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TOPICAL REVIEW

Single-molecule experiments in biological physics:

methods and applications.

F. Ritort

Departament de Fısica Fonamental, Facultat de Fısica, Universitat deBarcelona, Diagonal 647, 08028 Barcelona, Spain

E-mail: [email protected]

Abstract. I review single-molecule experiments (SME) in biological physics.Recent technological developments have provided the tools to design and buildscientific instruments of high enough sensitivity and precision to manipulate andvisualize individual molecules and measure microscopic forces. Using SME itis possible to: manipulate molecules one at a time and measure distributionsdescribing molecular properties; characterize the kinetics of biomolecular reactionsand; detect molecular intermediates. SME provide the additional informationabout thermodynamics and kinetics of biomolecular processes. This complementsinformation obtained in traditional bulk assays. In SME it is also possible tomeasure small energies and detect large Brownian deviations in biomolecularreactions, thereby offering new methods and systems to scrutinize the basicfoundations of statistical mechanics. This review is written at a very introductorylevel emphasizing the importance of SME to scientists interested in knowing thecommon playground of ideas and the interdisciplinary topics accessible by thesetechniques.

The review discusses SME from an experimental perspective, first exposingthe most common experimental methodologies and later presenting variousmolecular systems where such techniques have been applied. I briefly discussexperimental techniques such as atomic-force microscopy (AFM), laser opticaltweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) andsingle-molecule fluorescence (SMF). I then present several applications of SME tothe study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discussapplications of SME to the study of the nonequilibrium thermodynamics of smallsystems and the experimental verification of fluctuation theorems. I concludewith a discussion of open questions and future perspectives.

PACS numbers: 82.35.-x,82.37.-j,87.15.-v

http://arXiv.org/abs/cond-mat/0609378v1

Single-molecule experiments 2

Contents

1 Introduction 2

2 Why single molecules? 4

3 From physics to biology and back 6

4 Experimental techniques 10

4.1 Single-molecule manipulation techniques . . . . . . . . . . . . . . . . . 104.1.1 Atomic-force microscopy (AFM). . . . . . . . . . . . . . . . . . 104.1.2 Laser optical tweezers (LOT). . . . . . . . . . . . . . . . . . . . 124.1.3 Magnetic tweezers (MT). . . . . . . . . . . . . . . . . . . . . . 154.1.4 Biomembrane force probe (BFP). . . . . . . . . . . . . . . . . . 15

4.2 Single-molecule fluorescence techniques . . . . . . . . . . . . . . . . . . 17

5 Systems 18

5.1 Nucleic acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.1.1 DNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.1.2 RNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.1.3 DNA condensation. . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2 Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2.1 Protein-Protein interactions. . . . . . . . . . . . . . . . . . . . 275.2.2 Protein folding. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.3 Molecular motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6 Tests of nonequilibrium theories in statistical physics 37

7 Conclusions 42

8 List of abbreviations 43

1. Introduction

The study of single molecules has become a major theme of research in modernbiophysics. Specialized journals are devoted to this emerging field and every yearmore researchers become attracted to it. The history of single-molecule experiments isrelated to that of single-molecule imaging and has its roots in the invention of opticaltweezers and the scanning tunneling microscope. The possibility of manipulatingindividual entities has always attracted the scientist. Since the experimental discoveryof the nucleus of the atom by Rutherford it has become a major goal in physics tosearch for the ultimate constituents of matter. A similar trend is followed in modernbiology. There the main goal has been to characterize and understand the functionof all constituent parts of the living organisms and, ultimately, the chemistry of life.Despite the fact that biology and physics are very different sciences (most students inbiology rarely feel attracted by physics and vice-versa) the true fact is that these twosciences are to become much closer than ever in the new starting century. Althoughthere have been many notable contributions to molecular biology by physicists (likeMax Delbruck, Francis Crick, the Braggs just to cite a few names) the two scienceshave diverged over the past thirty years. Molecular biology has developed very specific


experimental methods, most of them borrowed from biochemistry. These methodsare largely unknown to physicists (PCR amplification, gene cloning,..). The currenttendency is for this temporary gap to progressively narrow. More physicists will learnabout the subtleties of biological matter and therefore become acquainted with someof the techniques and methods used by biologists. The marriage between physics andbiology may still take years, chemistry becoming the privileged witness of the union.

What is the benefit of such a marriage? On the one hand, physicists are becomingsteadily interested in the properties of biological matter. The kinetics of molecularmotors, the folding of biomolecules, the viscoelastic and rheological properties of thecell, the transport of matter through pores or channels, the physical properties ofmembranes and the structure of biological networks are just a few examples of subjectsakin to the expertise and interests of the physicist. On the other hand, biologists areinterested in the physical techniques and methods available from physics. Physics isa quantitative science while biology has been traditionally mostly descriptive [1]. It isnot surprising that the discovery of the double helix was made possible thanks to X-raydiffraction, an experimental technique discovered and used by physicists to determineatomic structures in crystals. More important, the biologist is steadily aware of thegreat complexity of biological matter, the large variety of biological forms and therelevance of trying to unify such knowledge. Physical abstraction can be importantto single out common themes and variations throughout this vast phenomenology. Inaddition, current experimental methods applied to biological systems are providinga huge amount of data that must be quantitatively analyzed by using sophisticatedmethods. The physicist can help a lot in this task.

It is fair to say that single-molecule experiments will contribute to bridge thegap between physics and biology. Single-molecule experiments (hereafter referred asSME) provide a new tool in physical biochemistry that allows to explore biochemicalprocesses at an unprecedented level. They offer a quantitative description of biologicalprocesses reminiscent of physicists approach. SME are made possible thanks in partto the advent of nanotechnologies. These, combined with microscale manufacturingtechniques, provide the technology required to design and build scientific instrumentsof enough sensitivity and precision to manipulate individual molecules and measuremicroscopic forces, thereby allowing experimentalists to investigate various physicaland biological processes. Nowadays, the most widespread and commercially availablesingle-molecule technique in biophysics labs is the atomic force microscope (AFM).This technique allows one to take images of individual molecules adsorbed intosurfaces. At the same time with the AFM it is possible to grab molecules one at a timeby attaching one end of the molecule to the AFM tip, the other being immobilized onthe surface. By moving the tip relative to the substrate it is then possible to pull themolecule away from the surface and exert mechanical force. The value of the breakageforce, the distance that the tip has to be retracted before the contact breaks and thedependence of these numbers on the speed of the moving tip are important informationabout the mechanical strength and location of the probed molecular bond. By pullingapart many molecules one at a time it is possible to quantitatively characterize thebreakage process, thereby giving precious information about molecular interactions.

There are several excellent reviews in SME, applications and methodologies. Mostof them fall into two categories. Either they are very introductory and cover generictopics on single-molecule manipulation or they are more specialized and specificallydevoted to discuss particular topics. It could not be otherwise. The field of singlemolecules is developing very fast and at the same time diversifying into many different


areas. Therefore it is very difficult to cover all the subjects in a review. SME deal withaspects related to instrumentation, their application to study many different systems(belonging to physics, chemistry and biology), theoretical modeling and numericalsimulations. Only in the area of optical tweezers, there is a complete resourceletter available with useful references until the year 2003 (which includes nearly 400references) [2]. This number of references is steadily growing every year.

The present review attempts to partially fill this gap by presenting an overviewof various topics from an experimental perspective, first exposing the most importantexperimental methodologies and later reviewing various molecular systems where suchtechniques have been applied. I also include a brief section describing the applicationsof SME to investigate thermodynamics at the molecular level. This review coversSME applied to biomolecules, it therefore does not touch upon applications of single-molecule techniques to other interesting subjects such as living cells or non-biologicallyinspired problems. It briefly discusses theoretical modeling and numerical simulations.When appropriate a few references about theoretical models and simulations are listedfor those readers who want to delve deeper into the subject. The selection of topics hasbeen naturally biased by my own taste and expertise. Although I have tried to coverthe most relevant existing literature it is unavoidable that some important work andpapers have been unduly omitted. I apologize in advance to these colleagues whosework may have been overlooked.

Very introductory reviews to SME can be found in [3, 4, 5, 6]. There are alsomore focused reviews on the mechanical properties of biomolecules [7, 8, 9, 10, 11],the elastic properties of proteins [12, 13, 14], mechanochemistry [15], single-moleculefluorescence [16, 17, 18] and instrumentation [19, 20]. Whole journal issues devotedto review SME, some of which have been published as books [21], can be found in [22]and proceedings of biophysics conferences often include a section on SME [23, 24]. Wemust also mention web pages with detailed information about specific single-moleculetechniques (for example, laser tweezers [25]) or excellent review journals [26]. Finally,reviews about the usefulness of SME to investigate the thermodynamics of molecularsystems can be found in [27, 28, 29].

2. Why single molecules?

SME are central to biological physics research [30]. These offer a complementary yetdifferent perspective to understand molecular processes. What are the advantagesof SME compared to traditional bulk assays? The main difference between singlemolecule and traditional biochemistry methods lies in the kind of average donewhen measuring the properties of the system. SME allow experimentalists to accessbiomolecular processes by following individual molecules. Using SME it is possible tomeasure distributions describing certain molecular properties, characterize the kineticsof biomolecular reactions and observe possible intermediates. SME provide additionalinformation about thermodynamics and kinetics that is sometimes difficult to obtainin bulk experiments. All this is complemented by powerful visualization methods(which allow to capture images and produce movies) that greatly help the scientist inthe interpretation and understanding of the experiments.

To better understand the advantages of SME let us consider the example ofprotein folding. A protein in water solution can exist in two possible conformations(folded and unfolded). In one conformation the protein is folded into its native stateforming a compact globular structure. Roughly speaking, the hydrophobic core is


buried inside the globule and stabilized by specific amino acid-amino acid interactionswhereas the hydrophilic amino acids are exposed to the outside on the surface ofthe globule. In the other conformation the protein is denatured or unfolded forminga random coil. At room temperature (e.g. 25◦C or 298◦K) the protein is in thenative state as this state has a free energy that is lower than that of the randomcoil. Upon heating (or increasing the concentration of denaturants such as urea),the protein can denature and change conformation from the native to the unfoldedstate. Most proteins typically denature at temperatures in the range 50◦C-80◦C, eachprotein being characterized (under given solvent conditions of salinity and pH) by amelting temperature, Tm, where the protein denatures. The full characterization ofthis transition is possible by using calorimetry bulk measurements where the protein ispurified inside a test tube. The enthalpy curve obtained in such measurements shows ajump in the enthalpy and a latent heat (similar to that observed in water at its boilingpoint). This is the characteristic signature of a first-order phase transition separatingtwo conformations. The same conclusion is reached and the same melting temperaturefound by carrying out other bulk measurements (such as UV absorbance).

What additional information can be obtained with single-molecule techniques? Itis a well known fact that during the folding process some proteins transiently visit anintermediate state, the molten globule state, characterized by a short lifetime. In suchstate proteins form a globular structure where, roughly speaking, the hydrophobicand hydrophilic parts are separated between the core and the surface of the globulebut specific contacts between amino acids are not yet fully formed. Due to its shortlifetime, the fraction of molecules that are in the molten globule state inside the testtube can be small enough to go unobserved in calorimetry measurements. The tinysignal they produce can be masked by that of the overwhelming number of correctlyfolded or totally unfolded molecules. In SME one can follow one protein at a time,therefore it is possible to separate molecules into three families: the native (N), theintermediate molten globule (I) and the unfolded (U).

By using single-molecule fluorescence it is possible to attach fluorescent moleculesto proteins, detect them by focusing light into a tiny spot, and watch proteins gothrough that spot for a short interval of time. Fluorescent proteins are chemicallysynthesized by attaching fluorescent dyes into specific residues of the amino acid chainsof the protein (see Figure 1). In single-molecule fluorescence resonance energy transfer(FRET) techniques, two different color dyes (e.g. green and red) can be positionedat specific locations of the protein. These locations stay close each other when theprotein is in its native state, only slightly close in the intermediate state and faraway in the unfolded state. Upon radiation of light with the appropriate frequencythe green dye (the donor) absorbs the radiation. A fraction of that intensity of lightis emitted to the observer (ID). The rest of intensity is emitted by the red dye (theacceptor) through a non-radiative resonance energy transfer mechanism between donorand acceptor (the condition being that the emission spectrum of the donor overlapswith the absorption spectrum of the acceptor). The light emitted by the acceptor hasalways lower frequency than that emitted by donor and part of the energy transferredto the acceptor is lost to the environment in the form of heat. The amount of non-radiative energy transfer between the green and the red dye depends on the distancebetween the dyes and defines the FRET efficiency, E = IA/(IA + ηID) where η isa correction factor that depends on the quantum yields of donor and acceptor. ForE = 1 all light absorbed by the donor is transferred to the acceptor whereas for E = 0the light is emitted only by the donor. The intensity of light emitted by the donor


and the acceptor that is detected by the observer changes as the distance between thetwo dyes changes. However the total amount of light emitted by the donor and theacceptor is constant, until photobleaching occurs. Therefore the intermittent exchangebetween the amount of light emitted at both wavelengths is an indirect measure of thedistance between the dyes, i.e. of the different conformations of the protein (providinga spectroscopic ruler).

Coming back to our previous example, measurements taken over many proteinsmight show a three-modal distribution indicating three possible conformations ofthe molecules (N,I,U). The fraction of molecules observed in each of these threestates (i.e. the statistical weight of each mode) would be a function of thetemperature and/or denaturant concentration. Below/Above the melting temperaturenearly all molecules are folded/unfolded. In the vicinity of the melting transition,intermediate conformations would be observable together with some native andunfolded conformations as well. Single-molecule techniques offer also the possibility tomeasure kinetic or time-dependent processes by following the trajectories of individualmolecules. The signal would execute transitions as the conformation of the proteinchanges, providing direct evidence of the existence of an intermediate state as well asinformation about the kinetic rates between the three states. Sometimes the proteinwould execute transitions from the unfolded to the itermediate state (U → I) to laterjump to the native state (I → N). In this case the molten globule is an intermediateon-pathway to the native state. In another scenario the protein directly folds intothe native state without first collapsing into the intermediate (U → N). In thiscase the molten globule would be an intermediate state off-pathway to the nativestate. The statistics of the residence times of the protein in each state providesextremely valuable information about the folding process. All this information isusually masked in bulk measurements where results are averaged over moleculesand time. SME complement standard spectroscopy and microscopy techniques inmolecular biology and biochemistry and therefore have to be viewed as a new sourceof valuable information to interpret biomolecular processes.

