Many-Particle Tracking with Nanometer Resolution in Three

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Many-Particle Tracking with Nanometer Resolution in Three Dimensions by Reflection Interference Contrast Microscopy Nathan G. Clack and Jay T. Groves* Department of Chemistry, University of California, Berkeley, California 94720 Received February 9, 2005. In Final Form: April 14, 2005 We have developed and characterized a method, based on reflection interference contrast microscopy, to simultaneously determine the three-dimensional positions of multiple particles in a colloidal monolayer. To evaluate this method, the interaction of 6.8 µm ((5%) diameter lipid-derivatized silica microspheres with an underlying planar borosilicate substrate is studied. Measured colloidal height distributions are consistent with expectations for an electrostatically levitated colloidal monolayer. The precision of the method is analyzed using experimental techniques in addition to computational bootstrapping algorithms. In its present implementation, this technique achieves 16 nm lateral and 1 nm vertical precision.

Introduction Colloidal systems have long attracted attention for the rich statistical physics they exhibit. Colloids have been widely employed as model systems for molecular phenomena in studies of phase transition dynamics such as crystal nucleation and glass transitions.1-7 The value of colloids in this context stems largely from their ability to exhibit collective behaviors while, at the same time, enabling direct imaging of the position and motion of individual particles. Recently, a variation of the traditional silica colloidal monolayer has emerged consisting of silica particles coated with biological lipid membranes. An interesting feature of these membrane-derivatized colloids is that the collective two-dimensional colloidal phase behavior is governed by interactions between the lipid membranes and, thus, can be used as a probe of molecular interactions at the membrane surface.8 A wealth of biological processes occur at the membrane surface, and the use of colloidal phase behavior to produce a robust readout of subtle molecular interactions is an attractive prospect. The sensitivity of this technique depends on the ability to locate the spatial coordinates of each particle in a colloidal monolayer precisely. Reflection interference contrast microscopy (RICM) is an imaging technique that achieves high precision by using optical interferometry to measure distances between reflecting surfaces. RICM has been widely applied to study adhesive interactions involving lipid bilayer vesicles,9-11 * To whom correspondence should be addressed. E-mail: [email protected]. (1) Murray, C. A.; Grier, D. G. Annu. Rev. Phys. Chem. 1996, 47, 421-462. (2) Aarts, D.; Schmidt, M.; Lekkerkerker, H. Science 2004, 304, 847850. (3) Poon, W. Science 2004, 304, 830-831. (4) Yethiraj, A.; van Blaaderen, A. Nature 2003, 421, 513-517. (5) Trappe, V.; Prasad, V.; Cipelletti, L.; Segre, P.; Weitz, D. Nature 2001, 411, 772-775. (6) Gasser, U.; Weeks, E.; Schofield, A.; Pusey, P.; Weitz, D. Science 2001, 292, 258-262. (7) Anderson, V.; Lekkerkerker, H. Nature 2002, 416, 811-815. (8) Baksh, M. M.; Jaros, M.; Groves, J. T. Nature 2004, 427, 139141. (9) Fang, N.; Chan, V.; Wan, K. T.; Mao, H. Q.; Leong, K. W. Colloids Surf., B-Biointerfaces 2002, 25, 347-362. (10) Albersdorfer, A.; Feder, T.; Sackmann, E. Biophys. J. 1997, 73, 245-257. (11) Radler, J.; Sackmann, E. Langmuir 1992, 8, 848-853.

