Introductory Lecture Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces explored with dynamic force spectroscopy Evan Evans Departments of Physics and Pathology University of British Columbia V ancouver BC Canada V 6T 1Z1 and Department of Biomedical Engineering Boston University Boston Massachusetts USA 02215 Received 21st December 1998 Beyond covalent connections within protein and lipid molecules weak noncovalent interactions between large molecules govern properties of cellular structure and interfacial adhesion in biology. These bonds and structures have limited lifetimes and so will fail under any level of force if pulled on for the right length of time. As such the strength of interaction is the level of force most likely to disrupt a bond on a particular time scale.For instance strength is zero on time scales longer than the natural lifetime for spontaneous dissociation. On the other hand if driven to unbind or change structure on time scales shorter than needed for diÜusive relaxation strength will reach an adiabatic limit set by the maximum gradient in a potential of mean force. Over the enormous span of time scales between spontaneous dissociation and adiabatic detachment theory predicts that bond breakage under steadily rising force occurs most frequently at a force determined by the rate of loading. Moreover the continuous plot (spectrum) of strength expressed on a scale of log (loading rate) provides a map of the prominent barriers e traversed in the energy landscape along the force-driven pathway and reveals the diÜerences in energy between barriers.Illustrated with results from recent laboratory measurements dynamic strength spectra provide a new view into the inner complexity of receptor»ligand interactions and receptor lipid anchoring. Introduction Well-recognized in biology ligand»receptor interactions are the fundament of nanoscale chemistry in recognition signalling activation regulation and other processes from outside to inside cells. Thus following the advent of atomic force microscopy (AFM) a decade ago,1 it was no surprise that researchers quickly seized the opportunity to test strengths of receptor»ligand bonds. Since then AFM and other sensitive force probes have been used to pull on a variety of molecules embedded in»or adhesively bonded to»surfaces.Applying these techniques experimentalists often imagine that probe force establishes a well-de–ned property of an interaction between molecules. Such expectations originate from the age-old creed of physics which states that strength is the maximum gradient [(dE/dx)max of an interaction potential or energy contour E(x) de–ned along the direction (x) of separation. Hence it is anticipated that detachment forces for diÜerent types of molecular interactions will follow a scale set by the ratio of bond energy to the eÜective Faraday Discuss. 1998 111 1»16 1 range of the interaction (bond length). This seems consistent with the standard model of biochemistry where the scale for bond strength is the free energy *G° reduction when molecules combine in solution as found from the equilibrium ratio keq[Dexp(*G°/kBT )] of bound to free constituents.As such the criterion for a strong bond should be simply a binding energy much larger than the thermal energy per molecule kBT . In marked contrast to these two paradigms we will see that even bonds with binding energies [40 kBT can fail under minuscule forces»more than 100-fold lower than the maximum energy gradient implied by energy/distance. Indeed we will –nd that measurement of molecular detachment force»no matter how precise the technique or how carefully performed»is not in itself a fundamental property of a molecular interaction. So what is the appropriate framework for describing strength of molecular bonds and how can we relate measurements of these forces to nanoscale chemistry ? When we test strength of molecular cohesion or adhesion at surfaces we determine the maximum level of force that a molecular attachment can support at the instant of failure.Unlike intimate covalent connections within protein and lipid molecules biomembrane structure and interfacial adhesion bonds involve noncovalent interactions between large macromolecules which have limited lifetimes and thus will fail under any level of force if pulled on for the right length of time. In other words when we speak of strength we should think of the force that is most likely to disrupt an adhesive bond or structural linkage on a particular time scale. At equilibrium for example bonds dissociate and reform under zero force.Thus an isolated bond has no strength on time scales longer than its natural lifetime ciation. On the other hand if detached within the time needed for diÜusive relaxation over the range of molecular interaction (e.g. x will reach and even exceed the adiabatic limit f=Bo*Eo/xb set by the maximum gradient in a potential of mean force. This is the situation in molecular dynamics (MD) simulations.2,3 t0\1/koff 0 for spontaneous (entropy-driven) dissob[ 1 nm]xb2/D\10~9 s in water) the strength of a bond From the slow limit set by spontaneous transition (from ls to months) to the ultrafast limit set by diÜusive relaxation (\ns) strength is governed by thermally activated kinetics under external force and thus depends on how the force is applied over time.Since application of force always requires a –nite interval of time the simplest way to parameterize the history of loading is to treat force as a ramp in time set by a constant loading rate rf\*f/*t. In fact a ramp of force is what single molecular attachments experience when a force probe and test surface are separated at constant speed (i.e. loading rate\probe stiÜness]speed). Using this parameterization and some nearly sixty year old physics4 for Brownian dynamics of chemical reactions in liquids we have shown that bond dissociation under steadily rising force occurs most frequently at a time determined by the rate of loading.5 Since loading rate is constant the time of dissociation speci–es the most likely rupture force»strength»which has the same dependence on loading rate.Of particular signi–cance the continuous plot of strength expressed on a scale of log (loading rate) maps the e most prominent barriers traversed in the energy landscape to distances along the force-driven pathway and reveals the splitting in energy between barriers. Thus strength vs. log (loading rate) e establishes the basis for a dynamic force spectroscopy (DFS) to probe the inner world of molecular-scale chemistry. Testing bond strength or structural transitions at diÜerent loading rates eÜectively probes the lifetime of a molecular complex under diÜerent levels of force. The experimental challenge is to measure forces over many orders of magnitude in loading rate. This dynamic requirement is dictated by the exponential of the energy diÜerence *E between the highest and lowest barriers divided by thermal energy i.e.exp(*Eb/kBT ) which can be enormous! b The strength spectra to be presented here will show that we can now cover six orders of magnitude in loading rate from \0.1 pN s~1 to D105 pN s~1 with a rather simple dynamic force probe which could be extended to D107 pN s~1 with complementary measurements using other probes. But more important than demonstrations of technique these spectra provide a new level of insight into the complexity of macromolecular interactions and structural linkages. First results from biotin»(strept)avidin6 and carbohydrate»L-selectin7 bond tests will show that a cascade of sharp energy barriers exists in receptor»ligand bonds where each barrier governs strength on a diÜerent time scale.We see then that these bonds cannot be simply idealized by a sole energy barrier and we cannot rely on the classical intuition about kinetics implicit in the detailed balance keq\ kon/koff where kon and koff are constants. Second tests of lipid extraction8 from membranes will show that anchoring of receptors to surface structure plays an important role in adhesion strength and can introduce unexpected transitions in the strengths of receptor»ligand attachments. In other Faraday Discuss. 