3. From physics to biology and back

It is fair to say that single-molecule techniques have been largely developed byphysicists. These new kind of measurements are providing lots of quantitativeinformation about molecular processes that have to be analyzed using statisticalmethods. This is very attractive to the physicist who can propose experimentsto test new theories or to investigate theories and analyze models to interpret theexperimental results. This statement can be illustrated with the following example.It is worth mentioning that one among the first single-molecule pulling experimentsrevealed that the elastic response of individual double stranded DNA (dsDNA)molecules are excellently described by the worm-like chain model introduced inpolymer theory by Kratky and Porod in 1949 [33] (see later in Sec. 5.1.1) . Bypulling an individual molecule it was possible to experimentally measure the forceas a function of the molecular extension, also called force-extension curve (FEC)[34, 35]. These results verified the prediction of the worm-like chain model for theFEC and provided the first direct mechanical estimate of the persistence length ofindividual DNA molecules (roughly speaking the persistence length is the distancealong the contour length of the molecule where the molecule keeps a straight directiondue to its bending rigidity) which was in agreement with previous light scattering


AC

B

Figure 1. Single-molecule detection using FRET. (A) A conformational changein a protein changes the relative intensities of light emitted by the donor and theacceptor. (B) Typical FRET efficiency trajectories and donor/acceptor intensitiesID, IA (Inset) for individual proteins trapped in vesicles. These show multiplefolding/unfolding events close to the midpoint folding transition. The arrowindicates when photobleaching occurs. (C) Probability distributions of FRETefficiencies showing the existence of two families of proteins (folded and unfolded).The average FRET efficiency is around 0.6 and agrees well with values obtainedin bulk assays. Figures taken from [31, 32].

measurements. By stretching the molecule above 60 pN (1pN = 10−12N) it was alsopossible to observe a plateau in the FEC at 65 pN (see Fig. 3C). This is characteristicof a first-order transition and interpreted as a structural change in the DNA moleculethat gets overstretched as the DNA double helix unwinds and bases get tilted inthe direction where the force is applied. The FEC of DNA (or any other polymer)in single-molecule pulling experiments is similar to the magnetization-field curve inmagnets, the load-deformation curves in plastic materials or the polarization-voltagecurves in dielectrics showing the physical flavor of such experiments.

A particular area of physics that can largely benefit from knowledge emergingfrom SME is statistical physics. SME allow one to measure forces in the range of afew piconewtons (a piconewton is approximately a trillionth of the weight of an apple)and have spatial resolution in the range of a nanometer. These are the ranges of forces


and extensions typically involved in many biomolecular reactions where high energybonds (such as ATP) are hydrolyzed and the energy released is subsequently used toperform mechanical work. Work values typically encountered in such reactions areof the order of a few kBT units. At room temperature T ≃ 300◦K and therefore1kBT ≃ 4 pN × nm ≃ 0.6 kcal/mol ≃ 2.5 kJ/mol (In the biophysics or molecularbiology community it is common to refer to energies in kBT or kcal/mol units whereaskJ/mol is preferred among the chemists). Most biomolecular reactions take place inan aqueous environment in the presence of water molecules. As the energy of thebiochemical reaction is not much different than the average kinetic energy carried byone water molecule such processes take place in a highly noisy environment. Therefore,we can imagine a molecular enzyme acting on a substrate carrying out a specificmolecular reaction impinged by hundreds of water molecules each nanosecond, eachof these molecules carrying enough kinetic energy to interfere in the process. Undersuch conditions we expect strong Brownian fluctuations in the behavior of the enzyme,which show up as rare and large deviations of its motion from the average behavior[36]. What if one water molecule carrying 10 times the average kinetic energy collideswith the enzyme while a particular biochemical reaction takes place? This happensfrom time to time and such large deviations must influence the behaviour of the motor.It is surprising to know that most of these work producing molecular machines have avery large efficiency where a large fraction of the energy consumed (typically around20-90%) is used as mechanical work, part of the rest of energy gets lost in the form ofheat released into the aqueous environment.

Fluctuations are well known to be the cause of some mutations that occur duringthe replication processes of DNA, when a new strand is synthesized from the parentalstrand and the genetic information is transmitted to a new generation of cells. Duringthe replication process many proteins interact with the DNA and participate in theprocess by self-assembling into a large complex. The replicating machinery is immersedin water and subjected to strong Brownian fluctuations. Under such harsh conditionsmutations occur frequently during the replicating process. However, what mostlysurprises from the replication process is not the fact that mutations are common butthat mutation rates are regulated inside the cell. Mutations are necessary as evolutiontakes advantage of them to produce better adapted individuals. However, mutationlevels during the replication process are kept under so tight control that mismatchesoccur as rarely as one every 109 replicated base pairs. To avoid the damaging effects ofnoise fluctuations, cells are endowed with a complex machinery of repair that is activeduring the crucial steps of the replicating process and important for the maintenance ofthe genome. Large fluctuations are expected to occur whenever a large number of fastmoving molecules clash simultaneously with the enzyme. Will these large deviationsaffect the performance of the enzyme? In which way will they alter its function? Evenmore interesting, are these deviations an integral part of the function and efficiencyof the enzyme? Such questions are just a few among many others that biophysicistsand statistical physicists are ready to confront.

The possibility to measure such tiny energies brings us close to what we candistinguish as an emerging area of science, i.e. how to understand and design molecularmotors that operate in the nanoscale and efficiently use chemical energy from naturallyavailable (or synthesized) sources to perform specifically designed functions. We mightcall this thermodynamics of small systems as the main goal of this discipline is tounderstand the performance of these small machines in a noisy environment. Suchterm was already coined by Hill many years ago when referring to thermodynamic


equilibrium properties of ensembles of small size systems where the equations ofstate depend on the ensemble or collectivity, i.e. the conditions or parametersthat are kept fixed in the ensemble [37]. However, the most important aspect ofmolecular machines is that they operate far from equilibrium by hydrolyzing sizableamounts of energy and taking advantage of large and rare deviations. The relationbetween the nonequilibrium properties of small machines and their thermodynamicproperties is shaping a new discipline in statistical physics, the so called nonequilibriumthermodynamics of small systems. The main facts behind this new discipline have beendiscussed in [28] at a very introductory level.

A related aspect of great interest to the statistical physicist is how to use SMEto test the basic foundations of statistical mechanics. This line of thought has seenimportant progress in recent years and we foresee that the exploration will continueand improve as more precise and quantitative measurements are becoming available.Examples are the study of the nonequilibrium work relations or fluctuation theoremsunder various conditions. Biological systems have been particularly useful in thisregard. The experimental access to small energies is interesting in non-linear systems,i.e. systems that do not respond in a linear way to an applied external perturbation.Systems of this type abound in molecular biology where conformational changes andmacromolecular interactions are of the all-or-none type. This is also referred as the lockand key interaction mechanism among molecular biologists, substrate-enzyme reactionsin biochemistry or activated behavior in the language of the physicist. In these type ofinteractions, a tiny variation of the external conditions can cause a big change in theoutcome of the reaction. This fact is behind the high sensitivity of protein structures tosingle amino acid mutations or the strong dependence of some enzymatic reactions toa small amount of some specific substances (e.g. activators or repressors). In proteins,although not all single amino acid changes lead to new folded structures, a few of themin some specific parts of the chain can have dramatic effects in the structure with lethalconsequences at the level of the cellular functions regulated by that protein. In physicalsystems such stability conditions are not so usually encountered. Upon the influence ofsmall perturbations physical systems usually respond in a smooth way albeit, of course,counterexamples also abound. The main difference between physical and biologicalsystems is that structure and function are intimately related in the latter. As a resultof evolution over millions of years a new kind of interactions and interrelationshipshave emerged between different parts of living matter (evolutionary constraints) whichare not expected to be common in other physical or chemical systems.

The idea of following individual biomolecules to understand processes that occurin a crowded environment like the cell pertains to the kind of abstractions typicalof a physicist. How has been received this idea by the community of biologists?The response is not yet uniform among the rows of biologists who, depending ontheir area of specialization, can feel more akin to the new techniques. Molecularbiologists and biochemists are probably the most receptive because single-moleculemethods offer complementary tools to investigate problems of their interest. Forexample, many processes that occur inside the cell such as DNA transcription andreplication, molecular transport, virus infection, DNA condensation, ATP generationcan be studied by using these new techniques. As we discussed in Sec. 2, thisapproach provides new relevant information to the molecular biologist which is usuallyunavailable with traditional techniques. A common criticism to single-moleculemethods is that molecular processes cannot be studied in vivo by following a moleculein its natural environment (e.g. a DNA replicating inside the nucleus). This is


indeed a limitation at present but it must be said that the same occurs in traditionalbiochemical assays. The specific conditions found in the cell cannot be reproducedin the test tube, which contains only a tiny fraction of the total number of cellconstituents. This limitation, however, is not seen as a drawback in the mind ofa physicist who is educated to explore simplified versions of complex and difficultproblems. The true fact is that more and more molecular biologists are becomingsteadily interested in adopting such techniques in their labs. This gives rise to anunprecedented excitement between physicists and biologists who are joining effortsand expertise to accomplish common scientific goals.

4. Experimental techniques

In this section I succinctly describe the experimental techniques mostly used in SME.We have to distinguish between techniques required to manipulate individual moleculesand techniques that allow to detect and follow in real time (but not manipulate)individual molecules. In the first class we have atomic force microscopy (AFM), laseroptical tweezers (LOT), magnetic tweezers (MT) and biomembrane force probe (BFP)to cite the most representative ones. Other techniques (such as glass microfibers) arenot of widespread use in SME and we are not going to discuss them here. In thesecond class, and in addition to AFM (which is also an imaging technique), there arepredominantly optical techniques such as single-molecule fluorescence (SMF), Ramanspectroscopy, two-photon spectroscopy and semiconductor quantum dot emission tocite the most common. Combination of manipulation and fluorescence techniques(e.g. laser tweezers with fluorescence) has already begun and will allow to explorenew phenomena with enhanced precision.

4.1. Single-molecule manipulation techniques

In this section the different techniques to manipulate individual molecules and measuremicroscopic forces are outlined. AFM are particularly useful because these can be usedto sweep surfaces and take images of individual molecules. At the same time, AFM canbe used to apply mechanical force on individual molecules. LOT cannot be used to takeimages of individual molecules but have the advantage that manipulation of individualmolecules can be more easily controlled, for example, in the study of molecular motors.The case of LOT has been chosen to be discussed in detail to emphasize the difficultiesand the methodology common to all techniques. All techniques discussed in thissection have complementary forces and loading rate regimes, each technique enablessome experiments that are not possible with the other. Most of the methods describedto capture video images and other details of the experimental LOT setup (such as theimplementation of force-clamp methods) are also applied to the other techniques.

4.1.1. Atomic-force microscopy (AFM). Probably the best well known among thesetechniques is atomic force microscopy (AFM). The AFM is a descendant of thescanning tunneling microscope invented by G. Binnig and H. Rohrer applied to obtainAngstrom resolution images of metallic surfaces using the quantum tunnel effect [38].The AFM [39] is based on the principle that a very soft cantilever with a tip that ismoved to the vicinity of a surface (metallic or insulating) can sense the roughness ofthe surface and deflect by an amount which is proportional to the proximity of the tipto the surface (Fig. 2A). The most important application of the AFM is imaging where


(A) Atomic force microscope (AFM) (B) Laser optical tweezers (LOT)

(C) Magnetic tweezers (MT) (D) Single-molecule fluorescence (SMF)

Time (sec)

FR

ET

eff

icie

nc

y

Figure 2. Experimental techniques: (A) Atomic force microscope (AFM);(B) Laser optical tweezers (LOT); (C) Magnetic tweezers; (D) Single-moleculefluorescence (SMF) using FRET.

it can work in various modes: the contact mode, tapping mode and the jumping mode[40]. For example, in the tapping mode the tip is made to oscillate close to the samplesurface. The amplitude of the oscillation is recorded and controlled by a feedbackloop mechanism that keeps such amplitude constant. When passing over a bump theamplitude decreases so the distance between tip and surface is increased to keep theamplitude of oscillation constant. When passing over a depression the tip is movedto the surface. This mode has the advantage that the transverse motion of the tipalong the surface is not influenced by shearing and frictional forces thereby avoidingdamage to the sample and noisy interference effects. A map of the distance of the tipto the sample provides an accurate topographic image of the surface. Other modes arepreferable depending on the particular system, for example the contact mode is usefulto take images of biological samples in fluids [41]. The use of the AFM for biomolecularimaging has been reviewed in several excellent papers [42, 43, 44, 45, 46, 47, 48].

The AFM is also used to manipulate and exert mechanical force on individualmolecules (Fig. 2A). As usual in single molecule tecniques, elaborated chemistryis often required to treat the surface and the tip. The surface has to be coated


with the molecules to be manipulated. The AFM tip also has to be coated withmolecules that can bind (either specifically or non-specifically) to the molecules onthe substrate. By moving the tip to the substrate a contact between the tip andone of the molecules adsorbed on the substrate is made. Retraction of the tip atconstant speed allows to measure the deflection of the tip in real time providing ameasure of the force acting on the molecule as a function of its extension, the so-called force-extension curve (FEC). The AFM covers forces in the [20 pN-10 nN]range depending on the stiffness of the cantilever. Typical values of the stiffness arein the range 10 − 1000 pN/nm. Although AFM is a very versatile and powerful toolit has a few drawbacks for manipulating single molecules. The most important one isprobably the presence of undesired interactions between tip and substrate (Van derWaals, electrostatic and adhesion forces) and the non-specificity of the attachmentsthat often occur between tip and substrate. When moving the tip to the substrate it iseasy to attach many molecules at a time. Moreover, it is difficult to control the specificlocation of the attachment between the tip and the molecule. Single molecule markers(e.g. polyproteins) and functionalization strategies have been specifically developedto overcome these limitations.

