SINGLE-MOLECULEBIOPHYSICS

EXPERIMENT AND THEORY

ADVANCES IN CHEMICAL PHYSICSVOLUME 146

EDITORIAL BOARD

Moungi G. Bawendi, Department of Chemistry, Massachusetts Institute of Technology,Cambridge, Massachusetts, USA

Kurt Binder, Condensed Matter Theory Group, Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany

William T. Coffey, Department of Electronics and Electrical Engineering, Trinity College,University of Dublin, Dublin, Ireland

Karl F. Freed, Department of Chemistry, James Franck Institute, University of Chicago,Chicago, Illinois, USA

Daan Frenkel, Department of Chemistry, Trinity College, University of Cambridge,Cambridge, United Kingdom

Pierre Gaspard, Center for Nonlinear Phenomena and Complex Systems, Université Libre deBruxelles, Brussels, Belgium

Martin Gruebele, School of Chemical Sciences and Beckman Institute, Director of Center forBiophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana,Illinois, USA

Jean-Pierre Hansen, Department of Chemistry, University of Cambridge, Cambridge, UnitedKingdom

Gerhard Hummer, Chief, Theoretical Biophysics Section, NIDDK-National Institutes ofHealth, Bethesda, Maryland, USA

Ronnie Kosloff, Department of Physical Chemistry, Institute of Chemistry and Fritz HaberCenter for Molecular Dynamics, The Hebrew University of Jerusalem, Israel

Ka Yee Lee, Department of Chemistry and The James Franck Institute, The University ofChicago, Chicago, Illinois, USA

Todd J. Martinez, Department of Chemistry, Stanford University, Stanford, California, USAShaul Mukamel, Department of Chemistry, University of California at Irvine, Irvine,

California, USAJose Onuchic, Department of Physics, Co-Director Center for Theoretical Biological Physics,

University of California at San Diego, La Jolla, California, USASteven Quake, Department of Physics, Stanford University, Stanford, California, USAMark Ratner, Department of Chemistry, Northwestern University, Evanston, Illinois, USADavid Reichmann, Department of Chemistry, Columbia University, New York, New York,

USAGeorge Schatz, Department of Chemistry, Northwestern University, Evanston, Illinois, USANorbert Scherer, Department of Chemistry, James Franck Institute, University of Chicago,

Chicago, Illinois, USASteven J. Sibener, Department of Chemistry, James Franck Institute, University of Chicago,

Chicago, Illinois, USAAndrei Tokmakoff, Department of Chemistry, Massachusetts Institute of Technology,

Cambridge, Massachusetts, USADonald G. Truhlar, Department of Chemistry, University of Minnesota, Minneapolis,

Minnesota, USAJohn C. Tully, Department of Chemistry, Yale University, New Haven, Connecticut, USA

SINGLE-MOLECULEBIOPHYSICS

EXPERIMENT AND THEORY

ADVANCES IN CHEMICAL PHYSICSVOLUME 146

Edited by

TAMIKI KOMATSUZAKI, MASARU KAWAKAMI,SATOSHI TAKAHASHI, HAW YANG, ROBERT J. SILBEY

Series Editors

STUART A. RICEDepartment of Chemistry

andThe James Franck InstituteThe University of Chicago

Chicago, Illinois

AARON R. DINNERDepartment of Chemistry

andThe James Franck InstituteThe University of Chicago

Chicago, Illinois

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

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CONTRIBUTORS

Rehana Afrin, Innovation Laboratory, Tokyo Institute of Technology, Midori-ku,Yokohama 226-8501, Japan

Akinori Baba, Physical Biology Unit, RIKEN Center for Developmental Biology,Kobe 650-0047, Japan

Jianshu Cao, Department of Chemistry, MIT, Cambridge, Massachusetts, 02139,USA

Ophir Flomenbom, Flomenbom-BPS, Louis Marshal 19, Tel-Aviv, Israel 62668

Irina V. Gopich, Laboratory of Chemical Physics, National Institute of Diabetesand Digestive and Kidney Diseases, National Institutes of Health, Bethesda,Maryland 20892, USA

Atsushi Ikai, Innovation Laboratory, Tokyo Institute of Technology, Midori-ku,Yokohama 226-8501, Japan

Masayuki Iwamoto, Department of Molecular Physiology and Biophysics, Uni-versity of Fukui Faculty of Medical Sciences, 23-3, Matsuokashimoaizuki,Eiheiji-cho, Yoshida-gun, Fukui 910-1193, Japan