1998 111 1»16 2 words we should not assume that a structural linkage of several molecules will fail at a speci–c weak connection nor that we can uniquely attach strong or weak labels to bonds in a linkage. Simultaneous kinetics over diÜerent energy landscapes in serial molecular linkages can lead to strength or weakness on diÜerent time scales.Dynamic crossovers in strength switch the site of failure from one location to another. Taken together these insights show that mechanical force can tune and switch time scales for kinetics in biomolecular reactions governed by complex energy landscapes which exposes a potentially new dimension in biochemical regulation and control. Theory of molecular kinetics under force in liquids We begin with an abstract of the physics that underlies the kinetics of bond dissociation and structural transitions in a liquid environment. Developed from Einsteinœs theory of Brownian motion these well-known concepts take advantage of the huge gap in time scale that separates rapid thermal impulses in liquids (\10~12 s) from slow processes in laboratory measurements (e.g.from 10~4 s to min in the case of force probe tests). Three equivalent formulations describe molecular kinetics in an overdamped liquid environment. The –rst is a microscopic perspective where molecules behave as particles with instantaneous positions or states x(t) governed by an overdamped Langevin equation of motion dx/dt\D/kBT [ f[+E]df ] The rate of change in state equals the instantaneous force scaled by the mobility of states or inverse of the damping coefficent c(\kBT /D). The deterministic force ([+E]f ) includes both the local gradient in molecular interaction potential E(x) and the external force f. An uncorrelated random force df from thermal impulses modulates the deterministic force and obeys the —uctuation»dissipation theorem where the integrated square —uctuation in a window of time can be Dexp[[/ df 2dt/(4k modeled as a Gaussian distribution BT )] with variance set by temperature and viscous damping.9 The microscopic physics also de–nes a stochastic process that has become the foundation of an important computational technique»Brownian dynamics or smart Monte Carlo (SMC)10 simulations.In this description the likelihood P(x]*x t]*t o x t) that a state x(t) will evolve to a new state x]*x over a time increment *t is speci–ed by the product of the equilibrium (long-time) Boltzmann weight for the step and a Gaussian weight for dynamics P(x]*x t]*t o x t)DexpM[(*E[f Æ*x)/kBT NexpM[o*x[(D/kBT ) f *t o2/(4D*t)N/(D*t)1@2 Finally on time scales that include many thermal impulses the overdamped dynamics can be cast in a continuum representation where the density of states o(x t) at location x and time t obeys Smoluchowski transport,9 do/dt\[+ Æ J J\D[ f[+E)o/k where the —ux of states BT [+o] re—ects both convection by force and spread by diÜusion.Although each description of the ultrafast kinetics brings to light important features Kramers4 demonstrated that Smoluchowski transport readily predicts the rate of escape from a deeply bound state when a large number of thermally activated steps are needed to pass a barrier in a dissipative environment. Escape from a bound state con–ned by a single barrier Starting far from equilibrium with all states con–ned inside the barrier the kinetics of escape are idealized as a stationary —ux of probability density along a preferential path from the deep energy minimum outward past the barrier via a saddle point in the energy surface.In real molecular interactions there can be many such paths and the paths can map out complex trajectories in con–guration space. However application of an external pulling force acts to select the reaction path which we express by a scalar coordinate x. Assumed to be bounded by steeply rising energy in other directions the energy landscape E(x) along this coordinate is illustrated schematically in Fig. 1(a). Governed by orientation h relative to the microscopic reaction coordinate external force adds a mechanical potential [fx(cos h) that tilts the energy landscape and diminishes the energy barrier E at the transition state (x\x b ts).When the tilted landscape is introduced into the Smoluchowski equation the stationary solution (J\constant in 1-D or\constant/xd~1 in d- Faraday Discuss. 1998 111 1»16 3 Fig. 1 Conceptual energy landscapes for bound states ììcœœ con–ned by sharp activation barriers. Oriented at an angle h to the molecular coordinate x external force f adds a mechanical potential [( f cos h)x that tilts the landscape and lowers the barrier. For sharp barriers the energy contours local to barriers»transition states ìì sœœ»are highly curved and change little in shape or location under force. (a) A single barrier under force. (b) A cascade of barriers under force.The inner barrier emerges to dominate kinetics when the outer barrier is driven below it by PkBT . dimensions) yields a generic expression for rate of escape from bound to unpopulated free states under force,5 c which drives escape. In a harmonic approximation l is derived from curvature koffB(D/lc lts)exp[[Eb( f )/kBT ] D/l The diÜusive nature of kinetics in liquids is embodied in the attempt frequency c lts which is the reciprocal of a characteristic time tD\lc lts(c/kBT ) set by damping and two length scales. The –rst length l represents con–nement in the bound state and de–nes the entropy gradient (do/dxB i l/l c\ c) (d2E/dx2) of the energy landscape local to the minimum i.e. lc\(2pkBT /ic)1@2. The second length c c l is the energy-weighted width of the barrier lts\/ dx exp[*E(x)ts/kBT ] local to the transition ts state x\xts also determined by curvature bB0.1»1 nm.On this scale the rate of escape increases exponentially with force koffB(1/t0) its\(d2E/dx2)ts of the energy landscape i.e. lts\ (2pkBT /its)1@2. Although force can displace and deform the width of the barrier [i.e. (its/2pkBT )1@2Bg( f )] the major impact of force arises in the thermal likelihood of reaching the exp[[E top of the energy barrier b( f )/kBT ]. For a sharp energy barrier the shape and location of the transition state are insensitive to force but force lowers the barrier in proportion to the therx mally averaged projection b\\xts cos h[ i.e. Eb( f )\Eb[fxb . As such thermal activation introduces the characteristic scale for force through the ratio of thermal energy to the distance xb x i.e.fb\kBT /xb which can be surprisingly small since kBT B4.1 pN nm at room temperature and b) as –rst postulated by Bell11 twenty years ago. But in contrast to the resonant frequency exp( f/f of bond excitations