Spatial and force resolution in the AFM are limited by thermal fluctuations.When the cantilever stage is held at a constant position the force acting on the tipand the extension between tip and substrate fluctuate. The respective fluctuations aregiven by 〈δx2〉 = kBT/k and 〈δF 2〉 = kBTk where kB is the Boltzmann constant, Tis the absolute temperature of the environment and k is the stiffness of the cantilever.At room temperature kBT ≃ 4 pN×nm and therefore

√

〈δF 2〉 ≃ 20 pN,√

〈δx2〉 ≃2 A if we take k ≃ 100 pN/nm. This shows that the signal-to-noise ratio for theforce is small for force values of just a few tens of pN. This is the range of forcescharacteristic of weak interactions therefore showing the limitations of AFMs to studythe mechanochemistry of weak interactions in the lower pN regime. In contrast, AFMsare ideal to investigate strong to covalent interactions. They have been mostly usedto probe relatively strong intermolecular and intramolecular interactions, e.g. pullingexperiments in biopolymers such as polysaccharides, proteins and nucleic acids.

4.1.2. Laser optical tweezers (LOT). The principle of LOT is based on the opticalgradient force generated by a focused beam of light acting on an object with an indexof refraction higher than that of the surrounding medium. Discovered by A. Ashkin in1970 [49, 50] the principle was developed more recently to trap dielectric particles byA. Ashkin and collaborators at the Bell Labs [51]. The application of gradient force bylight radiation pressure has been used to trap neutral atoms [52], eukaryotic cells [53]and virus and bacteria [54]. A good review on the origins of optical trapping can befound in [55]. In the basic experimental LOT setup a near-infrared laser is collimatedby a high numerical aperture water immersion lens. A micron-sized polystyrene orsilica bead is then trapped in the focus of the laser by exerting forces in the range0.1-100 pN depending on the size of the bead and the power of the laser. Typicalbead sizes are on the order of 1-3 microns and laser powers of a few hundreds ofmilliwatts to avoid the heating of the bead and undesired heat convection effects closeto the bead that could either damage the sample or affect the measurements. To avery good approximation the trapping potential is harmonic, therefore forces actingon the bead are directly proportional to the distance between the bead and the centerof the trap, F = kx where k is the stiffness constant of the trap. To determine thestiffness of the trap, noise measurements or Stokes force calibration are often used.


Typical values of the stiffness of the trap are 102 − 104 times smaller than AFMtips, therefore force resolution is at least 10 times better on the order of 0.1 pN.Major improvement in this basic setup is obtained by using dual counter propagatinglaser beams passing through two identical objectives [56] (Fig. 2B). There are severaladvantages in this more complex setup. First, the axial scattering force is reduced.Second, the trapping forces that can be reached (up to 200 pN) are higher than inthe one-beam setup. Finally, continued force calibration is not required because theforce is directly measured from the total amount of light deflected by the bead whichis collected by position sensitive detectors (PSD) located at the two opposite sides ofthe laser beams. The force is given by F = S/(Lc) where S is the radiation pressureflux, c is the speed of light, L is the distance that separates the bead (located betweenthe two objectives) and one of the objectives. This formula is valid for any size, shapeand refractive index of the bead. In this way there is no need for the calibration ofthe trap every time a new bead is captured.

Manipulation of individual molecules is carried out inside a fluids chamber madeout of two glass surfaces separated by a parafilm of 200 microns width. A fluidicssystem is designed in such a way that water and chemicals can be flowed and replacedat any time inside the chamber. A glass micropipette is inserted and fixed insidethe chamber and used to hold another bead by air suction. The chamber is thenmounted on a moving stage whose position is controlled by a piezo and positionedin front of the objective lens so that the laser can be focused inside the chamber.To manipulate individual molecules beads are coated with a chemical substance(e.g. avidin or streptavidin) that can bind specifically to its complementary molecule(biotin). The molecules of interest (e.g. DNA) are then biotinylated (i.e. labeled withbiotin molecules) at their ends so they can bind to the avidin (streptavidin) coatedbeads through a strong non-covalent bond. To avoid double attachments between thetwo ends of a single molecule and the same bead it is customary to differently labelthe molecule at its two ends. One end is then labeled with biotin, the other withdigoxigenin. Digoxigenin recognizes specifically its anti-dig antibody partner throughthe ”lock and key” interaction mechanism typical of antigen-antibody interactions.This is a weak bond so the biomolecule is often labeled with many dig molecules atone of its ends in order to increase the strength of the attachment. After incubation ofthe molecules with the beads (for instance the streptavidin beads) other beads coatedwith anti-dig are flowed inside the chamber. One bead is captured with the lasertrap and moved to the tip of the micropipette where it is held fixed by air suction.Incubated beads are then flowed inside the chamber and one bead is captured in thetrap. By moving the chamber relative to the trap the two beads approach each otheruntil a connection between the digoxigenin end of the molecule and the bead in themicropipette is established. The tether is then pulled by moving the chamber at agiven speed and the FEC measured, see Fig. 3.

The extension of the molecule can be monitored by using a CCD video camerathat uses a framegrabber to take pictures of the two beads and operates at a fewtens of a Hertz. Because spatial resolution is strongly limited by the pixel resolution(about 10 nm) other methods have to be implemented to resolve the position of thebead with higher accuracy. A standard procedure is to use a light lever or referencebeam where a low power light beam passing through a small lens in the frame of thechamber is collected by using additional position sensitive detectors. By recording theposition of the chamber it is possible to determine the extension of the tether down toa few nanometers of precision. Spatial resolution is however hampered by strong drift


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Figure 3. Pulling DNA using LOT. (A) Image taken by a CCD camera of thefluids chamber where manipulation of the DNA molecule takes place. The DNAis tethered between two beads. The upper bead is trapped in the optical wellwhereas the lower bead is immobilized on the tip of a micropipette and heldfixed by air suction. The presence of a DNA tether between the beads (invisiblein the real image but illustrated here as a thick black line) is detected by thepresence of a vertical force pointing downward acting on the trapped bead. (B)Experimental setup in DNA pulling experiments where the 3’ and 5’ ends of onestrand are attached to the beads through biotin-streptavidin and digoxigenin-antidig specific bonds. The force is then measured from the deviation of theupper bead respect to the center of the trap. By measuring the force (F) as afunction of the extension (X) it is possible to record the force-extension curve(FEC). (C) FEC in half λ-DNA (24000 base-pairs long). The blue-dashed line isthe worm-like chain prediction from polymer theory. It describes very well theelastic behavior of the DNA molecule up to forces ∼ 5 pN. Above 5 pN enthalpiccorrections are important. Note the overstretching transition that occurs at 65pN. See the more detailed discussion in Sec. 5.1.1.

effects in the optical components and the manipulation chamber. Depending on theexperimental setup the spatial resolution can reach the nanometer only in carefullyisolated environments (absence of air currents, mechanical and acoustic vibrations andtemperature oscillations). Force-clamp (also called force-feedback) methods that useacoustic-optic deflectors and incorporate a piezoelectric stage with capacitive positionsensing are providing better and more versatile instruments [57, 58]. LOT have beenwidely used to investigate nucleic acids and molecular motors.


4.1.3. Magnetic tweezers (MT). Magnetic tweezers (MT) design is based on theprinciple that a magnetized bead experiences a force when immersed in a magneticfield gradient F = −µ∇B. The basic setup is shown in Fig. 2C. A bead is trapped inthe magnetic field gradient generated by two strong magnets. Molecules are attachedto the surface of the magnetic bead and to a glass surface. A microscopic objective witha CCD camera is used to determine the position of the bead. Molecules are pulled bymoving the translation stage that supports the magnets. MT has several advantagescompared to AFM and LOT [59]. First, sensitivity to very low forces can be easilyachieved due to the low value of the stiffness of the magnetic trap. The typical rangeof forces is 10−2 pN-10 pN where the maximum value of the force depends on the sizeof the magnetic bead. Second, in the passive mode (when the magnets stage is keptfixed) the force acting on the bead can be kept constant because the spatial regionoccupied by the bead is small enough for the magnetic field gradient to be considereduniform. Therefore, although the bead position fluctuates the force is always constant.A constant force can be also achieved in the AFM and LOT setups by implementingforce-feedback control mechanisms (see Sec. 4.1.2). The main drawback of feedbackloops is their working frequency, typically limited to a few KHz, which do not allow todetect dynamical processes faster than milliseconds. Third, magnetic traps allow totwist molecules by rotating the magnets. Modifications of the basic setup by using athird bead to create a single chemical bond swivel allow also to measure torques [60].MT are calibrated in flow fields using the Stokes’ law or measuring Brownian motionin the direction transverse to the application of the force, k = KBT/〈δx2〉 where xdenotes the transverse coordinate. Typical values of the magnetic trap stiffness are10−4 pN/nm thereby one million times smaller than in AFMs and a thousand timessmaller than in LOT. Force-extension curves (FECs) can be recorded in real time bymoving the stage and measuring the transverse fluctuations 〈δx2〉. Force is measuredby using the expression F = kBT l/〈δx2〉 where l is the extension of the molecule.The value of l is determined using depth imaging techniques that provide excellentforce-position measurements. The smallness of the stiffness in MTs induces largefluctuations in the extension of the molecule on the order of 20 nm. MTs have beenextensively used to investigate elastic and torsional properties of DNA molecules.

4.1.4. Biomembrane force probe (BFP). Finally, we mention the biomembrane forceprobe technique developed by Evans and collaborators [61]. The basic experimentalsetup is shown in Fig. 4. In this setup a biotinylated red blood cell is pressurized bymicropipette suction into a spherical shape. The tip is made of a streptavidin coatedbead (left bead in Fig. 4) functionalized with some molecules (e.g. ligands). The otherbead is functionalized with complementary molecules (e.g. receptors) and kept fixedby air suction on the tip of the other micropipette (right). The blood cell acts likea spring so the force can be measured by calibrating the stiffness of the cell. This isdirectly related to the membrane tension and can be controlled by fine tuning of thepressurization of the micropipette (left). Typical stiffness values are in the range 0.1-1pN/nm. By moving the micropipette (right) using a piezo translator stage the twobeads approach each other until they touch. The micropipette is further retracted andligand-receptor interactions detected as rupture events. A CCD video camera recordsthe extension between the two beads with a resolution on the order of 10 nm. TheBFP has been mainly used to study ligand-receptor interactions.


Figure 4. BFP technique. (Upper figure) A red blood cell acts as a forcetransducer (symbolized as a spring in the figure) by transforming the pressuresuction applied on the pipette (-P) into the elastic stiffness of the cell membraneκs ∼ PRp where Rp is the pipette radius. A bead covered with ligands is thenattached to the cell (left bead). Another bead covered with receptors is thenimmobilized on the tip of another pipette (right bead). A ligand-receptor bond


4.2. Single-molecule fluorescence techniques

Single-molecule fluorescence (SMF) is based on the detection of light emitted byfluorophores that have been attached to the molecule under quest. Fluorophores areexcited from their ground state by absorbing light from an external light source. Afterinternal conversion and vibrational relaxation they emit fluorescent light in 10−9−10−7

seconds. Detection of single molecules is possible by exciting a very small volumewith light and observing the emitted signal. Typical volumes are on the order of thefemtoliter (10−15 l) corresponding to a water drop of diameter on the order of a micron.In diluted solutions (on the order of nanomolar concentration) the typical numberof photons intercepted by a molecule are estimated to be on the order of a millionphotons per second giving a number of photons emitted in such volume of a thousandphotons per second. The emitted light can be detected using sensitive photodetectorssuch as avalanche photodiodes and photomultipliers. The main advantage of SMF isits high-time resolution. This covers from the range of microseconds for individualevents up to picoseconds when identical experiments are repeated many times andlots of statistics are collected. SMF is a non-invasive technique that can be used tostudy biological samples in vivo. In general the spatial resolution in an optical systemis limited by the Rayleigh criterion (typically around 200 nm). However the limitimposed by the diffraction of light can be overcome by using other methods such asFIONA, a method based on centroid localization where nanometer precision can beachieved when a sufficient number of photons is collected [63, 64, 65]. Other methodsinclude SMF polarization measurements using total internal reflection fluorescence(TIRF) that allow to determine the orientation of individual molecules with tens ofmillisecond resolution [66]. With these methods it has been possible to determinethat myosin V, a two-headed molecular motor that translocates along actin filaments,walks in a hand-over way by alternating the role of the lead and trail heads during itsmotion [66, 67] (see Sec. 5.3).

A powerful SMF technique to detect conformational changes within 10 nm isfluorescence resonance energy transfer (FRET) discovered by Forster (sometimescalled Forster resonance energy transfer) and discussed already in Sec. 2. FRETis based on a quantum interaction mechanism between two fluorescent dyes that cantransfer energy when they are kept close enough (typically within a distance of 10 nm)and one of them (the so called donor) is excited by light. When the donor is excited byan external source of light the other dye (the so called acceptor) emits part of the lightat another wavelength through a non-radiative resonance energy transfer mechanismbetween donor and acceptor. The efficiency of energy transfer depends on the distancebetween donor and acceptor according to the formula E = E0/(1 + (R/R0)

6) whereR0 is Forster radius or the value of the distance above which the efficiency goes below50%. The value of R0 is a function of the fluorescence and absorption spectrum ofdonor and acceptor and the orientation between the electric dipoles of both molecules.Forster efficiency formula gives a spectroscopic ruler to determine distances betweenthe two dyes thereby allowing to identify conformational transitions in the biomolecule(Fig. 2D).

