The dissected chemical shift patterns for the salt-induced conformational change and other experimental data indicated that this conformational change caused a rigidification in the intrinsic hydrophobic cluster, leading to the observed amyloidogenicity.

Cyclic olefin copolymer as an X-ray compatible material for microfluidic devices

The combination of microfluidics and X-ray methods attracts a lot of attention from researchers as it brings together the high controllability of microfluidic sample environments and the small length scales probed by X-rays. In particular, the fields of biophysics and biology have benefited enormously from such approaches. We introduce a straightforward fabrication method for X-ray compatible microfluidic devices made solely from cyclic olefin copolymers. We benchmark the performance of the devices against other devices including more commonly used Kapton windows and obtain data of equal quality using small angle X-ray scattering. An advantage of the devices presented here is that no gluing between interfaces is necessary, rendering the production very reliable. As a biophysical application, we investigate the early time points of the assembly of vimentin intermediate filament proteins into higher-order structures. This weakly scattering protein system leads to high quality data in the new devices, thus opening up the way for numerous future applications.

Simultaneous Determination of Two Subdomain Folding Rates Using the "Transfer-Quench" Method

The investigation of the mechanism of protein folding is complicated by the context dependence of the rates of intramolecular contact formation. Methods based on site-specific labeling and ultrafast spectroscopic detection of fluorescence signals were developed for monitoring the rates of individual subdomain folding transitions in situ, in the context of the whole molecule. However, each site-specific labeling modification might affect rates of folding of near-neighbor structural elements, and thus limit the ability to resolve fine differences in rates of folding of these elements. Therefore, it is highly desirable to be able to study the rates of folding of two or more neighboring subdomain structures using a single mutant to facilitate resolution of the order and interdependence of such steps. Here, we report the development of the "Transfer-Quench" method for measuring the rate of formation of two structural elements using a single triple-labeled mutant. This method is based on Förster resonance energy transfer combined with fluorescence quenching. We placed the donor and acceptor at the loop ends, and a quencher at an α-helical element involved in the node forming the loop. The folding of the triple-labeled mutant is monitored by the acceptor emission. The formation of nonlocal contact (loop closure) increases the time-dependent acceptor emission, while the closure of the labeled helix turn reduces this emission. The method was applied in a study of the folding mechanism of the common model protein, the B domain of staphylococcal protein A. Only natural amino acids were used as probes, and thus possible structural perturbations were minimized. Tyr and Trp residues served as donor and acceptor at the ends of a long loop between helices I and II, and a Cys residue as a quencher for the acceptor. We found that the closure of the loop (segment 14-33) occurs with the same rate constant as the nucleation of helix HII (segment 33-29), in line with the nucleation-condensation model.

Recent advances in X-ray compatible microfluidics for applications in soft materials and life sciences

The increasingly narrow and brilliant beams at X-ray facilities reduce the requirements for both sample volume and data acquisition time. This creates new possibilities for the types and number of sample conditions that can be examined but simultaneously increases the demands in terms of sample preparation. Microfluidic-based sample preparation techniques have emerged as elegant alternatives that can be integrated directly into the experimental X-ray setup remedying several shortcomings of more traditional methods. We review the use of microfluidic devices in conjunction with X-ray measurements at synchrotron facilities in the context of 1) mapping large parameter spaces, 2) performing time resolved studies of mixing-induced kinetics, and 3) manipulating/processing samples in ways which are more demanding or not accessible on the macroscale. The review covers the past 15 years and focuses on applications where synchrotron data collection is performed in situ, i.e. directly on the microfluidic platform or on a sample jet from the microfluidic device. Considerations such as the choice of materials and microfluidic designs are addressed. The combination of microfluidic devices and measurements at large scale X-ray facilities is still emerging and far from mature, but it definitely offers an exciting array of new possibilities.