described in Bellœs model Kramers showed that the relevant attempt frequency is 1/tD\(ic its)1@2/2pc for overdamped transitions in liquids which is at least 1000-fold slower. With the Arrhenius dependence on initial barrier height and the attempt frequency Kramers classic result for spontaneous escape in the overdamped limit sets the scale for the transition rate i.e. 1/t0\(1/tD)exp([Eb/kBT ). Escape from a bound state con–ned by several barriers Although a naive model of chemical binding the single-sharp barrier model already captures the profound impact of force on thermally activated kinetics i.e.exponential ampli–cation of the forward rate for dissociation (and suppression of backward rate for reassociation) characterized by kBT /xb well below the adiabatic limit[E a small force scale b/xb ! However the energy landscapes of biomolecular bonds are expected to be much more complex because there are many sites of interaction involving large numbers of small molecules. This should produce a rough topography of barriers in an energy landscape and many possible pathways for unbinding. If again conceptualized as precipitous (sharp) energy maxima along a single pathway these prominent barriers are predicted to emerge under increasing force and dominate kinetics in succession as demonstrated by the sketch in Fig.1(b).5 An inner barrier is exposed when the force exceeds a crossover force fcB*Eb/*xb set by the splitting *Eb between barrier heights and separation in projected positions *xb . Depending on the diÜerence in barrier energies the crossovers occur at forces much Faraday Discuss. 1998 111 1»16 4 larger than the local thermal forces given by kBT /xb . Thus marked by these crossovers the kinetic rate constant is predicted to rise in a staircase of force-dependent exponentials that amplify the rate of transition less and less with each increase in thermal force scale. The transition rate for escape past a cascade of n sharp barriers is easily predicted with Kramers»Smoluchowski theory koff( f )B(1/t0)exp( f/f b0)/M1] ; li exp[ f*xb[*Eb]N i?n liBlts/lts 0 [\(its 0/its)1@2] plus diÜerences *xb\xb0[xb and energy *Eb\Eb0[Eb of inner barriers relative to the outermost which at low force begins with the steepest exponential dominated by the outermost barrier.At larger forces the rate crosses over to more shallow exponentials. The transition from one exponential regime to the next depends on the ratio of widths in location barrier as de–ned by Eb0 lts 0 and xb0 . We see then that a major consequence of structured energy landscapes is to make molecular interactions more durable (survive longer) at higher forces. f t[kBT /xb the forward transition Theory of force distributions in probe experiments Even with ultrasensitive probes and high resolution detection tests of molecular detachment yield a spread in force values.To understand the origin of the intrinsic uncertainty in force we have to examine the generic process of bond dissociation in laboratory experiments. Typically a probe decorated with a small amount of ligand»and a substrate studded with speci–c molecular receptors»are repeatedly touched together through steady precision movement to/from contact. If the surfaces are prepared with a sufficiently low density of reactive sites point contacts between the probe tip and the test surface will occasionally result in attachments (e.g. one attachment for every 5»10 touches). Under controlled touch infrequent bonding ensures a high probability of forming single molecular bonds (D95% con–dence for 1 attachment out of 10 touches).An attachment is exposed when the force transducer exhibits an extension or de—ection *x during surface t separation. Identi–ed by rapid recoil at breakage the rupture force is given by the maximum transducer extension * k x i.e. f\kf …*xt where is the spring constant of the transducer. Follow- t f ing many measurements detachment forces are then cumulated into a histogram. The peak in the distribution is the most likely the rupture force which is labelled bond strength. This approach has been reported many times in the literature over the past decade including studies of bond strength using AFM12h16 and other techniques.17,18 The exception to the generic description is that the frequency of attachment in most tests has been one for every touch which represents many molecular bonds and yields broad force distributions.Given that only a single molecular attachment forms on contact the crucial feature of the generic method is that the force experienced by the attachment prior to rupture is not constant but increases in time. This is shown clearly by two traces of attachment force vs. time in Fig. 2 taken from our experiments6 on single receptor»ligand bonds using a biomembrane force probe (BFP).19 In probe tests like these the linear rise of force with time is set by the product of separation speed v and transducer spring constant kf which is called the loading rate rf\kf vt . t (Note if soft structures like long polymers link the bond to a stiÜ probe the loading history can be nonlinear in time.20) Very diÜerent levels of force and time frame characterize the two detachment processes in Fig.2. Comparing these we see then that bond survival and breakage force depend on the rate of loading in reciprocal ways i.e. high speed loading]short lifetime but large detachment force whereas low speed loading]long lifetime but small detachment force which is the direct consequence of thermally activated kinetics. Statistics of transitions under increasing force To analyse bond breakage under steady loading we take advantage of the enormous gap in time (t scale between the ultrafast Brownian diÜusion DB10~10[10~9 s) and the time frame of laboratory experiments (D10~4 s to min). This means that the slowly increasing force in laboratory experiments is essentially stationary on the scale of the ultrafast kinetics.Thus dissociation rate merely becomes a function of the instantaneous force and the distribution of rupture times can be described in the limit of large statistics by a –rst-order (Markov) process with time-dependent rate constants. As force rises above the thermal force scale i.e. r Faraday Discuss. 1998 111 1»16 5 Fig. 2 Testing strength of single molecular attachments with the biomembrane force probe (BFP). The spring component of the BFP is a pressurized membrane capsule.19 Membrane tension sets the force constant kf (force/capsule extension) which is controlled by micropipet suction P and radius Rp kfBP]Rp . Using a red blood cell as the transducer the BFP stiÜness can be selected between 0.1 and 3 pN nm~1 to measure forces from 0.5 to 1000 pN.At the BFP tip a glass microbead of 1»2 lm diameter is glued to the membrane. The probe tip and red cell surfaces are bound covalently with heterobifunctional polyethylene oxide PEG polymers that carry glue components and test ligands.6 The BFP is operated in two orientations (modes) on the stages of inverted microscopes as illustrated by the following examples of fast and slow bond detachment (a) –rst the BFP (on the left) is kept stationary in the horizontal mode and the microbead test surface (on the right) is translated to/from contact with the BFP tip by precision piezo control. Video image processing is used to track the bead as shown by the simulated cursor ; a single high speed (D1000 frames s~1) scan