Difficulties associated to SMF are the expertise required to chemically attachfluorophores in biomolecules where it often consists of a ”try and repeat” procedure.FRET has the added complication that two dyes have to be chemically attachedto the same molecule at specific locations. Often it is not possible to know thedipolar orientation of the dyes which makes difficult to determine their distance


using the spectroscopic ruler. Combination of FRET with other techniques(e.g. electron microscopy or X-ray diffraction) helps to identify and characterizeconformational changes. A widespread problem in SMF is photobleaching offluorophores. Photobleaching is a process by which excited fluorophores undergoa chemical transformation (e.g. after reacting with oxygen) and stop fluorescing.Methods are currently employed to reduce such effect which still is a main nuisanceof SMF techniques.

SMF has been used to study molecular transport, protein folding andconformational transitions in enzymatic reactions. There is much current effort tocombine SMF with force measurements. This would allow to identify conformationalchanges with force jumps thereby giving precious information about biomolecularfunction.

5. Systems

Single-molecule techniques have been applied to a great variety of systems. Frompolymers to living cells many system properties have been characterized and studied.In what follows I provide a general overview of a personal selection of these problems.My choice is unavoidably biased by my specific knowledge of some of these questions.

5.1. Nucleic acids

5.1.1. DNA. Historically DNA is the most important player in molecular biology[68, 69]. Since the discovery of the double helix in 1953 [70] the structure of theDNA molecule has been studied under different conditions using crystallographic andbulk methods [71, 72]. DNA can be found in various structural forms and it is nowrecognized that the phase diagram of the molecule in the presence of force and torqueis rich and complex. Pulling experiments in DNA [73] use glass microfibers [74], LOT[75], MTs [76] or AFM [77]. Pioneering work in the study of the elastic properties ofDNA was carried out by Finzi, Smith and Bustamante in 1992 when they visualizedthe motion of fluorescent DNA molecules attached to micron-sized beads acted bymagnetic and hydrodynamic forces [34]. B-form DNA molecules 48 Kbps long (onebase pair -bp- is about 3 A long) of the λ-bacteriophage virus were stretched upto forces as high as 100 pN using AFM [77] and LOT [75]. DNA shows a elasticresponse at low forces (below 5 pN) dominated by entropic effects whereas at highforces (above 5 pN) enthalpic contributions start to be important. Pulling experimentsin DNA confirmed that B-DNA is an elastic molecule whose force-extension behaviorcan be well described using the worm-like chain model [35, 78, 79, 80, 81] introduced inpolymer theory by Kratky and Porod [33] ‡. Above 5 pN the FEC is well described bythe phenomeological extensible worm-like chain where the contour length L changesas a function of the applied force F by ∆L = LF/Y where Y is the Young elasticmodulus (Y ≃ 1 nN). In torsionally unconstrained DNA one end is immobilized inone bead, the other end of either one of the two strands (3’ or 5’) is immobilizedto another bead or surface (depending on the experimental setup). For torsionallyunconstrained DNA a transition is identified at an applied force of 65 pN where theB-DNA overstretchs into a new form (the so called S-form DNA or S-DNA) wherethe new extension of the molecule is approximately 1.7 times its original contour

‡ The solution of the model under the action of external force is equivalent to the solution of theclassical Heisenberg ferromagnetic chain in a magnetic field [82].


length. In the S form the double helix (characteristic of the B form) unwinds andall base pairs tilt along the force direction. The overstretching transition has a forceplateau characteristic of first-order phase transitions (see Fig. 3C). Curiously enoughthis extended form of DNA was anticipated 50 years ago from the measurement ofthe optical properties of fibers under tension [83]. A first order transition is alsofound when DNA melts when heated up above 65◦C. Although it has been suggestedthat S form is force-induced melted DNA [84, 85, 86] the current evidence suggeststhat S-DNA keeps the Watson-Crick base pairs intact in the absence of nicks alongthe DNA phosphodiester backbone. Noticeable salt dependence effects have beenreported for the elastic properties and overstretching transition in DNA due to itslarge electrostatic charge [87]. Various statistical models have been introduced inthe literature that investigate several aspects of DNA such as thermal denaturation[88, 89, 90, 91, 92, 93, 94, 95, 96] in the presence of force and torque [97, 98], bubbleformation [99, 100] and the overstretching transition [101, 102, 103, 104, 105, 106]. Theresponse of DNA to mechanical force is similar to that observed in other biopolymerssuch as peptides and polysacharides. These show an elastic response at low forceswhich is dominated by entropic effects whereas at high forces enthalpic contributionsand structural transitions are often observed [107, 108, 109, 110, 111].

Current experiments can now exert force and torque at the same time ontorsionally constrained DNA. In torsionally constrained DNA both strands areimmobilized at one end of the molecule. MT allow to rotate a magnetized beadattached to the end of a DNA molecule that is attached to a glass coverslip throughits other end [76]. DNA is a coiled molecule of 2 nm diameter covering one helicalturn every 10.5 bps equal to 3.4 nm, also called helical pitch. By exerting torque it ispossible to change the helical pitch of the molecule leading to a supercoiled molecule.The topological properties of a closed DNA molecule are determined by the so-calledlinking number Lk which is equal to the number of crossings between the two strands.In a closed DNA molecule (such as circular DNA from bacteria) Lk is a topologicalinvariant equal to the sum of twist (Tw) and writhe (Wr), Lk=Tw+Wr. The twistis the number of helical turns whereas the writhe is the number of loops occurringalong the DNA molecule. The amount of supercoiling, usually termed as superhelicaldensity σ, is measured as σ = Lk−Lk0

Lk0

where Lk0 is the linking number of torsionallyrelaxed DNA. Supercoiling is a biological important property of DNA. Supercoilingplays an active part in the regulation of the genome in both eukaryotes and bacteria(inside cells DNA is negatively supercoiled, σ ∼ −0.06) and is controlled by afamily of enzymes called topoisomerases (see below in Sec. 5.3). These are involvedin packaging, transcription, replication, repair and recombination of genomic DNA.Under the application of constant force the extension of the DNA molecule changesas the bead is rotated and the twist increases or decreases (Fig. 5 (A-B)). Under twistvarious structural transitions are observed [112, 113]. At very high forces a new formof DNA (called P-form) is found when the DNA is overtwisted and the extension ofthe molecule decreases [114]. In this new form bases are extruded from the inside ofthe backbone in a form that is reminiscent of the triple strand model for the structureof DNA proposed by Pauling in the 50’s (henceforth the name P for the phase)[115]. At low forces the DNA forms plectonemic supercoils (the coils often observedin telephone cords) if overtwisted and denatured bubbles if undertwisted. All thesebehaviors have been extensively studied and modeled [116, 117, 118, 119, 120, 121].They have resulted into a complex force-torque phase diagram of DNA [60, 11] (seeFig. 5 (C-D)). Conformational fluctuations have been shown also to be important in


(A) (B)

(C) (D)

Extension (µm) Torque (pN nm)

Fo

rce (

pN

)

Figure 5. Force-torque DNA measurements. (A) Experimental setup with MT.DNA can be twisted by exerting a torque through the rotation of two magnets.(B) Extension-twist curves showed a marked different behavior depending on thevalue of the constant applied force. If undertwisted the molecule forms bubblesat high forces, whereas it forms plectonemes at low forces. (C) Various FECsobtained by pulling on twisted DNA using LOT. The different plateaus indicatedifferent structural transitions. The possible DNA forms are: normal B-formDNA, overstretched (S-DNA), the highly overwound DNA Pauling (P) form,supercoiled and shortened Pauling (scP) form, and the underwound and denatured(L) form. (D) Phase diagram indicating all possible phases. Pictures (A,B) weretaken from [124]. Pictures (C,D) were taken from [11].

regulatory mechanisms such as protein-DNA interactions [122, 123].In another class of experiments the 3’ and 5’ ends on one end of the DNA molecule

are immobilized into a bead and a surface. By pulling apart the bead from thesurface the Watson-Crick base pairs connecting the two strands along the phosphatebackbone break and the DNA molecule opens like a zipper. Unzipping is the processwhere hydrogen bonds between complementary bases fall apart and the bases that areburied inside the helix become exposed to the solvent. It naturally occurs in variousbiomolecular processes. For example, the initiation process during DNA replication


is led by the exposure of specific DNA segments of the genome to the replicatingmachinery (a set of various multimeric protein complexes). The replication of DNA isthen determined by the advance of the replication fork which proceeds by untwistingand unzipping the DNA structure. Typical unzipping forces are on the order of 15 pNand are sequence dependent [125, 126, 77, 127, 128]. Below such force (e.g. around 10pN) the molecule does not unzip. Above that force (e.g. at 17 pN) unzipping proceedsfast with a signal that is a fingerprint of the DNA sequence. During the unzippingprocess, the recorded force/extension signal does strongly depend on the particularDNA sequence. By unzipping the molecule a repeated number of times a characteristicforce pattern emerges except for thermal fluctuations. This fact makes force unzippinga promising technique for DNA sequencing [129, 130, 131, 132]. Similar experimentsare being also conducted with RNA and will be discussed below in Sec. 5.1.2. Forceunzipping has been investigated using various statistical models [133, 134, 135, 136]which predict re-entrance of the transition due to excluded volume effects between thetwo strands [137, 138, 139]. At present, various technical precision limitations andnoise fluctuations due to the softness of the single stranded DNA (ssDNA) handleslimit the reliability of the sequencing procedure. Although at present it is possibleto resolve the unzipping of a DNA patch containing a few tens of base pairs, thedetection of the opening of just one base pair is an experimental challenge. Improveddetection resolution using two traps and combination of LOT with SMF [17] areexpected to provide far better accurate results. Other sequencing strategies are SMFmeasurements of DNA polymerase activity during the synthesis of the complementarystrand [140].

5.1.2. RNA. RNA is a very important player in molecular biology. It participatesin most processes where the genomic information that is kept inside the nucleus mustbe exported to the cytoplasm of the cell where it is translated into proteins that aresynthesized in the ribosome. The ribosome, one of the largest biological machines inthe cell, contains RNA as part of its structure as well as ribosomal proteins. RNA isconsidered a relic of the past [141] where the precursors of the first living cells (morethan 2 billion years ago) used the chemistry of RNA long before proteins took overmost of the essential functions of ancestral prokaryotic cells. The RNA world refers toa hypothetical scenario where the majority of important living functions were carriedout by ancient RNA molecules [142]. There are many functions where RNA is essential(e.g. in enzymatic and regulatory processes). Every few years new biological roles ofthe RNA are discovered. RNA and DNA are chemically very similar molecules. Themain difference of RNA with respect to DNA is the presence of the highly reactiveOH group in the sugar (ribose) and the replacement of thymine by uracil (adeninepairs with uracil) in RNA. Structurally they are also very different: RNA is found innature in single stranded form whereas DNA is found in double stranded form.

The elastic properties of synthesized double stranded RNA and DNA are verysimilar [143], but the single strand nature of RNA makes the difference. RNA is a morecomplex molecule than DNA. While complementariness is strict in DNA, RNA allowsfor additional non Watson-Crick base pairs (such as GU or GA) between the bases.Consequently it allows for more base pair interactions and a larger number of possiblestructures. Single stranded RNA molecules form complex secondary structures ofstems, junctions, loops, bulges and other motifs. The main thermodynamic stabilityof the molecule is derived from the complementarity of the bases and base stackinginteractions. However, secondary RNA structures fold into more complex three-


dimensional structures stabilized by specific interactions between different hydroxylgroups of the bases that bind divalent metal cations (e.g. magnesium). Tertiaryinteractions produce other sort of structural elements such as pseudoknots or kissingloops. In RNA the contribution to the free energy of the native state due to the tertiarystructure is a perturbation to the main contribution due to the secondary structure.In addition, the chemistry of RNA is much simpler than that of proteins (there are 4different nucleotides in RNA as compared to the 20 amino acids in proteins). This factmakes RNA easier to study at both theoretical and experimental level. RNA researchis very attractive to the biophysicist not only because RNA is less complex thanproteins, but also because RNA shows all important properties exhibited by proteins.RNA molecules can be unfolded under the action of mechanical force [144, 145, 146].Thermal and force denaturation experiments reveal that RNA folds into a native threedimensional structure in the same way proteins do. Understanding how RNA foldswill help to better understand the corresponding process in proteins [147, 148, 149].The problem of RNA folding has also motivated theoretical insight from the theoryof disordered systems in statistical physics [150, 151, 152, 153, 154, 155].