Consistent View of Polypeptide Chain Expansion in Chemical Denaturants from Multiple Experimental Methods

There has been a long-standing controversy regarding the effect of chemical denaturants on the dimensions of unfolded and intrinsically disordered proteins: A wide range of experimental techniques suggest that polypeptide chains expand with increasing denaturant concentration, but several studies using small-angle X-ray scattering (SAXS) have reported no such increase of the radius of gyration (Rg). This inconsistency challenges our current understanding of the mechanism of chemical denaturants, which are widely employed to investigate protein folding and stability. Here, we use a combination of single-molecule Förster resonance energy transfer (FRET), SAXS, dynamic light scattering (DLS), and two-focus fluorescence correlation spectroscopy (2f-FCS) to characterize the denaturant dependence of the unfolded state of the spectrin domain R17 and the intrinsically disordered protein ACTR in two different denaturants. Standard analysis of the primary data clearly indicates an expansion of the unfolded state with increasing denaturant concentration irrespective of the protein, denaturant, or experimental method used. This is the first case in which SAXS and FRET have yielded even qualitatively consistent results regarding expansion in denaturant when applied to the same proteins. To more directly illustrate this self-consistency, we used both SAXS and FRET data in a Bayesian procedure to refine structural ensembles representative of the observed unfolded state. This analysis demonstrates that both of these experimental probes are compatible with a common ensemble of protein configurations for each denaturant concentration. Furthermore, the resulting ensembles reproduce the trend of increasing hydrodynamic radius with denaturant concentration obtained by 2f-FCS and DLS. We were thus able to reconcile the results from all four experimental techniques quantitatively, to obtain a comprehensive structural picture of denaturant-induced unfolded state expansion, and to identify the most likely sources of earlier discrepancies.

Statistical Mechanical Model for pH-Induced Protein Folding: Application to Apomyoglobin

Despite the major role of pH in protein folding and stability, a quantitative understanding of the pH-induced protein folding mechanism remains elusive. Two conventional models, the Monod-Wyman-Changeux and Linderstrøm-Lang smeared charge models, respectively, have been used to analyze the formation/disruption of specific native structures and fluctuating non-native states. However, there are only a few models that can represent the overall kinetic events of folding/unfolding independent of the properties of relevant molecular species, which has hampered the efforts to systematically analyze pH-induced folding. Here, we constructed a statistical mechanical model that incorporates the protonation mechanism of conventional models along with a combined manual search and least-squares fitting procedure, which was used to investigate the folding of horse apomyoglobin over a wide pH range (2.2-6.7), with a time window ranging from ∼40 μs to ∼100 s, using continuous-/stopped-flow fluorescence at 8 °C. Quantitative analysis assuming a five-state sequential scheme indicated that (1) pH-induced folding/unfolding is represented by both specific binding and Coulombic interactions; (2) kinetic folding/unfolding intermediates share kinetic mechanisms with the equilibrium intermediate, indicating their equivalence; and (3) native-like properties are acquired successively during folding by intermediates and in transition states. This model could also be applied to a variety of association/dissociation processes.

Microsecond Rearrangements of Hydrophobic Clusters in an Initially Collapsed Globule Prime Structure Formation during the Folding of a Small Protein

Determining how polypeptide chain collapse initiates structure formation during protein folding is a long standing goal. It has been challenging to characterize experimentally the dynamics of the polypeptide chain, which lead to the formation of a compact kinetic molten globule (MG) in about a millisecond. In this study, the sub-millisecond events that occur early during the folding of monellin from the guanidine hydrochloride-unfolded state have been characterized using multiple fluorescence and fluorescence resonance energy transfer probes. The kinetic MG is shown to form in a noncooperative manner from the unfolded (U) state as a result of at least three different processes happening during the first millisecond of folding. Initial chain compaction completes within the first 37μs, and further compaction occurs only after structure formation commences at a few milliseconds of folding. The transient nonnative and native-like hydrophobic clusters with side chains of certain residues buried form during the initial chain collapse and the nonnative clusters quickly disassemble. Subsequently, partial chain desolvation occurs, leading to the formation of a kinetic MG. The initial chain compaction and subsequent chain rearrangement appear to be barrierless processes. The two structural rearrangements within the collapsed globule appear to prime the protein for the actual folding transition.

