What is the biological relevance of the specific bond properties revealed by single-molecule studies ? Philippe Robert, Anne-Marie Benoliel, Anne Pierres, Pierre Bongrand
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Philippe Robert, Anne-Marie Benoliel, Anne Pierres, Pierre Bongrand. What is the biological rel- evance of the specific bond properties revealed by single-molecule studies ?. Journal of Molecular Recognition, Wiley, 2007, 20, pp.432-447. hal-00321008
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This un-edited manuscript was accepted and iii) is it possible to relate this for publication by the Journal of information to molecular structure ? Molecular Recognition and published in volume 20, pp 432-447. It was published Keywords : laminar flow chamber, atomic on line on august 28, 2007 by Wiley force microscopy, biomembrane force probe, optical traps, surface-attached InterScience ( www.interscience.wiley.com molecules, binding strength, unbinding - DOI 10.1002/jmr.827) force, off-rate, Bell’s law
1 - INTRODUCTION What is the biological relevance of During the last decade, simultaneous the specific bond properties development of several methods allowing to revealed by single-molecule monitor bond formation and dissociation at the studies ? single molecule level yielded a new kind of information on molecular behaviour. The aim Philippe Robert 1,2,3 , Anne-Marie of this review is to discuss the input of this Benoliel 1,2,3 , Anne Pierres 1,2,3 and Pierre advance to current biological wisdom. For the Bongrand 1,2,34 sake of clarity and homogeneity, we shall focus on proteins. 1 INSERM UMR600, 2 CNRS UMR 6212, 3 Université de la Mediterranée Importance of molecular interactions. Life is based on molecular interactions. Indeed, considering proteins, enzymes need to bind specifically to substrates they will During the last decade, many authors took maintain in close proximity with adequate advantage of new methodologies based on reagents. Scaffolding proteins bind to each atomic force microscopy, biomembrane other in order to maintain the cell architecture. force probes, laminar flow chambers or Signalling is based on the formation of optical traps to study at the single molecule multimolecular complexes that will be level the formation and dissociation of generated through dedicated binding sites bonds between receptors and ligands frequently borne by widely spread structures attached to surfaces. Experiments provided such as SH2, SH3 or plecskstrin homology a wealth of data revealing the complexity of domains. Membrane receptors bind to specific bond response to mechanical forces and the ligands. Membrane adhesion receptors are a dependence of bond rupture on bond prominent example: nearly all steps of cell life history. These results supported the including survival, proliferation, existence of multiple binding states and/or differentiation, migration or activation are reaction pathways. Also, single bond studies heavily dependent on adhesive interactions. It allowed us to monitor attachments mediated is therefore not surprising that between 25 % by a few bonds. The aim of this review is to and 50 % of cell membrane molecules may discuss the impact of this new information well be adhesion receptors (Barclay, 1998). on our understanding of biological Also, it was stated in standard treatises that molecules and phenomena. The following “the biological functions of proteins almost points are discussed: i) which parameters do invariably depend on their direct physical we need to know in order to predict the interaction with other proteins” (Creighton, behaviour of an encounter between 1993). receptors and ligands, ii) which information Thus, it is not surprising that most is actually yielded by single-molecule studies biologists are deeply interested in molecular recognition and biomolecule interaction. However, while these phenomena are taught in 4 Corresponding author: Pr. Pierre Bongrand, every textbook and may be felt as well Laboratoire “Adhésion et Inflammation”, INSERM understood, several lines of research that UMR600, Parc de Luminy, Case 937, 13288 steadily increased during the last decade Marseille Cedex 09, France – Email : [email protected] 2 brought dramatic changes to our understanding Kramers (1940) to account for the rate of of molecular interactions. molecular reactions and basic analysis of the effect of force and attachment to surfaces Recent progress in studying molecular (Bell, 1978) was revived (Evans and Ritchie, interactions . 1997). Older reports formed the basis of a At least five major advances led to dramatic recent surge of theoretical analyses that are conceptual advances. intended to process and interpret currently i) extensive use of structural studies available experimental data. based on crystallography or nuclear magnetic v) Simultaneously, computer resonance yielded an increasing number of simulation evolved as a new approach for available molecular complexes known with understanding as well as predicting the angström resolution. Thus, we probably know behaviour of biomolecules. While thirty years fairly well what protein-protein binding ago, it appeared as a remarkable feat to interfaces look like (Lo Conte et al., 1999). It simulate the behaviour of a few tens of water seems a reasonable order of magnitude to molecules in a box (Dashevsky and Sarkisov, assume that the association of two protein 1974), it becomes feasible to simulate molecules will make several hundreds of interactions between proteins comprising squared angströms inaccessible to water, with thousands of atoms (Schueler-Furman et al., several tens of close interatomic contacts. 2005 ; Gray, 2006 ; Rueda et al., 2007) and ii) In addition to descriptive mimic force-induced bond rupture as studied information, systematic use of site-directed experimentally on models such as streptavidin- mutagenesis following the pioneering study of biotin interaction (Zhou et al., 2006). Cunningham et al. (1989) opened the Thus, it seems reasonable to examine possibility to assess the quantitative the impact of aformentioned lines of research importance of the interactions that were "seen". on the conceptual framework we should use to The basic principle consisted of systematically consider biomolecule interactions. replacing individual aminoacids constituting the binding surface with alanine and measuring An agenda for studying molecular the influence of this change on affinity. This interactions . approach yielded information on the influence A biologist willing to explore and understand on affinity of individual hydrogen bonds or the molecular interactions underlying cell ionic interactions. function will need the following three kinds of iii) Following the pioneering work of information. Tha et al. (1986) and Evans et al. (1989), several innovative methods were i) A first requirement consists of defining a set systematically used to monitor individual bond of quantitative parameters that are both formation and dissociation between surface- necessary and sufficient to account for attached biomolecules subjected to controlled molecular behaviour when they have been force in the piconewton range. These include measured. As an example, it has long been laminar flow chambers (Kaplanski et al., 1993 considered that the affinity constant might ; Alon et al., 1995 ; Pierres et al., 1996), account for most aspects of biomolecule atomic force microscopy (Florin et al., 1994 association. ;Lee et al., 1994 ; Hinterdorfer et al., 1996), optical tweezers (Miyata et al., 1996 ; Rinko et ii) Once useful parameters have been defined, al., 2004 ; Litvinov et al., 2005) biomembrane it is necessary to elaborate efficient methods force probes (Evans et al., 1994 ; Merkel et al., for measuring them. In fact, the development 1999). In addition to unprecedented accuracy, of powerful ways of studying individual bonds these methods yielded qualitatively new was certainly an incentive to look for more information such as bond response to accurate ways of describing and understanding mechanical forces. these bonds. iv) The need to interpret the new kind of information yielded by aforementioned iii) Finally, it is certainly useful to obtain methods was an incentive to reexamine the quantitative links between molecular structure physical basis of molecular interaction. Thus, and interaction properties. First, this would pioneering work initiated by Eyring (1935) and allow us to predict interaction parameters 3 between known molecules without a need to be considered. Here