Single-Molecule Biophysics: Experiment and Theory

Discover the experimental and theoretical developments in optical single-molecule spectroscopy that are changing the ways we think about molecules and atoms

The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This latest volume explores the advent of optical single-molecule spectroscopy, and how atomic force microscopy has empowered novel experiments on individual biomolecules, opening up new frontiers in molecular and cell biology and leading to new theoretical approaches and insights. Organized into two parts—one experimental, the other theoretical—this volume explores advances across the field of single-molecule biophysics, presenting new perspectives on the theoretical properties of atoms and molecules. Single-molecule experiments have provided fresh perspectives on questions such as how proteins fold to specific conformations from highly heterogeneous structures, how signal transductions take place on the molecular level, and how proteins behave in membranes and living cells.This volume is designed to further contribute to the rapid development of single-molecule biophysics research.

Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

• Language: English
• Publisher: Wiley
• Release date: Nov 16, 2011
• ISBN: 9781118131381

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Preface

Theoretical and experimental breakthroughs are strongly coupled: major advances in fundamental theoretical concepts are often triggered by novel experimental methods and observations. Similarly, new theoretical ideas suggest more experiments. Single-molecule studies are a clear demonstration of this paradigm. The advent of optical single-molecule spectroscopy and atomic force microscopy has empowered novel experiments on individual biomolecules, opening up new frontiers in molecular and cell biology. And these experiments led to new theoretical approaches and insights. The single-molecule approaches offer unique insights not only for the distribution of molecular properties, but also for the dynamics of individual molecules information that cannot be provided by conventional ensemble averaged measurements.

In the past fewyears, important advances have been made in several areas where data from single-molecule experiments have provided fresh new perspectives. Driving these developments are questions including, for example, how proteins fold to specific conformations from the highly heterogeneous structures, how signal transductions take place on the molecular level, as well how proteins behave in membranes and in living cells. A general problem arising from these new experimental observations is the theoretical underpinning for the roles of fluctuations in biochemical reactions. For example: Why biological systems can robustly perform their functions even with the free energy gain or loss of the reactions being comparable to the thermal energy, kBT ?

With a strong conviction that the integration of experimental developments and theoretical advances is essential toward resolving these issues, we have organized two international conferences focusing on identifying and articulating these issues. The first conference was entitled, Linking Single Molecule Spectroscopy and Energy Landscape Perspectives, held on December 3, 2008, at the FUKUOKA convention center, Fukuoka, Japan (organized by T. Komatsuzaki and H. Yang) during the 46th Annual Conference of Biophysical Society of Japan. The second conference was entitled, New Approaches to Complexity of Protein Dynamics by Single Molecule Measurements: Experiments and Theories, from December 7 to 9, 2008, held at the Institute for Protein Research (IPR), Osaka University, Japan (organized by S. Takahashi, T. Komatsuzaki, M. Kawakami).

This volume consists of contributions from participants of the above-mentioned two conferences, including invited speakers, discussants, and organizers. The content of this volume is organized into two parts: one is experimental, and the other is theoretical development on single-molecule biophysics. Part I focuses mainly on three experimental approaches: single-molecule fluorescence based mainly on fluorescence resonance energy transfer (FRET), atomic force microscopy (AFM) and diffracted X-ray tracking (DXT), and their applications to important biological phenomena. This part begins with experimental investigations of protein folding and the development of a new fluorescence method for a long time detection without tethering proteins to glass (Takahashi and Kamagata, Chapter 1) and is followed by conformational and dynamic properties of unfolded proteins based on the confocal detection of single-molecule fluorescence (Nettels and Schuler, Chapter 2), and a quantitative analysis of FRET signals in terms of cumulative distribution functions for telomere DNA (Okamoto and Terazima, Chapter 3). The topic then turns to AFM, which is capable of measuring the mechanical response of a single molecule to an applied force. A systematic AFM study of the mechanical property of the unbinding force of biomolecular complexes and rigidity (stiffness) of various biomolecules are reviewed (Ikai, Afrin, and Sekiguchi, Chapter 4). A novel dynamic force spectroscopy using AFM is discussed, in which a stretched single molecule is driven by an external oscillatory motion and both the static and dynamic mechanical properties of the molecule can be obtained through the deflection of an AFM cantilever (Kawakami and Taniguchi, Chapter 5). A recent breakthrough in single-molecule experiments is the DXT method, which monitors the movements of individual nanocrystals linked to a specific site of proteins at the picometer scale (Sasaki, Chapter 6). The DXT method revealed a twisting motion involved in the gating dynamics of a membrane potassium channel, KcsA (Oiki et al. Chapter 7). Finally, an exploration of complex kinetics at the association/dissociation of epidermal growth factor receptor and Grb2 in cellular signal transductions using an in vitro reconstructed system was reviewed (Takagi, Morimatsu, and Sako, Chapter 8).