through the center of the bead is used to track de—ection of the transducer (force) on a fast time scale at a resolution of 8»10 nm.Parts (b) and (c) show the BFP tip»substrate separation and force vs. time for rapid bond detachment in the horizontal mode. (b) The test microbead was moved towards the probe tip at a speed of D500 nm s~1. Stopped for D0.5 s after sensing contact at a preset impingement force of D[30 pN the test surface was then retracted at speed of D30 000 nm s~1. (c) Loaded at extremely fast rate the bond held the tip to the surface for D0.003 s (spike in force) and broke at D180 pN as the piezo continued to retract the test surface. The force —uctuations were due to position uncertainties ]BFP stiÜness. (d) In the vertical mode re—ection interference contrast is used to image the BFP tip as it is translated by piezo control along the optical axis to/from contact with a coverglass test surface.Standard video (30 frames s~1) processing of the circular interference pattern reveals elevation of the tip at a resolution of 2»5 nm. Transducer de—ection (force) is obtained from the diÜerence between piezo translation and bead displacement. Parts (e) and (f) show the BFP tip» substrate separation and force vs. time for a slow bond detachment in the vertical mode. (e) The probe was moved towards the coverglass test surface at a speed of D20 nm s~1. After sensing contact at a preset impingement force of D[3 pN the probe was retracted at slow speed of D1 nm s~1. (f ) Loaded at extremely slow rate the bond held the tip to the surface for D24 s and broke at D3 pN as the piezo continued to retract the probe (dashed trajectory).The —uctuations in tip position were due to thermal excitations of the BFP with mean square displacement DkBT /kf . Stretch of the PEG polymers that linked the bond to the glass surfaces is shown by the slight upward movement of the tip (D15 nm) under force prior to detachment. Due to polymer (k below 10 pN s~1 had to be obtained compliance the true loading rate felt by a bond at nominal rates f vt) from the actual force vs. time. Faraday Discuss. 1998 111 1»16 6 on ]0). Thus the likelihood S(t) of remaining in the bound state (escape) rate increases extremely rapidly. Moreover the molecules drift apart faster than diÜusion can recombine them from positions beyond the con–ning barrier so the backward rate for reassociation quickly vanishes (k is dominated by the forward process i.e.dS(t)/dtB[koff(t)S(t) or equivalently S(t)\ exp[[/0?t koff(t@)dt@]. The probability density p(t)\koff(t)S(t) for detachment between times t and t]*t describes the distribution of lifetimes. Since instantaneous force is the product of time and loading rate ( f\rf t) the probability density p( f ) for detachment between forces f and f]*f is given by the distribution of lifetimes p(t),5 p( f )\(1/rf)koff( f )exp[[(1/rf)P koff( f @)df @] 0?f noting the statistical identity p(t)dt\p( f )df. The peak in the distribution of forces de–nes the force f * for most frequent transition which is strength. Analytically the location of a distribution peak is found from dp( f )/df\0 which establishes a transcendental equation that relates the strength f * to loading rate rf [koff]f/f*\rf[d loge(koff)/df ]f/f* Although somewhat forbidding this expression yields a simple result for strength as a function of loading rate in the case of a single sharp energy barrier f *\f loge(rf/rf 0 ) recalling that the rate is modelled by an exponential in force koffB(1/t0)exp( f/fb).Governed by a thermal scale for loading rate rf0\fb/t0 the most likely force»strength»simply shifts upward linearly with the logarithm of loading rate multiplied by the thermal force fb . Similarly the curvature of the distribution local to the peak 1/Df2\[[1/p( f )][d2p( f )/df 2]f/f* can be used to estimate a Gaussian width for uncertainty in the force distribution, f\fb .Hence even without experi- Dynamic force spectroscopy b b Df2\1/M[d loge(koff)/df ]2[[d2 loge(koff)/df2]Nf/f* For a sharp energy barrier this again yields a simple result D mental uncertainty the distribution of forces is broadened by thermal activation (kinetics) ! In the context of experiments the signature of a major sharp barrier is predicted to be a straight line in a plot of most frequent probe force f * vs. log(loading rate) as illustrated in Fig. 3(a). This linear regime can span orders of magnitude in rate as determined by the ratio of barrier energy E 1/tD and height E of the activation barrier. (a) Linear spectrum predicted for a single Fig. 3 Dynamic strength spectra de–ned by most likely bond detachment force f * vs.log (loading rate\ rf/rf 0 ) where the loading rate scale rf0\( fb /tD)exp([Eb/kBT ) is set by thermal force fb\kBT /xb diÜusive e b attempt frequency sharp energy barrier. The logarithmic intercept at zero force (represented by \) is determined by the barrier height and the microscopic diÜusion time loge(rf 0)\[Eb/kBT ]loge( fb /tD). (b) Piece-wise linear spectrum for a cascade of two sharp energy barriers. The abrupt increase in slope from one thermal force scale to the next shows that the outer barrier has been suppressed and that the inner barrier has become the dominant kinetic impedance to detachment [cf. Fig. 1(b)]. The diÜerence between logarithmic intercepts (represented by \) is governed by the splitting in barrier energies and the ratio of thermal force scales loge(* rf 0)B[*Eb/kBT ] *loge( fb ).7 Faraday Discuss. 1998 111 1»16 xb\Sxts cos hT along the direction of force. Moreover to thermal energy k f BT . The slope of this line maps the thermally averaged projection of the microscopic transition state to a distance the logarithmic intercept at zero force re—ects the magnitude of barrier energy as given by b loge(rf 0)\[Eb/kBT ]loge( fb/tD). Setting the scale for loading rate the ratio fb/tD involves the microscopic attempt frequency 1/tD . Assuming that attempt frequency is weakly aÜected by point mutations the simple linear-log behavior exposes a unique opportunity to quantitate the resulting chemical modi–cations in energy and/or location of barriers.Such changes in microscopic properties can be derived from the shift in the logarithmic intercept and/or change in slope *Eb/kBT B [*loge(rf 0)]*loge( fb). Taken together these features demonstrate that the plot of most frequent probe force vs. log(probe loading rate) represents a dynamic spectral image of an activation barrier. [Although unknown attempt frequency can be estimated from the damping factor indicated by MD simulations. Values for damping factor seem to be typically on the order of cB10~8 pN s nm~1 (equivalent to Stokes drag on a 1 nm size sphere in water) e.g. cB2]10~8 pN s nm~1 in simulations of biotin»streptavidin separation2 and cB5]10~8 pN s nm~1 in simulations of lipid extraction from a bilayer.3 Since the product of molecular lengths lc lts should lie in the range D0.01»0.1 nm2 the attempt frequency is expected to be in the range 1/tDB 109»1010 s~1 and the microscopic scale for loading rate in the range fb/tDB1010»1011 pN s~1.The eÜective loading rate in the slowest MD simulations2,3 is even higher P1012 pN s~1.] As described earlier the most idealized view of a complex molecular energy landscape is a cascade of sharp activation barriers which leads to a staircase of exponential increases in the rate constant under force. Using this