are two important perform lengthy and delicate experiments. examples. Second, this would markedly improve our A prominent step in the development understanding of biological phenomena. Thus, of immune responses is the interaction of T an important effort was done in building so- lymphocytes and antigen presenting cells called docking algorithms intended to predict exposing on their membranes cognate the interaction between two molecules or to complexes formed between molecules encoded devise a synthetic molecules with a capacity to in the major histocompatibility complex and bind to a biologically important mediator. This antigen-derived oligopeptides of about 10 may be particularly useful for drug design aminoacid residues (pMHC). Indeed, a major (Brooijmans and Kuntz, 2003). Also, this is task of T lymphocytes is to scan cells certainly useful to summarize data. composing a living organism to detect possible abnormalities, essentially the expression of The aim of the present review is to provide a foreign structures likely to be encoded by brief description of recent progress along these potentially harmful microorganisms (see e.g. three lines of research, with a special Bongrand and Malissen, 1998, for more details emphasis on methodological points. As on this task and involved challenge). Now, an mentioned above, we shall focus on protein important feature of this interaction is that a interactions. Even with this restriction, it is not given T lymphocyte may display different feasible to do justice to all advances performed responses depending on the interaction during the past years and we apologize for the properties of its membrane receptor (T cell omission of important work. receptor, abbreviated as TCR) and pMHC. While immunologists had long tried to relate 2 - LOOKING FOR A SUITABLE SET OF the outcome of interaction with affinity PARAMETERS TO ACCOUNT FOR (Ashwell, 2004), it appeared in the early MOLECULAR INTERACTIONS nineties that different peptide ligands recognized by a TCR with similar affinity The affinity constant . could induce widely different responses The law of mass action is a basic rule that (Matsui et al., 1994). What then might be the defines the amount of moles of complex interaction parameter determining the T cell formed between two reactants, say A and B, in response ? equilibrium: An other example is integrin regulation. Integrins are important cell A + B AB (1) membrane receptors that mediate a number of key interactions, such as adhesion to A common way of expressing the law of mass extracellular matrices or lymphocyte adhesion action is: to other cells. An important property of integrins is that their binding efficiency is [A eq ] [B eq ]/[AB eq ] = K d = 1/K a (2) highly regulated, in order that cells may bind to appropriate surfaces (see Vitte et al., 2005 Where eq stands for the equilibrium conditions, for a review). Now, while recent studies and K d and K a are the dissociation constant and clearly established the integrin capacity to the affinity constant, that are expressed in mole display major conformational changes with and mole -1 respectively (see Bongrand, 1999, concomitant affinity modification (e.g. for some additional remarks). Shimaoka et al., 2001), intriguing experiments As was emphasized by Alan Williams showed that affinity was not the only (1991) in the early nineties "The concept of parameter involved in integrin regulation: affinity dominated most thinking about indeed, Cai and Wright (1995) showed that a complex biological reactions for many years". monoclonal antibody could induce a high This means that about 15 years ago biologists affinity conformation in CR3, an integrin were entitled to think that the affinity constant complement receptor of phagocytic cells, but accounted for most important properties of any this antibody displayed similar binding intermolecular reaction. However, at this affinity to both active and inactive forms of moment, several important experimental CR3. Thus, rigorous thermodynamic reasoning findings suggested that other parameters had to showed that activity regulation performed by 4 this antibody was not based on affinity. What organism is repeatedly stimulated with a given then might be the basis of increased integrin antigen, the "efficiency" of the antibodies efficiency ? produced to get rid of the antigen will progressively increase. While it was first Kinetic constants: the on-rate and off-rate . thought that this improvement was essentially Several reports suggested that kinetic due to an increase of affinity, Foote and reasoning might provide an answer to Milstein (1991) reported that in addition to the aforementioned questions. This consisted of affinity increase, there was a shift towards an replacing equation (2) with (3) for describing a antibody family with an extremely high bimolecular reactions: association rate (k on ), suggesting a selection mechanism "with a premium of binding target d [AB]/dt = k on [A] [B] - k off [AB] (3) antigens rapidly".
This kinetic view was related to the A third example, that raised a major thermodynamic description through the simple interest of the biological community in equation: biophysical aspects of cell adhesion is the interaction of blood leukocytes with the blood Ka = k on /k off (4) vessels leading to adhesion and subsequent transmigration to peripheral tissues. This An important consequence of (4) is that two phenomenon is a key step of inflammation, reactions of similar affinity might display which plays an essential role in the organism widely different timescales. Thus, some defence against aggression (Harlan and Liu, receptors might form rapidly fairly transient 1992). It has long been found, using intravital bonds, while others with similar affinity might microscopy, that local activation of endothelial require higher amounts of time to form durable cells lining the blood vessels allowed them to bonds. Several examples supported the interest capture flowing white blood cells in of this concept. remarkable way involving at last two steps (Figure 1). First, cells undergo a nearly hundredfold velocity decrease and display a jerky displacement in contact with the vessel walls. Their velocity is then reduced to a few micrometers per second. This is called rolling. Cells then stop completely, which is a prerequisite for the transmigration step. The molecular basis of this phenomenon was Figure 1: Capture of flowing leukocytes by demonstrated by Lawrence and Springer activated endothelial cells. The arrest of flowing (1991) who used a laminar flow chamber to leukocytes on inflamed blood vessels involves demonstrate that rolling could be initiated and several sequential steps including tethering, maintained by an interaction between induction of rolling (often mediated by selectins) and firm arrest (requiring integrins). endothelial receptors belonging to the selectin family and ligands on the leukocyte surface. First, in their aforementioned paper, Complete stop could be achieved through an Matsui et al. (1994) provided experimental interaction between a leukocyte integrin (such support to the hypothesis that the outcome of as LFA-1, also called CD11aCD18) and its interaction between T cell receptor and pMHC ligand on endothelial cells (e.g. ICAM-1, also ligand was determined by the lifetime of denominated as CD54). While selectins could interaction rather than the affinity. A widely tether leukocytes to endothelial cells, they quoted model suggested to explain were unable to stop them completely. experimental data (McKeithan, 1995) relied on Conversely, integrins could stop leukocytes the involvement of biochemical reactions only if their motion had been slowed down by requiring a minimal occupation time to trigger selectins. A reasonable interpretation of these cell a signalling cascade in T lymphocytes. findings was that selectins had high association and dissociation rate, while integrins might A second example is the so-called display comparable affinity and lower kinetic maturation of the antibody response: when an constants. 5
importance of the link between molecules and The reports from Foote and Milstein (1991) surfaces). and Lawrence and Springer (1991) indeed arose the interest of the biological community in kinetic aspects of intermolecular reactions (Williams, 1991). Interestingly, available methodologies based on surface plasmon resonance provided a suitable way of measuring these constants when receptor and ligand molecules were available (Schuck, 1997 ; Rich and Myszka, 2006).