Part II focuses on the theoretical progress in single-molecule data analyses. In general, the observed time traces from single molecule are contaminated by several internal noises in addition to external noises arising from experimental settings. For example, the origin of the fluctuation in the FRET data ranges from photophysics, such as blinking and bleaching to different quantum yields of two dye molecules. It is therefore of crucial importance to recognize the existence of two distinct, but complementary stages, in the analyses of single-molecule time series: The first is of extracting the time trace of a desired physical quantity, such as an interdye distance from a noisy signal and the second is of constructing the underlying mechanisms from a scalar time series, such as multidimensional energy landscapes and networks composed of states in a kinetic scheme. Part II includes new theoretical frameworks to extract the scalar time trace of a desired physical quantity buried in a noisy time signal observed in single-molecule experiments, which are designed as an unbiased and quantitative interpretation of the data (Yang, Chapter 9), a comprehensive review of a theory of the FRET efficiency histograms obtained from single-molecule photon counting experiments, which is designed to separate the time trace of photon trajectories in the diffusion process into the distance fluctuation between dye molecules and the other components (Gopich and Szabo, Chapter 10), a new theoretical framework to construct local equilibrium states and the corresponding multidimensional energy landscape from a scalar time series without a priori postulation of the concept of local equilibration and the detailed balance (Baba and Komatsuzaki, Chapter 11), a generalized Michaelis-Menten rate equation for nonequilibrium steady-state turnover reactions in which the original kinetic network model is mapped onto a flux network with unbalanced population currents and the concentration dependence of substrate for the average turnover rate derived (Wu and Cao, Chapter 12), a new construction scheme of a reduced form of the underlying multisubstate kinetic scheme for time trace when composed of two states, where the connections between the nodes in the network can have multiexponentialwaiting time probability density functions (Flomenbom, Chapter 13), a systematic survey of discrepancies found between numerical simulations andAFM experiments for mechanical unfolding of proteins including a caution of oversimplifications due to the projections of the intrinsic multidimensional free energy surface onto a low dimension (Yew, Olmsted, and Paci, Chapter 14), and the exploration of different types of mechanochemical coupling mechanisms (i.e., loose- and tight-coupling scenarios) functioning in myosin II in terms of the mean velocity and velocity fluctuation at various ATP concentration (Takagi and Nishikawa, Chapter 15).

We note, however, that the subject matter included herein should not be regarded as solved; rather, they indicate topics that have been identified for which solutions with various levels of completeness have been provided. It is therefore hoped that the ideas contained in this volume will motivate further innovations in both experiment and theory, and especially their closer interactions in the near future. We finally acknowledge the financial supports for the above two conferences from the following organizations and programs: (1) Japan Science and Technology Agency, Promoting Globalization on Basic Research Programs, (2) Japan Science and Technology Agency, Core Research for Evolutional Science and Technology (CREST), and (3) The Institute for Protein Research, Osaka University.

T. Komatsuzaki

M. Kawakami

S. Takahashi

H. Yang

R. J. Silbey

Part One

Developments on Single-Molecule Experiments

Chapter 1

Staring at a Protein: Ensemble and Single-Molecule Investigations on Protein-Folding Dynamics

Satoshi Takahashi* and Kiyoto Kamagata

Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Miyagi 980-8577, Japan and CREST, JST Kawaguchi, Saitama 332-0012, Japan

I. Introduction

A. Structural Properties of Folded Proteins

Proteins are natural heteropolymers that possess a remarkable property to fold to their native conformations autonomously, where they perform various physiological functions [1]. Proteins become unfolded in solutions containing high concentrations of denaturants, however, the folded conformations are usually regenerated once the concentration of the denaturants is reduced [2]. This observation demonstrates that the folded conformation is determined by the primary sequence. It further suggests that the folded conformation is predictable. Despite intensive investigations conducted over the past 40 years, the prediction of protein structures still presents an extremely difficult task [3]. In fact, the current situation is that even the prediction of the foldability of the sequences created by single mutation of natural proteins is difficult, reflecting our lack of understanding of the molecular principles governing protein folding. The processes involved in the selection of the folded structures from the unfolded conformations for actual proteins, that is, the dynamic process of protein folding, remains an important subject [4].

Four structural properties of folded proteins distinguish them from other synthetic and biological polymers and from the unfolded proteins. First, proteins are abundant in secondary structures, which are mainly stabilized by hydrogen bonds between main-chain amides. Second, proteins are always compact, and the interior of proteins is packed nearly perfectly, similarly to crystals of organic compounds. Third, the interior of proteins is mostly dehydrated. No water molecule is usually observed in the core domain of proteins. The compactness and the absence of water are related to the fact that the major driving force of protein folding is the hydrophobic interaction. Fourth, the folded conformation of proteins basically consists of a single topology. In contrast, the unfolded proteins possess no secondary structures, and are in expanded conformations with fully solvated polypeptides. The unfolded proteins comprise an astronomical number of heterogeneous conformations that are interconverting into each other. Consequently, the dynamic process of protein folding involves a myriad of molecular events that lead the unfolded proteins to the distinct conformation. The important question persists: How are the four structural properties of the folded proteins organized in the dynamic process of protein folding?