cells,10,12 and even the pretarsal pads of ants.13 The first application of RICM to track individual colloidal particles was develeoped by Ra¨dler and Sackmann11 to compliment a total internal reflection microscopy (TIRM) method developed by Frej and Prieve.14 Both these methods rely on dynamic observation of the height of a single colloidal sphere above an underlying substrate to estimate the interaction potential. Traditionally, applications of RICM and TIRM have been limited to the study of single colloidal particles. A recent study has explored the extension of TIRM to multiparticle tracking.15 Here, RICM is used to simultaneously observe the lateral motion of many particles in a colloidal monolayer as well as their out-of-plane fluctuations. RICM is an attractive imaging method for its simplicity: no laser, specialized optics, or difficult alignments are necessary. Additionally, since RICM is based on interferometry, it can be used to probe a relatively large vertical range, as compared with that of TIRM. In the following, interactions between membrane-coated silica particles and an underlying glass substrate are monitored by RICM. Changes in membrane composition, and the corresponding changes in surface charge density, are observed to alter the colloidal height distribution, as expected for electrostatically levitated colloidal particles. Using a combination of experimental and computational techniques, we determine the precision of this RICM-based tracking method to be 16 nm laterally and 1 nm vertically in its present implementation. This high spatial resolution confirms that RICM studies of membrane-coated colloidal particles could yield information down to macromolecular length scales while, at the same time, remaining practically applicable to statistically relevant numbers of particles. Materials and Methods Small unilamellar vesicles (SUVs) of desired composition were made by mixing the desired components (0.5 mol % N-(Texas red sulfonyl)-1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (TRDPPE) and 0-10 mol % 1,2-dimyristoyl-sn-glycero-3-[phospho(12) Simson, R.; Wallraff, E.; Faix, J.; Niewohner, J.; Gerisch, G.; Sackmann, E. Biophys. J. 1998, 74, 514-522. (13) Federle, W.; Riehle, M.; Curtis, A. S. G.; Full, R. J. Integr. Comp. Biol. 2002, 42, 1100-1106. (14) Prieve, D.; Frej, N. Langmuir 1990, 6, 396-403. (15) Wu, H.-J.; Bevan, M. A. Langmuir 2004, 21, 1244-1254.

10.1021/la050372r CCC: $30.25 © 2005 American Chemical Society Published on Web 06/03/2005

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Langmuir, Vol. 21, No. 14, 2005 6431 coverslip-water interface. Each sphere in the field of view produces a height-dependent interference pattern, as shown in Figure 1C.

Results and Discussion

Figure 1. Reflection interference contrast microscopy (RICM) of lipid-derivatized silica microspheres. (A) Schematic illustrating the geometry of interferogram formation. Monochromatic rays, E1 and E2, reflecting off a coverslip and from a lipidcoated silica microsphere interfere at the image point I(x,y). The intensity at I(x,y) is the integrated contributions from each ray incident at the image point. (B) Fluorescence images of 6.8 µm diameter silica microspheres each coated with a uniform, fluid lipid bilayer (0.5 mol % TR-DPPE, 6 mol % DMPS, 96.5 mol % DMOPC). (C) RICM images of the same microspheres, consisting of height-dependent interferograms corresponding to each microsphere. l-serine] (DMPS) in 1,2-dimyristoleoyl-sn-glycero-3-phosphocholine (DMOPC)) in chloroform. The mixture was then evaporated until it was visibly dry and hydrated with deionized water at 4 °C for 15 min. SUVs were then formed by sonication and ultracentrifugation (166 000g, 2.5 h, 4 °C). Bilayers were deposited on 6.84 µm ((5%) diameter silica spheres (Bangs Labs, Fischer, IN) by adding a 1:1 mixture of SUVs and 250 mM NaCl/ 10 mM TrisCl pH 7.2 to an equal volume of microspheres (10% solids in water) and rinsing thoroughly. Working buffers for ionic strength experiments were prepared as dilutions of a stock buffer containing 90 mM NaCl and 10 mM HEPES at pH 7.2. The experimental setup is schematically illustrated in Figure 1A. Coated microspheres were allowed to gravitationally settle to the bottom of a glass-bottomed well plate (LabTek, Nalge Nunc, Rochester, NY) to form a colloidal monolayer with a 25% surface area density. After 15 min, all microspheres had settled, and the resulting colloidal monolayer was viewed using a Nikon T300 inverted fluorescence microscope mounted with a Nikon 1.3NA 100X Plan Fluor oil-immersion objective. The quality of lipid bilayer deposition was verified by epifluorescence microscopy. The fluorescent intensity of well-coated colloidal particles, such as those shown in Figure 1B, appears homogeneous. For RICM (Figure 1C), the sample was illuminated by light from a mercury arc lamp filtered by a 541-551 nm bandpass filter; the aperture diaphragm was set to provide a small illumination numerical aperture (INA ) 0.42) and, hence, minimal angular variation in illumination light. This is important for maximizing contrast between interference fringes. The field diaphragm was partially closed in order to produce a sharply focused shadow in the image plane (upper left corner of Figure 1C). This was used to facilitate reproducible focusing on the

