Explaining Non-Zero Separation Distances between Attached Bacteria

Explaining Non-Zero Separation Distances between Attached Bacteria and Surfaces Measured by Total Internal ... Yan He, Hung-Wing Li, and Edward S. Yeu...
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Langmuir 2002, 18, 5247-5255

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Explaining Non-Zero Separation Distances between Attached Bacteria and Surfaces Measured by Total Internal Reflection Aqueous Fluorescence Microscopy Lisa V. Smith,‡ Lukas K. Tamm,† and Roseanne M. Ford*,‡ Department of Chemical Engineering, School of Engineering and Applied Science, and Department of Molecular Physiology and Biological Physics, School of Medicine, University of Virginia, Charlottesville, Virginia 22904-4741 Received December 10, 2001. In Final Form: April 2, 2002 To relate observed separation distances between bacteria and surfaces to the forces governing adhesion, we need measurements of absolute distance that are accurate as well as precise. In this paper we examine factors that possibly contribute to a larger than expected separation distance for Escherichia coli attached to quartz and implications for using total internal reflection aqueous fluorescence (TIRAF) microscopy in quantitative studies. TIRAF was used to determine relative separation distances between bacteria and surfaces with an uncertainty of approximately 12 nm. This error in relative distances can be attributed to the uncertainty associated with the parameter values used to calculate the separation distance from light intensity measurements and to the uncertainty in the orientation of each individual cell with respect to the surface, which alters the effect that the curvature of the cell has on the separation distance. Absolute distances determined with TIRAF are overestimated by as much as 26 nm. The main source of error contributing to this value is caused by the averaging that occurs within each image pixel over the curvature of the body of a rod-shaped bacterium. Scattering of laser light off the microscope slide and the cell, and roughness of the bacterial and quartz surfaces also contribute to the overestimation. Liposomes were constructed to serve as a simple model of bacteria for which some of these factors have a reduced effect.

Introduction Classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which describes electrostatic and van der Waals interactions, has been used qualitatively and quantitatively to describe microbial adhesion to various surfaces.1 DLVO theory for a suspension of Escherichia coli2 in high ionic strength buffer predicts an energy maximum that acts as a barrier to direct contact between the cell and the substratum, and a secondary energy minimum that is deep enough to allow adhesion at about 3 nm from the quartz surface.3 However, most of the distances that we have calculated on the basis of total internal reflection aqueous fluorescence (TIRAF) microscopy observations were about 50 nm away from the surface and none were closer than 30 nm. While a majority of the separation distances reported in the literature are between 30 and 100 nm,4-8 Truskey and co-workers9 were able to obtain separation distances as close as 15 nm for focal contacts of endothelial cells using total internal reflection

fluorescence microscopy (TIRFM), and Izzard and Lochner10 were able to obtain separation distances as close as 10 nm for focal contacts of chick heart fibroblasts using interference reflection microscopy (IRM). In this paper we discuss factors that possibly contribute to a larger than expected separation distance for bacteria attached to quartz and implications for using TIRAF in quantitative studies. The factor that seems to be most important is averaging within each pixel over the curvature of the body of a rod-shaped bacterium. The uncertainties of the parameters used in Gingell’s equations11 relating light intensity to distance, scattering of laser light off of the cell and off of the microscope slide, and roughness of the bacterial surface and the quartz surface also have an effect. Liposomes were constructed to serve as a simple model of bacteria for which some of these factors have a reduced effect.

* Corresponding author. Telephone: 434-924-6283. Fax: 434982-2658. E-mail: [email protected]. † Department of Molecular Physiology and Biological Physics, School of Medicine. ‡ Department of Chemical Engineering, School of Engineering and Applied Science.