In the past 10 years, we have investigated the dynamics of protein folding based on the four structural properties described above. To detect transient species, we developed time-resolved experimental systems based on rapid solution mixing and ensemble detection [5]. Additionally, we developed a single-molecule fluorescence detection system to monitor the dynamics of individual proteins [6]. In Section II, we summarize our efforts in the ensemble experiments. In Section III, we describe our recent trials in single-molecule experiments. Finally, we offer our perspectives on the investigation of protein-folding dynamics.

B. Cooperativity in the Folding Transitions

Although the unfolded state of a protein comprises an astronomical number of conformations, the observable process of protein folding is surprisingly simple. For many small proteins with chain lengths of <100 residues (small proteins), the folding is cooperative and occurs as the two-state transition from the unfolded state to the native state, implying that the states are separated by an energy barrier (Fig. 1) [7]. The two-state transition is established for many small proteins in both equilibrium and kinetic measurements [8]. Consequently, intermediates other than the unfolded and native states were unidentifiable, even in time-resolved observations, although it is important that the involvement of a small amount of the intermediate was sometimes pointed out in the folding kinetics of small proteins [9]. The cooperativity is a remarkable property of proteins, whose origin bears central importance for elucidation of folding phenomena.

Figure 1. Cooperativity in the folding transition of proteins. (a) Small proteins with <100 residues usually demonstrate the two-state transition from the unfolded state to the folded state that are separated by a distinct energy barrier. (b) Medium proteins with >100 residues frequently possess one or more intermediates in addition to the unfolded and folded states. In some cases, the intermediates are called the molten globule state. However, the transitions between any pair of the unfolded state, the intermediate, and the native state are still cooperative.

It is particularly interesting that the cooperativity depends on the chain length. For proteins >100 residues (medium proteins), the folding transition occurs as a multistep process involving one or more intermediate states (Fig. 1) [8]. Accordingly, the perfect cooperativity observed in small proteins is not maintained in medium proteins. It is important, however, that the transitions between any pair of the unfolded state, intermediates, and native state are still cooperative. Many single-domain proteins with >200 residues (large proteins) fail to fold autonomously, and require cellular machineries that prevent the formation of misfolded structures. Proteins with much larger chain lengths (e.g., 1000 residues) are not rare. These proteins are usually composed of multiple domains, each of which folds independently. The dependency of the folding cooperativity on the chain length suggests that the folding transitions are controlled by the properties of proteins as polymeric molecules.

Various properties of the intermediates of medium proteins have been investigated. The equilibrium intermediates are usually observed under mildly denaturing conditions, and are sometimes termed as the molten globule state, which is collapsed and possesses a large amount of secondary structure [10]. Although the state is highly fluctuating, it possesses partially formed tertiary contacts that are indispensable for the stability of the state. During the kinetic process from the unfolded to the native state in medium proteins, the kinetic intermediates usually appear within the mixing dead time of the stopped-flow apparatus (a few milliseconds) [11]. The conformational properties of the kinetic intermediates resemble that of the molten globule intermediates [12]. Because of the limited time resolution and structural information, it remains unknown how and why the intermediate conformations are constructed, and why the folding transitions are highly cooperative.

II. Ensemble Investigations of Protein Folding

A. Strategies for Ensemble Investigations

Conformational investigations of protein folding have been hampered by the speed of the processes. To initiate the folding, it is usually necessary to dilute the highly concentrated denaturants in solutions containing the unfolded proteins. The conventional stopped-flow apparatus can achieve the mixing dead time of, at most, several milliseconds. We used a continuous-flow rapid mixing technique that can achieve a time resolution of several hundreds of microseconds, and can drastically enlarge the accessible time window for kinetic investigations of protein folding [13]. In some special applications, a mixing dead time as short as 11 μs can be achieved [14]. The other advantage of the continuous-flow technique is its applicability to a variety of spectroscopic and scattering methods. Transient spectra can be obtained easily by placing the mixing device inside of conventional spectrometers and by changing the device's location relative to the observation point. We used circular dichroism (CD) [5] and Fourier transform infrared (FTIR) [15] spectroscopies to observe secondary structures and hydration of the main chain amides. To detect compactness and overall shape, we used small-angle X-ray scattering (SAXS) technique [16].

To obtain general and specific features of protein folding, we investigated folding dynamics of proteins with different chain lengths, secondary structure contents, and topologies. These include α-helical proteins, such as cytochrome c (cyt c) (5, 6, 13, 14, 16), apomyoglobin (ApoMb) [17, 18], and heme oxygenase [19]. In addition, single-chain monellin (SMN) [20, 21] was selected as an example of proteins containing β-sheet (Fig. 2).

Figure 2. Structures of proteins mainly discussed in this review. (a) Cytochrome c. The heme group and its axially coordinated ligands are shown in the expanded view in the circle. (b) Apomyoglobin. The main-chain structure of myoglobin without heme was presented with labels denoting helixes. Helix F and the C-terminal region are fluctuating in ApoMb [25]. (c) Single-chain monellin. (d) Heme oxygenase.