Kiyoto Kamagata, Institute of Multidisciplinary Research for Advanced Mate-rials, Tohoku University, Sendai, Miyagi 980-8577, Japan; Core Research forEvolutional Science and Technology (CREST), Japan Science and Technol-ogy Agency (JST), Kawaguchi, Saitama 332-0012, Japan

Masaru Kawakami, School of Materials Science, Japan Advanced Institute ofScience and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa 923-1292,Japan; PRESTO of Japan Science and Technology Corporation (JST), 4-1-8Honcho Kawaguchi, Saitama 332-0012, Japan

Tamiki Komatsuzaki, Molecule & Life Nonlinear Sciences Laboratory, ResearchInstitute for Electronic Science, Hokkaido University, Kita 20 Nishi 10,Kita-ku, Sapporo 001-0020, Japan; Core Research for Evolutional Scienceand Technology (CREST), Japan Science and Technology Agency (JST),4-1-8, Honcho, Kawaguchi, Saitama 332-0012, Japan

Takashi Konno, Department of Molecular Physiology and Biophysics, Universityof Fukui Faculty of Medical Sciences, 23-3, Matsuokashimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui 910-1193, Japan

v

vi Contributors

Miki Morimatsu, Laboratories for Nanobiology, Graduate School of Frontier Bio-sciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan;Core Research for Evolutional Science and Technology (CREST), Japan Sci-ence and Technology Agency (JST), 1-3 Yamadaoka, Suita, Osaka 565-0871,Japan

Daniel Nettels, Biochemisches Institut, Universität Zürich, Winterthurerstr.190, 8057 Zürich, Switzerland

Masatoshi Nishikawa, Department of Mathematical and Life Sciences,Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526,Japan; Core Research for Evolutional Science and Technology (CREST),Japan Science and Technology Agency (JST), 1-3 Yamadaoka, Suita, Osaka565-0871, Japan

Shigetoshi Oiki, Department of Molecular Physiology and Biophysics, Uni-versity of Fukui Faculty of Medical Sciences, 23-3, Matsuokashimoaizuki,Eiheiji-cho, Yoshida-gun, Fukui 910-1193, Japan

Kenji Okamoto, Department of Chemistry, Graduate School of Science, KyotoUniversity, Kitashirakawa-oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan

Peter D. Olmsted, School of Physics and Astronomy, University of Leeds, LeedsLS2 9JT, UK

Emanuele Paci, Institute of Molecular and Cellular Biology, University of Leeds,Leeds LS2 9JT, UK

Yasushi Sako, Cellular Informatics Laboratory, RIKEN, 2-1 Hirosawa, Wako351-0198, Japan

Yuji C. Sasaki, Department of Advanced Materials Science, Graduate School ofFrontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, KashiwaCity, Chiba, 277-8561, Japan

Benjamin Schuler, Biochemisches Institut, Universität Zürich, Winterthurerstr.190, 8057 Zürich, Switzerland

Hiroshi Sekiguchi, Laboratory of Biodynamics, Tokyo Institute of Technology,Midori-ku, Yokohama 226-8501, Japan; Department of Advanced MaterialsScience, Graduate School of Frontier Sciences, The University of Tokyo,5-1-5 Kashiwanoha, Kashiwa city, Chiba, 277-8561, Japan

Hirofumi Shimizu, Department of Molecular Physiology and Biophysics, Uni-versity of Fukui Faculty of Medical Sciences, 23-3, Matsuokashimoaizuki,Eiheiji-cho, Yoshida-gun, Fukui 910-1193, Japan

Contributors vii

Attila Szabo, Laboratory of Chemical Physics, National Institute of Diabetesand Digestive and Kidney Diseases, National Institutes of Health, Bethesda,Maryland 20892, USA

Hiroaki Takagi, Department of Physics, Nara Medical University, 840 Shijo-cho,Kashihara Nara 634-8521, Japan; Core Research for Evolutional Science andTechnology (CREST), Japan Science and Technology Agency (JST), 1-3Yamadaoka, Suita, Osaka 565-0871, Japan

Satoshi Takahashi, Institute of Multidisciplinary Research for Advanced Mate-rials, Tohoku University, Sendai, Miyagi 980-8577, Japan; Core Research forEvolutional Science and Technology (CREST), Japan Science and Technol-ogy Agency (JST), Kawaguchi, Saitama 332-0012, Japan