Single-Molecule FRET Spectroscopy and the Polymer Physics of Unfolded and Intrinsically Disordered Proteins

The properties of unfolded proteins have long been of interest because of their importance to the protein folding process. Recently, the surprising prevalence of unstructured regions or entirely disordered proteins under physiological conditions has led to the realization that such intrinsically disordered proteins can be functional even in the absence of a folded structure. However, owing to their broad conformational distributions, many of the properties of unstructured proteins are difficult to describe with the established concepts of structural biology. We have thus seen a reemergence of polymer physics as a versatile framework for understanding their structure and dynamics. An important driving force for these developments has been single-molecule spectroscopy, as it allows structural heterogeneity, intramolecular distance distributions, and dynamics to be quantified over a wide range of timescales and solution conditions. Polymer concepts provide an important basis for relating the physical properties of unstructured proteins to folding and function.

Emerging applications of small angle solution scattering in structural biology

Small angle solution X-ray and neutron scattering recently resurfaced as powerful tools to address an array of biological problems including folding, intrinsic disorder, conformational transitions, macromolecular crowding, and self or hetero-assembling of biomacromolecules. In addition, small angle solution scattering complements crystallography, nuclear magnetic resonance spectroscopy, and other structural methods to aid in the structure determinations of multidomain or multicomponent proteins or nucleoprotein assemblies. Neutron scattering with hydrogen/deuterium contrast variation, or X-ray scattering with sucrose contrast variation to a certain extent, is a convenient tool for characterizing the organizations of two-component systems such as a nucleoprotein or a lipid-protein assembly. Time-resolved small and wide-angle solution scattering to study biological processes in real time, and the use of localized heavy-atom labeling and anomalous solution scattering for applications as FRET-like molecular rulers, are amongst promising newer developments. Despite the challenges in data analysis and interpretation, these X-ray/neutron solution scattering based approaches hold great promise for understanding a wide variety of complex processes prevalent in the biological milieu.

Sequence and temperature dependence of the end-to-end collision dynamics of single-stranded DNA

Intramolecular collision dynamics play an essential role in biomolecular folding and function and, increasingly, in the performance of biomimetic technologies. To date, however, the quantitative studies of dynamics of single-stranded nucleic acids have been limited. Thus motivated, here we investigate the sequence composition, chain-length, viscosity, and temperature dependencies of the end-to-end collision dynamics of single-stranded DNAs. We find that both the absolute collision rate and the temperature dependencies of these dynamics are base-composition dependent, suggesting that base stacking interactions are a significant contributor. For example, whereas the end-to-end collision dynamics of poly-thymine exhibit simple, linear Arrhenius behavior, the behavior of longer poly-adenine constructs is more complicated. Specifically, 20- and 25-adenine constructs exhibit biphasic temperature dependencies, with their temperature dependences becoming effectively indistinguishable from that of poly-thymine above 335 K for 20-adenines and 328 K for 25-adenines. The differing Arrhenius behaviors of poly-thymine and poly-adenine and the chain-length dependence of the temperature at which poly-adenine crosses over to behave like poly-thymine can be explained by a barrier friction mechanism in which, at low temperatures, the energy barrier for the local rearrangement of poly-adenine becomes the dominant contributor to its end-to-end collision dynamics.

Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy

The dimensions of unfolded and intrinsically disordered proteins are highly dependent on their amino acid composition and solution conditions, especially salt and denaturant concentration. However, the quantitative implications of this behavior have remained unclear, largely because the effective theta-state, the central reference point for the underlying polymer collapse transition, has eluded experimental determination. Here, we used single-molecule fluorescence spectroscopy and two-focus correlation spectroscopy to determine the theta points for six different proteins. While the scaling exponents of all proteins converge to 0.62 ± 0.03 at high denaturant concentrations, as expected for a polymer in good solvent, the scaling regime in water strongly depends on sequence composition. The resulting average scaling exponent of 0.46 ± 0.05 for the four foldable protein sequences in our study suggests that the aqueous cellular milieu is close to effective theta conditions for unfolded proteins. In contrast, two intrinsically disordered proteins do not reach the Θ-point under any of our solvent conditions, which may reflect the optimization of their expanded state for the interactions with cellular partners. Sequence analyses based on our results imply that foldable sequences with more compact unfolded states are a more recent result of protein evolution.