Interaction between bound molecules: there is a need for two functions rather than two constant parameters to account for molecular behaviour. Figure 2: Effect of force on the energy Since the late seventies, it became more and landscape. The figure shows i) bold line : a simple more apparent that the conventional kinetic energy well with a barrier (abscissa a). ii) thin line : description of molecular interactions as the alteration induced by an external force equal to described in standard textbooks of physical 10 % of the maximal slope of the native curve. The chemistry was insufficient to deal with barrier position is not markedly changed, and important biological processes. Indeed, Kramers's theory may be used, leading to Bell's law. iii) broken line : the alteration induced by an biologically relevant intermolecular reactions external force equal to about 90% of the maximal often involve bound molecules. This is obvious slope of the native curve. The barrier is very low when we consider cell adhesion, but and approximations used to derive Bell's law are no intracellular processes also frequently involve longer valid. multimolecular assemblies. Thus, molecular interactions often involve molecules bound to These points were indeed discussed in an large size complexes. insightful and premonitory theoretical paper by George Bell (1978): he clearly emphasized at A first important consequence is that least two important points: i) the kinetics of bonds formed between attached molecules are bond association and dissociation may be frequently subjected to mechanical forces that widely different when molecules are freely are likely to alter their lifetime. Thus, several moving (3D conditions) and when they are experimental data suggested that adhesive bound to surfaces (2D interactions). ii) the strength might behave as a physiologically effect of forces on intermolecular bonds should relevant parameter in the triggering of defence be dependent on specific structural parameters processes such as phagocytosis (Capo et al., (e.g. the location of energy barriers on 1978) or T-lymphocyte-mediated cytotoxicity energy/distance curves) that might vary (Bongrand et al., 1983). independently of affinity. Indeed, Bell proposed a simple exponential dependence of A second point is that the rate of bond the off-rate on disrupting force following a formation between attached molecules cannot formula that is now currently denominated as be derived from properties measured in Bell's law: solution. The most obvious illustration of this fact may be that 2-dimensional (2D) and 3- koff (F) = k off (0) exp(F/F°) = k off (0) exp(F a/k BT) dimensional (3D) on-rates have different (5) dimensions (Dustin et al., 1996 ; Pierres et al., 2001). Also, association between bound where k B is Boltzmann's constant, T is the molecules may be heavily dependent on absolute temperature, and a is the distance properties such as binding length or flexibility between the energy minimum and the that are not important in solution (see Pierres et maximum of the energy barrier on the force al., 1998a, for additional remarks and Jeppesen distance curve (Figure 2). An intuitive et al., 2001, for a spectacular illustration of the explanation for this law was that the rate of bond rupture might be viewed as the product of 6
"attempt frequency" to escape and the of microfilament elongation (Kovar et al., probability of success for a given attempt. A 2004). force F should decrease the activation barrier (Figure 2) by F a, thus increasing by There is a need for information allowing us exp(F a/k BT), according to Boltzmann's law, to derive the properties of multivalent the probability that a complex had sufficient interactions from single bond parameters . energy to break the bond. Note that in contrast It is striking that the efficiency of with Bell, several authors chose to make us of many bond species was found to be related to parameter F° (i.e. k BT/ a) instead of a. Indeed, their capacity to form dimers or multimers. F° may be used as a phenomenological Here are some examples. parameter without any reference to the energy The aforementioned ligand of LFA-1, landscape structure. ICAM-1/CD54, an ubiquitous molecule, was reported to occur as a dimer on cell Thus, predicting the formation and dissociation membranes, and this dimerization seemed of bonds between attached molecules should important for adhesive activity (Miller et al., require at least a knowledge of two functions 1995). rather than two parameters (Pierres et al., Cadherins are a prominent family of 1996), i.e. the probability k on (d) of bond homotypic calcium-dependent adhesion formation as a function of the distance between molecules that play a key role in maintaining the anchoring points of the molecule, and the tissue integrity (Wheelock et al., 2003). In a frequency koff (F) or rupture of a bond very elegant study, Yap et al. (1997) made subjected to a force F. Note that even this set cells express modified cadherin with an of parameters may prove insufficient in the intracytoplasmic moiety that allows the future. Thus, the force-mediated rupture of a induction of lateral clustering at will by mere bond may be dependent on the force addition of a membrane-permeable drug. This orientation in addition to its intensity (Astroff clustering was concluded to be required for et al., 2006 ; Ke et al., 2007). cadherins to exert efficiently their adhesive function. There is some experimental support to the Antibody molecules have long been view that this information is indeed relevant to shown to be multivalent. It has also been biological situations. Thus, elegant studies by recognized that the potential of an antibody to Patel et al. (1995) strongly suggested that the capture its cognate antigen was not always selectin capacity to tether leukocytes to entirely accounted for by affinity , which led endothelial cells under flow was at least partly immunologists to use the empirical concept of due to the length of these molecules, which avidity which seemed related to the capacity allowed them to interact with their ligand at of an antibody sample to form multivalent sufficient distance to avoid excessive repulsion bonds. by the pericellular matrix of interacting cells. Integrins are a prominent example that This concept is fully consistent with another has been already mentioned. report by VonAndrian et al. (1995) who CR3/CD11bCD18 is an integrin receptor for showed that selectins needed to be located on complement components that is found on the tip of cell membrane protrusions to mediate neutrophils and macrophages. It has long been rolling, thus emphasizing the importance of known that this receptor was fairly inefficient interaction range. on resting cells and it required some kind of An other point that was less frequently activation. As described above, activation was considered is the relationship between cell sometimes found to be related to a suitable rheological properties and mechanical conformational change resulting in increased properties of the bonds formed by cytoskeletal affinity or association rate. However, another constituents, such as actin and actin binding hypothesis was supported by other proteins. Indeed, cell deformation under force experiments. Indeed, Detmers et al. (1987) is tightly related to the kinetics of attachment used colloidal gold labelling and electron to and detachment from actin microfilaments microscopy to report that treatment of of molecules such as alpha actinin neutrophils with PMA, a well known protein (Wachsstock et al., 1994). Also, cell capacity kinase C activator, induced both CR3 to generate forces is related to the mechanisms activation and clustering of these receptors into 7 aggregates of a few (two to six) integrins. equilibrium constant in a standard medium (of Further experiments showed that the mere known composition, temperature and pressure) clustering of receptors on a membrane could may be considered as fully defined. On the be sufficient to activate adhesion contrary, aforementioned parameters (Hermanowski-Vosatka et al., 1988). Note that concerning surface-attached molecules are the importance of receptor clustering in dependent on many extrinsic factors. If these integrin activation was supported by a number are not adequately controlled, experimental of experimental reports (Yauch et al., 1997 ; data obtained with a given experimental setup Hato et al., 1998) may not be relevant to other situations. Here are a few examples. As a consequence, it is important to provide links between multivalent attachment The effect of a force applied to a bond and the properties of single bonds. However, may depend on the stiffness of linker this raises major difficulties: molecules. Thus, when Evans et al. (1999) i) linking the rupture of multivalent subjected molecular bonds to a disruptive force attachments to the behaviour of individual increasing linearly with respect to time, the bond requires assumptions relative to the dependence of the unbinding force (i.e. the sharing of forces between bonds and the force at the moment of rupture) on the rate of possibility of rebinding. As discussed in force increase might depend quantitatively and theoretical studies (Seifert, 2000 ; Erdmann even