TIRAF Microscopy. TIRAF microscopy is a technique that has been used to measure the distance between an actively swimming bacterium and a surface.8 In this technique, an evanescent wave is generated in an aqueous suspension of bacteria by reflecting a laser beam off a quartz/water interface at the top of a sample chamber. The evanescent wave excites a fluorescent marker included in the sample bacterial suspension and illuminates the fluid to a depth of about 100 nm (based on the characteristic exponential decay depth).12 Because fluorescein-dextran (MW 3000) is too large to pass through pores in a cell wall, bacteria that are close to the surface will appear as dark

(1) Hermansson, M. Colloids Surf., B 1999, 14, 105-119. (2) Armstrong, J. B.; Adler, J.; Dahl, M. M. J. Bacteriol. 1967, 93, 390-398. (3) Vigeant, M. A. S.; Ford, R. M. Appl. Environ. Microbiol. 1997, 63, 3474-3479. (4) Ong, Y.-L.; Razatos, A.; Georgious, G.; Sharma, M. M. Langmuir 1999, 15, 2719-2725. (5) Lanni, F.; Waggoner, A. S.; Taylor, D. L. J. Cell Biol. 1985, 100, 1091-1102. (6) Robertson, S. K.; Bike, S. G. Langmuir 1998, 14, 928-934. (7) Fletcher, M. J. Bacteriol. 1988, 170, 2027-2030. (8) Vigeant, M. A.-S.; Wagner, M.; Tamm, L. K.; Ford, R. M. Langmuir 2001, 17, 2235-2242. (9) Truskey, G. A.; Burmeister, J. S.; Grapa, E.; Reichert, W. M. J. Cell Sci. 1992, 103, 491-499.

Background

(10) Izzard, C. S.; Lochner, L. R. J. Cell Sci. 1976, 21, 129-159. (11) Gingell, D.; Heavens, O. S.; Mellor, J. S. J. Cell Sci. 1987, 87, 677-693. (12) Tamm, L. K. In Optical Microscopy: Emerging Methods and Applications; Academic Press: San Diego, 1993; pp 295-337.

10.1021/la0117855 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/22/2002

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Figure 1. Example TIRAF image. The line that passes behind one of the cells represents the analysis box along which light intensity values are extracted. The elliptical area illuminated by laser-stimulated fluorescence is outlined with a dotted line, and the bright spots caused by photon scattering are indicated by arrows.

spots on a bright background, as seen in Figure 1. The bright spot next to each bacterium in the image is caused by photons scattering off the surface of the cell and exciting the proximate fluorescent marker molecules, which creates a local increase in light intensity. The line that passes behind one of the cells in Figure 1 shows where light intensity values are extracted for determining the separation distance. Gingell’s Relationship. The theory underlying TIRAF microscopy11,13,14-17 and its application to motile bacteria8 have been described in detail elsewhere. Gingell and coworkers11 related the separation distance between a cell and a surface to the ratio of the light intensity at the location of a cell and the light intensity of the background at the same location. (A typographical correction to these equations as given by Vigeant et al. is located in Appendix A.) The form of this relationship depends on the nature of the wave in each of the media and more specifically on the refractive index of quartz, the refractive index of the aqueous fluid in which the bacteria are suspended, the refractive index and thickness of the cell envelope, and the refractive index of the cell cytoplasm. For our experimental system, the evanescent wave is transformed back into a continuous wave in the cell wall and then again into an evanescent wave in the cytoplasm of the cell, where its exponentially decreasing amplitude reaches an insignificant value.11 Figure 2 shows the wave form as it passes through the different media of a bacterial suspension as well as values of the parameters that are necessary for describing this system. In liposome suspensions the wave behaves similarly; it becomes continuous in the lipid bilayer and evanescent in the inner fluid of the liposome. Table 1 lists the parameter values used in calculations for liposomes. The differences between liposomes and bacteria in terms of parameter values are the refractive index of the inner fluid and the thickness of the membrane. Figure 3 shows the form of Gingell’s relationship for bacteria and for liposomes. Materials and Methods Bacterial Strains. In addition to HCB1 (AW405), which is a wild-type E. coli that has six to eight flagella positioned around its cell body and swims in a run and tumble pattern resembling molecular diffusion, a smooth-swimming mutant (HCB437) and two nonmotile mutants (HCB136 and HCB5pil-) were used in (13) Gingell, D.; Heavens, O. J. Microsc. 1996, 182, 141-148. (14) Gingell, D.; Todd, I.; Bailey, J. J. Cell Biol. 1985, 100, 13341338. (15) Heavens, O. S. J. Cell Sci. 1990, 95, 175-176. (16) Mellor, J. S.; Gingell, D.; Heavens, O. S. J. Mod. Opt. 1988, 35, 623-628. (17) Todd, I.; Mellor, J. S.; Gingell, D. J. Cell Sci. 1988, 89, 107-114.