prescription the most likely force vs. log(loading rate) is predicted to follow a simple spectrum of piece-wise continuous linear regimes with ascending slopes as shown in Fig. 3(b). The abrupt increase in slope from one regime to the next signi–es that an outer barrier has been suppressed by force and that an inner barrier has become the dominant kinetic impedance to escape as sketched in Fig.1(b). These dynamic crossovers occur at somewhat higher forces than the stationary crossovers in rate constant as shown by the analytical approximation f cdynB*Eb/*xb]kBT [loge(xb @ /xb)]/*xb *x where b\xb @ [xb and *Eb\Eb @ [Eb represent adjacent prominent barriers. In contrast to the idealized theory the shape of a strength spectrum could be nonlinear and a challenge to interpret because force can distort physical potentials and molecular structure. Surprisingly the results from recent probe experiments to be shown next yield linear plots for strength vs. log(loading rate) with one or more well-de–ned regimes which allows the spectra to be interpreted in terms of sharp activation barriers.Energy landscapes of receptorñligand bonds Not well-appreciated in biology is that energy landscapes of receptor»ligand bonds can be rugged terrains with more than one prominent activation barrier. The inner barriers are undetectable in test-tube assays but are important since they establish diÜerent time scales for kinetics under force. With two unrelated pairs of molecules we will demonstrate that dynamic force measurements can be used to reveal these hidden barriers. The –rst pair of molecules will be the ligand biotin (a vitamin) and the protein receptor streptavidin (from bacteria) or avidin (a closely similar protein from hen egg white).21 This complex is used widely in biotechnology because it has one of the highest affinity noncovalent bonds in biology with a force-free lifetime on the order of days.22 The second pair of molecules will be a sialylated (carbohydrate) short peptide ligand§ and the Lselectin receptor resident in the outer membrane of blood leukocytes.Although weaker in affinity with a lifetime of D1 s or less the carbohydrate»L-selectin bond plays a crucial role in the initial capture of leukocytes from blood circulation at sites of injury or infection.23 In preparation for both experiments the ligand was covalently anchored to a glass microbead along with a chemical glue for attachment of the bead to the BFP transducer [as noted in Fig. 2(a)]. A similarly pre- § Note the actual ligand used in the tests was a short peptide chimera of the biological molecule called P-selectin glycoprotein ligand (PSGL1) which was constructed by Genetics Institute and obtained through collaboration with Scott Simon at Baylor College of Medicine.The generic label carbohydrate will be used for convenience. Faraday Discuss. 1998 111 1»16 8 Fig. 4 On the left are examples of force histograms taken from tests of single biotin»streptavidin bonds which demonstrate the shift in peak location and increase in width with increase in loading rate (top histogram 0.05 pN s~1 middle histogram 20 pN s~1 bottom histogram 60 000 pN s~1). Superposed on the histograms are Gaussian –ts used to determine the most frequent rupture force»bond strength. Governed ideally by the thermal force fb standard deviations p of the distributions also re—ected uncertainties in posifB[ f b2](kf*x)2](rf*tv)2]1@2.f tion *x and video sampling time *tv i.e. p increased from ^1 pN at As pf the slowest rate to ^60 pN at the fastest rate the standard error in mean force»the uncertainty in strength» ranged from ^0.3 to ^5 pN. On the right are complete dynamic strength spectra for both biotin»streptavidin slopes of the linear regimes seen in the spectra map activation barriers at positions along the direction of force. (open circles) and biotin»avidin (closed triangles) bonds.6 De–ned as thermal energy kBT /distance xb the The common high strength regime in the biotin»streptavidin and biotin»avidin spectra place the innermost x barrier at bB0.12 nm.Separate intermediate strength regimes place the next barrier at xbB0.5 nm for biotin»streptavidin and xbB0.3 nm for biotin»avidin (with a slight reduction in slope below 38 pN suggesting that the biotin»avidin barrier extends to D0.5 nm). Only well-de–ned in the biotin»avidin spectrum a low x strength regime implies a distal barrier at bB3 ( nm. Also marked \AFM) is the biotin»streptavidin strength measured recently by AFM at D105 pN s~1 using a carbon nanotube as the tip.14 This and the earlier measurements of biotin»avidin bond strength13 at loading rates of D6]104 pN s~1 also correlate with the high strength regime shown here. pared microbead was used as the test surface for probing biotin»(strept)avidin bonds whereas a white blood cell (granulocyte) taken from a small blood sample was used as the test surface for probing carbohydrate»L-selectin bonds.kf vt is preselected by setting the transducer force constant k in the range 0.1»3 pN f [Methods In testing molecular bonds the density of reactive sites must be reduced signi–cantly as mentioned earlier so that only 1 out of 7»10 touches results in a molecular attachment. Assumed to be governed by Poisson statistics this ensures that 90»95% of the attachments are single bonds. To obtain strength spectra with the BFP technique detachment forces are measured over a six order of magnitude range in loading rate from 0.05 pN s~1 to 100 000 pN s~1. The loading rate nm v ~1 and the piezo retraction speed in the range 1»30 000 nm s~1 as described in Fig.2. From t thousands of repeated touches at –xed loading rate histograms of detachment forces are compiled at many rates and Gaussian –ts are used to locate the peak in each histogram. These most probable values of force are then plotted as a function of log (loading rate) which yields the dynamic e strength spectrum.] Biotin (strept)avidin bonds Because of high affinity the –rst ligand»receptor pair chosen by researchers for testing with AFM was biotin and streptavidin ; which was soon followed by biotin and avidin.12h14 Deduced from a broad distribution of AFM forces it was concluded that the strength of a biotin»streptavidin 9 Faraday Discuss. 1998 111 1»16 bond lies in a range of D200»300 pN and somewhat lower for biotin»avidin D160 pN. However the examples of force histograms and the strength spectra6 in Fig.4 show that biotin»streptavidin (and biotin»avidin) bond strengths fall continuously from D200 pN to DpN with each decade increase in time scale for rupture from 10~3 to 102 s which clearly demonstrates the thermally activated nature of bond breakage. Moreover distinct linear regimes with abrupt changes in slope imply sharp barriers which can be analysed using the idealized theory.6 First above 85 pN there is a common high strength regime for both biotin»streptavidin and biotin»avidin with a slope of fbB34 pN. This locates a barrier deep in the binding pocket at xbB0.12 nm. Below 85 pN the fbB8 pN slope in the biotin»streptavidin spectrum maps the next activation barrier at xbB0.5 nm whereas the steeper slope fbB13»14 pN between 38 and 85 pN in the biotin»avidin spectrum x indicates that its next barrier maps to bB0.3 nm.Interestingly a slight curvature and reduction in slope between 38 and 11 pN suggests that the barrier in biotin»avidin extends to D0.5 nm. Below 11 pN the biotin»avidin