Integrative structural modeling with small angle X-ray scattering profiles

Recent technological advances enabled high-throughput collection of Small Angle X-ray Scattering (SAXS) profiles of biological macromolecules. Thus, computational methods for integrating SAXS profiles into structural modeling are needed more than ever. Here, we review specifically the use of SAXS profiles for the structural modeling of proteins, nucleic acids, and their complexes. First, the approaches for computing theoretical SAXS profiles from structures are presented. Second, computational methods for predicting protein structures, dynamics of proteins in solution, and assembly structures are covered. Third, we discuss the use of SAXS profiles in integrative structure modeling approaches that depend simultaneously on several data types.

Small-angle X-ray scattering and single-molecule FRET spectroscopy produce highly divergent views of the low-denaturant unfolded state

The results of more than a dozen single-molecule Förster resonance energy transfer (smFRET) experiments suggest that chemically unfolded polypeptides invariably collapse from an expanded random coil to more compact dimensions as the denaturant concentration is reduced. In sharp contrast, small-angle X-ray scattering (SAXS) studies suggest that, at least for single-domain proteins at non-zero denaturant concentrations, such compaction may be rare. Here, we explore this discrepancy by studying protein L, a protein previously studied by SAXS (at 5 °C), which suggested fixed unfolded-state dimensions from 1.4 to 5 M guanidine hydrochloride (GuHCl), and by smFRET (at 25 °C), which suggested that, in contrast, the chain contracts by 15-30% over this same denaturant range. Repeating the earlier SAXS study under the same conditions employed in the smFRET studies, we observe little, if any, evidence that the unfolded state of protein L contracts as the concentration of GuHCl is reduced. For example, scattering profiles (and thus the shape and dimensions) collected within ∼4 ms after dilution to as low as 0.67 M GuHCl are effectively indistinguishable from those observed at equilibrium at higher denaturant. Our results thus argue that the disagreement between SAXS and smFRET is statistically significant and that the experimental evidence in favor of obligate polypeptide collapse at low denaturant cannot be considered conclusive yet.

A comparative study of the second-order hydrophobic moments for globular proteins: the consensus scale of hydrophobicity and the CHARMM partial atomic charges

In this paper, the second-order hydrophobic moment for fifteen globular proteins in 150 nonhomologous protein chains was performed in a comparative study involving two sets of hydrophobicity: one selected from the consensus scale and the other derived from the CHARMM partial atomic charges. These proteins were divided into three groups, based on their number of residues (N) and the asphericity (δ). Proteins in Group I were spherical and those in Groups II and III were prolate. The size of the proteins is represented by the mean radius of gyration (R_g ), which follows the Flory scaling law, R_g ∝ N^ν. The mean value of v was 0.35, which is similar to a polymer chain in a poor solvent. The spatial distributions of the second-order moment for each of the proteins, obtained from the two sets of hydrophobicity, were compared using the Pearson correlation coefficient; the results reveal that there is a strong correlation between the two data sets for each protein structure when the CHARMM partial atomic charges, |q_i| ≥ 0.3, assigned for polar atoms, are used. The locations at which these distributions vanish and approach a negative value are at approximately 50% of the percentage of solvent accessibility, indicating that there is a transition point from hydrophobic interior to hydrophilic exterior in the proteins. This may suggest that there is a position for the proteins to determine the residues at exposed sites beyond this range.

How, when and why proteins collapse: the relation to folding

Unfolded proteins under strongly denaturing conditions are highly expanded. However, when the conditions are more close to native, an unfolded protein may collapse to a compact globular structure distinct from the folded state. This transition is akin to the coil-globule transition of homopolymers. Single-molecule FRET experiments have been particularly conducive in revealing the collapsed state under conditions of coexistence with the folded state. The collapse can be even more readily observed in natively unfolded proteins. Time-resolved studies, using FRET and small-angle scattering, have shown that the collapse transition is a very fast event, probably occurring on the submicrosecond time scale. The forces driving collapse are likely to involve both hydrophobic and backbone interactions. The loss of configurational entropy during collapse makes the unfolded state less stable compared to the folded state, thus facilitating folding.