In RICM images of colloidal monolayers, each microsphere forms a radially symmetric interferogram centered about its lateral position. The amplitude of intensity oscillations in the interferogram of a single microsphere decays monotonically with distance from the center, such that the interferogram is fully contained within the radius of the microsphere. Thus, closely neighboring microspheres can be analyzed individually, without considering the effects of reflection interference from neighbors. The interferogram of a single microsphere is dependent on the height of the microsphere above the coverslip. The three-dimensional location of observed particles was estimated by fitting, in a least-squares sense, images of individual spheres to interferograms calculated according to the nonplanar interface image formation theory of Wiegand and Sackmann.16 This methodology approximates the illumination source as monochromatic, pseudocoherent, and angularly limited by the illumination aperture. The surface of the coverslip and microsphere are treated as ideal planar and spherical surfaces, respectively. The normalized intensity at a point, I, in the interferogram is calculated by numerically integrating over all interfering rays incident upon that point using adaptive Labato quadrature to a precision of 1 × 10-6.16 The contribution from a particular incident ray is calculated by ray-tracing backward to solve for the effective path length and intensity, as schematically outlined in Figure 2A. At every optical interface, reflection and transmission coefficients are calculated according to the Fresnel reflection coefficients,17 so as to properly account for the specific angle of incidence. Integration is restricted to rays that fall within the cone of collected light subtended by the numerical aperture (NA) of the objective and that of the illuminating light as limited by the illumination numerical aperture (INA) (Figure 2B). Rays that undergo multiple reflections are attenuated at each optical interface and, as a result, do not contribute significantly to the overall interference profile. Hence, in this ray-tracing procedure, multiple reflections were not considered. The interference profile produced by each microsphere is strongly height dependent, as seen in Figure 3A and B. By recording images at four frames per second, a sequence of uncorrelated heights can be determined (Figure 3C). Data Processing. There are two central steps necessary when processing the RICM images of multiple microspheres: (i) rough location of the lateral position of individual interferograms in the field of view and (ii) analysis of the individual interferograms to determine the three-dimensional position of particles with high precision. We employ image correlation18,19 in the approach to both steps. Image correlation is a computational tool that, in this context, is equivalent to a filtering operation where the filter kernel consists of calculated RICM interferograms. Since the filter may be applied globally to an experimentally obtained image using the fast Fourier transform, image correlation is ideal for laterally localizing (16) Wiegand, G.; Neumaier, K. R.; Sackmann, E. Appl. Opt. 1998, 37, 6892-6905. (17) Hecht, E.; Zajac, A. Optics, 3rd ed.; Addison-Wesley: Boston, MA, 1997. (18) Nicholson, W. V.; Glaeser, R. M. J. Struct. Biol. 2001, 133, 90101. (19) Cheezum, M.; Walker, W.; Guilford, W. Biophys. J. 2001, 81, 2378-2388.

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Figure 2. (A) Schematic illustrating the geometry used to calculate interferograms by the nonplanar interface method. The intensity at a point in the image, I, is calculated by integrating the contributions of rays incident at I. Contributing rays can be traced backward to a source point S. The effective path length of the ray is a sum of the distances l1 and l2 corrected for the extra distance, l3, a wave front must travel after encountering the point, S, before encountering the image point, I. The different indices of refraction are accounted for when calculating the intensity and effective path length of the ray. (B) Rays contributing to the intensity at I originate from within the cone of illumination light determined by the illumination numerical aperture (INA) of the microscope. Because these rays must also be collected by the objective, they are also constrained to fall within the cone of collected light determined by the numerical aperture (NA) of the objective.

Figure 4. Image processing. (A) An observed RICM image of a microsphere is correlated with a number of calculated heightdependent correlation kernels in order to estimate lateral and vertical position. (B) Three represented correlation kernels for the full palette that would typically include 1250 kernels evenly spanning the range from 0 to 250 nm. (C) The correlation response is strongly location dependent, enabling estimation of lateral position with 16 nm precision. (D) Height of the microsphere above the glass coverslip is estimated with 1 nm precision by finding the height-dependent kernel that gives the greatest correlation response at the center of the interferogram.