spectrum exhibits a very low strength regime (dashed line) with a slope of fbB1.4 pN that maps to xbB3 nm. A similar low strength regime is indicated by results from the slowest test of biotin»streptavidin bonds; but it was not possible to perform tests at loading rates below 0.05 pN s~1 as needed to verify the existence of this regime. In addition to the map of barrier locations the logarithmic intercepts found by extrapolation of each linear regime to zero force also yield estimates of the energy diÜerences between activation barriers within each landscape as well as energy diÜerences between related barriers of biotin»avidin and biotin» streptavidin landscapes.However instead of discussing barrier heights it is more illuminating to examine how the 1-D map of barrier locations compares with detailed molecular simulations of biotin»(strept)avidin interactions. In separate MD simulations,2 biotin was extracted from a binding pocket of streptavidin and avidin by pulling on the outer end with a pseudo-mechanical spring. Consistent with the numerous bonds to small molecules in the binding pocket simulations yield a —uctuating superposition of many attractions»buÜeted by steric collisions»along the unbinding trajectories.This is shown by a pro–le of instantaneous energy calculated over a slow D500 ps extraction of biotin from avidin [Fig. 5(a) kindly provided by Professor K. Schulten and coworkers Beckman Institute University of Illinois]. Even with the enormous and fast changes in energy simple qualitative features appear in the pro–le that provide important clues to the thermally averaged free energy landscape relevant on laboratory time scales. In particular transition states are readily identi–ed by regions with rari–ed statistics where biotin passes quickly. Taking a simple coarse-grained average over D20 ps windows [Fig. 5(b)] smooths over the strong rapid —uctuations and exposes locations of activation barriers. First within an initial displacement of 0.1»0.2 nm the spring force in the simulations revealed abrupt detachment of biotin from a nest of hydrogen bonds water bridges and nonpolar interactions deep in the binding pocket.Next forces reached maximal Fig. 5 (a) Pro–le of instantaneous energy computed for interaction between biotin and avidin over a halfnanosecond extraction from the binding pocket in the simulations of Israilev et al.2 (kindly provided by Professor K. Schulten and coworkers University of Illinois). Separating regions of rapid intense —uctuations locations of rari–ed statistics coincide with maximal forces in the simulations which signify the presence of transition states. (b) Coarse-grained average over the fast degrees of freedom which yields an approximate potential of mean force.5 Arrows mark barrier locations derived from the intermediate and high strength regimes of the spectrum for biotin»avidin in Fig.4. Faraday Discuss. 1998 111 1»16 10 kBT /distance xb the slope of the high strength regime places the innermost barrier at Fig. 6 On the left are examples of force histograms taken from tests of single carbohydrate (sialylated PSGL1 short peptide chimera)»L-selectin bonds which demonstrate shift in peak location and increase in width with increase in loading rate (top histogram 10 pN s~1 middle histogram 850 pN s~1 bottom histogram 13 000 pN s~1). Superposed on the histograms are Gaussian –ts used to determine the most frequent rupture force» bond strength. On the right is the complete dynamic spectrum of strength vs. log(loading rate).De–ned as thermal energy xbB0.06 nm. The intermediate strength regime places the next barrier at xbB0.3 nm. The low strength regime implies a barrier further out at xbB1.2 nm. values followed by sudden displacements of biotin at a distance of D0.4 nm (and D0.5 nm in the biotin»streptavidin simulation). Finally biotin was observed to still cling to peripheral polar groups at D1.4 nm in the avidin simulation. As labelled in Fig. 5(b) the locations of activation barriers derived from the high and intermediate strength regimes of the laboratory spectra in Fig. 4 correlate well with regions of rari–ed statistics and the qualitative appearance of the energy landscape. The conclusion is that these transition states inferred from the simulations persist on long time scales.However the outer barrier indicated by the low strength regime is 2»3-fold more distant than the last transition state seen in the MD simulation ; this is perhaps due to interactions with the peripheral —exible loops24h27 which border the channel that leads to the binding pocket. More puzzling however extrapolation of the lowest strength regime to zero force implies that bond strength vanishes below a threshold loading rate of D0.0006 pN s~1 for biotin»avidin. In other words the spontaneous oÜ rate would be D1 per hour. This is 50-fold faster than the rate of D1 per 55 hours that we measured for spontaneous dissociation of PEG»biotin from probe tips in free solution and found previously for biotin by others.22 Hence some nontrivial eÜect remains that accounts for the signi–cant increase in rate of dissociation under extremely small forces below 5 pN.CarbohydrateñL-selectin bonds In contrast to the high affinity biotin»(strept)avidin bonds carbohydrate»L-selectin bonds with modest affinity stop white cells at vessel walls in the circulation.23 Numerous bonds to other surface (integrin) receptors then form between the white cell and vessel wall to sustain adhesion and enable subsequent movement into the surrounding tissue. On its initial arrest from the blood —ow the white cell can be subjected to forces of D100 pN in a time frame of milliseconds which implies loading rates of 104»105 pN s~1. With this functional requirement in mind we now examine recent tests of carbohydrate»L-selectin bonds under dynamic loading in probe tests.From the results7 presented in Fig. 6 we again see a sequence of high intermediate and low strength regimes for carbohydrate»L-selectin bonds where strength also falls continuously from 11 Faraday Discuss. 1998 111 1»16 b bB3.4 pN that sets the outermost barrier at xbB1.2 nm. Using the logarithmic intercepts found D200 pN to DpN but over fewer decades in time scale for detachment from 10~3 to 1 s. The high strength regime has a very steep slope of fbB70 pN that maps an inner barrier to a small distance xbB0.06 nm along the direction of force. Although we lack detailed molecular information about L-selectin binding the small value of x seems to imply that the microscopic reaction coordinate deviates signi–cantly from the macroscopic orientation of force.For example if the ligand was bound to the side of the receptor pulling parallel to the axis of the receptor along the surface normal could result in a large orientation angle h relative to the microscopic pathway and weak coupling of force to the energy landscape. Departing from the high strength regime below 70 pN f the intermediate strength regime with a slope of bB13 pN places the next activation barrier at xf bB0.3 nm. Finally below D20 pN the spectrum exhibits a low strength regime with a slope of by extrapolation of each linear regime to zero force the diÜerences in energy between the inner activation barriers are calculated to be only 2»3 kBT . As for biotin»(strept)avidin bonds the innermost barrier deep in the binding pocket provides strength on short time