Yukinori Taniguchi, School of Materials Science, Japan Advanced Institute ofScience and Technology (JAIST) 1-1 Asahidai, Nomi, Ishikawa 923-1292,Japan; Japan Society for the Promotion of Science (JSPS), 8 Ichibancho,Chiyoda-ku, Tokyo 102-8472, Japan

Masahide Terazima, Department of Chemistry, Graduate School of Science,Kyoto University, Kitashirakawa-oiwakecho, Sakyo-ku, Kyoto 606-8502,Japan

Jianlan Wu, Department of Chemistry, MIT, Cambridge, Massachusetts, 02139,USA

Haw Yang, Department of Chemistry, Princeton University, Princeton, NJ 08544,USA

Zu Thur Yew, Institute of Molecular and Cellular Biology, University of Leeds,Leeds LS2 9JT, UK

PREFACE TO THE SERIES

Advances in science often involve initial development of individual specializedfields of study within traditional disciplines, followed by broadening and over-lapping, or even merging, of those specialized fields, leading to a blurring of thelines between traditional disciplines. The pace of that blurring has accelerated inthe last few decades, and much of the important and exciting research carried outtoday seeks to synthesize elements from different fields of knowledge. Examplesof such research areas include biophysics and studies of nanostructured materials.As the study of the forces that govern the structure and dynamics of molecularsystems, chemical physics encompasses these and many other emerging researchdirections. Unfortunately, the flood of scientific literature has been accompaniedby losses in the shared vocabulary and approaches of the traditional disciplines,and there is much pressure from scientific journals to be ever more concise in thedescriptions of studies, to the point that much valuable experience, if recorded atall, is hidden in supplements and dissipated with time. These trends in scienceand publishing make this series, Advances in Chemical Physics, a much neededresource.

The Advances in Chemical Physics is devoted to helping the reader obtaingeneral information about a wide variety of topics in chemical physics, a fieldthat we interpret very broadly. Our intent is to have experts present comprehensiveanalyses of subjects of interest and to encourage the expression of individual pointsof view. We hope that this approach to the presentation of an overview of a subjectwill both stimulate new research and serve as a personalized learning text forbeginners in a field.

Stuart A. Rice

Aaron R. Dinner

ix

CONTENTS

xiiiPreface

part one Developments on Single-Molecule Experiments

3Staring at a Protein: Ensemble and Single-MoleculeInvestigations on Protein-Folding Dynamics

By Satoshi Takahashi and Kiyoto Kamagata

23Single-Molecule FRET of Protein-Folding Dynamics

By Daniel Nettels and Benjamin Schuler

49Quantitative Analysis of Single-Molecule FRET Signals and itsApplication to Telomere DNA

By Kenji Okamoto and Masahide Terazima

71

Force to Unbind Ligand–Receptor Complexes and the InternalRigidity of Globular Proteins Probed by Single-Molecule ForceSpectroscopy

By Atsushi Ikai, Rehana Afrin, and Hiroshi Sekiguchi

89Recent Advances in Single-Molecule Biophysics with the Use ofAtomic Force Microscopy

By Masaru Kawakami and Yukinori Taniguchi

133Dynamical Single-Molecule Observations of Membrane ProteinUsing High-Energy Probes

By Yuji C. Sasaki

147Single-Molecular Gating Dynamics for the KcsA PotassiumChannel

By Shigetoshi Oiki, Hirofumi Shimizu, Masayuki Iwamoto, andTakashi Konno

xi

xii contents

195Static and Dynamic Disorder in IN VITRO ReconstitutedReceptor–Adaptor Interaction

By Hiroaki Takagi, Miki Morimatsu, and Yasushi Sako

part two Developments on Single-Molecule Theories andAnalyses

219Change-Point Localization and Wavelet Spectral Analysis ofSingle-Molecule Time Series

By Haw Yang

245Theory of Single-Molecule FRET Efficiency Histograms

By Irina V. Gopich and Attila Szabo

299Multidimensional Energy Landscapes in Single-MoleculeBiophysics

By Akinori Baba and Tamiki Komatsuzaki

329Generalized Michaelis–Menten Equation for ConformationModulated Monomeric Enzymes

By Jianlan Wu and Jianshu Cao

367Making it Possible: Constructing a Reliable Mechanism from aFinite Trajectory

By Ophir Flomenbom

395Free Energy Landscapes of Proteins: Insights from MechanicalProbes

By Zu Thur Yew, Peter D. Olmsted, and Emanuele Paci

419Mechanochemical Coupling Revealed by the FluctuationAnalysis of Different Biomolecular Motors