Glass microfibers, AFM and LOT have been used to stretch and unzip RNAmolecules. The latter is by now the most accurate technique to resolve forces on theorder of the pN and distances on the order of a few nanometers that are observed inthe unfolding of small RNA hairpins. The first RNA pulling experiments were carriedout in the Bustamante lab [156] where the P5ab RNA hairpin (a derivative of theL121 Tetrahymena rybozyme) was studied. In such experiments an RNA hairpin isstretched in a force-ramping experiment and the FEC recorded. The molecule is foundto unzip at forces around 15pN resulting into a denaturated single stranded RNA form(ssRNA). The RNA molecule also hops between the folded and the unfolded statesat a critical value of the extension or force applied on the molecule where the foldedand unfolded conformations are equally populated. Pulling RNA (or DNA) hairpinshas additional complications as compared to the case of stretching dsDNA. Being thehairpin a few tens of base pairs long the gain in extension after the molecule unfolds isbetween 10 and 50 nm. Such extension is too short to manipulate the RNA moleculeusing micron-sized beads. To pull on the RNA hairpin, two hybrid RNA/DNA handlesare synthesized and annealed to the RNA molecule at its flanking sides. The handlesare typically a few hundreds base pairs long so the whole construct is approximatelya few hundred nanometers long when fully extended. The experimental setup and atypical FEC is shown in Fig. 6 (A-B). Upon increasing of the force the RNA hairpinunfolds, the extension of the molecule increases and the force drops in response to theretraction of the trapped bead that follows to the sudden gain in molecular extension.If the force is relaxed back then the hairpin refolds again showing a sudden increase inthe force upon formation of the hairpin. Several thermodynamic and kinetic propertiescan be investigated in these experiments. By pulling slowly enough (the lowest valueof the pulling speed being limited by low-frequency drift effects in the instrument)one can infer the mechanical work necessary to unfold the hairpin which is equal tothe area below the FEC. After subtraction of the reversible work required to stretchthe hybrids handles and the unfolded ssRNA, the free energy difference between thefolded and unfolded state at zero force and room temperature can be inferred [156].The value of the folding free energy obtained for RNA secondary structures agreeswell with theoretical estimates by Mfold [157, 158]. By repeatedly pulling-relaxingthe molecule many times, hysteresis is often observed in the FECs. The averageunfolding force is always larger than the average refolding force. Kinetic properties


Time (seconds)

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Figure 6. RNA pulling experiments using LOT. (A) Experimental setup. AnRNA molecule is inserted between two hybrid RNA/DNA handles. The force (F)and extension (X) of the molecular assembly are measured as the micropipette ismoved. (B) FEC of a 20 bps RNA hairpin in a pulling cycle. During the stretchingpart of the cycle (red curve) the elastic response of the handles is followed by thesudden release of extension and a drop in the force corresponding to the unfoldingof the RNA molecule. During the relaxation part of the cycle (blue curve) theRNA molecule folds back again. (C) Hopping experiments. If the force is heldconstant the RNA molecule hops between the folded and unfolded conformations.The vertical axis represents the position of a reference laser beam for the chamberwhich is related to the molecular extension.

can be studied by pulling the hairpin at different rates and measuring the breakageor dissociation force distribution during unfolding. Combined with the measurementof the refolding force distribution along the retracting part of the cycle it is possibleto identify the location of the transition state and the free-energy landscape of themolecule as a function of its extension [159]. Pulling experiments using LOT areusually carried out near equilibrium conditions. AFMs allow to perform dynamic forcespectroscopy measurements of RNA dissociation far from equilibrium by exploring afew orders of magnitude of loading rates [160]. These studies reveal that the averagedissociation force increases logarithmically with the pulling speed as has been foundin the study of intermolecular protein-protein interactions (see Sec. 5.2.1). Similarexperiments have been carried out to investigate the kinetics of short DNA hairpinsusing SMF [161, 162] or AFM [163, 164, 165, 166, 167] finding slower kinetics ofunfolding/refolding depending on the length of the sequence as predicted by some


theoretical models [133, 168]. Mechanical unfolding of single RNA molecules throughnanopores has been also proposed as a method to determine the secondary structure[169]. The unzipping of RNA hairpins has motivated several theoretical studies ofthermodynamic [170, 171, 172] and kinetic properties [173, 174, 175, 176, 177].

Other related experiments provide additional insight on the kinetics of unfoldingof the molecule. For example, if a constant force that is close to a critical value ismaintained by a force feedback mechanism then the RNA molecule hops between thefolded and unfolded states (Fig. 6C) (the mechanism being similar to the openingand closure activity that is observed in single ion channels [178]). Hopping can beinvestigated in two different modes: 1) the passive mode where the position of themicropipette and the trap are kept fixed; 2) the force-feedback mode where the forceis maintained constant by using a piezo controller that corrects the position of themicropipette every time there is a change in the force (see Sec. 4.1.2). Working atthe vicinity of the critical extension or force (where the molecule hops between thefolded and unfolded conformations) it is found that the molecule follows exponentialkinetics. The probability distribution of the residence times in the folded (unfolded)conformations is well described by an exponential function whose width is equalto the inverse of the kinetic rates of unfolding (folding). The dependence of theserates on the applied force gives accurate information about the height and positionof the kinetic barrier. The hopping kinetics of RNA hairpins has been modeled byCocco and collaborators who have introduced a one-dimensional representation ofthe possible configurations of the molecule in terms of the number of sequentiallyopen base pairs starting from the beginning of the fork [179, 180]. Models for theexperimental setup where the distance between the micropipette and the center ofthe trap are the appropriate control parameter have been considered in [181] whereasa detailed analysis of the influence of the experimental setup (length of the handles,stiffness of the trap, bandwith of data collection, time delay of the force-feedbackmechanism) on the measurement of the intrinsic molecular kinetic rates of the RNAmolecule in the different modes (passive or force-feedback) has been carried out in[182, 183]. Passive force clamp methods operating without force-feedback have beenalso implemented in dual laser traps by taking advantage of the anharmonic regionof the trapping potential. Studies of the hopping kinetics of a tetraloop DNA hairpinshow that the hopping frequency increases with the stiffness of the trap [184, 185].

Two-states behavior is usually found during the unfolding and refolding of shortRNA hairpins [156, 186]. Experiments have been carried out in more complexmolecules such as the full Tetrahymena thermophila rybozyme L21 (containingapproximately 400 nucleotides) using FRET [187] or LOT [188]. LOT made alsopossible the mechanical unfolding of the Escherichia coli 1540 bps-long 16S ribosomalRNA by the group of D. Chatenay [189]. The resulting FECs reveal a series of complexrips that correspond to the opening of different domains of the molecule. Other studieshave investigated specific RNA motifs such as internal bulges [189] , the transactivationresponse region (TAR) RNA derived from the human immunodeficiency virus (HIV)[190] and three-helix junction RNA molecules [191, 192, 193]. These experimentsshow that force unfolding proceeds through the successive opening of domains whereasforce refolding is a much more complex process where various folding pathways andtrapped intermediates are often observed [194, 195, 196, 197]. The kinetic behavior ofRNA molecules shares many resemblances to what has been observed in proteins (seeSec. 5.2.2), often showing misfolded structures [198], reinforcing the observation thatthe free-energy landscape underlying the folding dynamics is more rugged in RNA


than in proteins [199, 200, 201].

5.1.3. DNA condensation. The nuclear genome is not isolated but surrounded bymany different proteins engaged in its maintenance and regulation [202, 203]. Proteinsare also responsible for the compaction of eukaryotic DNA inside the nucleus of thecell [204]. The nuclear DNA is condensed with proteins into a huge molecular complexcalled chromatin. Linear compaction defined as the ratio between the length of fullyextended DNA to the length of the condensed DNA reaches values on the order of104−105. The basic unit of the condensed DNA is the nucleosome core particle, a flatdisk of 11 nm diameter with 146 bps of supercoiled DNA wrapped around a histoneoctamer formed by pairs of histones H2A, H2B, H3, H4. The main force stabilizingthe nucleosome particle is the electrostatic attraction between the negatively chargedphosphate backbone of DNA and the protonated (positively charged) arginine andlysine lateral chains of histones. Nucleosome particles are destabilized and readilydissociate at low salt concentrations [205]. Nucleosomes are connected to each otherby segments of variable length of linker DNA (around 60 bps) forming a beads in astring structure. The histone H1 stabilizes the structure of the nucleosome by fixingthe entry and exit angle of the wrapping DNA. Chromatin organizes into differentstructures at different lengthscales [206]. The nucleosome is the minimal unit in suchorganization, also called the 10 nm fiber. At physiological salt values nucleosomes forma complex and dense structure recognized as the 30 nm fiber formed by the folding ofnucleosomes into a yet unknown three-dimensional structure [207, 208, 209].

There are few experimental single-molecule studies of DNA condensation. Thefirst study used LOT to pull chicken erythrocyte chromatin fibers [210]. Itshowed irreversible force-extension cycles above 20 pN interpreted as due to themechanical removal of histone cores from native chromatin. SMF and AFMimaging have explored the assembly kinetics of chromatin from Xenopus eggs andDrosophila embryos [211]. None of these preliminary studies could identify thedynamics of individual nucleosomes. Subsequent studies analyzed the condensationof reconstituted chromatin fibers of λ-phage DNA suspended between two beads andexposed to Xenopus laevis egg extract [212, 213]. The fiber condensed under a constantfrictional Stokes force. The rate of condensation decreased considerably under appliedforce and no condensation events were observed at forces exceeding 10 pN. Stronginhibition of chromatin assembly in chromatin fibers above 10 pN has been alsoobserved in MT studies [214]. After the fiber had condensed subsequent FECs revealeda series of force jumps between 15 and 40 pN attributed to the release of the wrappedhistone octamer. After all releasing events have taken place the FEC characteristicof naked DNA was recovered. However, due to the large amount of different typeof proteins in the cell extract, it is difficult to tell which jumps correspond to otherbound proteins and which jumps are due to the unravelling of the histone octamer.Similar experiments have been carried out in the study of nucleosomal arrays ofreconstituted pure histones [215]. FECs reveal a series of disruptive events attributedto the unwrapping of individual nucleosomes containing 80 bp of dsDNA (Fig. 7A). Single-molecule force measurements to test higher order chromatin structures havebeen applied to investigate the protein scaffold of mitotic chromosomes [216].

Recent studies of DNA condensation have considered synthetic condensing agentsmuch simpler than protein histones such as shell crosslinked nanospheres [218] anddendrimers [219]. Dendrimers are synthetic branched polymers that are synthesizedvia an initiator core terminating (after a repeated series of steps) with amino NH2


D

A C

B

A

Figure 7. FECs in DNA condensation using LOT. (A) Mechanical disruptionof nucleosomal arrays. Experimental setup. (B) Nucleosomal arrays repeatedlystretched three times (first -black-, second -red-, third -blue-) up to a maximumforce of 50pN. The unwrapping of individual nucleosomes is observed as jumps inthe FEC. As the array is repeatedly pulled the number of remaining nucleosomesin the fiber decreases. Figure taken from [215]. (C) Condensation of DNAmolecules with polyaminoamide (PAMAM) dendrimers (Experimental setup).(D) FECs of DNA fibers (red curves) condensed with dendrimers of generationG8 (diameter of particles around 10 nm) [217]. The black curve is the FEC ofnaked DNA before condensation. The red curves show hysteresis between thestretch and release part of the cycle, the presence of a slack (due to the presenceof uncondensed segments in the fiber) and a decondensing force plateau around10 pN.

groups on the surface [220, 221]. Questions such as the importance of charge,shape and size in the condensed state have been recently considered by studyingPAMAM (polyaminoamide) dendrimers condensed with λ-phage DNA using LOT[217]. FECs in dendrimers show a force plateau around 10pN, characteristic of adecondensation transition between a condensed and an extended phase (Fig. 7B).These experiments also reveal that residual inter-dendrimer electrostatic interactionskeep the structure of the condensed state as revealed by the salt dependence of the forcevalue from the plateaux, similar to what has been found in the condensation of DNAby other polycationic complexes such as eukaryotic condensin and trivalent cations


like hexaammine cobalt (CoHex) and spermidine [222, 223, 224]. The mechanism bywhich nucleosomes form and arrange into a compact globular structure has been thesubject of many theoretical and numerical studies [225, 226, 227, 228, 229, 230, 231,232, 233, 234, 235, 236, 237].

5.2. Proteins

Many single-molecule studies have investigated in detail the mechanochemistry ofsome relevant proteins. Two category of protein systems must be distinguished: 1)Those where an energy source (e.g. from ATP or GTP hydrolisis) is not required;2) those where catalytic functions driven by high energy phosphate compounds (e.g.ATP or GTP hydrolisis) are necessary. The first class of proteins is closer in spirit tomanipulation experiments of single nucleic acids in which molecular interactions areprobed either by mechanical force or observed using optical imaging techniques. Thesecond class of proteins includes the study of many molecular motors and enzymes.Due to the large number and the importance of the studies on ATP-dependent motorsa whole section is devoted below to them.

5.2.1. Protein-Protein interactions. Proteins have important regulatory functionsas demonstrated by Jacob and Monod in the early 60’s with the discovery of theLac repressor. Proteins can participate in chemical signaling at the intra andintermolecular level. The successful development of an organism relies on thecoordination of myriads of signals transmitted among a large number of proteinsall participating in a structurally complex and highly dynamic web of interactions.Developmental processes such as cellular association, differentiation, patterning andreproduction all are controlled mainly by proteins.

A large of number of studies have focused in the study of protein-proteininteractions of the ligand-receptor type [238]. These interactions are governed bywhat in biological terms has become known as ”lock and key” mechanism. Proteinscan interact and recognize each other by assembling into larger complexes by mutualcomplementarity and fit of their molecular surfaces. Allostery refers to the regulationof such interaction by changes in either one or both proteins. Protein-proteininteractions are studied in dynamic force spectroscopy using AFM, BFP and LOT.The first type of measurements are the most common. Samples are prepared bycoating a substrate with ligand molecules and the tip of an AFM with receptormolecules. The substrate is then moved towards the tip until a few contacts betweenligand and receptor molecules are formed. Ideally one would like to have justone molecular contact between the tip and the substrate. In general this is notpossible and the concentration of the proteins has to be carefully tuned to ensurethat just one connection is often established between tip and substrate (implyingthat the large majority of contact trials are unsuccessful and a connection is rarelyestablished). Upon retraction of the tip the extension of the protein-protein contactincreases and the force increases up to a value where the contact breaks. Therupture of the contact is stochastic, therefore upon repetition of the experimentseveral times (each time a new contact has to be sought) the value of the ruptureforce is always different, the overall rupture process being described by a breakageforce distribution. The rupture force distribution depends in a non-trivial way onthe retraction rate of the tip. Typically, the larger is the retraction rate the higheris the average rupture force which grows approximately as the logarithm of the


loading rate. Kramer theories for chemical reactions [239, 240, 241] extended byBell in the 70’s to include the effect of mechanical force on bond dissociation[242],have been adapted by Evans and Ritchie [243, 244, 245] to interpret the observedrate dependencies. Dynamic force spectroscopy [61, 62] has become nowadays astandard method to probe the strength of molecular bonds. It has been appliedto the study of biotin-avidin and biotin-streptavidin interactions [246, 247, 248],antigen-antibody interactions [249, 250, 251], P-selectin/ligand interactions [252, 253],adhesion forces in lipid bilayers [254], substrate-protein adsorption forces [255],cadherin mediated intermolecular interactions [256, 257] , carbohydrate-protein bonds[258], proteoglycans [259, 260], antibody-peptide interactions [261] just to cite a fewexamples. Typical rupture force distributions are shown in Fig. 8. The problem ofbond rupture has been extended to multiple bonds in several configurations (series,parallel, zipper) [62, 262, 263]. An annoyance inherent to dynamic force spectroscopyin ligand-receptor studies is that after a rupture event occurs a contact has to beestablished again. As discussed below, this is different from what happens whenstudying intramolecular interactions where the initial set of bonds can be reformedagain by moving back the surface to the tip.