scales (\0.03 s) which is sufficient to meet the functional requirements noted earlier.Even though only 4»6 kBT higher in energy the outermost activation barrier extends the lifetime of the bond almost 100-fold (to D1 s) beyond that set by the innermost barrier. Energy landscapes for anchoring lipids in membranes Lipids and acylated proteins are anchored in bilayers by hydrophobic interactions. The handbook28 correlation for free energy of transfer from aggregates (e.g. micelles or bilayers) to water is a linear proportionality of D1 kBT per aliphatic carbon for lysophosphatidylcholines (PCs) and not quite double D1.7 kBT per carbon for diacylPCs although little evidence exists for diacyl lipids with chain lengths longer than 10»12 carbons.This reinforces the established view that anchoring potential increases with hydrophobic surface area embedded in the bilayer.29 Partition and solubility provide important static-equilibrium assays but represent energetic measures of strong vs. weak anchoring»not strength»which is the force needed to extract a molecule. Based on the hydrophobic energy scale for exposure to water the energy landscape for hydrophobic anchoring in bilayers should simply rise linearly with displacement along the bilayer normal. Treating the embedded molecule as a cylinder with radius rm the surface energy per unit area for creating a water/nonpolar interface and the circumference of the cylinder (i.e. energy/length B30 mJ m~2]2pr or 7 kBT nm~2]2prm) suggest naively that the molecular extraction force should m be a constant set by molecular size fB180 pN]r (nm).Taking a radius D0.5 nm for a lipid the m anchoring force would be D100 pN. On the other hand we will see next that lipids can be extracted from membrane bilayers with forces as small as D1 pN if performed over seconds! Over the range of anchoring strengths between 0 and 100 pN the missing ingredient is thermally activated kinetics. By comparison lipid pull-out forces in MD simulations3 were [200 pN even under the slowest extraction of D10~8 s and increased with speed apparently due to viscous damping. Strength of hydrophobic anchoring in —uid membranes was tested by extraction of single receptor lipids from giant bilayer vesicles prepared with two lipid compositions pure stearoyloleoylphosphatidylcholine (SOPC) (C18 0/1) and a 1 1 mixture of SOPC plus cholesterol (CHOL)» somewhat similar to membranes that encapsulate cells.Doped in the vesicle bilayers at extremely low concentration (\0.0001%) the receptor lipids were a special lipid construct of biotin»PEG» distearoylphosphatidylethanolamine (DSPE) (diC18:0) kindly provided by INEX Pharmaceuticals Burnaby B.C. Canada. Plotted in Fig. 7 we see little structure in the spectra for receptor lipid anchoring and much lower forces compared to the spectra in Figs. 5 and 6 for receptor»ligand bonds.8 Over nearly four orders of magnitude in loading rate only a single linear strength regime is found for extraction of the receptor lipids from SOPC CHOL bilayers.The f low slope of bB2.4 pN places a barrier at a distance xbB1.7 nm along the direction of force. Two linear regimes are found for lipid extraction from pure SOPC bilayers with a modest diÜerence in slopes. The initial slope of fbB3.4 pN locates an outer barrier at xbB1.2 nm and the second slope of fbB6.1 pN implies an inner barrier at xbB0.7 nm. Consistent with the simple concept of hydrophobic interaction the locations of the outermost barriers for both types of bilayers are comparable to (but slightly less than) the hydrophobic half thickness of the bilayer Faraday Discuss. 1998 111 1»16 12 Fig. 7 On the left are examples of force histograms taken from tests of receptor lipid (biotin»PEG»DSPE) extraction from mixed SOPC CHOL vesicle bilayers which demonstrate shift in peak location and increase in width with increase in loading rate (top histogram 2 pN s~1 middle histogram 200 pN s~1 bottom histogram 5 000 pN s~1).Superposed on the histograms are Gaussian –ts used to determine the most frequent extraction force»anchoring strength. On the right are the complete dynamic spectra of strength vs. log(loading rate) for extraction of receptor lipids from SOPC (closed boxes) and mixed SOPC CHOL bilayers (open circles). De–ned as thermal energy kBT /distance xb the slopes of the initial linear regimes map activation barriers at xbB1.2 nm for extraction from SOPC and xbB1.7 nm for extraction from SOPC CHOL along the direction normal to the bilayer. Not seen in the SOPC CHOL spectrum the break in slope for the SOPC spectrum places a weak inner barrier at xbB0.7 nm.which is increased by cholesterol. Addition of cholesterol to SOPC bilayers increases the outer activation barrier by D2 kBT as shown by the shift between logarithmic intercepts of the initial regimes for SOPC CHOL and SOPC. Quite unexpected the break in slope in the spectrum for SOPC reveals an inner transition state near the middle of the hydrophobic monolayer which appears to be D2 kBT below the outer barrier. Perhaps coincidental the location of this transition state derived from the thermal force scale correlates with the position of the unsaturated bond in the oleoyl chain of SOPC. Completely speculative the split in activation barriers could re—ect an entropic bottle neck as chains transiently pass the average position of the unsaturated group.Very puzzling the bilayer residence time of D0.01 s derived from the logarithmic intercept of these spectra at zero force is much shorter than implied by the lack of perceptible dissociation from an isolated vesicle over the the time scale of 1 h. Without an explanation at present we see again (as for biotin»avidin bonds) that very small forces must strongly aÜect the shape of the soft outer transition state. In any case anchoring of lipids and acylated proteins in bilayers will always be weak unless the molecules are extracted very rapidly from the bilayer. Strong vs. weak bonds in serial linkages For a serial linkage of n identical bonds the rate of breakage under force is simply increased by a factor n koffB(n/t0)exp( f/fb) if the bond kinetics are uncorrelated.This increases the thermal scale for loading rate rf0\nfb/t0 and shifts the strength spectrum along the log (loading rate) axis by a loge(n) which reduces strength at a given loading rate by [fb loge(n). In contrast to a factor of e simple shift along the log(loading rate) axis we expect the strength of a multiple linkage of dissimilar bonds to be limited by the weakest bond and naively that strong vs. weak should be de–ned by the energy barriers sustaining the bonds. However theory shows that this anticipated hierarchy is only correct for some sets of bonds; other sets will exhibit unexpected switching from strong to 13 Faraday Discuss. 