By Hiroaki Takagi and Masatoshi Nishikawa

437Author Index

467Subject Index

PREFACE

Theoretical and experimental breakthroughs are strongly coupled: major advancesin fundamental theoretical concepts are often triggered by novel experimentalmethods and observations. Similarly, new theoretical ideas suggest more exper-iments. Single-molecule studies are a clear demonstration of this paradigm. Theadvent of optical single-molecule spectroscopy and atomic force microscopy hasempowered novel experiments on individual biomolecules, opening up new fron-tiers in molecular and cell biology. And these experiments led to new theoreticalapproaches and insights. The single-molecule approaches offer unique insights notonly for the distribution of molecular properties, but also for the dynamics of indi-vidual molecules information that cannot be provided by conventional ensembleaveraged measurements.

In the past few years, important advances have been made in several areas wheredata from single-molecule experiments have provided fresh new perspectives.Driving these developments are questions including, for example, how proteinsfold to specific conformations from the highly heterogeneous structures, how sig-nal transductions take place on the molecular level, as well how proteins behave inmembranes and in living cells. A general problem arising from these new exper-imental observations is the theoretical underpinning for the roles of fluctuationsin biochemical reactions. For example: Why biological systems can robustly per-form their functions even with the free energy gain or loss of the reactions beingcomparable to the thermal energy, kBT ?

With a strong conviction that the integration of experimental developmentsand theoretical advances is essential toward resolving these issues, we have orga-nized two international conferences focusing on identifying and articulating theseissues. The first conference was entitled, Linking Single Molecule Spectroscopyand Energy Landscape Perspectives, held on December 3, 2008, at the FUKUOKAconvention center, Fukuoka, Japan (organized by T. Komatsuzaki and H. Yang)during the 46th Annual Conference of Biophysical Society of Japan. The secondconference was entitled, New Approaches to Complexity of Protein Dynamics bySingle Molecule Measurements: Experiments and Theories, from December 7 to9, 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-mentionedtwo conferences, including invited speakers, discussants, and organizers. The con-tent of this volume is organized into two parts: one is experimental, and the otheris theoretical development on single-molecule biophysics. Part I focuses mainly

xiii

xiv preface

on three experimental approaches: single-molecule fluorescence based mainly onfluorescence resonance energy transfer (FRET), atomic force microscopy (AFM)and diffracted X-ray tracking (DXT), and their applications to important biologicalphenomena. This part begins with experimental investigations of protein foldingand the development of a new fluorescence method for a long time detectionwithout tethering proteins to glass (Takahashi and Kamagata, Chapter 1) and isfollowed by conformational and dynamic properties of unfolded proteins basedon the confocal detection of single-molecule fluorescence (Nettels and Schuler,Chapter 2), and a quantitative analysis of FRET signals in terms of cumulativedistribution functions for telomere DNA (Okamoto and Terazima, Chapter 3). Thetopic then turns to AFM, which is capable of measuring the mechanical response ofa single molecule to an applied force. A systematic AFM study of the mechanicalproperty of the unbinding force of biomolecular complexes and rigidity (stiffness)of various biomolecules are reviewed (Ikai, Afrin, and Sekiguchi, Chapter 4). Anovel dynamic force spectroscopy using AFM is discussed, in which a stretchedsingle molecule is driven by an external oscillatory motion and both the staticand dynamic mechanical properties of the molecule can be obtained through thedeflection of an AFM cantilever (Kawakami and Taniguchi, Chapter 5). A recentbreakthrough in single-molecule experiments is the DXT method, which moni-tors the movements of individual nanocrystals linked to a specific site of proteinsat the picometer scale (Sasaki, Chapter 6). The DXT method revealed a twist-ing motion involved in the gating dynamics of a membrane potassium channel,KcsA (Oiki et al. Chapter 7). Finally, an exploration of complex kinetics at theassociation/dissociation of epidermal growth factor receptor and Grb2 in cellularsignal 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 byseveral internal noises in addition to external noises arising from experimentalsettings. For example, the origin of the fluctuation in the FRET data ranges fromphotophysics, such as blinking and bleaching to different quantum yields of twodye molecules. It is therefore of crucial importance to recognize the existence oftwo distinct, but complementary stages, in the analyses of single-molecule timeseries: The first is of extracting the time trace of a desired physical quantity, suchas an interdye distance from a noisy signal and the second is of constructing theunderlying mechanisms from a scalar time series, such as multidimensional energylandscapes and networks composed of states in a kinetic scheme. Part II includesnew theoretical frameworks to extract the scalar time trace of a desired physicalquantity 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 histogramsobtained from single-molecule photon counting experiments, which is designed