qualitatively on the nature of the linker. and Schwarz, 2004), these properties may Also, when Chen et al. (2000) studied the force dramatically influence bond rupture. Indeed, required to separate cells from concanavalin- the lifetime of a divalent attachment may be A-coated atomic force microscopy tip, close to the lifetime of a single bond in the increasing cell rigidity with glutaraldehyde absence of rebinding, whereas active rebinding resulted in twofold increase of the separation may increase this lifetime by several orders of force. This finding may be highly relevant to magnitude. This possibility is also exemplified the physiology of cell adhesion, since older by a recent report by Gopalakrishnan et al. investigations showed that cell detachment (2005) who used computer simulation to show from a surface might follow a decrease of that ligand dissociation from a surface might membrane stiffness, with subsequent decrease be strongly influenced by receptor clustering. of adhesive strength (Rees et al., 1977 ; Badley ii) when multiple bonds are allowed to et al., 1980). Clearly, linker mechanical form between surfaces, the rate of bond properties may be easily overlooked when formation is usually dependent on the number forces parameters are measured on bonds and position of already existing bonds as well involving cell membrane molecules, since as molecular length and flexibility (see e.g. results are dependent on cell mechanical Pierres et al., 1998a, for a simple treatment of a properties which are fairly complex. representative example). Thus, the only rigorous way of The significance of association rates is extracting single bond properties from probably even more dependent on experimental studies is to study attachments environmental parameters than that of mediated by single bonds . This explains the unbinding forces. Indeed, experimental outstanding impact of single bond studies on association rates are not only dependent on the our understanding of molecular interactions. length and flexibility of interacting molecules but also on their mobility and on the A point of caution: importance of defining topography of surrounding surfaces (Huang et intrinsic association parameters . al., 2004). It is important to emphasize a major difficulty underlying the experimental study of bond In summary , bond formation and dissociation formation between surface-attached molecules. between biomolecules is often dependent on When molecular associations are studied in parameters that are not accounted by standard solution, measured thermodynamic and kinetic 3D association and dissociation rates. It is constants may be considered as fairly intrinsic necessary to determine force-dependent to the studied binding sites: when molecular dissociation rate and distance-dependent species A and B have been defined, the association rates . These quantities are highly 8 complex since i) functions are obviously more reader is referred to a recent review for more complex than constant numbers, ii) they are details (Pierres et al., 2006). dependent on molecular environment, and iii) as will be shown below, a third cause of Basic principle s. As shown on Figure 3, the complexity is the multiplicity of binding states, principle consists of monitoring the motion of which was clearly revealed by single molecule a receptor-bearing cell or particle along a studies. ligand-coated surface in presence of a laminar shear flow. The velocity of a particle of radius 3 - WHICH PARAMETERS CAN BE a close to the surface is on the order of aG, OBTAINED WITH SINGLE MOLECULE where G is the wall shear rate (in second -1). STUDIES? The hydrodynamic force on a sphere attached to the surface is ≈ 32 µ a 2 G, where µ is the The aim of the present section is to medium viscosity. When the sphere is provide a brief description of currently maintained at rest by a single bond, the force available methods of studying single bond on the bond may be 5-10 fold higher at most, formation and dissociation in order to discuss depending on the length of the lever arm (see the reliability and significance of experimental Figure 3B). data. At least four approaches were repeatedly In many laboratories, flow chambers used during the last decade: flow chambers, were used with a shear rate on the order of atomic force microscopy (AFM), 100 s -1 or more, to mimic physiological biomembrane force probes (BFP) and optical conditions in blood vessels. In this case, the tweezers. Although much interesting Reynold's number is low enough to warrant information was obtained with the latter complete neglect of inertial effects. The approach (Miyata et al., 1996 ; Rinko et al., velocity of a particle of 5 µm radius is on the 2004 ; Litvinov et al, 2005), we shall consider order of 500 µm/s, allowing a contact duration only on the one hand flow chambers, and on of about 0.1 millisecond between receptor and the other hand AFM and BFP, since these ligands of total length of 50 nm. If a cell is methods were probably used most often and stopped by a bond, it may be subjected to a they yield fairly complementary information, force of order of the 100 pN, and the bond may making comparison fruitful. experience a rupture force of several hundreds of pN, unless cells undergo extensive deformation such a extension of long membrane tethers (Schmidtke et al., 2000). These conditions were mostly used to study interactions between selectin molecules and their ligands. We found it more rewarding to operate flow chambers at a much lower shear rate ranging between about 1-10 s -1 and replacing cells with microspheres of about 1.4 µm radius. In this case, the intermolecular contact time for bond formation might be higher than 1 millisecond, and the force on a bond Figure 3: Studying ligand-receptor interaction in maintaining cells at rest was less that about 5 the flow chamber . A: a receptor-coated particle is pN. Under these conditions, it appeared driven along a ligand-coated surface by a possible to monitor single bond formation and hydrodynamic flow. The unperturbed flow velocity dissociation between involving most adhesion at distance z from the surface is Gz, where G is the receptors, including integrins, cadherins, wall shear rate. B: a particle maintained at rest by a bond is subjected to a hydrodynamic force F and collagen, fibronectin, members of the torque T. The force on the bond is dependent on the immunoglobulin superfamily, and antibodies, shape of the particle surface. as well as selectins. Another advantage of this setup is that freely moving spheres are easily Studying single bonds with flow chambers . followed, and their position could be easily We shall only present major conclusions. The determined with an accuracy of about 50 nm with a simple image processing system. The 9 moment of bond formation and dissociation et al., 2002) and about 218 pN for L-selectin could thus be followed with high accuracy. (Alon et al., 1997). The spontaneous dissociation rate also varied on a large range, -1 Results obtained with flow chambers . as exemplified by CD2-CD48 (k off = 7.8 s , Bond rupture: Bell's law first seemed to Pierres et coll., 1996a) and α2β1 integrin - -1 account for a number of reported results . collagen (k off = 0.01 s after integrin activation An experiment easily yields hundreds ; Masson-Gadais et al., 1999). of particle trajectories (Figure 4A) that may be used to detect a number of arrests of widely Bond rupture: Multiplicity of binding states . varying duration. Values of arrest durations Soon after the first determination of can be used to obtain unbinding curves by bond lifetime with a flow chamber (Kaplanski plotting the probability P for particles to et al., 1993), it appeared that unbinding plots remain at rest at time t after initial stop (Fig did not always follow monophasic kinetics 4b) . Assuming simple dissociation kinetics, P (Pierres et al., 1995) in accordance with is expected to be equal to exp(- k off t), and the previous studies made with conventional dissociation rate is simply the slope of the methods of chemical kinetics (Beeson et al., curve on a semi-log plot. If the experiment is 1994 ; Foote et al., 1994). Thus, it was shown repeated with different values of the shear rate, at the single bond level that ligand-receptor the dependence of k off on the force can be couples such as antigen-antibody (Pierres et determined provided the force on the bond is al., 1995), Streptavidin-biotin (Pierres et al., determined with simple reasoning (Pierres et 2002), integrin-fibronectin (Vitte et al., 2004a) al., 1995 ; Alon et al., 1995). A simple way of or C-cadherin/C-cadherin (Pierres et al., 2007) varying specifically the force consisted of could display a series of binding states with changing the medium viscosity (Mège et al., different lifetimes. As will be discussed below, 1986 ; Chen et al., 2001). The force might thus this situation accounts for a variety of results be increased without changing the kinetics. that have been formulated in different ways such as dependence of rupture on bond history (Pincet et al., 2005 ; Marshall et al., 2005) or bond heterogeneity (Raible et al., 2006). Also, this imposes a tremendous complexity on the concept and experimental determination of association rates.