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Figure 2. Schematic showing the form of the wave as it passes into a bacterium suspended in the sample chamber. A continuous wave is indicated by a straight line; an evanescent wave, by a wavy line. Values for the parameters used in Gingell’s relationship to determine the distance between the quartz and a bacterium are given with references shown in parentheses.

Figure 3. Gingell’s relationship for the separation distance between the surface of a bacterium or a liposome and the substratum. R is the ratio of the light intensity where a colloid is present to an estimate of the light intensity in the same location without a colloid present. Table 1. Liposome Parameters Used in Gingell’s Relationship parameter

value

ref

refractive index of sucrose solution refractive index of lipid bilayer refractive index of glucose solution thickness of bilayer

1.3379 1.45 1.3356 5 nm

18 15 18 19

these studies. HCB437 does not have the ability to change the rotational direction of its flagella to clockwise and thus constantly runs. HCB136 is a paralyzed mutant, which means that it does not have the ability to rotate its flagella. HCB5pil- is a nonflagellated mutant that also has no ability to express pili. Bacterial Preparation. Bacteria were grown from frozen stock as batches in tryptone broth at 30 °C and aerated by agitation on a shaker table (Lab-Line Orbit Environ-shaker, Dubuque, IA) at 150 rpm. Tryptone broth consists of 10 g of tryptone, 5 g of sodium chloride, and 1 L of water and has a pH of 6.7. A 1 mL aliquot of the midexponential phase culture was filtered through a 0.45 µm filter (Millipore, Bedford, MA) and resuspended in 25 mL of phosphate buffer to remove spent media and arrest cell division while maintaining cell motility.20 The phosphate buffer used in this study consists of 11.2 g of potassium hydrogen phosphate, 4.8 g of potassium dihydrogen phosphate, 0.029 g of ethylenediaminetetraacetic acid, and 1 L of water and (18) CRC Handbook of Chemistry and Physics, 81st ed.; Lide, D. R., Ed.; CRC Press: Washington, DC, 2000; pp 8-57 to 8-83. (19) Liposomes: A Practical Approach; New, R. R. C., Ed.; IRL Press: New York, 1990; p 301. (20) Berg, H. C.; Turner, L. Biophys. J. 1990, 58, 919-930.