Figure 3. Height dependence of interferograms. RICM images of a microsphere estimated to be 100 nm (A) and 130 nm (B) above a borosilicate coverslip. (C) Estimated height of the microsphere over time. Height fluctuations are uncorrelated from frame to frame. This microsphere was coated with a fluid lipid bilayer (3 mol % DMPS, 0.5 mol % TR-DPPE, 96.5 mol % DMOPC).

and estimating the height of colloidal particles imaged by RICM. In real space, this corresponds to locating the lateral position of each particle by maximizing the correlation response under translation of the kernel. Height information is obtained from the phase of the most highly correlated kernel. A library of 1250 correlation kernels was calculated for microsphere heights, equally spaced over the range from

0 to 250 nm, using the nonplanar interface theory outlined above. Three such kernels from this set are shown in Figure 4B. Kernels from the library were then correlated, one by one, with the experimentally obtained image to obtain a correlation response as a function of height. By applying a threshold, individual peaks were isolated to obtain a rough estimate of the location of each particle in the image. Focusing on individual interferograms and interpolating to achieve subpixel resolution, estimates of the height and lateral location of the particle image were refined by minimizing the least-squares error between calculated and observed images. A typical correlation result is plotted as a function of lateral position and height in Figure 4C and D. Colloidal Interactions. To test the viability of the three-dimensional particle tracking method described here, we studied the interactions between lipid-coated colloidal particles and an underlying borosilicate coverslip.

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Interactions of single micron-sized colloidal particles with planar substrates are well described by DerjaguinLandau-Verwey-Overbeek (DLVO)20 theory and have been experimentally characterized by both RICM11 and TIRM.14,21,22 For colloidal spheres more than a few nanometers from the underlying substrate, dispersion forces may be neglected.23 Hence, only electrostatic and gravitational forces are considered. For electrostatically levitated microspheres, the equilibrium height distribution depends on the solution ionic strength as well as the surface charge densities of the particle and substrate. Ionic strength is a readily adjustable parameter, and for lipid membrane-coated microspheres, the surface charge density can be varied simply by changing the composition of the coating lipid membrane. Both these approaches were used to alter the colloidal height distribution and validate the RICM-based method presented here as a tracking strategy. Typically, RICM movies with 50-70 colloidal particles in the field of view were recorded for a length of 700 frames, yielding a minimum of 35 000 estimated three-dimensional positions. Tracking the lateral diffusion of free particles revealed a constant lateral diffusion coefficient of 0.03 ( 0.005 µm2/s for 6.8 µm ((5%) diameter lipidcoated silica microspheres that was independent of membrane composition. This value corresponds to half the value predicted from the Stokes-Einstein relation. This reduction in mobility likely results from hydrodynamic drag between the particle and underlying substrate. Measurements of the particle height distributions were used to characterize interactions with the underlying substrate. First, a series of lipid-derivatized colloids were prepared using membrane coatings with varying composition to span a range of surface charge densities. The concentration of the negatively charged lipid, DMPS, in the bilayer was adjusted between 0 and 10 mol %. Under the experimental conditions of this work, only a fraction of the DMPS lipid headgroups are deprotonated and carry a net negative charge.24 Nonetheless, increasing DMPS concentration increases negative surface charge density and, consequently, electrostatic repulsion from the negatively charged borosilicate coverslip. The equilibrium height increases with increasing DMPS concentration, as the data shown in Figure 5A reveal. In the second approach, a constant membrane composition is maintained while altering ionic strength. Increasing ionic strength decreases the electrostatic repulsion, causing colloidal height distributions to decrease in height (Figure 5B). Interpreting histograms of observed microsphere heights in terms of a Boltzmann distribution permits estimation of the height-dependent potential in which the particles are suspended. Including electrostatic and gravitational components, the height-dependent potential energy, U(h), of a colloidal microsphere above a planar substrate is of the form

U(h) ) Ψ0e

-κh

+ Fgh

(1)

( ) ( ) ( ) kBT e

2

tanh

eψs eψb tanh 4kBT 4kBT

microsphere radius, e is the charge of an electron, T is the temperature, and kB is Boltzmann’s constant. Ψ0 is an effective electrostatic potential resulting from superposition of the surface potential of the planar borosilicate substrate, ψs, and the surface potential of the lipid-coated microsphere, ψb. Ψ0 is derived from Poisson-Boltzmann theory using the Derjaguin and linear superposition approximations. These approximations are appropriate because the radius of the particles used in these experiments is much greater than the Debye length.23,25 The resulting equilibrium height is given by

( )

heq ) κ-1 ln

κΨ0 Fg

(3)

For microspheres of a particular size and density at a fixed temperature, the equilibrium height may be adjusted

with

Ψ0 ) 16R

Figure 5. (A) Height distributions for populations of silica microspheres derivatized with fluid lipid membranes containing different mole percents of the acidic lipid DMPS as labeled. (B) Height distributions for colloidal populations at varying ionic strengths, as indicated. (C) Height distributions were interpreted in terms of a Boltzmann distribution to estimate the potential about equilibrium. These estimated height-dependent potentials were fit according to eq 1. A typical fit is shown. All lipid membranes consist of DMOPC, 0.5% TR-DPPE, and DMPS.