Bond rupture: catch bonds behave at variance with Bell's law . The concept of catch-bonds was put forward nearly twenty years ago by Dembo et al. (1988). The basic idea was that while a disruptive force should decrease bond affinity, as shown with thermodynamic reasoning, it Figure 4: Unbinding curves may be obtained was in principle conceivable that it might with a flow chamber . A: a typical trajectory increase bond lifetime. A few years later, revealing a binding event. B: the distribution of when in vitro systems were used to study the binding events durations is used to build an rolling phenomenon, it was reported that a unbinding plot. A straight line (bold curve) is suggestive of a monophasic reaction. Curvature minimal shear force was required to allow (thin line) is indicative of bond strengthening that rolling (Finger et al., 1996), but it was only may be due to delayed formation of additional recently that flow chambers allowed clearcut bonds or strengthening of a single bond. demonstration that catch bonds actually existed, as exemplified with bacterial receptors Many experimental data were (Thomas et al., 2002) or P-selectin (Marshall et consistent with Bell's law (Alon et al., 1995 ; al., 2003). Pierres et al., 1996a ; Alon et al., 1997 ; Chen et al., 2001) with a force constant varying on a Bond formation: measuring association rates nearly 100 fold range since reported F° was 2.4 with the flow chamber . pN for outer fragments of E-cadherins (Perret 10
Flow chambers are in principle well suited to range was estimated at 10 nm and the binding measure association rates provided these are frequency between molecules maintained at not too high. This may be explained as binding distance was estimated at 0.0012 s -1. follows: consider a molecule of binding range A major difficulty in studying r passing near a ligand with a velocity v. As a association rates is that the complexity of rule of thumb, the contact time will be of order energy landscapes makes their definition quite of r/v and the local concentration during arbitrary: indeed, defining a molecule as bound 3 passage will be about 1/r (in molecule per unit when a threshold force F t during a threshold of volume). if we express r in nanometer and v period of time t t, the bound state depends on in µm/s, the probability p that a contact might these parameters (Figure 5). Also, depending result in binding might be of order of on the shape of the energy landscape, the probability that a molecular encounter of 3 2 p = k on * (r/1000v) * (10/6r ) ≈ k on /( 600 v r ) duration dt might result in binding may vary as (6) a power of dt higher than 1. This adds to the definition of k on a complexity that has not been -1 -1 where k on is expressed in Mole s and the thoroughly discussed, to the best of our number of molecules per mole is written as 6 knowledge (see e.g. Pierres et al., 2007, for an 10 23 . experimental study illustrating this point. Taking the binding range as about 20 nm, which matches the length of many adhesion molecules, and using velocities of order of 10 µm/s, it is concluded that the association rate may be a limiting parameter for binding if it is lower than about 2.4 10 6 M -1s-1. Note that this is probably an underestimate since the mobility of surface-attached binding sites is likely to be lower than in free molecules (however, the difference may be moderate: Pierres et al., 1998a). Note also that if k on is higher than the limit we calculated, the binding frequencies measured with the flow chamber only reflect Figure 5: ligand-receptor interactions are often the number of ligand-receptor encounters, i.e. multiphasic . The curve shows a sequence of bound binding site densities on interacting surfaces. states of decreasing stability. The horizontal bracket However, the experimental shows a group of minima representing what is determination of association rates with flow called a bound state. The proportion of complexes chambers is made difficult due to the following occupying b 0, b 1, b2 depends on bond history. State reason: a high shear rate is required to make b3 may be too weak to be detected, but it may encounter time short enough to comply with influence binding kinetics. Thus, if transition from aforementioned condition. However, a high b3 to b 2 is slow enough, the attachment probability shear rate generates a high disruptive force may vary as a power of contact duration. which makes break nascent bonds. A possible way of overcoming this Studying multivalent attachments with a flow limitation might be to use particles of smaller chamber . radius than cells. Indeed, this will increase the As emphasized, unravelling biologically ratio between the particle velocity and the relevant phenomena requires not only a hydrodynamic force. However, a new quantitative understanding of single bond difficulty is the importance of Brownian behaviour but also a good knowledge of motion that makes particle motion very combinations rules. As an example, the complex. However, this may be used to obtain integrin-mediated attachment of monocytic an estimate of the binding range. Computer cells to fibronectin-coated surfaces was studied simulation may then be required to process under flow (Vitte et al., 2004a): unexpectedly, experimental data. This approach was used to when cell surface integrins were clustered with study the rate of bond formation between antibodies, a simultaneous increase of binding surfaces decorated with outer domains of duration and binding frequency was found. cadherin 11 (Pierres et al., 1998b). The binding Since it was checked that cross-linking 11
antibodies did not change integrin quantity was called the unbinding force (F u). conformation, the simplest interpretation of After performing hundreds of cycles, it was these experiments was that monovalent possible to obtain the frequency distribution of encounters between integrins and fibronectin unbinding forces (Figure 6B). In the molecules resulted in a majority of transient pioneering study made on avidin-biotin couple associations that were too short to be detected, (Florin et al., 1994), the hypothesis that single while receptor clustering might result in strong bonds were observed was based on the finding potentialization of interactions, thus markedly that the unbinding force appeared as an integer raising the proportion of detectable multiple of a constant value of 160 pN. In interactions. many studies, the surface density of binding molecules was made low enough that only a Studying single bonds with atomic force small fraction of contact/retraction cycles microscopy or biomembrane force probes . revealed binding events. Thus, if binding was a While selectins were the first molecules rare events, the probability of simultaneous studied at the single bond level with flow occurrence of multiple bonds was deemed chambers (Kaplanski et al., 1993 ; Alon et al., negligible based on Poisson law. 1995), avidin-biotin interaction was first Although the cycle and contact chosen for AFM studies in view of its duration were subject to wide variations exceptionnally high affinity, on the order of between different reports, typical values for the 10 15 M -1 (Florin e al., 1994 ; Lee et al., 1994). contact time were on the order of 50-100 ms, cantilever velocity was on the order of 100- 1000 nm/s, and cantilever stiffness on the order of 0.1 N/m. The impingement force during contact might be on the order of several hundreds of pN (Hinterdorfer et al., 1996 ; Ros et al., 1998 ; Fritz et al., 1998). While only "unbinding forces", i.e. the maximum force supported by a bond, were first reported, it was soon recognized that bond rupture should be considered as a stochastic event. It was first indicated by Evans et al. (1997) that the most probable force at the
Figure 6: Information yielded by AFM and BFP . moment of rupture should be proportional to the loading rate r (i.e. the rate of force increase A : An unbinding force (F u) can be measured . B: information can be extracted from the frequency per unit of time). However, the relationship distribution of F u. C: a plot of F u (either mean or between the unbinding force distribution and peak) versus the rate of force increase gives some the loading rate is fairly complex and depends information on the energy landscape (Figure 5). on the precise form of function k off (F). Using However, several assumptions may be required to Bell's law as the standard model, the following extract this information. Also, objective separation equation if often used (Merkel et al., 1999 ; of the curve into straight segment lines may not be Yuan et al., 2000 ; Perret et al., 2004 ; Rinko et straightforward. al., 2004)