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Figure 4. Close-up view of a sample TIRAF image. A plot showing the magnitude of the light intensity (in arbitrary units) across the center of the bacterium is superimposed on the image. Arrows show the position of a bacterium and its reflection in the image and on the plot. has a pH of 7.1. The resulting concentration of cells in suspension was on the order of 106-107 cells/mL. TIRAF Microscopy. The materials and methods used in the TIRAF experiments were as described by Vigeant et al.8 with a few modifications. The stock solution of fluorescein-dextran (5 mg/mL) was filter sterilized with 0.2 µm Acrodisc syringe filters (Pall Corporation, Ann Arbor, MI), stored in 50 µL aliquots in a freezer at -20 °C to prevent growth of microorganisms, and thawed prior to its addition to a bacterial suspension. Quartz microscope slides were rinsed in acetone instead of methanol. For the experiments performed to evaluate the significance of light scattering off of a cell and field scattering off of the microscope slide, measurements of the laser light were made with a 488 nm narrow-band-pass filter and 50% neutral density filter instead of the FT510 dichroic mirror and 520 nm long-pass filter (Chroma Optics, Brattleboro, VT) normally used to measure fluorescent light. An 8 W argon ion laser (Coherent Innova Series 300, Palo Alto, CA) was run in constant power mode at 0.7 W instead of 0.3 W to improve image quality. Images were captured for up to 2 min at a rate of two frames per second. Since the sample chamber is situated with the quartz microscope slide at the top, it was necessary to invert the chamber for 5 min and allow nonmotile bacteria to settle onto the surface so that they could be observed. For experiments with motile strains, the sample chamber was placed onto the microscope stage immediately after being loaded. To investigate whether inverting the chamber affected our results, we compared samples of wild-type E. coli and smooth-swimming E. coli that had been inverted to samples that had not been inverted. We found that initially resting the chamber upside-down caused more cells to be immobile and fewer cells to be swimming freely near the surface. Despite this change in the proportion of behaviors observed near the surface, we do not expect the average separation distance for cells exhibiting each type of behavior to change. TIRAF Data Analysis. Light intensity values were extracted from the TIRAF images with an analysis box using the public domain NIH Image program (developed at the U.S. National Institutes of Health and available on the Internet at http:// rsb.info.nih.gov/nih-image/). The analysis box was 1 pixel wide, instead of 3 pixels wide as in previous work, and 162 pixels long, which was used to produce a good curve fit of the background. Light intensity values and an image of the cell from which they were obtained are shown in Figure 4. The lowest point of the dip corresponds to the light intensity at the location of the cell, and the background light intensity at the same location is estimated by fitting a second-order polynomial across the light intensity profile. Separation distances were determined from Gingell’s relationship with an iterative root-finding scheme built into MATLAB version 5.0. Quartz Surface Roughness. The ten-point mean roughness of the quartz substratum was determined with a scanning probe atomic force microscope (Molecular Imaging, Inc., Phoenix, AZ) equipped with Nanoprobe cantilevers (PARK Scientific, Sunnyvale, CA). The cantilevers have Si3N4 integral tips at least 50 nm in diameter with spring constants of 0.3 and 0.06 nm-1. The deflection and height were measured in contact mode with

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Figure 5. Separation distance over time of an immobile nonflagellated pili-less E. coli. From our calculations, this particular immobile cell was located 62 ( 2 nm from the surface during the 25 s time period that it was observed and sampled distances from 54 to 66 nm. constant force at four positions on the microscope slide: one at a 25 µm2 scale and three at a 5 µm2 scale. Liposomes. Liposomes were prepared using an improved gentle hydration method described by Akashi et al.21 and composed of 90% phosphatidylcholine and 10% phosphatidylserine. The inclusion of charged lipids (such as negatively charged phosphatidylserine) is required for successful preparation of giant unilamellar liposomes. It was adequate to dry the lipid film for only 0.5 h instead of 6 h. The solution enclosed inside the liposomes consisted of 100 mM glucose, 50 mM potassium chloride, 20 mM N-(2-hydroxyethyl)piperazine-N′(2-ethanesulfonic acid) (HEPES), and 1 mM ethylene glycol-bis(β-aminoethyl ether)-N,N,N ′,N ′-tetraacetic acid (EGTA). The liposomes were suspended in a solution identical to the internal fluid except that it contained 100 mM sucrose instead of glucose. The difference in density of the internal and external media ensured that the liposomes would float to the top of the TIRAF sample chamber and approach the surface of the quartz microscope slide. The solutions were designed to have the same osmolarity to prevent swelling or shrinking of the liposomes, and the osmolarity was determined to be 220 mmol/kg with a vapor pressure osmometer (Wescor 5500, Logan, UT). The pH of both solutions was adjusted to 7.2 with potassium hydroxide.