B. Stepwise Folding of Cytochrome c

Cytochrome c is a small globular protein with 104 amino acid residues and possesses a heme prosthetic group that is attached covalently to the main chain. At pH 7 and 2, cyt c is, respectively, in the folded and unfolded states. In the folded conformation, the heme group is surrounded by three helices termed N-terminal, C-terminal, and 60's helices. Additionally, the heme possesses two axially coordinated residues: histidine-18 (His18) and methionine-80 (Met80) (Fig. 2). The unfolded protein at pH 2 is expanded and possesses no specific structures. Furthermore, the protein forms the molten globule intermediate at pH 2 in the presence of a high concentration of salt [22]. The protein also forms another intermediate in the course of kinetic folding, in which the non-native histidine (either His26 or His33) is coordinated to the heme in place of the native methionine [23]. Because the misligation decelerates the folding kinetics, the form is sometimes termed the misfolded state. The formation of the misligated conformation can be minimized by conducting the refolding reaction at pH 4.5, where histidine residues are primarily in the protonated state and cannot coordinate to heme. Consequently, by changing pH from 2.0 to 4.5, we can monitor the folding kinetics of cyt c, which is unaffected by the misligated conformation [24].

To detect changes in the secondary structures in the folding kinetics after the pH jump of cyt c, we conducted time-resolved CD measurements using the continuous-flow device [5]. The negative ellipticity in the far ultraviolet (UV) region is useful as an index of the α-helix formation. The CD spectrum for the initial acid unfolded state (U) showed that the helical content is 10%. The spectrum does not change at 400 μs after the pH jump, demonstrating that the helix formation is not coupled to the formation of the initial intermediate (I). The kinetic changes in the CD spectra after 400 μs can be well approximated by two exponential phases. The first phase (2100 s-1) corresponds to the formation of the second intermediate (II), whose helical content was 35%. The second phase (150 s-1) corresponds to the conversion of the second intermediate to the native state (N) possessing the helical content of 50%. Consequently, the sequential folding scheme with two intermediates (Scheme 1)

can explain the observed CD spectra. These results, demonstrating the major helix formation in the time domain after 400 μs, are in sharp contrast to the premise that the secondary structure formation occurs immediately after the initiation of folding.

To detect the compactness in the cyt c folding, the second of the four structural properties of the native proteins, we next conducted time-resolved SAXS experiments [16]. We constructed a time-resolved SAXS detection system based on a rapid mixing device and the intense X-ray source from the synchrotron facility at SPring8. The radii of gyration (Rg) of the acid unfolded (U) and the native (N) states of cyt c were, respectively, 24.3 and 13.9 Å. In contrast to the kinetic CD results, the SAXS results demonstrated a considerable reduction in Rg from 24.3 to 21.1 Å within the observation dead time (160 μs). The Rg value was interpreted to correspond to that of the initial intermediate (I). All other kinetic data were explained consistently based on the sequential folding scheme with two intermediates (Scheme 1). The second intermediate (II) was shown to possess the Rg value of 17.8 Å. We showed the changes in α-helical content and Rg in the two-dimensional (2D) plot, which clearly demonstrated that the reduction in Rg is the first kinetic event in the stepwise folding of cyt c (Fig. 3).

Figure 3. Changes in the secondary structure content and the compactness in the process of kinetic folding of cytochrome c (triangles), apomyoglobin (circles), and SMN (rectangles). The secondary structure content was estimated based on analyses of the kinetic CD spectra for the intermediate state. The radii of gyration were estimated from analysis of the small angle X-ray scattering data. The figure was modified from Fig. 4 of an earlier report [20].

C. Collapse and Search Mechanism in Apomyoglobin Folding

Next, we conducted time-resolved CD and SAXS experiments on the folding of apoMb [18]. Apomyoglobin is the apo form of myoglobin with 153 residues, in which the prosthetic heme group is surrounded by eight helices designated as A–H (Fig. 2B). Upon the extraction of heme, apoMb maintains the folded structure except for fluctuating regions (e.g., the F helix and the C-terminus) [25]. The ApoMb shows stepwise equilibrium unfolding. The native conformation (N) is stable at pH 6. The protein becomes the acid unfolded state at pH 2.0 (Uacid), which possesses a small helical content of 10% [26]. In addition, the equilibrium intermediate, sometimes termed as the molten globule state, becomes stabilized at pH 4.2, which possesses a partial helical content of 33% located at helices A, G, and H and a part of helix B [27]. In the kinetic stopped-flow experiments, apoMb was demonstrated to form a burst phase intermediate, whose hydrogen deuterium exchange pattern resembles that of the static molten globule state [12]. Accordingly, we expected to detect how the molten globule state is organized from Uacid by application of the rapid mixing technique.

We conducted pH-jump refolding experiments of apoMb from pH 2.0 to 6.0 [18]. Within the observation deadtime of 300 μs, the protein showed a rapid collapse to form the initial intermediate (I1). The Rg values of Uacid and I1 are, respectively, 29.7 and 23.7 Å. In addition, the helical content of I1 is 30 30%. Next, we detected an increase in the helical content, which corresponds to the formation of the second intermediate (I2). The helix content of I2 is 44% and the Rg value is identical to that of I1. Finally, the conversion of I2 to N was observed with a time constant of 49 ms. Consequently, the folding of apoMb is explainable by the linear folding scheme (Scheme 2):

The kinetic changes in α-helical content and Rg were plotted in the 2D plot (Fig. 3). The folding of apoMb occurs as a stepwise process in which a considerable collapse occurs as the initial step of the folding dynamics.