Basic principle. F* = F° ln (r /k (0) F°) (7) The basic principle consisted of coating an off
AFM tip with a low density of receptor Note that the average unbinding force
AFM or BFP. Indeed, the latter approach was Thus, AFM and BFP forcefully demonstrated applied to streptavidin-biotin (Florin et al., that Bells' law held only on restricted domains 1994 ; Merkel et al., 1999 ; Yuan et al., 2000), of loading rates. selectin-ligand couples, and particularly P- selectin/PSGL1 (Fritz et al., 1998 ; Hanley et Catch bonds were also evidenced with AFM al., 2003 ; Evans et al., 2004), Integrins (Zhang and BFP . et al., 2002 ; Li et al., 2003) or cadherins While catch bonds were demonstrated by (Baumgartner et al. 2000 ; Perret et al., 2002 ; Thomas et al. (2002) with a flow chamber, Panorchan et al., 2006). Marshall et al. (2003) found with both flow experiments and atomic force microscopy that Merkel et al. (1999) soon showed that the P-selectin/PSGL-1 couple displayed a Equation (7) applied only over a limited range catch bond behaviour. This conclusion was of loading rates, and plots of F* versus r confirmed by a collaboration between E. Evans appeared as a sequence of line segments, and C. Zhu (Evans et al., 2004) with the which was interpreted as revealing a biomembrane force probe. This was interpreted succession of energy barriers that had to be as a consequence of the occurrence of two overcome for complex dissociation. The dissociation pathways for the P-selectin/PSGL- distance between each barrier and the energy 1 complex. minimum was calculated as k BT/F°, according to equation (5). This first report was rapidly Studying the rate of bond formation with AFM confirmed by other investigators who reported and BFP . multiple segments in F*/r plots revealing a Several authors attempted to estimate growing complexity. association rates at the single molecule level with AFM or BFP. The first quantitative report As an example, while a study of the homotypic was probably authored by Hinterdorfer et al. interaction between the two distal domains of (1996) who studied the interaction between an E cadherin (EC12) yielded a dissociation rate albumin-coated surface and an AFM tip coated -1 koff and a force constant F° equal to 0.45 s with specific antibodies. They estimated the and 2.4 pN respectively with a flow chamber range of the interaction by subjecting the AFM (Perret et al., 2002), Panorchan et al. (2006) tip to rapid vertical movement and slow lateral reported values of 1.09 s -1 /13 pN, and 4 s -1 /41 displacement, and determining the binding pN with an atomic force microscope operated probability as a function of position near a with a loading rate of 1,000 and 10,000 pN/s surface coated with albumin at low density. respectively. Finally, using a biomembrane Estimating that binding could occur when the force probe, Perret et al., disclosed a hierarchy tip was less than 6 nm from the surface, and of four substates displayed by complexes assuming that the binding frequency was formed with EC12 or the entire five-domain constant when the distance was lower than the extracellular region of E cadherin (EC15): threshold value, they could derive a tentative parameters were respectively about 10 s -1/6pN, association constant from the binding 0.7 s -1/6 pN, 0.01 s -1/5 pN and 10 -5-10 -6 s -1/3- probability. They obtained an estimate of 5 10 4 4pN. In order to reveal these widely different M-1 s -1 that they considered as satisfactory on binding states, it was necessary to improve the the basis of reported values obtained on usual procedure involving constant loading soluble molecules with conventional methods rate. The authors took advantage of a special (although much higher values were often "jump ramp" procedure to detect very transient reported). complexes. In their study of VE-cadherin, Baumgartner et al. (2000) estimated at 10 3-10 4 This multiplicity of binding states was not M-1s-1 the association rate of these molecules. unique to E-cadherin. Thus, Li et al. (2003) This falls within the range reported with studied the interaction between a fibronectin measurements made on cadherins with surface fragment and α5βintegrin : Bell parameters plasmon resonance (Syed et al., 2002). were respectively 0.13 s -1/10 pN and 33.5 s - In addition to these attempts at 1/48 pN when the loading rates fell in the 20- estimating association rates, several authors 10,000 and 10,000-50,000 pN/s range. reported that the binding probability increased as a function of the duration of contact during 13 receptor and ligand-coated surfaces (Fritz et - A more complete argument consists of al., 1998). comparing results obtained with serial dilutions of binding sites: if the frequency of Reliability and significance of measured binding events decreases as a linear function of parameters. surface receptor density, but event duration or Before concluding this experimental section, strength remain constant, it seems reasonable we shall consider four pending problems. to assume that single bonds are detected. Although this conclusion seems reasonable, it Can we really measure and even define may be pointed out that there remain a association rates ? possibility of an error: indeed, suppose only An association rate k on may be defined by divalent attachments are detectable, and assuming that the probability that an encounter receptor solution contains a proportion of of duration dt between two molecules will molecular aggregates (which is quite common: result in bond formation is k on .dt. There are Vitte et al., 2004). In this case, it is possible to two problems with this definition: i) since the observe linearly decreasing frequency of energy landscape of the molecular complex identical events. probably involves a huge number of minima - A definitive proof would thus require to (see e.g. Ansari et al., 1985) there is no check the precise density and distribution of objective way of defining the region we shall binding sites on surfaces (imaging mode AFM call "bound". Thus, as often discussed in the might be useful for this purpose) in order to description of flow chamber experiments, a rule out the requirement for aggregates in view particle is defined as arrested when its of the frequency of binding events. This is by displacement during a time interval τ is less no means easy. than a threshold distance ξ. This requires an - A reasonable argument might be that the arbitrary choice. ii) simple kinetic reasoning properties (strength or duration) of observed shows that the probability that a sufficient binding events match the expected order of number of energy barriers be overcome during magnitude on the basis of other published a molecular encounter, the probability of bond reports. However, while this argument also formation during a period of time dt may be seems reasonable, the multiplicity of binding proportional to a power of dt, which makes states and possibility that a combination of "apparent" association rates time dependent. incomplete bonds might resemble a single full Thus, "apparent" association rates might attachment makes also this argument increase together with encounter time. This questionable. might provide an explanation for the low value Thus, it must be accepted that despite of the association rate we obtained with adequate controls the conclusion that single cadherin moieties (Pierres et al, 1998b). The bonds are studied may often be considered as existence of ultrashort undetectable binding reasonable, although not formally proven. states was indeed demonstrated in recent studies (Vitte et al., 2004a ; Pierres et al., How can we relate the properties of 2007). attachments mediated by a few bonds to single- bond parameters? How can we prove that we are actually As emphasized in the first section of this measuring single bonds ? review, many important biological interactions As previously argued (Zhu et al., 2002), It is are mediated by parallel bonds. An important difficult to prove formally that single bonds are example is antigen binding by antibodies. actually detected for several reasons: Indeed, antibodies are multivalent and it has - An argument used in many AFM studies is long been known that the efficiency (often that when a low proportion of cycles reveal called "avidity") of antibody samples is often detectable binding events, only a low related to their capacity to form multivalent proportion of these events should involve bonds. It is therefore of interest to mention multiple bonds according to Poisson's law. recent experimental studies using dynamic However, it must be emphasized that this force spectroscopy to analyze parallel bonds argument holds only if it has been proved that between antibodies and antigens such as mucin single bonds are actually detectable. (Sulchek et al., 2005) or chelated uranyl (Odorico et al., 2007). Results clearly suggest 14 that multivalency can result in dramatic Table 1. Analysis of P-Selectin/PSGL1 interaction enhancement of receptor efficiency. at the single molecule level