(2)

The inverse Debye length, κ-1, is dependent on the ionic strength.23 The height, h, is the smallest distance between the planar substrate and the bottom of the microsphere. Fg is the force due to gravity on the submerged microsphere,  is the dielectric constant of the buffer, R is the

(20) Prieve, D. C. Adv. Colloid Interface Sci. 1999, 82, 93-125. (21) Bevan, M. A.; Prieve, D. C. J. Chem. Phys. 2000, 113, 12281236. (22) von Grunberg, H. H.; Helden, L.; Leiderer, P.; Bechinger, C. J. Chem. Phys. 2001, 114, 10094-10104. (23) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, NY, 1989. (24) Leckband, D. E.; Helm, C. A.; Israelachvili, J. Biochemistry 1993, 32, 4974-4974. (25) Behrens, S.; Grier, D. J. Chem. Phys. 2001, 115, 6716-6721.

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by either changing ionic strength, and hence κ, or changing the surface potentials, and hence Ψ0. Estimates of heq and κ-1 can be made by fitting measured Boltzmann-weighted height probability distributions to eq 1. A typical fit is shown in Figure 5C. For experiments involving no added salt, typical ionic strengths were in the range of 10-20 µM, as determined by fitting. These ionic strength values are consistent with expected concentrations of dissolved CO3- from exposure to air. Adding salt altered distributions as shown in Figure 5B. Estimates of ionic strength, as obtained by fitting, will be lower than actual values if height distributions are broadened by random errors in height estimation. Here, ionic strength estimates obtained by fitting were within 50% of expected values and consistently lower than expected. The most significant factor broadening height distributions is likely inaccurate height estimation caused by polydispersity in particle diameter. In the above experiments, the colloidal particles were functionalized with lipid bilayers, but within the realm of validity of the Derjaguin approximation,23 untreated silica microspheres suspended above a planar supported bilayer on the borosilicate coverslip would yield equivalent results. This is a consequence of the symmetry between ψb and ψs inherent in eq 2. Comparison of height distributions between colloids prepared according to these two scenarios using supported bilayers consisting of 10% DMPS (0.5% TR-DPPE, 98.5% DMOPC) confirms this equivalency. Precision. The precision with which this RICM-based imaging and analysis method locates particles is estimated using a combination of experimental and computational techniques. First, particles apparently bound to the substrate in a high ionic strength (250 mM NaCl) solution were observed. Position measurements of these presumably immobile particles varied no more than 20 nm laterally and less than 1 nm vertically, providing upper bounds on instrument noise effects. These are only upper bounds, however, because the immobilized particles are still subject to some thermal motion. Localization precision was further characterized using a computational bootstrap resampling26 method. Since the interferogram of a single microsphere is radially symmetric, the intensity of pixels equidistant from the image center should be independently and identically distributed. Hence, by shuffling the order of pixels at equivalent radial distances, a collection of new images can be generated that are representative of the noise distribution in the original image. This procedure allows estimation of the spread in particle locations due to image noise on an image-by-image basis. The effects of adding zero-mean Gaussian noise (1% variance) to images and comparing location estimates were also explored. Both computational techniques indicated heights could be resolved with 1 nm precision while lateral positions could be resolved with a precision of 16 nm. Accuracy. Although relative positions may be determined precisely using RICM, measurement of absolute coverslip-microsphere separation distances is more error prone. Difficulties in microscope focus, reproducing microsphere polydispersity, and determination of the interference pattern at zero height all contribute to an observed deviation of 5 nm in the reproducibility of measured equilibrium heights. The effect of polydispersity on estimated heights was observed most clearly for (26) Press: W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipies in C: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992.