preface xv

to separate the time trace of photon trajectories in the diffusion process into thedistance fluctuation between dye molecules and the other components (Gopichand Szabo, Chapter 10), a new theoretical framework to construct local equilib-rium states and the corresponding multidimensional energy landscape from a scalartime series without a priori postulation of the concept of local equilibration and thedetailed balance (Baba and Komatsuzaki, Chapter 11), a generalized Michaelis–Menten rate equation for nonequilibrium steady-state turnover reactions in whichthe original kinetic network model is mapped onto a flux network with unbalancedpopulation currents and the concentration dependence of substrate for the averageturnover rate derived (Wu and Cao, Chapter 12), a new construction scheme of areduced form of the underlying multisubstate kinetic scheme for time trace whencomposed of two states, where the connections between the nodes in the networkcan have multiexponential waiting time probability density functions (Flomenbom,Chapter 13), a systematic survey of discrepancies found between numerical simu-lations and AFM experiments for mechanical unfolding of proteins including a cau-tion of oversimplifications due to the projections of the intrinsic multidimensionalfree 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 themean velocity and velocity fluctuation at various ATP concentration (Takagi andNishikawa, Chapter 15).

We note, however, that the subject matter included herein should not be regardedas solved; rather, they indicate topics that have been identified for which solutionswith various levels of completeness have been provided. It is therefore hopedthat the ideas contained in this volume will motivate further innovations in bothexperiment and theory, and especially their closer interactions in the near future.

We finally acknowledge the financial supports for the above two conferencesfrom the following organizations and programs: (1) Japan Science and TechnologyAgency, Promoting Globalization on Basic Research Programs, (2) Japan Scienceand Technology Agency, Core Research for Evolutional Science and Technology(CREST), and (3) The Institute for Protein Research, Osaka University.

T. KomatsuzakiM. KawakamiS. Takahashi

H. YangR. J. Silbey

PART ONE

DEVELOPMENTS ONSINGLE-MOLECULE EXPERIMENTS

STARING AT A PROTEIN: ENSEMBLE ANDSINGLE-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

CONTENTS

I. IntroductionA. Structural Properties of Folded ProteinsB. Cooperativity in the Folding Transitions

II. Ensemble Investigations of Protein FoldingA. Strategies for Ensemble InvestigationsB. Stepwise Folding of Cytochrome cC. Collapse and Search Mechanism in Apomyoglobin FoldingD. Folding Pathway Depends on Secondary StructuresE. Scaling Behavior in the Initial IntermediatesF. Two-State and Multistate Transitions Are Likely Determined by the Collapse TransitionG. Main-Chain Solvation and Desolvation Dynamics

III. Single-Molecule Investigations of Protein FoldingA. Development of a Single-Molecule Detection SystemB. Slow Conformational Dynamics Observed in the Unfolded cyt cC. Diversity of Conformational Dynamics in the Unfolded Proteins

IV. Summary and PerspectiveAcknowledgmentsReferences

∗To whom correspondence should be addressed.

Single-Molecule Biophysics: Experiment and Theory, Advances in Chemical Physics, Volume 146.Edited by Tamiki Komatsuzaki, Masaru Kawakami, Satoshi Takahashi, Haw Yang, andRobert J. Silbey.© 2012 John Wiley & Sons, Inc. Published 2012 by John Wiley & Sons, Inc.