Based on the observations of the folding of apoMb and cyt c, we proposed the collapse and search mechanism [18]. The initial kinetic event is the rapid collapse occurring within the mixing dead time. The secondary structure contents in the initial intermediates are minor and depend on the proteins. The collapsed intermediate eventually converts to the second intermediate, which contains increased amounts of the secondary structures and closely resembles the molten globule state observed in the equilibrium condition. The stepwise processes occurring after the collapse are likely to be associated with the search process for the correct folded structures.

D. Folding Pathway Depends on Secondary Structures

To characterize the folding pathway of a β-sheet protein, next we investigated the folding of SMN [28]. Single-chain monellin is a 94-residue protein consisting of a five-stranded β-sheet and an α-helix (Fig. 2) and at pH 9.4 retains the native conformation (N). In contrast, SMN at pH 13 possesses the unfolded conformation (U). The time-resolved observation of the folding of SMN initiated using a pH-jump from 13.0 to 9.4 demonstrated that the initial collapse occurs within 300 μs [20]. The Rg value for U is 25.5 Å, which becomes 18.2 Å after the collapse. The CD spectrum for the conformation at 300 μs was almost identical to that of U. Consequently, the initial intermediate (I1) formed after the collapse possesses only a limited amount of secondary structures. The I1 state converts to the next intermediate (I2) with the increase in negative CD ellipticity, suggesting the partial formation of the secondary structures. The Rg value for I2 is 15.4 Å, and is comparable to that of N (15.8 Å). Finally, the formation of N was observed in the increase in the negative ellipticity, corresponding to development of the β-sheet structure. Consequently, the folding scheme of SMN resembles those of cyt c and apoMb (Scheme 3):

The folding of SMN was demonstrated again to follow the collapse and search process, in which the formation of the collapsed conformation precedes the formation of the secondary structure.

It is remarkable that the collapse and search mechanism was observed for both α-helical and β-sheet proteins. However, the kinetic steps involved in the secondary structure formation differ between the two classes of proteins. The difference can be visualized in the 2D plot describing the conformational landscape of proteins (Fig. 3). The unfolded states are commonly expanded with a small amount of secondary structures, and are located in the lower right of the plot. In contrast, the folded conformations are compact and possess high contents of secondary structures, and are shown in the upper left. The folding intermediate states connect these states to form pathways. In the case for α-helical proteins, the pathways traverse the plot diagonally. It is particularly interesting that the pathway for SMN is distinct and L-shaped, corresponding to the formation of the β-sheet structure that occurs as the slower step. This difference in the α-helical and β-sheet proteins was predicted by theoretical calculations [29] and might be attributed to the abundance of middle-range interactions that are necessary for the formation of a β-sheet [30].

E. Scaling Behavior in the Initial Intermediates

Next, we characterized the folding of heme oxygenase (HO), which is the largest single-domain protein (263 residues) ever investigated using the time-resolved SAXS method. Heme oxygenase is an α-helical protein [31] (Fig. 2) and shows a reversible acid unfolding transition [19]. The investigation of the folding of HO was severely hampered by the facile aggregation of the intermediates and by the parallel-folding pathways. To identify the processes reflecting the folding of the monomeric form, we analyzed the concentration dependence of the time-resolved data and conducted the double-jump experiments. The series of experiments showed that the major part of the sample forms the burst phase intermediate (I1) immediately after the pH jump, which subsequently forms the second intermediate (I2). The I2 state easily forms dimeric and higher multimeric conformations. The sample immediately after the pH jump further contains the minor (I′) component, which is likely to be the non-native proline isomer and folds slowly. The average Rg value of I1 and I′, determined by the time-resolved SAXS, is 26.1 Å. The average α-helical content is 50%. Consequently, the folding scheme of HO can be described as follows (Scheme 4):

The folding dynamics for the monomeric and major component of HO can therefore be described by the collapse and search mechanism.

To examine the properties of the initial collapse, we show the Rg values of the initial intermediates for different proteins as the function of chain lengths [19] (Fig. 4). The Rg values of the native proteins on a logarithmic scale are linearly dependent on the logarithm of the chain length with a slope of . For the native proteins, the scaling exponent of reflects the tight packing of proteins [32]. Regarding the unfolded proteins, the scaling exponent is , demonstrating that the unfolded proteins can be considered as random coils with excluded volume effects [33]. The scaling exponent for the initial intermediates is close to , suggesting that the Rg values for the collapsed conformation are not controlled directly by the individual sequences. We proposed that the initial conformations are rather controlled by a property of the unfolded state of proteins as polymers.

Figure 4. Scaling relationship observed for the Rg and the number of amino acid residues, N, for the native (circles), the intermediate (open rectangles and triangles), and the unfolded state in the presence of high concentration of denaturant (crosses). Data for kinetic intermediates obtained in our investigations were presented as open rectangles. Data obtained for the unfolded state in the absence of the denaturant (filled rectangles) are distinct from those of the medium and large proteins (open rectangles). Modified from Fig. 5 of an earlier report [19].