Residual structure in unfolded proteins

The denatured state ensemble (DSE) of unfolded proteins, once considered to be well-modeled by an energetically featureless random coil, is now well-known to contain flickering elements of residual structure. The position and nature of DSE residual structure may provide clues toward deciphering the protein folding code. This review focuses on recent advances in our understanding of the nature of DSE collapse under folding conditions, the quantification of the stability of residual structure in the DSE, the determination of the location and types of residues involved in thermodynamically significant residual structure and advances in detection of long-range interactions in the DSE.

Automated microfluidic sample-preparation platform for high-throughput structural investigation of proteins by small-angle X-ray scattering

A new microfluidic sample-preparation system is presented for the structural investigation of proteins using small-angle X-ray scattering (SAXS) at synchrotrons. The system includes hardware and software features for precise fluidic control, sample mixing by diffusion, automated X-ray exposure control, UV absorbance measurements and automated data analysis. As little as 15 µl of sample is required to perform a complete analysis cycle, including sample mixing, SAXS measurement, continuous UV absorbance measurements, and cleaning of the channels and X-ray cell with buffer. The complete analysis cycle can be performed in less than 3 min. Bovine serum albumin was used as a model protein to characterize the mixing efficiency and sample consumption of the system. The N2 fragment of an adaptor protein (p120-RasGAP) was used to demonstrate how the device can be used to survey the structural space of a protein by screening a wide set of conditions using high-throughput techniques.

A circumventing role for the non-native intermediate in the folding of β-lactoglobulin

Folding experiments have suggested that some proteins have kinetic intermediates with a non-native structure. A simple G ̅o model does not explain such non-native intermediates. Therefore, the folding energy landscape of proteins with non-native intermediates should have characteristic properties. To identify such properties, we investigated the folding of bovine β-lactoglobulin (βLG). This protein has an intermediate with a non-native α-helical structure, although its native form is predominantly composed of β-structure. In this study, we prepared mutants whose α-helical and β-sheet propensities are modified and observed their folding using a stopped-flow circular dichroism apparatus. One interesting finding was that E44L, whose β-sheet propensity was increased, showed a folding intermediate with an amount of β-structure similar to that of the wild type, though its folding took longer. Thus, the intermediate seems to be a trapped intermediate. The high α-helical propensity of the wild-type sequence likely causes the folding pathway to circumvent such time-consuming intermediates. We propose that the role of the non-native intermediate is to control the pathway at the beginning of the folding reaction.

Minireview: structural insights into early folding events using continuous-flow time-resolved small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) is a powerful method for obtaining quantitative structural information on the size and shape of proteins, and it is increasingly used in kinetic studies of folding and association reactions. In this minireview, we discuss recent developments in using SAXS to obtain structural information on the unfolded ensemble and early folding intermediates of proteins using continuous-flow mixing devices. Interfacing of these micromachined devices to SAXS beamlines has allowed access to the microsecond time regime. The experimental constraints in implementation of turbulence and laminar flow-based mixers with SAXS detection and a comparison of the two approaches are presented. Current improvements and future prospects of microsecond time-resolved SAXS and the synergy with ab initio structure prediction and molecular dynamics simulations are discussed.

Time resolved SAXS and RNA folding

Small angle X-ray scattering provides low resolution structural information about macromolecules in solution. When coupled with rapid mixing methods, SAXS reports time-dependent conformational changes of RNA induced by the addition of Mg(2+) to trigger folding. Thus time-resolved SAXS provides unique information about the global or overall structures of transient intermediates populated during folding. Notably, SAXS provides information about the earliest folding events, which can evade detection by other methods.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

The length and viscosity dependence of end-to-end collision rates in single-stranded DNA