Is Bell's description convenient, and is it Method Bell parameters Reference sufficiently accurate to summarize /Loading rate k (0) F° pN experimental data? off second -1 At the present time, Bell's law remains the Flow chamber 0.95 82 Alon et al., standard way of describing bond rupture and 1995 extracting simple parameters from AFM/10 4 - 10 5 0.022 16.6 Fritz et al., experimental data, as acknowledged in both pN/s 1998 experimental (Chen et al., 2001 ; Rinko et al., Flow chamber 2.4 104 Smith et al., 2004 ; Perret et al., 2004) and theoretical 1999 (Pereverzev et al., 2005 ; Dudko et al., 2006 ; AFM/5x10 3- 0.22 30 Hanley et Lou et al., 2007) reports. However, it seems 6x10 5pN/s al., 2004 now well established that we must abandon the BFP/300-3x10 4 0.37 18 Evans et al., earlier view that a single pair of parameters pN/s 2004 koff (0) and F° can fit experimental observations in all accessible situations (Alon et al., 1995 ; This table displays estimates of Bell’s parameters for PSGL1-P-Selectin interaction reported by Fritz et al., 1998). This is exemplified by a several investigators using AFM, BFP or flow comparison of several parameters reported for chambers. the same molecular couple, i.e. P- selectin/PSGL1 (Table 1). The main reason for Conclusion . this situation stems from the multiplicity of The aim of this section was to review the type binding states that is usually observed in of information that was obtained during the studied ligand-receptor couples. There are two last decade when flow chambers, atomic force consequences for this situation: microscopes or biomembrane force probes - Different transitions may be observed under were used to study bond formation and different situations. Indeed, it was suggested dissociation at the single molecule level. that AFM or BFP often probed transitions from more stable binding states than flow chambers Bond rupture . At the present time, Bell's law (Pierres et al., 2002 & 2007). Thus, in a study remains the standard way of describing bond of streptavidin-biotin interaction, the distance rupture. However, this is more and more between energy barriers estimated with Bell's difficult to use since a given set of parameters law on the basis of AFM or BFP data (Merkel (k off and F°) can only be used in a limited et al., 1999 ; Yuan et al., 2000) ranged between number of conditions. Therefore, there is 0.05 an 1 nm whereas the flow chamber probably a need to determine which revealed two barriers 1.3 nm apart, at some physiological situation is relevant to a given distance from the minimum energy state. Also, set of Bell's parameters. Thus, adhesion in a in a study made on C-cadherin homotypic flow chamber operated under a wall shear rate interaction (Pierres et al., 2007), Results were of 100-200 s -1 is probably well representative consistent with the existence of two barriers of leukocyte-endothelium adhesion in blood 2.15 nm apart. vessels. The disruptive forces experiences by - Since what is called a "bound state" is in fact bonds in a flow chamber operated at lower a mixture of different molecular states, the shear rate may be comparable to the force proportion of these isoforms may be dependent required to extend microvilli, i.e. several tens on the history of complex preparation in of piconewtons (Shao et al., 1998). It would absence of equilibrium, as was demonstrated certainly be useful to determine which loading directly (Pincet et al., 2005). rate is most representative of physiological Thus, describing bond rupture with situations. Bell's law and a single set of parameters is only feasible in a limited range of experimental Bond formation . The most common way of conditions (i.e. loading rate in AFM describing bond formation between experiments, and shear rate in flow chamber individual attached molecules is based on two experiments). parameters, i.e. binding range and binding frequency for two molecules maintained within 15 binding range (Hinterdorfer et al., 1996 ; Fritz number of dimensions of the relevant space et al., 1998 ; Pierres et al., 1998b). As may be strongly increased. previously emphasized, these parameters are A simplification that was considered as likely to be highly dependent on surface acceptable until a few years ago was suggested structure and environmental conditions. It must by H. Eyring (1935) who elaborated the be emphasized that a different approach should transition state theory of reaction rates. The be used to study the rate of bond formation main assumption was that there was a single between surfaces that have been aligned by a preferred path for a bimolecular reaction. This sufficient number of bonds. In this case, the path was supposed to follow the bottom of a relevant formalism that has been developed for valley in the energy landscape. The reaction many years is the use of 2D affinity constant, could thus be viewed as a 1-dimensional and association and dissociation rates (see e.g. displacement along the energy/distance curve Zhu et al., 2007). (Figure 3). The dissociation rate could then be calculated by using the Boltzmann velocity 4 - RELATIONSHIP BETWEEN BINDING distribution to determine the particle flux PARAMETERS AND STRUCTURE OF across the energy barrier opposing the exit. BINDING SITES A following step was achieved by Kramers (1940), who took care of viscosity by While a quantitative description of molecular studying the escape rate of a particle interactions is per se of utmost interest to experiencing a random Langevin force as well understand and model cell processes such as as viscous drage in a well. signalling or adhesion (Bell et al., 1984), it More recently, following a seminal would be of prominent interest to relate these intuition by Bell (1978), Evans and Ritchie parameters to molecular structure. Indeed, in (1997) built on these early reports to achieve a addition to its intellectual appeal, a reliable quantitative analysis of the effect of forces on method of deriving interaction parameters particle escape (or bond rupture). Following from molecular structure would allow us to Bell's remark that the energy U(x) becomes U - take advantage of all structural information Fx in presence of force, the diffusion current available in data banks and avoid lengthy and J(x) may be written as: delicate experiments.
There are currently to ways of relating J(x) = - D ∂c/ ∂x - (Dc/k BT) (dU/dx - F) cell interaction parameters to their structure: (8) while a purely theoretical approach is conceivable, computer simulations are more where D is the diffusion coefficient and c(x,t) and more widely used to illuminate the the particle concentration. Assuming a behaviour of biomolecules. stationary state (J is constant, c only depends While a thorough review of both on x), and writing that the total number of approaches would not fall into the scope of this particle (i.e. ∫ c(x) dx) is one, we can calculate review, it is certainly warranted to give a brief the escape frequency 1/J. Now, assuming that sketch of recent attempts relevant to the F is low enough not to alter drastically the phenomena we studied. shape of the potential, the escape rate may be viewed as a product of four terms (Evans and Theoretical approach . Ritchie, 1997 ; Lin et al., 2007): A theoretical basis for Bell's law .