5.2.2. Protein folding. SME allow to investigate intramolecular interactions inproteins. Pioneering studies have been carried out by pulling the muscle proteintitin. The sarcomere is a repeating unit found in fibers of muscle cells responsible forcontractile motion. The sarcomere is a highly complex structure 2.5 µm long madeout of thick (myosin) and thin (actin) filaments and a third filament (titin). Titinconnects the Z-disk to the M-line in the sarcomere, and is a huge modular proteinresponsible for the passive elastic properties of the muscle. Titin is formed by tandempseudorepeats of many different protein domains such as the immunoglobule (Ig)and the fibronectin type III (fnIII) domains. The characterization of the mechanicalproperties of modular proteins like this one is very important because they are presentin the cytoskeleton and the extracellular matrix of all eukaryotic cells. AFM and LOTpulling experiments in proteins were first carried out in titin [264, 265, 266] by thegroups of H. Gaub in Munich and C. Bustamante in Berkeley. Upon application offorce titin unravels in a series of force jumps, one jump corresponding to the unfoldingof an individual module. A FEC reveals a characteristic sawtooth pattern as shownin Fig. 9. Due to the heterogeneous structure of the module sequence in modularproteins (such us titin) it is difficult to identify which specific module correspondsto which unfolding event. Considerable progress has been later achieved in thegroup of J. Fernandez using protein engineering techniques to construct homomericpolyproteins, i.e. tandems of identical repeats of a protein such as the I27 moduleof titin [267, 268, 13] (similar constructs have been synthesized in the T4 lysozyme[269]). The study of polyproteins of I27 allows to carry out detailed studies of themechanical stability and unfolding/refolding kinetics of a single molecule.

Similar studies have been conducted in other modular proteins such as tenascin[270], triple helical coiled coils of spectrin [271] bacteriorhodopsin [272] and the cellularadhesion molecule Mel-CAM [273]. In all cases the unfolding kinetics is well describedby a two-state process where the distribution of ripping forces and FECs dependson the loading rate. The distributions are also influenced by the polymer spacersand the instrument limitations [274, 275]. These studies provide insight also on therole of the different structural elements of the protein on its mechanical stability,such as β-sheets and α-helices, the main building blocks of the secondary structure


A B C

Steady ramp

1000pN/sec

Steady ramp

100pN/sec

BFP force error

Figure 8. Mechanical strength of trans-bonded cadherin fragments. (A,B) Forcehistograms in steady ramp protocols at 100 pN/sec and 1000 pN/sec. Forcedistributions shift to larger forces as the loading rate increases (C) Logarithmicrate dependence of the average rupture force over nearly 4 orders of magnitudein loading rates. The dotted line corresponds to the measurement error in force.The error increases with the loading rate because of viscous corrections appearingdue to probe damping. Figure taken from [257].

in proteins. Experimentally it has been also found that as a rule β-sheets are morerobust elements than α-helices [276]. The geometry of the pulling, whether unzippingor shearing β-strands, and the point of application of the force also determines the finalmechanical stability of the protein [13, 14]. The influence of specific solvent conditionson protein stability can also be studied using the AFM. In this line interesting studieshave been carried out by the Discher’s group on the mechanical stability of a vascularcell adhesion molecule (VCAM-1), a tandem of seven Ig domains that are stabilizedby disulfide bonds and that can be destabilized in the presence of reducing agents[277]. Simultaneous force experiments and reduction of disulfide bonds (to SH) can bestudied on single molecules [277, 278, 279]. Finally, the study of force unfolding kineticsin proteins has motivated various theoretical and numerical studies [280, 281, 282].

Protein folding, the process by which a molecule folds into a three dimensionalfunctionally active structure, is still a major unsolved problem in modern biophysics.


A

B

Figure 9. Pulling multi-modular proteins with AFM. (A) Experimental setup.A laser beam is deflected by the cantilever tip of the AFM. The amount of thedeflection is detected in a position sensitive detector (PSD). (B) The characteristicsaw-tooth pattern of force obtained by pulling on a recombinant construct of Ig27domains from titin. Figure taken from [4].

The dynamics of such process has many aspects and complications, for example manyproteins need to be assisted by some other proteins (chaperons) to become efficientlyand quickly folded [283]. A fascinating aspect of SME is the possibility to investigatefolding under applied force in a single molecule, i.e. the equivalent of protein foldingin bulk experiments but with force being the externally controlled variable. Uponpulling the protein is unfolded, while upon retraction of the positioner the proteincan fold back again into its native structure. The process should be similar to thatobserved in RNA molecules. However, there are two inconveniences or difficulties thatmake the study of force-folding of proteins with AFM more difficult than RNA foldingusing LOT. The first difficulty is found in the high value of the stiffness of the AFMtip (typically 100 times larger than that of a LOT, see Sec. 4.1.1) which considerablyincreases thermal fluctuations in the force making difficult to control the value of


the force during the refolding process. The second inconvenience is related to theexperimental difficulties of unequivocally identifying individual molecules due to manynon-specific interactions between tip and substrate. To overcome this second limitationthe synthesis of polyproteins has been used in order to identify true unfolding events.The study of force-folding kinetics in proteins has been carried out by measuringthe force-clamp relaxation (i.e. the force is maintained constant by using a feedbackloop) of polyproteins that have been previously mechanically unfolded. However, itis unclear whether in such conditions the folding kinetics of individual modules mightbe affected by the folding kinetics of other modules. Recent AFM measurementsby the group of J. Fernandez in polyubiquitin proteins (ubiquitin is an ubiquitousand highly conserved eukaryotic protein in charge of signalling for the proteosomaldegradation of proteins, among other functions) using the force-clamp technique [284]have shown that the refolding kinetics is not a two-state process but a multiple pathwaydynamical process determined by the roughness of the free-energy landscape of themolecule [285, 286] (see however [287, 288, 289, 290] for a discussion of these results andalternative interpretations). Similar observations have been reported in RNA pullingexperiments [198]. These studies suggest the existence of intermediate states along theunfolding/folding pathway of proteins. Evidence for intermediates has been obtainedin the study of the unfolding kinetics of titin with AFM [291, 292, 293]. Recently, LOThave been also used to investigate the folding kinetics of RNAseH enzyme revealingthe presence of an intermediate conformation of the protein, probably the moltenglobule state observed in thermal denaturation experiments [294]. This work pavesthe way to investigate other proteins using LOT. SME in proteins are expected togreatly contribute to our current understanding of protein folding from a statisticalphysics approach [295, 296, 297].

Fluorescence spectroscopy has been also used to investigate and detect thepresence of intermediate states in proteins. Different methods are used to immobilizeand observe proteins: passive adsorption, specific tethering, trapping inside polymergels or vesicle encapsulation [18]. In this last technique proteins are encapsulatedinside vesicle cells of size larger than the protein but smaller than the laser beamsection allowing for a mild immobilization of the protein. Haran and collaborators haveshown that two-state folders, well characterized by bulk biochemistry methods, displayexponential kinetics in their relaxation [31]. Adenylate kinase, an enzyme 214 aminoacids long that catalyzes the production of ATP from ADP, shows a heterogeneousand slow dynamics characterized by multiple folding pathways [32]. These results arein agreement with the conclusions obtained in the aforementioned force-clamp AFMstudies on polyubiquitin [285] and FRET studies on RNAse P (a transfer RNA thatcontains a catalytic RNA subunit) [298].

5.3. Molecular motors

One of the great applications of SME is the possibility to follow individual molecularmachines in real time while they carry out specific molecular tasks [299]. Molecularmotors are proteins that typically use the energy extracted from available sources,such as chemical gradients or high energy phosphate compounds (e.g. ATP or GTP)to exert mechanical work (Fig. 10). For example, in ATP hydrolisis a molecule ofATP is broken into ADP and inorganic phosphate Pi (ATP → ADP + Pi) in ahighly irreversible reaction that releases around 7 kcal/mol ≃ 12 kBT . The chemicalprocess by which motors utilize the energy stored in the high energy bonds of the ATP


molecules to perform mechanical work is based on two hypothesized mechanisms: 1)Power stroke generation or 2) Brownian ratchet mechanism. In the first mechanismeither the production of ADP or the release of the inorganic phosphate during theATP hydrolysis cycle induces a conformational change in the substrate that is tightlycoupled to the generation of force and motion in the motor. In the second mechanism,the motor diffuses reversibly along the substrate. Unidirectional movement is producedby rectification of thermal fluctuations induced by the conformational change in theprotein caused by ATP hydrolisis. By steady repetition of a mechanochemical cycle(one or more ATP molecules are hydrolyzed per cycle) the motor carries out importantcellular functions. Motors are characterized by the so called processivity or number ofturnover cycles the motor does before detaching from the substrate. Processivities ofmolecular motors can vary by several orders of magnitude, depending on the type ofmotor and the presence of other regulating factors. For example, the muscle myosin IImotors work in large assemblies, each myosin having a processivity around 1, meaningthat each myosin performs one mechanochemical cycle on average before detachingfrom the substrate. In the other extreme of the scale there are DNA polymerases(DNApols, enzymes involved in the replication of the DNA) in eukaryotes whichshow processivities that range from 1 (adding approximately one nucleotide beforedetaching) up to a several thousands or even millions. However, in the presence ofsliding clamps (proteins with the shape of a doughnut that encircle the DNA andtightly bind DNApols [300]) processivities go up to 109.

Molecular motors are magnificent objects from the point of view of their efficiency.If we define the efficiency rate as the ratio between the useful work performed bythe motor and the energy released in the hydrolysis of one ATP molecule in onemechanochemical cycle, then typical values for the efficiencies are around several tensper cent reaching also the value of 97% in some cases (like in the F1-ATPase, seebelow). For example, out of the 20 kBT obtained from ATP hydrolysis, kinesin canexert a mechanical work of 12 kBT at every step, having an efficiency of around 60%.Such large efficiencies are rarely found in macroscopic systems (motors of cars haveefficiencies in the range 20-30%) meaning that molecular motors have been designed byevolution to efficiently operate in a highly noisy environment [301]. Molecular motorsare expected to be essential constituents of future nanodevices. Single-molecule devicesthat operate out of equilibrium and are capable of transforming externally suppliedenergy into mechanical work are currently being studied [302].

Two major classes of molecular motors have been experimentally studied usingsingle-molecule techniques. One class corresponds to molecular motors involved inseveral transport processes inside the cell cytoplasm such as the aforementionedkinesin, dynein and myosin [303]. Single-molecule measurements in molecular motorswere carried out by Block and coworkers, who studied a single kinesin on a microtubulerail. Kinesin and dynein are both microtubule associated proteins (MAPs) involvedin the transport of organelles and vesicles along microtubules in the cytoplasm of thecell. They move in opposite directions with respect to the polarity of the microtubule.Using LOT it is possible to attach one kinesin molecule to a bead captured in anoptical trap and measure the force exerted on the bead while the kinesin walks alongthe microtubule [304, 305]. Kinesins are found to move in 8 nm steps at an averagespeed of 2 microns per second [306]. Kinesins move in a hand-over-hand way byalternate exchange between the head of the molecule (that makes a strong bond withthe β-tubulin domain of the microtubule while ATP is hydrolyzed) and the otherhead that detaches from the substrate [307]. The average velocity of kinesin has


Actin filament

Streptavidin

ADP-Pi

ADP

Kinesin

Helicase Ribosome

F1-ATPase

A

C

B

D

Figure 10. Examples of molecular machines: (A) Kinesin walking along amicrotubule and transporting a cargo (not shown). (B) F1-ATP synthase is theproton pump responsible of synthesizing ATP in the mitochondria of eukaryoticcells. (C) Helicases are forerunners of the DNA polymerase that unwind DNAby transforming dsDNA into two strands of ssDNA. (D) The ribosome is amongthe largest molecular machines inside the cytoplasm of the cell and is in chargeof manufacturing proteins.

been shown to depend on the value and direction of the applied force [308, 309] witha stall force around 7 pN required to arrest the motion [310, 311]. Kinesin alsoshows backward steps during its motion suggesting a Brownian ratchet mechanism[312, 311]. Depolymerazing kinesin motors of the cytoskeleton and extraction ofmembrane nanotubes by kinesins have been also investigated in SMF experiments[313, 314]. Dynein has also been studied and shown to display steps that are multipleof 8 nm [315] depending on the applied force. The force generation mechanism is stillunknown [316].

Myosins are a large class of proteins responsible for muscular cell contractionthat walk along actin filaments [317]. Two main types of myosins have been studiedin SME: monomeric (single head) and dimeric (two heads) motors. Examples of singlehead myosins are myosin-I, myosin II and myosin IXb [318, 319, 320]. Examplesof two-headed myosins are myosin V and myosin VI [321, 322, 66]. LOT and SMFmeasurements have shown that myosins moves along actin in steps of average sizeabout 10 nm in single head myosins [323, 324] and 36 nm for the two headed myosinV [67].

Another motor that has been extensively studied using SMF techniques is theprotein machine F0, F1-ATP synthase, a proton pump that synthesizes ATP in the


mitochondria, the power plant of eukaryotic cells. The F0, F1-ATP synthase dissociatesin two parts, F0 (the proton channel) and F1 (often called F1-ATPase). The latteris a complex made out of a shaft containing two different types of 3 tubular subunitseach (called α and β) and a central subunit called γ. By engineering appropriatemutations in the complex, Kinosita and coworkers [325] immobilized the shaft to asurface and attached the central γ subunit to a fluorescent actin filament (Fig. 10B).In the presence of ATP the actin filament was observed to rotate in steps of 120degrees [326, 327, 328] which were later resolved into substeps of 30 and 90 degrees,each substep corresponding to different phases of the mechanochemical cycle of ATPsynthesis [329]. F1-ATPase motors have also the capability to be integrated withnanoelectrochemical systems to produce functional nanomechanical devices [330].