Intramolecular dynamics play an essential role in the folding and function of biomolecules and, increasingly, in the operation of many biomimetic technologies. Thus motivated we have employed both experiment and simulation to characterize the end-to-end collision dynamics of unstructured, single-stranded DNAs ranging from 6 to 26 bases. We find that, because of the size and flexibility of the optical reporters employed experimentally, end-to-end collision dynamics exhibit little length dependence at length scales <11 bases. For longer constructs, however, the end-to-end collision rate exhibits a power-law relationship to polymer length with an exponent of -3.49 +/- 0.13. This represents a significantly stronger length dependence than observed experimentally for unstructured polypeptides or predicted by polymer scaling arguments. Simulations indicate, however, that the larger exponent stems from electrostatic effects that become important over the rather short length scale of these highly charged polymers. Finally, we have found that the end-to-end collision rate also depends linearly on solvent viscosity, with an experimentally significant, nonzero intercept (the extrapolated rate at zero viscosity) that is independent of chain length--n observation that sheds new light on the origins of the "internal friction" observed in the dynamics of many polymer systems.

Hydrodynamic selection of the kinetic pathway of a polymer coil-globule transition

Recently, the role of hydrodynamic interactions in the selection of a kinetic pathway for phase transitions has attracted considerable attention. Here we study this problem numerically by taking as an example a coil-globule transition of a single polymer, which is a prototype model of protein folding. When a swollen polymer collapses into a globule state, hydrodynamic interactions accelerate the transition. We find, on the other hand, that when a rather compact polymer collapses into the same final state, hydrodynamic interactions decelerate the transition due to a slow squeezing process of the solvent. We reveal that the degree of the initial enhancement of anisotropy of the polymer configuration determines whether hydrodynamic interactions accelerate or decelerate the collapsing dynamics. We also discuss the possible relevance of squeezing flow effects in protein folding.

Coherent multidimensional vibrational spectroscopy of biomolecules: concepts, simulations, and challenges

The response of complex molecules to sequences of femtosecond infrared pulses provides a unique window into their structure, dynamics, and fluctuating environments. Herein we survey the basic principles of modern two-dimensional infrared (2DIR) spectroscopy, which analogous to those of multidimensional NMR spectroscopy. The perturbative approach for computing the nonlinear optical response of coupled localized chromophores is introduced and applied to the amide backbone transitions of proteins, liquid water, membrane lipids, and amyloid fibrils. The signals are analyzed using classical molecular dynamics simulations combined with an effective fluctuating Hamiltonian for coupled localized anharmonic vibrations whose dependence on the local electrostatic environment is parameterized by an ab initio map. Several simulation methods, (cumulant expansion of Gaussian fluctuation, quasiparticle scattering, the stochastic Liouville equations, direct numerical propagation) are surveyed. Chirality-induced techniques which dramatically enhance the resolution are demonstrated. Signatures of conformational and hydrogen-bonding fluctuations, protein folding, and chemical-exchange processes are discussed.

Early closure of a long loop in the refolding of adenylate kinase: a possible key role of non-local interactions in the initial folding steps

Most globular protein chains, when transferred from high to low denaturant concentrations, collapse instantly before they refold to their native state. The initial compaction of the protein molecule is assumed to have a key effect on the folding pathway, but it is not known whether the earliest structures formed during or instantly after collapse are defined by local or by non-local interactions--that is, by secondary structural elements or by loop closure of long segments of the protein chain. Stable closure of one or several long loops can reduce the chain entropy at a very early stage and can prevent the protein from following non-productive pathways whose number grows exponentially with the length of the protein chain. In Escherichia coli adenylate kinase (AK), about seven long loops define the topology of the native structure. We selected four loop-forming sections of the chain and probed the time course of loop formation during refolding of AK. We labeled the termini of the loop segments with tryptophan and cysteine-5-amidosalicylic acid. This donor-acceptor pair of probes used with fluorescence resonance excitation energy transfer spectroscopy (FRET) is suitable for detecting very short distances and thus is able to distinguish between random and specific compactions. Refolding of AK was initiated by stopped-flow mixing, followed simultaneously by donor and acceptor fluorescence, and analyzed in terms of energy transfer efficiency and distance. In the collapsed state of AK, observed after the 5-ms dead time of the instrument, one of the selected segments shows a native-like separation of its termini; it forms a loop already in the collapsed state. A second segment that includes the first but is longer by 15 residues shows an almost native-like separation of its termini. In contrast, a segment that is shorter but part of the second segment shows a distance separation of its termini as high as a segment that spans almost the whole protein chain. We conclude that a specific network of non-local interactions, the closure of one or several loops, can play an important role in determining the protein folding pathway at its early phases.