The structure of a complex formed by koff ≈ (D/l 0la ) exp [(- E° a + a F)/k BT] two rigid macromolecules may be defined (9) with five independent parameters (e.g. a distance and four angles). The energy D represents the particle diffusion coefficient. landscape of the complex may thus be viewed This is likely to be much lower than in free as a hypersurface in a 6-dimensional space. state due to different phenomena including The interaction between molecules may be hydrodynamic effects (Evans and Ritchie, viewed as a motion of a point defining the 1997) and the microstructure of the energy complex on this hypersurface. Since proteins curve (Zwanzig, 1988 ; Hyeon and Thirumalai, are quite flexible (Rueda et al., 2007), the 2003)
16
l0 represents the width (or the reciprocal of the to external forces (Evans et al., 2004 ; curvature) of the energy well, and l a represents Pereverzev et al., 2005). Note that the reality the width of the energy barrier opposing the of multiple pathways is also supported by particle escape. Finally, the exponential term molecular dynamics simulation (Martinez et represents the escape probability that may be al., 2005). approximated as the sum of the zero force activation energy and the product of the force Reexamination of Kramers theory. and the distance of the barrier to the minimum The increasing flow of experimental studies on energy. This approximation is acceptable if the single bond rupture was an incentive to barrier is fairly steep. reexamine the basis of Kramers theory, and it was an incentive to study theoretical Extracting barrier position from force relationships between experimental results and spectroscopy data free energy profiles (Hummer and Szabo, 2001 Assuming the existence of a series of sharp & 2003 ; Dudko et al., 2003). As clearly barriers, Evans et al. predicted that the plot of explained in recent reports (Dudko et al., 2006 most probable unbinding force versus the ; Lin et al., 2007), it seems now possible to logarithm of the loading rate should appear as state that Bell's law is an acceptable a sequence of linear segments with ascending approximation when the pulling speed is low slope (Evans et al., 1997 ; Merkel et al., 1999) enough. However, at high pulling speed, it may and they concluded that the time required to happen that the force experienced by the bond cross a series of barriers was the sum of times is close to the maximum slope of the binding required to pass each barrier. potential along the reaction coordinate. In this case, there is no longer any sharp barrier on the
1/k = ∑ t off (n) exp(- F/F°(n)) free energy profile and the unbinding force (10) may be proportional to r 2/3 rather than r (r is the loading rate), following an insightful analysis Where n refers to the nth barrier. Note that from Garg (1995). Further, some important this result was based on several assumptions points were added. concerning particle equilibration between - First, it was emphasized that the statistical barriers. distribution of unbinding forces conveyed However, this simple interpretation was useful information. A useful guideline (Dudko recently questioned for several reasons. et al., 2006) is that Bell's law may no longer be Even if Bell's equation is valid for the passage applicable when the variance of the unbinding of a single barrier, it may be difficult to relate force is dependent on the loading rate. This is dissociation kinetics to the shape of the important since this may indicate that energy/distance curve. Indeed, Strunz et al. curvature of the F u versus r plot may not be (2000) showed that even with a single indicative of an actual energy barrier. intermediate barrier, different dissociation - Also, it was noticed that additional kinetics could be observed when forces were information could be obtained by varying the varied. Also, Derényi et al. (2004) way of exposing bond to forces. Thus, Lin et demonstrated that when the curve contained a al. (2007) concluded that a constant force number N of barriers, plots of most probable experiment was better suited to obtain the unbinding force might display up to N(N+1)/2 activation energy of the bond, and a constant segments. loading rate might be useful to extract the critical force corresponding to the maximal Single path approximation. slope of the energy/distance curve. Also, Braun Bartolo et al. (2002) questioned the single path et al. (2005) pointed out the potential interest assumption in a theoretical study. Interestingly, of periodic loading. the interest of the point raised by these authors was soon supported by the experimental Conclusion . demonstration of the reality of catch bonds While Bell's law remains the standard way of (Thomas et al., 2002 ; Marshall et al., 2003) describing experimental data, much whose rupture behaviour was found consistent theoretical work is currently devoted to the with the hypothesis that there indeed were two analysis of quantitative relationship between dissociation pathways with different sensitivity these data and energy landscapes. The interest 17 of this current line of research is increased by molecules at the single cell level. Most studies present attempts made at taking advantage of were devoted to the monitoring of the rupture computer simulation to predict fine aspects of of bond subjected to a constant or steadily molecular behaviour more and more closely growing external force. The standard way of related to measurable properties. expressing results is based on Bell's hypothesis that the dissociation rate of a bond subjected to Computer simulation. an external force F increases exponentially Molecular dynamics was applied for more than with respect to F. two decades to simulate protein behaviour, and It was initially considered that bond there is much interest in the development of rupture might be viewed as the passage of a algorithms for predicting the capacity of single energy barrier in a single reaction path, synthetic molecules to interact with following a scheme elaborated by Eyring and biologically important targets (Brooijmans and Kramers during the first half of the twentieth Kuntz, 2003). While the reliability of available century. In this case, it was felt relatively easy methods has long been felt insufficient, to extract from experimental data the continuous progress makes it more and more spontaneous dissociation rate of a bond, as warranted to use simulations as an additional well as the height of the energy barrier and its tool both to help understand and predict distance to the energy minimum. experimental data. Systematic ways of testing During the last years, it became more new methods such as CAPRI (critical and more obvious that this standard framework assessment of protein interactions) markedly was unable to account for all the complexity of increased the credibility of current approaches actual bonds. It is likely that bond formation (Schueler-Furman et al., 1995). and dissociation may follow more than one Thus, while Evans et al. (Evans and path in the complex energy landscape, and Ritchie, 1997 ; Merkel et al., 1999) were able each path involves several energy barriers. As to compare their experimental results on the a consequence, more work is required to draw rupture of spectravidin-biotin bonds with full benefit of recent experimental advances: earlier simulations (Tavan et al., 1996 ; i) Firstly, it would be useful to define criteria Izrailev et al., 97), there was a gap of several to assess the biological relevance of the orders of magnitude between the pulling multiple reaction paths that are disclosed by duration in simulated and actuel experiments. ultrasensitive experimental devices. This Recently, this difference was overcome by requires a quantitative analysis of the Zhou et al. (2006) with a so-called "hybrid conditions of encounter between biomolecules simulation technique" consisting of decoupling composing living cells. the motion of the tip and molecular ii) Secondly, in order to rule out any ambiguity equilibration. It was thus possible to simulate in the extraction of structural information on realistic loading rates. Experiments suggested molecular complexes from dissociation the occurrence of three energy barriers in experiments, it is necessary to improve the accordance with the experimental report from procedure of single bond analysis by using Merkel et al. (1999). Also, the authors were more appropriate and/or systematic ways of able to link energy barriers to the disruption of varying the force cycles. well identified hydrogen bonds. iii) Thirdly, much effort must be done to rule Thus, it is likely that computer out possible causes of interpretation errors in experiment will complement more and more order to rule out misinterpretations due to the efficiently single molecule experiments to unexpected occurrence of multivalent yield an accurate view of protein dynamics. attachment, or to inexact estimate of the forces actually experienced by tested bonds. 5 - SUMMARY iv) Fourthly, measuring association rates probably requires extensive information on During the last decade, numerous energy landscapes (as obtained by studying investigators used new approaches based on bond rupture), topographic distribution and atomic force microscopy, biomembrane force environment of binding molecules as well as probes, laminar flow chamber or optical geometrical and mechanical properties of tweezers to study bond formation and linkers. dissociation between ligand and receptor 18
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