Several theories have been proposed to explain the collapse transition of polymers and proteins. The simplest of them is Flory's homopolymer theory, in which hydrophobic polymers without sequence-dependent interaction become collapsed in poor solvents at temperatures below the θ temperature (Tθ) [34]. The scaling exponent of the collapsed polymers, called globules, was predicted to be , reflecting the homogeneous density of monomers. Consequently, the observation for the initially collapsed conformation is consistent with the coil–globule transition. The extension of Flory's theory to random heteropolymers similarly predicts the presence of the collapsed and extended conformations possessing scaling exponents of and , respectively [35]. We conclude that the collapse transition, generally observed in the initial phase of folding, reflects the properties of the unfolded proteins as the polymeric molecules.

F. Two-State and Multistate Transitions Are Likely Determined by the Collapse Transition

The collapse behavior of small proteins is distinct from that of medium proteins. Small proteins with <100 residues usually demonstrate a two-state transition in the folding kinetics. The stopped-flow SAXS experiments showed that IgG binding domain of protein L with 62 residues possesses the expanded Rg value immediately after the initiation of the folding reaction [36]. Because the Rg value is almost identical to that of the unfolded state, the protein shows no collapse until the moment of folding. Similarly, two other small proteins were reported to possess expanded Rg after the start of folding (Fig. 4) [37]. In contrast, the folding of medium proteins with >100 residues involves distinct intermediate states. The initial event in the folding is always a pronounced collapse. Consequently, a clear distinction can be made between small and medium proteins in the involvement of intermediate states and in the collapse behavior.

We propose that the difference between small and medium proteins, separated roughly at 100 residues, might be explained by the chain-length dependency of the coil–globule transition [19]. Based on the extension of the Flory's theory to heteropolymers by Bryngelson and Wolynes [35], it can be predicted that Tθ of the unfolded proteins depends on the chain length because the average hydrophobicity of medium proteins becomes higher as a result of a larger amount of residues located inside of proteins. Regarding small proteins, Tθ is lower than room temperature, and the unfolded proteins remain in the coil state in the absence of the denaturants. In contrast, medium proteins possess Tθ that is higher than the room temperature, causing the collapse of the unfolded proteins in the absence of denaturant and the formation of the intermediates. Consequently, the heteropolymer theory can explain the distinct collapse behaviors and intermediate formation between small and medium proteins.

The two-state folding is believed to be a general property of small proteins [8]. However, recent re-examinations have revealed the deviation of many small proteins from the perfect two-state transitions [9]. We suggest that the unfolded state of proteins possess both the coil and globule conformations corresponding, respectively, to the expanded and compact unfolded states, and that the relative stabilities of the two states are primarily dependent on the chain lengths with a modulation by the primary sequences. Therefore, we consider that the collapse dynamics are important for understanding of the folding of both small and medium proteins.

G. Main-Chain Solvation and Desolvation Dynamics

The third of the four structural properties of the native proteins is the absence of water in the interior. Because the peptide groups are polar, they are solvated in the unfolded state of proteins [38]. Both the carbonyl group and the amide protons are involved in hydrogen bonding with water. The free energy of the peptide solvation is largely enthalpic and is estimated as −14 kcal mol−1 [39]. Consequently, the desolvation from the unfolded state of proteins is expected to cause marked kinetic barriers to protein folding. It is important to detect how the desolvation is coupled to the dynamics of protein folding.

To observe the desolvation around the polypeptide backbone, we used FTIR and detected amide I′ absorption. The amide I′ is mainly attributed to the C=O stretching vibration of the amide group, is sensitive to subtle changes in secondary structures, and can differentiate the solvated and desolvated amides because amide I′ shows a low-frequency shift upon hydrogen-bond formation with water. We developed a time-resolved FTIR system that is based on the rapid mixing device and FTIR microscope [15], and followed the dynamics of the apoMb folding by the pD jump [17]. We detected a rapid increase in the solvated helix to 25% at the fastest detectable point (100 μs), which decreases to the content of N (14%) mainly in the time domain after 10 ms in accordance with the formation of N. In contrast, the amount of the desolvated helix is only 19% at 100 μs, whose conversion to the level of N (39%) occurs after 10 ms. Consequently, the largest amount of desolvation occurs at the rate-limiting step in the folding of apoMb (i.e., the conversion of I2 to N).

Next, we conducted time-resolved FTIR experiments on the folding of SMN initiated by the pD jump [21]. We treated the entire set of the time-resolved spectra of amide I′ by the singular value decomposition, and interpreted the data on the basis of the linear-folding scheme (Scheme 3). The amide I′ spectra for I1 and I2 revealed the stepwise formation of secondary structures. In I1, there exists a considerable amount of solvated helix. However, the typical signature of the β-sheet was absent. Consequently, I1 possesses a fluctuating helix, but no β-sheet. In contrast, I2 possesses a line corresponding to solvated helix and the major and minor lines assignable to β-sheet. The major and minor lines are both shifted to the lower wavenumbers compared to those of N, demonstrating the low-frequency shift in the intrinsic frequency of amide I′ for the β-sheet. We attributed the shift to the solvation of β-sheet in I2. Together with the presence of solvated helix, we proposed that the core of I2 formed between the β-sheet and the α-helix is solvated. The time-resolved observation on the folding of SMN again supported that the rate-limiting folding step is associated with the major desolvation around the backbone.