Hierarchical folding mechanism of apomyoglobin revealed by ultra-fast H/D exchange coupled with 2D NMR

The earliest steps in the folding of proteins are complete on an extremely rapid time scale that is difficult to access experimentally. We have used rapid-mixing quench-flow methods to extend the time resolution of folding studies on apomyoglobin and elucidate the structural and dynamic features of members of the ensemble of intermediate states that are populated on a submillisecond time scale during this process. The picture that emerges is of a continuum of rapidly interconverting states. Even after only 0.4 ms of refolding time a compact state is formed that contains major parts of the A, G, and H helices, which are sufficiently well folded to protect amides from exchange. The B, C, and E helix regions fold more slowly and fluctuate rapidly between open and closed states as they search docking sites on this core; the secondary structure in these regions becomes stabilized as the refolding time is increased from 0.4 to 6 ms. No further stabilization occurs in the A, G, H core at 6 ms of folding time. These studies begin to time-resolve a progression of compact states between the fully unfolded and native folded states and confirm the presence an ensemble of intermediates that interconvert in a hierarchical sequence as the protein searches conformational space on its folding trajectory.

Dehydration of main-chain amides in the final folding step of single-chain monellin revealed by time-resolved infrared spectroscopy

Kinetic IR spectroscopy was used to reveal beta-sheet formation and water expulsion in the folding of single-chain monellin (SMN) composed of a five-stranded beta-sheet and an alpha-helix. The time-resolved IR spectra between 100 mus and 10 s were analyzed based on two consecutive intermediates, I(1) and I(2), appearing within 100 mus and with a time constant of approximately 100 ms, respectively. The initial unfolded state showed broad amide I' corresponded to a fluctuating conformation. In contrast, I(1) possessed a feature at 1,636 cm(-1) for solvated helix and weak features assignable to turns, demonstrating the rapid formation of helix and turns. I(2) possessed a line for solvated helix at 1,637 cm(-1) and major and minor lines for beta-sheet at 1,625 and 1,680 cm(-1), respectively. The splitting of the major and minor lines is smaller than that of the native state, implying an incomplete formation of the beta-sheet. Furthermore, both major and minor lines demonstrated a low-frequency shift compared to those of the native state, which was interpreted to be caused by hydration of the C O group in the beta-sheet. Together with the identification of solvated helix, the core domain of I(2) was interpreted as being hydrated. Finally, slow conversion of the water-penetrated core of I(2) to the dehydrated core of the native state was observed. We propose that both the expulsion of water, hydrogen-bonded to main-chain amides, and the completion of the secondary structure formation contribute to the energetic barrier of the rate-limiting step in SMN folding.

Small-angle X-ray scattering of reduced ribonuclease A: effects of solution conditions and comparisons with a computational model of unfolded proteins

The disulfide-reduced form of bovine ribonuclease A, with the Cys thiols irreversibly blocked, was characterized by small-angle x-ray scattering. To help resolve the conflicting results and interpretations from previous studies of this model unfolded protein, we measured scattering profiles using a range of solution conditions and compared them with the profiles predicted by a computational model for a random-coil polypeptide. Analysis of the simulated and experimental profiles reveals that scattering intensities at intermediate angles, corresponding to interatomic distances in the range of 5-20 A, are particularly sensitive to changes in solvation and can be used to assess the internal scaling behavior of the polypeptide chain, expressed as a mass fractal dimension, D(m). This region of the scattering curve is also much less sensitive to experimental artifacts than is the very small angle regime (the Guinier region) that has been more typically used to characterize unfolded proteins. The experimental small-angle x-ray scattering profiles closely matched those predicted by the computational model assuming relatively small solvation energies. The scaling behavior of the polypeptide approaches that of a well-solvated polymer under conditions where it has a large net charge and at high urea concentrations. At lower urea concentrations and neutral pH, the behavior of the chain approaches that expected for theta-conditions, where the effects of slightly unfavorable interactions with solvent balance those of excluded volume, leading to scaling behavior comparable to that of an idealized random walk chain. Though detectable, the shift toward more compact conformations at lower urea concentrations does not correspond to a transition to a globule state and is associated with little or no reduction in conformational entropy. This type of collapse, therefore, is unlikely to greatly reduce the conformational search for the native state.