3

4 satoshi takahashi and kiyoto kamagata

I. INTRODUCTION

A. Structural Properties of Folded Proteins

Proteins are natural heteropolymers that possess a remarkable property to foldto their native conformations autonomously, where they perform various phys-iological functions [1]. Proteins become unfolded in solutions containing highconcentrations of denaturants, however, the folded conformations are usually re-generated once the concentration of the denaturants is reduced [2]. This observationdemonstrates that the folded conformation is determined by the primary sequence.It further suggests that the folded conformation is predictable. Despite intensiveinvestigations conducted over the past 40 years, the prediction of protein structuresstill presents an extremely difficult task [3]. In fact, the current situation is thateven the prediction of the foldability of the sequences created by single mutationof natural proteins is difficult, reflecting our lack of understanding of the molecularprinciples governing protein folding. The processes involved in the selection ofthe 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 othersynthetic and biological polymers and from the unfolded proteins. First, proteinsare abundant in secondary structures, which are mainly stabilized by hydrogenbonds between main-chain amides. Second, proteins are always compact, andthe interior of proteins is packed nearly perfectly, similarly to crystals of organiccompounds. Third, the interior of proteins is mostly dehydrated. No watermolecule is usually observed in the core domain of proteins. The compactnessand the absence of water are related to the fact that the major driving force ofprotein folding is the hydrophobic interaction. Fourth, the folded conformationof proteins basically consists of a single topology. In contrast, the unfoldedproteins possess no secondary structures, and are in expanded conformationswith fully solvated polypeptides. The unfolded proteins comprise an astronomicalnumber of heterogeneous conformations that are interconverting into each other.Consequently, the dynamic process of protein folding involves a myriad ofmolecular events that lead the unfolded proteins to the distinct conformation. Theimportant question persists: How are the four structural properties of the foldedproteins organized in the dynamic process of protein folding?

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

staring at a protein 5

B. Cooperativity in the Folding Transitions

Although the unfolded state of a protein comprises an astronomical number ofconformations, the observable process of protein folding is surprisingly simple.For many small proteins with chain lengths of 100 residues (medium proteins), the folding transition occurs asa multistep process involving one or more intermediate states (Fig. 1) [8]. Ac-cordingly, the perfect cooperativity observed in small proteins is not maintainedin medium proteins. It is important, however, that the transitions between anypair of the unfolded state, intermediates, and native state are still cooperative.Many single-domain proteins with >200 residues (large proteins) fail to fold au-tonomously, and require cellular machineries that prevent the formation of mis-folded structures. Proteins with much larger chain lengths (e.g., 1000 residues)are not rare. These proteins are usually composed of multiple domains, each ofwhich folds independently. The dependency of the folding cooperativity on thechain length suggests that the folding transitions are controlled by the propertiesof proteins as polymeric molecules.

Figure 1. Cooperativity in the folding transition of proteins. (a) Small proteins with 100 residues frequently possess oneor more intermediates in addition to the unfolded and folded states. In some cases, the intermediatesare called the molten globule state. However, the transitions between any pair of the unfolded state, theintermediate, and the native state are still cooperative.

6 satoshi takahashi and kiyoto kamagata

Various properties of the intermediates of medium proteins have been investi-gated. The equilibrium intermediates are usually observed under mildly denaturingconditions, and are sometimes termed as the molten globule state, which is col-lapsed and possesses a large amount of secondary structure [10]. Although the stateis highly fluctuating, it possesses partially formed tertiary contacts that are indis-pensable for the stability of the state. During the kinetic process from the unfoldedto the native state in medium proteins, the kinetic intermediates usually appearwithin the mixing dead time of the stopped-flow apparatus (a few milliseconds)[11]. The conformational properties of the kinetic intermediates resemble that ofthe molten globule intermediates [12]. Because of the limited time resolution andstructural information, it remains unknown how and why the intermediate confor-mations 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 speedof the processes. To initiate the folding, it is usually necessary to dilute the highlyconcentrated denaturants in solutions containing the unfolded proteins. The con-ventional stopped-flow apparatus can achieve the mixing dead time of, at most,several milliseconds. We used a continuous-flow rapid mixing technique that canachieve a time resolution of several hundreds of microseconds, and can drasticallyenlarge the accessible time window for kinetic investigations of protein folding[13]. In some special applications, a mixing dead time as short as ∼11 �s can beachieved [14]. The other advantage of the continuous-flow technique is its applica-bility to a variety of spectroscopic and scattering methods. Transient spectra can beobtained easily by placing the mixing device inside of conventional spectrometersand by changing the device’s location relative to the observation point. We usedcircular dichroism (CD) [5] and Fourier transform infrared (FTIR) [15] spectro-scopies 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 fold-ing dynamics of proteins with different chain lengths, secondary structure contents,and topologies. These include �-helical proteins, such as cytochrome c (cyt c) (5,6, 13, 14, 16), apomyoglobin (ApoMb) [17, 18], and heme oxygenase [19]. Inaddition, single-chain monellin (SMN) [20, 21] was selected as an example ofproteins containing �-sheet (Fig. 2).