The initial collapse transition in protein folding is expected to be coupled to the replacement of water around the hydrophobic side chains by other hydrophobic groups. Consequently, the majority of water surrounding unfolded proteins is expected to be excluded from the vicinity of proteins in the collapse process. However, time-resolved IR measurements demonstrated that many water molecules are still solvated around the main-chain amides in the collapsed conformation and desolvation occur at the rate-determining step [17, 20]. We suggest that the dehydration dynamics contribute to the energy barrier between the collapsed intermediate and the native state.

III. Single-Molecule Investigations of Protein Folding

A. Development of a Single-Molecule Detection System

The fourth of the important properties of the folded conformations of proteins is structural uniqueness. The scaling relationship demonstrated that the unfolded proteins are categorized as random coils, suggesting that all the conformational degrees of freedom of the main-chain are mutually independent and that the number of the conformations in the unfolded state is astronomical [33]. In surprising contrast, the folded proteins basically possess a single topology. How the number of the conformations of the unfolded proteins decreases with the progress of the folding reaction is an important question that has remained unanswered. In addition, the dynamic properties of individual proteins in the unfolded and intermediate states are important. Because of ensemble averaging, these properties cannot be investigated based on conventional methods. Single-molecule methods must be used for observation of the inhomogeneity and the dynamics of unfolded proteins.

To detect single proteins, we took advantage of the fluorescence detection of proteins labeled by fluorescent dyes. The major obstacle to fluorescence detection from single molecules is not the efficiency of collecting photons, but the efficiency of discriminating the signal photons from the background photons. To this end, two methods have been proposed. The first is confocal microscopy, in which the signals from the tightly focused point of the microscopic lens are selectively collected and the background from the molecules outside of the focal point is eliminated. The second is total internal reflection microscopy, in which the laser excitation is spatially confined within the evanescent field created at the interface between the optical plate and water and the signals originating from the proteins attached on the plate are obtained selectively. However, these methods entail respective drawbacks for their application to protein folding. Using confocal microscopy, a single molecule can be detected for the periods of only a few milliseconds because of the diffusion of molecules from the focus point [40]. For total internal reflection microscopy, the sample fixation on the optical surface frequently causes artifacts on the properties of proteins, especially in the unfolded state [41]. Therefore, we developed a new method for detection of fluorescence from single molecules flowing freely in solution for an extended time period [6].

The developed method is based on the flow capillary, imaging detectors, and lenses having moderate numerical aperture (NA) values (Fig. 5) [6]. In conventional experiments, lenses with high NA values are used. However, such lenses possess short focal depths and cannot collect photons from molecules outside of the focusing area. Using the developed method, the larger focal depths of the lenses with the moderate NA values enabled us to image the larger cross-section of the capillary. Consequently, by adjusting the concentration of the samples adequate for observation of single molecules and by imaging the capillary, it is possible to obtain signals from single molecules. The background level of the system is higher than that of the confocal system. We can state that the system enables the detection of single molecules without fixation at the expense of the efficiencies of collecting photons and of reducing backgrounds.

Figure 5. Schematic representation of the single-molecule detection system. The dilute solution of sample proteins labeled using a fluorophore is introduced to a capillary at a constant flow speed. The excitation laser is introduced coaxially to the cell, and fluorescence from molecules flowing in the cell was imaged on a CCD camera.

Many factors affected the performance of our system. In our initial model, we used a camera lens with the NA value of 0.33. Because the lens had focal depth of 11 μm, a large area of the cross-section of the flow capillary with an inner diameter of 75 μm was imaged. Our later systems used a lens with the NA value of 0.5, which increases the efficiency of collecting photons by >2. Although flow capillaries with narrower diameters are desirable, the difficulty in flowing samples slowly prevented the use of the narrower capillary. The sample concentration was another important variable, which was again affected by the diameter of the flow capillary. For an inner diameter of 75 μm, the adequate concentration for detection of single molecules is the femtomolar level. However, at this extremely low concentration, the samples easily adsorb on the walls of the flow systems, making the adjustment of sample concentration extremely difficult. Additional improvement in the method of sample flow and collecting photons are necessary for the easier detection of single molecules.

B. Slow Conformational Dynamics Observed in the Unfolded cyt c

We selected cyt c from Saccharomyces cerevisiae as the first example for single-molecule measurements [6]. The C-terminal cysteine of cyt c was labeled using a fluorophore, Alexa 532 (cyt c-Alexa). The unfolding transition of cyt c-Alexa was examined using bulk titration experiments. In the absence of denaturant, cyt c-Alexa is in the native state, whose fluorescence intensity is weak because of the quenching by the heme group located in the vicinity of Alexa. In contrast, in the presence of a high concentration of denaturant, the fluorescence intensity is increased because the distance between Alexa and heme becomes large. We further identified the intermediate for the sample in the mildly denaturing condition that possesses the fluorescence intensity in the middle of those of the unfolded and folded conformations.