1998 111 1»16 weak and vice versa as loading rate increases.In the determination of strong vs. weak at a particular retraction rate the important parameters are both the spontaneous rates of dissociation set by barrier energies and the thermal force scales that characterize e-fold changes in the dissociation rates of bonds under force. Again invoking the simple sharp barrier model we can easily establish a phase diagram [cf. Fig. 8(a)] of the most likely site for breakage in a two-bond linkage. Assuming that both bonds are characterized by the same diÜusive time scale t for simplicity the D rate of uncorrelated breakage is the combined rates for each bond koffB(1/t0)exp( f/fb)M1]exp[[*Eb/kBT ]f*(1/fb)]N 1/ f t and specify the spontaneous rate and thermal force scale of the fast bond (smallest 0 *E and *(1/f represent the diÜerences in barrier energy and *Eb[0) relative to the fast bond.The comwhere barrier energy) as the reference ; b reciprocal thermal force scale for the slow bond (i.e. bined rate and the predicted strength spectrum predict that the fast bond will remain the expected *E weak bond so long as the following inequality holds b/kBT [f*(1/fb). This will always be the case when the thermal force scale for the fast bond is less than the thermal force scale for the slow *(1/f bond [i.e. b)\0 or equivalently *(xb)[0]. On the other hand if the thermal force scale for *E the fast bond is larger then there will be a crossover force where b/kBT Of *(1/fb) ; this strongHweak bond phase boundary is sketched in Fig. 8(a). Now the fast bond will be the strong bond and the slow bond will be the most likely site of failure which is not anticipated in the traditional view.To demonstrate the importance of this concept imagine that the selectin receptor was linked to b ) b ) b Faraday Discuss. 1998 111 1»16 b) a vesicle bilayer by a lipid anchor and then the strengths of carbohydrate ligand bonds to the selectin were probed as in the leukocyte tests. Purely hypothetical Fig. 8(b) shows that at slow loading rates the carbohydrate»selectin bond would most likely detach because lipid anchoring is b[0 characterizes a slow bond relative to a fast bond as de–ned by spontaneous oÜ rates) ; the horizontal b Fig. 8 (a) Phase diagram for de–nition of strongHweak bonds in a serial linkage of two bonds sustained by single sharp energy barriers.The vertical axis is the diÜerence in barrier heights *E for the two bonds (*E axis is the product f*(1/f of applied force f and the diÜerence *(1/f in reciprocal thermal force scales. In the traditional view strong weak equates to slow fast. But for bonds in series this diagram shows that there can be unexpected switching of these attributes under force. (b) Hypothetical strength of carbohydrate bonds to selectins if linked by lipid anchors to membranes. Simultaneous kinetics over diÜerent energy landscapes for the carbohydrate»selectin bond and lipid anchoring predicts a dynamic crossover in site for detachment when pulled on by a probe decorated with the carbohydrate ligand. At slow rates of loading the lipid anchor is stronger than the carbohydrate»selectin bond which is the most likely site of detachment.On the other hand at fast rates of loading the carbohydrate»selectin bond is stronger than lipid anchoring strength which then becomes the most likely site of detachment. 14 stronger. On the other hand under fast loading the carbohydrate»selectin bond becomes strong and the lipid anchor weak by comparison. Hence the lipid-anchored selectin would most likely be pulled out of the membrane by the carbohydrate ligand attached to the probe. In contrast to the image of inner activation barriers in a complex bond we see that the signature of a strong to weak bond metamorphosis in a serial linkage of bonds is an abrupt reduction in slope from one linear strength regime to the next with increase in loading rate.Summary Recent laboratory probe experiments con–rm that bond breakage and molecular detachment occur at forces determined by the loading rate. Measured under steadily rising force over an enormous span of loading rates the spectra of strength vs. log (loading rate) yield images of the e prominent barriers traversed in the energy landscapes along force-driven pathways in unbinding. Simple analysis of the spectra provides a view into the inner complexity of biomolecular interactions and structural cohesion as noted in the following list of highlights. (1) Examining two unrelated receptor»ligand bonds we –nd a similar sequence of linear strength regimes vs. log(loading rate). These regimes reveal a cascade of three activation barriers for both receptor»ligand interactions although quite diÜerent in energy scale.The innermost barrier deep in the binding domain is responsible for the high strength perceived on short time scales and the major portion of total activation energy. The more distal barriers lead to weakness on long time scales but signi–cantly extend bond lifetime in the absence of force. The intriguing question is why did nature structure energy landscapes in receptor»ligand bonds and create a sequence of time scales for ampli–cation of kinetics under force ? Answering this question is likely to introduce a new perspective of biological chemistry. (2) No surprise anchoring strengths of lipids in bilayers are consistent with nearly structureless hydrophobic potentials although small inner barriers do appear in some cases.Most signi–cant the small thermal force scale set by acyl chain length results in very weak anchoring strength unless the molecules are extracted extremely rapidly from the bilayer. Still to be con–rmed integral membrane proteins should be much more strongly anchored to membranes since hydrophilic groups at the interfaces will contribute major activation barriers with large thermal force scales. (3) Dissimilar bonds in a serial linkage can unexpectedly switch from strong to weak and shift the most likely site for failure between bonds as loading rate increases. Such behaviour is not only a major factor in cohesive and adhesive strength but is likely to be important in signalling and regulation of biochemical pathways inside cells.Acknowledgement It is important to credit the individuals who carried out the experiments and developed the instrumentation described in this paper since many of the results are yet to be published. Tests of biotin»(strept)avidin bonds were performed by Andrew Leung (University of British Columbia) and Pierre Nassoy (now at lœInstitut Curie in Paris). Computer control of the biomembrane force probe assembly and video image processing was developed by Ken Ritchie (now at Nagoya University in Japan). Tests of carbohydrate»L-selectin bonds were also performed by Andrew Leung in collaboration with Scott Simon (from Baylor College of Medicine in Houston) and Dan Hammer (from University of Pennsylvania in Philadelphia). Tests of lipid anchoring in bilayer membranes were performed by Florian Ludwig (University of British Columbia).The work was supported by grants HL54700 and HL 31579 from the US National Institutes of Health grant MT7477 from the Medical Research Council of Canada and the Canadian Institute for Advanced Research Program in Science of Soft Surfaces and Interfaces. References 1 G. Binnig C. F. Quate and C. H. Gerber Phys. Rev. L ett. 1986 56 930; B. Drake C. B. Prater A. L. Weisenhorn S. A. C. Gould T. R. Albrecht C. F. Quate D. S. Cannell H. G. Hansma and P. K. Hansma Science 1989 243 1586. 2 H. Grubmuller B. Heymann and P. Tavan Science 1996 271 997; S. Izrailev S. Stepaniants M. Balsera Y. Oono and K. Schulten Biophys. J. 1997 72 1568. 15 Faraday Discuss. 1998 111 1»16 3 S-J.Marrink O. Berger P. Tieleman and F. Jahnig Biophys. J. 1998 74 931. 4 H. A. Kramers Physica (Amsterdam) 1940 7 284; P. Hanggi P. Talkner and M. Borkovec Rev. Mod. Phys. 1990 62 251. 5 E. Evans and K. 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Paper 8/09884K Faraday Discuss. 1998 111 1»16 16