B. Stepwise Folding of Cytochrome c

Cytochrome c is a small globular protein with 104 amino acid residues and pos-sesses a heme prosthetic group that is attached covalently to the main chain.

staring at a protein 7

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

At pH 7 and 2, cyt c is, respectively, in the folded and unfolded states. In the foldedconformation, the heme group is surrounded by three helices termed N-terminal,C-terminal, and 60’s helices. Additionally, the heme possesses two axially coor-dinated residues: histidine-18 (His18) and methionine-80 (Met80) (Fig. 2). Theunfolded protein at pH 2 is expanded and possesses no specific structures. Further-more, the protein forms the molten globule intermediate at pH 2 in the presenceof a high concentration of salt [22]. The protein also forms another intermediatein the course of kinetic folding, in which the non-native histidine (either His26 orHis33) is coordinated to the heme in place of the native methionine [23]. Becausethe misligation decelerates the folding kinetics, the form is sometimes termed themisfolded state. The formation of the misligated conformation can be minimizedby conducting the refolding reaction at pH 4.5, where histidine residues are pri-marily in the protonated state and cannot coordinate to heme. Consequently, bychanging pH from 2.0 to 4.5, we can monitor the folding kinetics of cyt c, whichis unaffected by the misligated conformation [24].

To detect changes in the secondary structures in the folding kinetics after the pHjump 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

8 satoshi takahashi and kiyoto kamagata

as an index of the �-helix formation. The CD spectrum for the initial acid unfoldedstate (U) showed that the helical content is ∼10%. The spectrum does not changeat 400 �s after the pH jump, demonstrating that the helix formation is not coupledto the formation of the initial intermediate (I). The kinetic changes in the CDspectra after 400 �s can be well approximated by two exponential phases. Thefirst phase (2100 s−1) corresponds to the formation of the second intermediate(II), whose helical content was ∼35%. The second phase (150 s−1) correspondsto the conversion of the second intermediate to the native state (N) possessing thehelical content of ∼50%. Consequently, the sequential folding scheme with twointermediates (Scheme 1)

U � I� II� NScheme 1

can explain the observed CD spectra. These results, demonstrating the major helixformation in the time domain after 400 �s, are in sharp contrast to the premisethat the secondary structure formation occurs immediately after the initiation offolding.

To detect the compactness in the cyt c folding, the second of the four structuralproperties of the native proteins, we next conducted time-resolved SAXS exper-iments [16]. We constructed a time-resolved SAXS detection system based on arapid mixing device and the intense X-ray source from the synchrotron facility atSPring8. 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 CDresults, the SAXS results demonstrated a considerable reduction in Rg from 24.3to 21.1 Å within the observation dead time (160 �s). The Rg value was inter-preted to correspond to that of the initial intermediate (I). All other kinetic datawere explained consistently based on the sequential folding scheme with two in-termediates (Scheme 1). The second intermediate (II) was shown to possess theRg value of 17.8 Å. We showed the changes in �-helical content and Rg in thetwo-dimensional (2D) plot, which clearly demonstrated that the reduction in Rg isthe first kinetic event in the stepwise folding of cyt c (Fig. 3).

C. Collapse and Search Mechanism in Apomyoglobin Folding

Next, we conducted time-resolved CD and SAXS experiments on the folding ofapoMb [18]. Apomyoglobin is the apo form of myoglobin with 153 residues,in which the prosthetic heme group is surrounded by eight helices designatedas A–H (Fig. 2B). Upon the extraction of heme, apoMb maintains the foldedstructure 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),

staring at a protein 9

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

which possesses a small helical content of ∼10% [26]. In addition, the equilibriumintermediate, sometimes termed as the molten globule state, becomes stabilizedat pH 4.2, which possesses a partial helical content of ∼33% located at helicesA, 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 fromUacid 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 �s, the protein showed a rapid col-lapse 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%. Next,we detected an increase in the helical content, which corresponds to the formationof the second intermediate (I2). The helix content of I2 is ∼44% and the Rg valueis identical to that of I1. Finally, the conversion of I2 to N was observed with atime constant of 49 ms. Consequently, the folding of apoMb is explainable by thelinear folding scheme (Scheme 2):

Uacid � I1 � I2 � NScheme 2

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

10 satoshi takahashi and kiyoto kamagata

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 col-lapse occurring within the mixing dead time. The secondary structure contents inthe initial intermediates are minor and depend on the proteins. The collapsed inter-mediate eventually converts to the second intermediate, which contains increasedamounts of the secondary structures and closely resembles the molten globule stateobserved in the equilibrium condition. The stepwise processes occurring afterthe collapse are likely to be associated with the search process for the correctfolded structures.