X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution

Crystallography supplies unparalleled detail on structural information critical for mechanistic analyses; however, it is restricted to describing low energy conformations of macromolecules within crystal lattices. Small angle X-ray scattering (SAXS) offers complementary information about macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, but without the size limitations inherent in NMR and electron microscopy studies. Together these techniques can allow multi-scale modeling to create complete and accurate images of macromolecules for modeling allosteric mechanisms, supramolecular complexes, and dynamic molecular machines acting in diverse processes ranging from eukaryotic DNA replication, recombination and repair to microbial membrane secretion and assembly systems. This review addresses both theoretical and practical concepts, concerns and considerations for using these techniques in conjunction with computational methods to productively combine solution scattering data with high-resolution structures. Detailed aspects of SAXS experimental results are considered with a focus on data interpretation tools suitable to model protein and nucleic acid macromolecular structures, including membrane protein, RNA, DNA, and protein-nucleic acid complexes. The methods discussed provide the basis to examine molecular interactions in solution and to study macromolecular flexibility and conformational changes that have become increasingly relevant for accurate understanding, simulation, and prediction of mechanisms in structural cell biology and nanotechnology.

Solvation and desolvation dynamics in apomyoglobin folding monitored by time-resolved infrared spectroscopy

Solvation and desolvation dynamics around helices during the kinetic folding process of apomyoglobin (apoMb) were investigated by using time-resolved infrared (IR) spectroscopy based on continuous-flow rapid mixing devices and an IR microscope. The folding of apoMb can be described by the collapse and search mechanism, in which the initial collapse occurring within several hundreds of microseconds is followed by the search for the correct secondary and tertiary structures. The time-resolved IR measurements showed a significant increase in solvated helix possessing a component of amide I' at 1633 cm(-1) within 100 mus after initiating the folding by a pD jump from pD2.2 to 6.0. In contrast, there was a minor increase in buried helices having amide I' at 1652 cm(-1) in this time domain. The observations demonstrate that the initially collapsed conformation of apoMb possesses a large amount of solvated helices, and suggest that much water is retained inside the collapsed domain. The contents of solvated and buried helices decrease and increase, respectively, in the time domain after the collapse, showing that the stepwise desolvation around helices is associated with the conformational search process. Interestingly, the largest changes in solvated and buried helices were observed at the final rate-limiting step of the apoMb folding. The persistence of the solvated helix until the final stage of apoMb folding suggests that the dissociation of hydrogen bonds between water and main-chain amides contributes to the energy barrier in the rate-determining step of the folding.

Microsecond Hydrophobic Collapse in the Folding of Escherichia coli Dihydrofolate Reductase, an α/β-Type Protein

Using small-angle X-ray scattering combined with a continuous-flow mixing device, we monitored the microsecond compaction dynamics in the folding of Escherichia coli dihydrofolate reductase, an alpha/beta-type protein. A significant collapse of the radius of gyration from 30 A to 23.2 A occurs within 300 micros after the initiation of refolding by a urea dilution jump. The subsequent folding after the major chain collapse occurs on a considerably longer time-scale. The protein folding trajectories constructed by comparing the development of the compactness and the secondary structure suggest that the specific hydrophobic collapse model rather than the framework model better explains the experimental observations. The folding trajectory of this alpha/beta-type protein is located between those of alpha-helical and beta-sheet proteins, suggesting that native structure determines the folding landscape.