We obtained the single-molecule fluorescence traces of cyt c-Alexa under mildly denaturing conditions based on the developed device. We identified high-and low-intensity species in the observed traces, and assigned them to the unfolded and intermediate state, respectively. As we increased the concentration of denaturant, the occurrence of the unfolded state was increased and that of the intermediate was decreased. Accordingly, the single-molecule results were consistent with the ensemble results. To obtain dynamic information of the unfolded cyt c, we calculated the autocorrelation of the single-molecule time series data. Although the autocorrelation of the traces assignable to the intermediate decays within the time resolution of the system (several milliseconds), the autocorrelation for the unfolded cyt c decays slowly with a time constant of 15 ms. The observation indicates the existence of the slow dynamic motions for the unfolded cyt c. Consequently, single-molecule measurements revealed that the unfolded cyt c has slow dynamic motion on the order of 10 ms.

C. Diversity of Conformational Dynamics in the Unfolded Proteins

To compare the time constant obtained for the unfolded state of cyt c, we listed the corresponding time constants reported for many unfolded proteins (Table I, [42–46]). It is particularly interesting that the time constants and the number of the observed dynamics differ from protein to protein. For example, cold shock protein shows only fast dynamics with a time constant of 50 ns [47]. In contrast, cyt c and ribonuclease HI possess extremely slow dynamics with a time constant longer than 10 ms [6, 48]. Note that there might exist faster and/or slower dynamics in addition to the listed time constants, which were undetectable in the reported experiments because of experimental limitations. Consequently, the time scale of the dynamic motions of the unfolded proteins ranges from tens of nanoseconds to seconds.

Table I Reported Time Constants for the Dynamics of Various Denatured Proteins.a

The wide range of the time scales, encompassing eight orders of magnitude, is expected to correspond to the diverse structural dynamics in the unfolded proteins, and likely reflects the fact that the unfolded proteins are not perfect random coils. It was proposed that dynamics in the nanosecond range is the time for the loop closure [49], which could be identified in the random coils. The slower dynamics in the microsecond time domain likely corresponds to the formation and the disruption of specific structures in the unfolded state. It also suggests that the unfolded proteins possess residual structures and are not random coils. The current conclusion is in contrast to the suggestion from the scaling behavior in Rg of the unfolded proteins [33]. The size dependency of the unfolded proteins can be explained consistently by assuming random coils. To understand the conflicting aspects, we propose that the unfolded ensemble of proteins is a mixture of random coils and nonrandom coils with specific structures. Although most unfolded proteins are random coils, some of them possess specific structures, such as a part of secondary structures and native-like topology, which were detected in single-molecule experiments.

IV. Summary and Perspective

We will summarize the results of the ensemble and single-molecule investigations in the order of the molecular events in protein folding (Fig. 6). The unfolded proteins in the presence of a high concentration of denaturants or in the extreme pH solutions are mainly in the random coils with the excluded volume effect. However, some fractions of proteins possess residual structures and cause the slow conformational dynamics detected at the single-molecule level. Upon the jump of the solution to physiological conditions, a marked collapse occurs within several hundreds of microseconds. While the conformation of the initially collapsed proteins obeys the scaling law expected for the globules, the conformation is not random. For example, the tertiary contacts in the core domain of apoMb are already established [50]. Consequently, important interactions required for the construction of the native conformation are likely to be formed in the collapse phase. After the collapse, the native conformation was constructed in a stepwise manner in a much longer time domain ranging from milliseconds to seconds, which is designated as the search phase. The desolvation of main-chain amides is linked strongly to the steps in the search phase, and is likely to contribute to the energy barrier of the rate-determining step.

Figure 6. Structural events involved in the folding processes of proteins larger than 100 residues. The unfolded state (shaded) comprises many conformations that are mutually interconverting. Some conformations are pseudostable and cause slow dynamics detected at the single-molecule experiments. Once the sample is brought to the physiological condition, the conformation might act as the nucleation site for the collapse, which occurs rapidly in the microsecond time domain. The collapsed intermediate possesses specific structures that are important for construction of a folded structure. The hydrated water molecules around the main-chain amides are still present in the collapsed intermediate. Dehydration of the main-chain amides is associated with the formation of the native conformation and contributes to the largest energy barrier for protein folding.

Many events, such as those outlined above, demand further clarification. First, the mechanism of the collapse that enables the formation of specific structures in the initially collapsed state should be investigated. In fact, many recent controversies are related to the collapse phenomenon. For example, in time-resolved SAXS measurements, small proteins, such as protein L and ubiquitin, were demonstrated to be expanded in the unfolded state in the absence of the denaturants [36, 37]. However, the single-molecule Förster resonance energy transfer (FRET) measurements for the small proteins demonstrate that the unfolded proteins are collapsed [51]. Cyt c reportedly collapses from the unfolded state to the first detectable state with a single time constant of 50 μs [14, 52]. However, a careful examination of the process suggested that the collapse occurs in two phases with time constants of <20 and 100 μs [53]. Consequently, the nature of the collapse should be further investigated with the improved time resolution and with the