D. Folding Pathway Depends on Secondary Structures

To characterize the folding pathway of a �-sheet protein, next we investigated thefolding of SMN [28]. Single-chain monellin is a 94-residue protein consisting ofa five-stranded �-sheet and an �-helix (Fig. 2) and at pH 9.4 retains the nativeconformation (N). In contrast, SMN at pH 13 possesses the unfolded conforma-tion (U). The time-resolved observation of the folding of SMN initiated usinga pH-jump from 13.0 to 9.4 demonstrated that the initial collapse occurs within300 �s [20]. The Rg value for U is 25.5 Å, which becomes 18.2 Å after the col-lapse. The CD spectrum for the conformation at 300 �s was almost identical tothat of U. Consequently, the initial intermediate (I1) formed after the collapse pos-sesses only a limited amount of secondary structures. The I1 state converts to thenext intermediate (I2) with the increase in negative CD ellipticity, suggesting thepartial formation of the secondary structures. The Rg value for I2 is 15.4 Å, and iscomparable to that of N (15.8 Å). Finally, the formation of N was observed in theincrease in the negative ellipticity, corresponding to development of the �-sheetstructure. Consequently, the folding scheme of SMN resembles those of cyt c andapoMb (Scheme 3):

U � I1 � I2 � NScheme 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 for-mation of the secondary structure.

It is remarkable that the “collapse and search” mechanism was observed for both�-helical and �-sheet proteins. However, the kinetic steps involved in the secondarystructure formation differ between the two classes of proteins. The difference canbe visualized in the 2D plot describing the conformational landscape of proteins(Fig. 3). The unfolded states are commonly expanded with a small amount ofsecondary structures, and are located in the lower right of the plot. In contrast,the folded conformations are compact and possess high contents of secondarystructures, and are shown in the upper left. The folding intermediate states connect

staring at a protein 11

these states to form “pathways”. In the case for �-helical proteins, the pathwaystraverse the plot diagonally. It is particularly interesting that the pathway for SMN isdistinct and L-shaped, corresponding to the formation of the �-sheet structure thatoccurs as the slower step. This difference in the �-helical and �-sheet proteins waspredicted by theoretical calculations [29] and might be attributed to the abundanceof middle-range interactions that are necessary for the formation of a �-sheet [30].

E. Scaling Behavior in the Initial Intermediates

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

U � I1 � I2 � N, U′ � I′ � NScheme 4

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

To examine the properties of the initial collapse, we show the Rg values of theinitial 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 linearlydependent on the logarithm of the chain length with a slope of ∼ 13 . For the nativeproteins, the scaling exponent of ∼ 13 reflects the tight packing of proteins [32].Regarding the unfolded proteins, the scaling exponent is ∼ 35 , demonstrating thatthe unfolded proteins can be considered as random coils with excluded volumeeffects [33]. The scaling exponent for the initial intermediates is close to ∼ 13 ,suggesting that the Rg values for the collapsed conformation are not controlleddirectly by the individual sequences. We proposed that the initial conformationsare rather controlled by a property of the unfolded state of proteins as polymers.

12 satoshi takahashi and kiyoto kamagata

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 thepresence of high concentration of denaturant (crosses). Data for kinetic intermediates obtained in ourinvestigations were presented as open rectangles. Data obtained for the unfolded state in the absenceof the denaturant (filled rectangles) are distinct from those of the medium and large proteins (openrectangles). Modified from Fig. 5 of an earlier report [19].

Several theories have been proposed to explain the collapse transition of poly-mers and proteins. The simplest of them is Flory’s homopolymer theory, in whichhydrophobic polymers without sequence-dependent interaction become collapsedin poor solvents at temperatures below the � temperature (T�) [34]. The scalingexponent of the collapsed polymers, called globules, was predicted to be 13 , reflect-ing the homogeneous density of monomers. Consequently, the observation for theinitially collapsed conformation is consistent with the coil–globule transition. Theextension of Flory’s theory to random heteropolymers similarly predicts the pres-ence of the collapsed and extended conformations possessing scaling exponentsof 13 and

35 , respectively [35]. We conclude that the collapse transition, generally

observed in the initial phase of folding, reflects the properties of the unfoldedproteins as the polymeric molecules.

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

The collapse behavior of small proteins is distinct from that of medium proteins.Small proteins with