A second class of motors are those that interact with the DNA and participate inmaintenance tasks of the genome such as transcription and replication. Examples areDNA polymerases (DNApols), DNA translocases, RNA polymerases (RNApols) andDNA topoisomerases. DNApols have been studied using LOT and MT. Studies havebeen carried out in [331] with the T7 DNApol (belonging to the bacteriophage T7 andcharacterized by having a high processivity of several thousands base pairs) and in theBensimon group [332] who studied the sequenase (a mutant of T7 DNApol lacking theexonuclease site) and the Klenow DNApol (a fragment of Escherichia coli DNApolI lacking exonuclease activity). In these experiments a ssDNA containing a DNAprimer required for the initiation of replication is tethered between one immobilizedsurface and one detector bead that measures the force acting on the molecule. Afterflowing DNApol, ATP and other nucleotides (NTP) inside the chamber the tetherextension of the molecule is recorded at a constant applied force as a function of timeas the ssDNA is converted into dsDNA. From these measurements it is possible torecover the number of replicated nucleotides as a function of time and the speed ofthe motor. In all cases the replicating activity was found to decrease with the appliedforce ceasing at around 40pN in the case of the T7 DNApol above which exonucleaseactivity was observed. Models of the mechanochemical cycle of DNApol have beenproposed for T7 which qualitatively reproduce the dependence of the net replicationrate as a function of the opposing load [333, 334]. Another class of enzymes that movein specific directions along dsDNA are translocases. These are regulatory enzymesimportant during transport and replication processes which sometimes show sequencedependent bidirectional motion. FtsK, a translocase of Escherichia coli involved inchromosome seggregation and cellular division, has been shown to move at an averagespeed of 5 Kbp/s and against loads up to 60 pN [335, 336].

A related experimental setup has been applied to investigate the transcriptiondynamics of RNApol. This is a processive enzyme that synthesizes a ssRNA strand bytranslocating along dsDNA without the need of a primer [339]. The newly synthesizedstrand, messenger RNA, codes for the amino acid sequence of proteins which aresynthesized in the ribosome [340]. Transcription consists of three main steps: initiationof the transcribing complex, elongation and termination [341]. Pioneering SME ontranscription were carried out in the T7 RNApol by the groups of Block, Gelles andLandick using LOT [342, 343]. Under an applied force the rate of RNA transcriptiondid not change much but the process stalled at around 20-30 pN. Similar results havebeen found in studies of the transcription dynamics of Escherichia coli RNApol underassisting or opposing force [344, 337] (see Fig. 11 (A-C)). The recent development of anultra-stable trap with Angstrom-level resolution has shown discrete steps of averagearound 3.5 A for the step size of the enzyme indicative of a mechanochemical cycle


Distance (Å)

Dis

tance

(Å

)

Auto

corr

ela

tion

B

C

A

D E F

time (s)

3.4 Å

Figure 11. RNApol motion in E. coli using LOT. (A) Experimental setup inforce-flow measurements. LOT are used to trap beads but forces are applied onthe RNApol-DNA molecular complex using the Stokes drag force acting on theleft bead immersed in the flow. In this scheme force assists RNA transcriptionas the DNA tether between beads increases in length as a function of time.(B) The contour length of the DNA tether as a function of time (blue curve)and (C) the transcription rate (red curve) as a function of the contour length.Pauses (temporary arrests of transcription) are shown as vertical arrows. (D)Experimental setup in a ultrastable LOT. The right trapped bead is located in theregion of the trap where the stiffness vanishes. This creates a force-clamp whereonly the right bead moves determining the extension of the complex. (E) Motion ofRNApol resolved in discrete steps of 3.4 A . (F) Average autocorrelation functionobtained from the position histograms showing peaks at distances multiples of 3.4A . Pictures (A-C) taken from [337]. Pictures (D-F) taken from [338].

of one bp at a time [345, 338] (Fig. 11 (D-F)). The dynamics of RNApol displaysa complex behavior sensitive to DNA sequence with pauses (temporary halts totranscription) and arrests (permanent halts). Many aspects of the elongation processin RNApol are not well understood. For example the distribution of residence timesfor pauses shows strong statistical variations in their frequency and duration [346].Many of these features are also found in DNA replication and are expected to beimportant in the regulation of gene expression [347].

Another type of DNA-protein motor that has attracted considerable attentionrecently are virus packaging motors. The packaging motor of bacteriophage virusφ29 encapsulates DNA inside the heads of the virus. It has been shown to be a


highly processive motor capable to work against loads of up to approximately 50pN[348]. These experiments have stimulated very interesting theoretical activity in thepackaging problem [349, 350, 351].

SME have been also applied to the study of topoisomerases. These are a largeclass of enzymes present in both prokaryotes and eukaryotes and are very importantin the maintenance of the genome. Topoisomerases act on the topology of DNA, theirmain task being to relax and introduce supercoils in DNA by cutting the phosphatebackbone of ssDNA and dsDNA. For example, relaxing stress of supercoiled DNAis important for transcription, replication and recombination. There are two majorfamilies of topoisomerases: type I and type II. Type I topoisomerases relax DNAsupercoils by changing the linking number (for a definition see Sec. 5.1.1) in one unit(∆Lk = −1) without ATP consumption. Type II topoisomerases change the linkingnumber by 2 being capable of introducing supercoils in DNA, ∆Lk = ±2, thereforeconsuming ATP. SME using MT are ideal to study the action of topoisomerases. Bytwisting the bead attached to a DNA molecule it is possible to build up torsional stressin the molecule and follow the subsequent relaxation upon addition of topoisomerase inthe buffer. Examples include the study of topoisomerase II in Drosophila melanogaster[352, 353], the observed torque dependence of kinetics in eukaryotic topoisomerase I[124, 354]. Also, DNA gyrase, a topoisomerase II of prokaryotes known to introducenegative supercoils, has been studied [355] using the bead tracking method [60].Related studies have been conducted with Escherichia coli topoisomerase IV, an ATP-dependent enzyme that removes positive (but not negative) supercoils [356]. Most ofthese experiments have been carried out using MT [357] or SMF where limited spatialresolution hinders time-dependent aspects of the kinetics such as pauses or stalls, seehowever [355].

Recent studies on helicases, however, have already identified such effects.Helicases are yet another class of DNA-protein motors crucial during DNA replicationthat have been studied with SME. Helicases are forerunners of the DNApol thatunwind DNA by transforming dsDNA into two strands of ssDNA, a necessary step forthe advance of the replication fork during DNA replication. DNA unwinding has beenstudied in the RecBCD helicase/nuclease of E. coli [358, 359] and in the Rep helicaseusing SMF assays [360]. RNA helicases play also an important part in the infectioncycle of many viruses by making two strands of ssRNA (available to produce newvirus copies) from a double stranded RNA (dsRNA) synthesized inside the infectedcell. Recent studies of the NS3 helicase, part of the protein machinery of hepatitis Cvirus, has been recently studied using LOT showing a great richness of kinetic effectsincluding pauses, arrests or even reversal of the motor followed by rewinding of thepreviously unwound dsRNA [361]. Finally we mention the study of the molecularcomplex of the ribosome, an experimental challenge to the biophysicist using single-molecule methods [362, 363, 364].

Molecular motors have inspired a large number of theoretical studies in statisticalphysics [365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376]. All motors studiedup to now show generic properties such as ATP and load dependence of their averagevelocity. For example the average speed as a function of ATP concentration followsthe Michaelis-Menten kinetics. Also, there is some evidence that kinetic phenomenasuch as pauses, arrests and backtracking motion are generic features of motors. Onewonders whether it exists a relationship between these dynamical features of motorsand their astonishing mechanical efficiency.


6. Tests of nonequilibrium theories in statistical physics

Recently there has been a lot of interest in applying single-molecule techniquesto explore physical theories in systems out of equilibrium. The use of newmicromanipulation tools in the exploration of the behavior of tiny objects (such asbiomolecules and motors) embedded in a thermal environment opens the possibilityto investigate how these systems exchange energy with their environment. Thisquestion is of great interest both at a fundamental and practical level. From afundamental point of view, the comprehension of how biomolecules operating veryfar from equilibrium are so efficient (see discussion in Sec. 3) raises the questionwhether such tiny systems exploit rare and large deviations from their average behaviorby rectifying thermal fluctuations from the bath. From a practical point of view,this might help in the design of efficient nanomotors in the future. The study ofsuch questions is steadily becoming an active area of research, nowadays referredto as Nonequilibrium thermodynamics of small systems [28, 29]. Such discipline isbecoming quite popular among statistical physicists who recognize there new aspectsof thermodynamics where large Brownian fluctuations are of pivotal importance ascompared to fluctuations in macroscopic (or large) systems [36]. In macroscopicsystems, fluctuations represent just small deviations respect to the average behavior.For example, an ideal gas of N molecules in thermal contact with a bath at temperatureT has an average total kinetic energy of (3/2)NkBT . However, the total energy is nota conserved quantity but fluctuates, its spectrum being a Gaussian distribution ofvariance (3/2)N(kBT )2. Therefore, relative deviations of the energy are on the order1/

√N respect to the average value. For macroscopic systems such deviations are very

small: for N = 1012 (this is the typical number of molecules in a 1 ml test tube atnanomolar concentrations), then relative deviations are on the order of 10−6, henceexperimentally unobservable by calorimetry methods. For a few molecules, N ∼ O(1)relative deviations are on the same order and fluctuations are measurable. SME, byallowing to study molecules one at a time, grant access to such large deviations thatare inaccessible in bulk experiments which use a macroscopic number of molecules.As a rule of thumb we can say that in nonequilibrium processes in small systems thetypical amount of energy exchanged with the environment is a few times kBT , maybefrom 1 to 1000 but not much more. As often happens when establishing the limits ofvalidity of certain regimes, there is not a well defined frontier separating the small-sizeregime from the large-size regime.

The name thermodynamics of small systems was already coined by T. L. Hill [37]who showed the importance of the statistical ensemble in thermodynamic relations.A main result of statistical mechanics is the independence of the equation of stateon the statistical ensemble in the thermodynamic limit. Such independence breaksdown in small systems due to the contribution of fluctuations which depend onthe type of statistical ensemble considered (e.g for the case of a stretched polymer[377]). The search for a new thermodynamic description of small systems has givenrise to microcanonical ensemble theory of phase transitions [378] and new classicalstatistics such as that embodied in Tsallis-entropy [379] and Beck’s theory [380] (fora review see [381]). From the current point of view, the most important aspect ofbiomolecular complexes is that they operate far from equilibrium, yet the possiblerelationship between nonequilibrium behavior and biological function is still unknown.The combination of small size and nonequilibrium behavior appears as the playgroundfor the striking behavior observed in molecular complexes inside the living cell.


Since the beginning of the 90’s some exact results in statistical mechanics haveprovided a mathematical description of energy fluctuations (in the form of heatand work) for nonequilibrium systems. This new class of results go under thename of fluctuation theorems (FTs) and provide a solid theoretical basis to quantifyenergy fluctuations in nonequilibrium systems [382, 383, 29]. FTs describe energyfluctuations in systems while they execute transitions between different types of states.For these fluctuations to be observable the system has to be small enough and/oroperate over short periods of time, otherwise the measured properties approach themacroscopic limit where fluctuations get masked by the dominant average behavior.Most fluctuation theorems are of the form,

P (+S)

P (−S)= exp

( SkB

)

, (1)

where S has the dimensions of an entropy that may represent heat and/or workproduced during a given time interval. The precise mathematical form of relationssuch as (1) (for instance, the precise definition of S or whether they are valid at finitetime intervals or just in the limit where the time interval goes to infinity) dependson the particular nonequilibrium conditions (e.g. whether the systems starts in anequilibrium Gibbs state, or whether the system is in a nonequilibrium steady state,or whether the system executes transitions between steady states, etc..).

Various categories of FTs have been introduced and experimentally validated [29].The differences between various FTs can be illustrated by introducing the concept ofthe control parameter. The control parameter (let us say λ) is a value or a set ofvalues that, once specified, fully characterizes a given stationary state of the system(either equilibrium or nonequilibrium). Upon variation of the control parameter asystem that is initially in a well defined state will evolve toward a new state. Ingeneral, if the control parameter is varied with time according to a given protocol,{λ(t); 0 ≤ t ≤ tf} the system will evolve along a given trajectory or path. If, aftertime tf , the value of the control parameter is kept fixed at the value λ(tf ) then thesystem will eventually settle into a new stationary state. Along a given path thesystem will exchange energy with its environment in the form of heat and work. Thevalues of the heat and work will depend on the path followed by the system. Uponrepetition of the same experiment an infinite number of times (the protocol λ(t) beingthe same for all experiments), there will be a heat/work distribution characterizing theprotocol λ(t). Generally speaking, FTs relate the amounts of work or heat exchangedbetween the system and its environment for a given nonequilibrium process and itscorresponding time-reversed process. The time-reversed process is defined as follows.Let us consider a given nonequilibrium process (we call it forward, denoted by F)characterized by the protocol λF (t) of duration tf . In the reverse process (denoted byR) the system starts at t = 0 in a stationary state at the value λF (tf ) and the controlparameter is varied for the same duration tf as in the forward process according to theprotocol λR(t) = λF (tf −t). FTs depend on the type of initial state and the particulartype of dynamics (deterministic versus stochastic) or thermostatted conditions.