Clack and Groves

substrate-bound microspheres. Individual immobilized microspheres would appear to fluctuate less than 1 nm in height about their respective means, but the mean heights were typically distributed over an interval of 10-15 nm. For these samples, location of each microsphere in the field of view exhibited no correlation with apparent mean heights. We conclude, therefore, that these systematic deviations result from polydispersity of microsphere diameter. To account for this type of error when analyzing height fluctuations in a colloidal population, histograms of height fluctuations were characterized independently of the mean population height. First, population height is estimated as an average of all recorded heights. Then a histogram is built of all fluctuations away from the mean height of each individual microsphere to characterize the height distribution. This amounts to making independent determinations of the mean and variance of a distribution and was found to work well for the system studied here. Conclusion The RICM-based method for simultaneous localization of multiple particles in three dimensions with nanometer resolution, as introduced here, is useful for the characterization of collective behavior in colloidal monolayers. Application of this method to the study of membranecoated colloidal particles should be useful for the design of experiments probing membrane interactions. For instance, particles may be coated with membranes to adhere via a specific bridging interaction between surfacebound ligands and receptors such as cell adhesion molecules. By tracking many of these adhering particles in three dimensions using the described method, the length of the receptor-ligand bridging interaction may be determined with nanometer precision. Cell membranes typically display a richly decorated surface of proteins and carbohydrates that create a complex three-dimensional character. Architectural constraints imposed by topographical features on cell surfaces have been implicated in protein pattern formation in artificial bilayer junctions27 and intercellular junctions between immune cells.28-31 Supported bilayers offer a natural environment for functional incorporation of membrane-associated proteins32-38 and have even proven competent in the formation of hybrid live cell-supported membrane junctions. In these intermembrane junctions, patterns, which are putatively linked to biological function in the immune synapse,31 seem to form in accordance with steric constraints imposed by the sizes of proteins in an interface. For instance, tall adhesion molecules in the immune synapse would, presumably, sterically hinder the binding of the short T-cell receptor (TCR) to the major histocompatibility complex (MHC) molecule30 were it not for the rearrangement of proteins into patterns. Probes of protein (27) Parthasarathy, R.; Groves, J. T. Proc. Natl. Acad. Sci. 2004, 101, 12798-12803. (28) Groves, J. T.; Dustin, M. L. J. Immunol. Methods 2003, 278, 19-32. (29) Qi, S. Y.; Groves, J. T.; Chakraborty, A. K. Proc. Natl. Acad. Sci. 2001, 98, 6548-6553. (30) Shaw, A.; Dustin, M. Immunity 1997, 6, 361-369. (31) Li, Q.; Dinner, A.; Qi, S.; Irvine, D.; Huppa, J.; Davis, M.; Chakraborty, A. Nature Immunol. 2004, 5, 791-799. (32) Sackmann, E. Science 1996, 271, 43-48. (33) Groves, J.; Ulman, N.; Boxer, S. Science 1997, 275, 651-653. (34) Kalb, E.; Frey, S.; Tamm, L. K. Biochim. Biophys. Acta 1992, 1103, 307-316. (35) Puu, G.; Artursson, E.; Gustafson, I.; Lundstrom, M.; Jass, J. Biosens. Bioelectron. 2000, 15, 31-41. (36) Shen, W.; Boxer, S.; Knoll, W.; Frank, C. Biomacromolecules 2001, 2, 70-79. (37) Wagner, M.; Tamm, L. Biophys. J. 2000, 79, 1400-1414. (38) Kiessling, V.; Tamm, L. K. Biophys. J. 2003, 84, 408-418.

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height in intermembrane junctions, such as fluorescence resonance energy transfer (FRET),39 fluorescence interference contrast microscopy (FLIC),27,38 and the surface forces apparatus (SFA),40-42 have been informative be(39) Kim, M.; Carman, C.; Springer, T. Science 2003, 301, 17201725. (40) Leckband, D.; Sivasankar, S. Curr. Opin. Cell Biol. 2000, 12, 587-592. (41) Sivasankar, S.; Gumbiner, B.; Leckband, D. Biophys. J. 2001, 80, 1758-1768. (42) Zhu, B.; Chappuis-Flament, S.; Wong, E.; Jensen, I.; Gumbiner, B.; Leckband, D. Biophys. J. 2003, 84, 4033-4042.

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cause of their nanometer sensitivity, but they require elaborate techniques and instrumentation. This has the practical consequence of making individual measurements time-consuming or expensive, thus reducing the experimental parameter space one can effectively explore. We anticipate that the combination of statistical analysis enabled by many-particle tracking with the precision afforded by RICM will facilitate study of the molecular topography of membrane surfaces. LA050372R