Despite of the fact that most of these theorems are treated as distinct they are infact closely related [29]. The main hypothesis for all theorems is the validity of someform of microscopic reversibility or local detailed balance (see however [384, 385, 386]).Major classes of FTs include the transient FT (TFT) and the steady state FT (SSFT):

• The transient FT (TFT). In the TFT the system initially starts in an equilibrium(Boltzmann-Gibbs) state and is driven away from equilibrium by the action of


time-dependent forces that derive from a time-dependent potential Vλ(t). Thepotential depends on time through the value of the control parameter λ(t). Atany time during the process the system in an unknown transient nonequilibriumstate. If the value of λ is kept fixed then the system relaxes into a new equilibriumstate. The TFT was introduced by Evans and Searles [387] in thermostattedsystems and later extended by Crooks to Markov processes [388].

• The steady state FT (SSFT). In the SSFT the system is in a nonequilibriumsteady state where it exchanges net heat and work with the environment. Theexistence of the SSFT was numerically anticipated by Evans and collaborators forthermostated systems [389] and demonstrated for deterministic Anosov systemsby Gallavotti and Cohen [390]. The entropy production S by the system (equal tothe heat exchanged by the system divided by the temperature of the environment)satisfies the relation (1) in the asymptotic limit of large times t → ∞ and for

bounded energy fluctuations, σ = |S|t

< σ∗ where σ∗ is a model dependentquantity. Other class of SSFTs include stochastic dynamics [391], Markov chains[392, 393] or the case where the system initially starts in a steady state [394] andexecutes transitions between different steady states [395, 396].

The first experimental tests of FTs were carried out by Ciliberto and coworkersfor the Gallavoti-Cohen FT in Rayleigh-Bernard convection [397] and turbulent flows[398]. Later on FTs were tested for beads trapped in an optical potential and movedthorugh water at low Reynolds numbers. The motion of the bead is then well describedby a Langevin equation that includes a friction (non-conservative) force, a confining(conservative) potential and a source of stochastic noise. Experiments have beencarried out by Evans and collaborators who have tested the validity of the TFT[399, 400], and by Liphardt and collaborators for a bead executing transitions betweendifferent steady states [401]. The validity of the TFT has been also recently tested fornon-Gaussian optical trap potentials [402].

Particularly relevant to the single molecule context is the FT by Crooks [388, 403]which relates the work distributions measured along the forward (F) and reverse (R)paths,

PF (W )

PR(−W )= exp

(W − ∆G

kBT

)

, (2)

where PF (W ), PR(−W ) are the work distributions along the F and R processesrespectively, and ∆G is the free energy difference between the equilibrium statescorresponding to the final value of the control parameter λf = λ(tf ) and the initial oneλi = λ(0). A particular result of (2) is the Jarzynski equality [404, 405] that is obtainedfrom (2) by rewriting it as PR(−W ) = exp

(

−W+∆GkBT

)

PF (W ) and integrating both sidesof the equation between W = −∞ and W = ∞. Because of the normalization propertyof probability distributions, the left hand side is equal to 1 and the Jarzynski equalityreads,

< exp(

− W

kBT

)

>F = exp(

− ∆G

kBT

)

or

∆G = −kBT log(

< exp(

− W

kBT

)

>F

)

, (3)

where < ... >F denotes an average over an infinite number of trajectories all themgenerated by a given forward protocol λF (t). Relations similar to Jarzynski’s equalitycan be traced back in the free-energy perturbation identity derived by Zwanzig


[406] and a generalized fluctuation-dissipation relation proposed by Bochkov andKuzovlev [407]. The Jarzynski equality and the FT by Crooks can be used torecover equilibrium free-energy differences between different molecular states by usingnonequilibrium SME using LOT [408, 409, 410]. In 2002, the Jarzynski equality wastested to pull the P5ab RNA hairpin, a derivative of the Tetrahymena TermophilaL21 ribozyme [411]. However, in that case the molecule was pulled not too far fromequilibrium. The Jarzynski equality and related identities for athermal systems havebeen recently put under scrutiny in other systems [412, 413, 414]. The Jarzynskiequality and the FT by Crooks have inspired several theoretical papers discussingother related exact results [415, 416, 417, 418, 419, 420], free-energy recovery fromnumerical simulations [421, 422, 423, 424, 425, 426], bias and error estimates forfree-energy differences [427, 428, 429, 430, 431, 432, 433], applications either tosingle-molecule pulling experiments [186, 434, 435], enzyme kinetics [436, 437] orsolvable models [438, 439, 440, 441, 442, 443]. In addition, analytical studies on smallsystems thermodynamics show that work/heat distributions display non-Gaussian tailsdescribing large and rare deviations from the average and/or most probable behavior[415, 416, 444, 445, 446, 447]. These theoretical studies open the way to investigatethe possible relevance of these large deviations in other nonequilibrium systems incondensed matter physics [397, 398, 448, 449].

The FT by Crooks can be applied and tested by measuring the unfolding andrefolding work distributions in single molecule pulling experiments. For example, letus consider the case of a molecule (e.g. a DNA or RNA hairpin or a protein) initiallyin thermal equilibrium in the folded (F) or native state. By applying mechanicalforce (e.g. using AFM or LOT) the molecule can be mechanically unfolded and theconformation of the molecule changed from the native to the unfolded (U) state.The unfolding event is observed by the presence of a rip in the FEC of the molecule(Fig. 12B). During the unfolding process the tip of the cantilever or the bead in thetrap exerts a mechanical work on the molecule that is given by,

W =

∫ xf

x0

Fdx (4)

where x0, xf are the initial and final extension of the molecule. In (4) we are assumingthat the molecular extension x is the externally controlled parameter (i.e. λ ≡ x) whichis not necessarily the case. However the corrections introduced by using (4) are shownto be often small. The work (4) done upon the molecule along a given path correspondsto the area below the FEC that is limited by the initial and final extensions, x0 and xf

(grey shaded area in Fig. 12B). Because the unfolding of the molecule is a stochastic(i.e. random) process, the value of the force at which the molecule unfolds changesfrom experiment to experiment and so does the value of the mechanical work requiredto unfold the molecule. Upon repetition of the experiment many times a distributionof unfolding work values for the molecule to go from the folded (F) to the unfolded (U)state is obtained, PF→U (W ). A related work distribution can be obtained if we reversethe pulling process by releasing the molecular extension at the same speed at whichthe molecule was previously pulled, to allow the molecule to go from the unfolded (U)to the folded (F) state. In that case the molecule refolds by performing mechanicalwork on the cantilever or the optical trap. Upon repetition of the folding processmany times the work distribution, PU→F (W ) can be also measured. The unfoldingand refolding work distributions can then be measured in stretching/releasing cycles,an example is shown in Fig. 12C.


G∆

Dissipation approx. 30kBT

W/kBT

PF

U(W

) , P

U

F(-

W)

Folding (U F)

Unfolding (F U)

Extension (nm)

Fo

rce

(pN

)

W

0 nt 77 nt25

20

15

10

360 380 400

G C

C G

G C

G U

C G

A U

C G

G C

G C

G C

A CC A

G G

U C

G CG CG U

U AG C

C GU A

C GU A

G CA U

G A G

A G

U GA

A

G C

U A

U A

U G

G C

G A

GA

GU

U

3´5´F F

STEM

HELIX 1

HELIX 2

A

(A) (B)

(C)

Figure 12. Recovery of folding free energies in a three-helix junction RNAmolecule [193]. (A) Secondary structure of the junction containing one stem andtwo helices. (B) Typical force-extension curves during the unfolding process. Thegray area corresponds to the work exerted on the molecule for one of the unfoldingcurves. (C) Work distributions for the unfolding or forward paths (F → U) andthe refolding or reverse (U → F ) paths obtained from 1200 pulls. According tothe FT by Crooks (2) both distributions cross at W = ∆G. After subtracting thefree energy contribution coming from stretching the handles and the ssRNA thesemeasurements provide a direct measure of the free energy of the native structure.

The FT by Crooks has been tested in different types of RNA moleculesand the method has been shown capable of recovering free-energies under strongnonequilibrium conditions [193]. From (2) we observe that PF (∆G) = PR(−∆G) sothe forward and reverse work probability distributions cross each other at W = ∆G.By repeatedly measuring the irreversible mechanical work exerted upon the moleculeduring the unfolding process and the mechanical work delivered by the molecule to theLOT instrument during the refolding process it has been possible to reconstruct theunfolding and refolding work probability distributions, PF→U (W ) and PU→F (−W ),and extract the value of the work W = ∆G at which both distributions cross each other(Fig. 12C). The work probability distributions where measured along the unfoldingand refolding pathways for a three-way junction RNA molecule and found to stronglydeviate from a Gaussian distribution [193] (Fig. 12C). These experimental results pave


the way for other related studies, for example in molecular dynamics simulations [450].These kind of studies will expand in the future to cover more complex cases and

other nonequilibrium situations such as the free-energy recovery of folding free energiesin native states in proteins or free energies in misfolded structures and intermediatestates in RNA molecules and proteins. Ultimately FTs, when combined with SME, willoffer an excellent opportunity to characterize and understand the possible biologicalrelevance of large deviations and extremal fluctuations in molecular systems.

7. Conclusions

In this review I have discussed the potential of SME to investigate various topicsin molecular biophysics and statistical mechanics. After a brief discussion of themost widely used experimental techniques I have presented applications to variousmolecular systems. As stressed in the Introduction this review does not exhaust allrelevant applications of SME. By focusing on the field of molecular biophysics I justcovered a small fraction of problems. Other areas such as cellular biophysics andcondensed matter physics are progressively incorporating such techniques in the labs.

What is the future of SME? We can foresee two aspects of SME whosedevelopment will be crucial for the progress in the field: development of new andbetter instruments and development of new and better protocols of chemical synthesis.

A major contribution to the progress of the field will come from instrumentationdesign with enhanced spatial and temporal resolution, Recently, the developmentof an ultra-stable optical trap with Angstrom-level resolution has allowed for thedirect observation of base-pair stepping during the transcriptional elongation of E.coli RNApol [345, 338]. Future developments to improve spatial detection willcertainly include optical tweezers with dual traps [451]. Combination of SMFtechniques for imaging with force measurements open also the way to more sensitivemeasurements. Single molecule FRET can be combined with LOT to measure forcesand correlate them with conformational changes [452]. Also total internal reflectionfluorescence (TIRF) techniques capable of monitoring the position of a moleculealong a vertical direction using a calibrated evanescent wave can be combined withAFM measurements [453]. Instruments that can manipulate molecules at differenttemperatures and forces will grant access to the potential energy surface of themolecule. Along this direction, AFM and LOT that include various temperaturecontrollers have been already developed [454, 455, 456]. Finally, LOT with multipletraps offer interesting possibilities in the near future although it is not yet clear how touse them to manipulate molecular complexes in a controlled way [457]. Holographictweezers offer also exciting possibilities [458] however we must first learn how tocalibrate them in order to measure forces.

Also, the development of better protocols to synthesize molecular systems willfacilitate the outcome of the experiments. SME may present a considerable difficultyregarding the preparation of the samples, specially in those cases where biologicalactivity is required. It is commonly said that SME are 100% noise and 100%signal. Uncertainties in experimental conditions and sample preparation imply thatexperiments have to be repeated several times until good results are obtained. Usually,just a few molecules show the interesting behavior one is looking for, the rest simplydo not work. By synthesizing better complexes and having a good control on thechemistry it will be possible to carry out more efficient experiments and investigatenew problems. A good example of potentially interesting SME, where the chemical


synthesis of the molecular complex to manipulate is the rate-limiting step, is foundin the study of intermolecular interactions, for example protein-protein interactions(Sec.5.2.1). Most studies on intermolecular interactions use the AFM. Unfortunatelywith such technique it is difficult to repeteadly form and dissociate the same set ofmolecular interactions. This experiment is more feasible using LOT where, in addition,non specific interactions between substrate and the molecule are more efficientlyavoided. The chemical synthesis of appropriate handles (e.g. carbon nanotubes)for protein complexes will facilitate such experiments. We can foresee future SME toinvestigate protein-protein aggregation processes that are crucial in many biologicalprocesses.

SME are fascinating but difficult at the same time. They require imagination andstrenuous efforts. SME are redefining the shape and composition of modern researchteams. These must include researchers with expertises and knowledge covering a widerange of topics. SME represent one of the most interdisciplinary fields at present thatwill require the combined efforts of biologists, chemists and physicists. SME representa good example of the new trends in modern science that will reshape the way we aregoing to do research in this century.

Acknowledgments. I warmly thank M. Carrion-Vazquez for useful suggestionson the manuscript. Observations by an anonymous referee are also acknowledged. Iwish to thank also S. Dummont, J. Gore, M. Manosas and P. Sollich for a criticalreading of parts of the manuscript. I acknowledge the warm hospitality during pastyears of the Bustamante, Tinoco and Liphardt labs at UC Berkeley where I had thegreat opportunity to learn about this fascinating subject. I am grateful to all mycollaborators, much of whose work has been described in this review, including C.Bustamante, D. Collin, G. E. Crooks, J. Gore, J. M. Huguet, C. Jarzynski, I. Junier,P. Li, J. Liphardt, M. Manosas, S. Mihardja, D. Navajas, S. Saxon, S. Smith, R.Sunyer, I. Tinoco, E. Trepagnier, J. D. Wen. This work has been supported by theEuropean community (STIPCO network), the SPHINX ESF program, the Spanishresearch council (Grants FIS2004-3454,NAN2004-09348) and the Catalan government(Distincio de la Generalitat 2001-2005).

8. List of abbreviations

ADP Adenosine diphosphate

AFM Atomic force microscopy

ATP Adenosine triphosphate

BFP Biomembrane force probe

dsDNA Double stranded DNA

dsRNA Double stranded RNA

DNA Deoxyribonucleic acid

DNApol DNA polymerase

FEC Force-extension curve

FRET Fluorescence resonance energy transfer

FT Fluctuation Theorem

MT Magnetic tweezers

LOT Laser optical tweezers


RNA Ribonucleic acid

RNApol RNA polymerase

SME Single-molecule experiments

SMF Single-molecule fluorescence

ssDNA Single stranded DNA

ssRNA Single stranded RNA

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