Results and Discussion Pili-less Nonflagellated Mutant of E. coli. For an immobilized nonflagellated bacterium without the ability to express pili, we expected to obtain separation distances near zero. However, the distances that we measured were much larger than this. Immobile cells were identified as those that showed no visible movement over time. Images recorded during the experiment are similar to those shown in Figures 1 and 4, and an example of the distances determined from the images over time is shown in Figure 5. Each distance determined is the smallest value obtained for that bacterium at a particular time and thus the closest detectable location relative to the quartz surface. The population of 11 observed immobile cells was determined to be an average of 61 ( 8 nm from the surface. The discrepancy between this experimental result and DLVO theory predictions prompted us to examine the sensitivity of Gingell’s relationship to the parameters used to describe our experimental system. Sensitivity Analysis. A sensitivity analysis was performed on the parameters used in Gingell’s equations relating the amount of fluorescence generated between a cell and a surface and the width of that gap. The parameter values normally used in our calculations, which were (21) Akashi, K.-I.; Miyata, H.; Itoh, H.; Kinosita, K., Jr. Biophys. J. 1996, 71, 3242-3250.

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Figure 7. Diagram showing the size of a cell relative to the size of the pixels (with binning, thicker lines) and subpixels (without binning, thinner lines). The gray area highlights the pixel within which the cell is in contact with the substratum.

Figure 6. Sensitivity of the calculated separation distance to the parameters of the cell. The high values used for the refractive index of the cell envelope, the thickness of the cell envelope, and the refractive index of the cytoplasm were 1.46, 31 nm, and 1.37, respectively. The low values used were 1.39, 26 nm, and 1.36. The set of parameter values normally used in our calculations are those that were shown in Figure 2. The dashdot box shows the amount of error in the separation distance that is caused by the uncertainty in the cell parameters when the reported value is 31 nm.

shown in Figure 2, were selected as the base case. Increasing the values of the cell envelope thickness, the cell envelope refractive index, or the cytoplasm refractive index, or decreasing the value of the buffer refractive index, reduces the calculated separation distance between a cell and a surface. The parameter that had the largest effect on the calculated separation distance was the buffer refractive index, but it was measured directly and thus is well-known. Although we normally use a refractive index for lipid bilayers to represent the entire cell envelope, this parameter has the smallest effect on the calculated separation distance. Other authors cite TIRAF’s theoretical vertical resolution limit as 2 nm for a high-index substratum11 and 10 nm for a low-index substratum22 on the basis of the sensitivity of distance calculations to the refractive index of cell cytoplasm alone because it is the most influential of the cell parameters. Because parameter values for bacteria are particularly difficult to estimate, we included all of them in a combined sensitivity analysis. The low value of the cell envelope refractive index (1.39) was selected because the refractive index must be at least this large for the waveform to remain continuous in the cell envelope and the same set of equations to be applicable. The high value (1.46) was selected because the refractive index cannot be greater than that of quartz. Low and high values for the other two cell parameters were taken from the literature. Values reported for the thickness of the cell envelope ranged from 26 to 31 nm.23,24 The refractive index of cytoplasm has been determined by immersion refractometry to be between 1.36 and 1.37.11 Figure 6 shows the ratio of the signal to background light intensities as a function of the separation distance between a bacterium and a quartz substratum for three combinations of the cell parameters. Higher values produced smaller separation distances than normal (22) Geggier, P.; Fuhr, G. Appl. Phys. A 1999, 68, 505-513. (23) The Physiology and Biochemistry of Prokaryotes; White, D., Ed.; Oxford University Press: New York, 1995; p 378. (24) Leduc, M.; Frehel, C.; Siegel, E.; van Heijenoort, J. J. Gen. Microbiol. 1989, 135, 1243-1254.

values, and lower values produced larger separation distances than normal values. The smallest ratio of light intensities (R ) 0.407 35) that we obtained from all of our experiments with bacteria was for an attached paralyzed mutant estimated to be 31 nm from the surface. Accounting for the uncertainty in cell parameters alone, the gap width for this cell most likely would be between 30 and 39 nm. The closer a cell is to the surface, the less sensitive the distance measurement is to uncertainty in any of the parameters. Therefore, any uncertainty in the parameters used in Gingell’s relationship will be less important at smaller separation distances. Furthermore, using a substrate with a high refractive index (n1 ∼ 1.85) would make the distance measurements nearly independent of cell parameters11 and should be considered for future measurements. Regardless of how much the parameters deviate from their true values, the light intensity must be zero at one position in order to obtain a zero separation distance with Gingell’s equations. Thus, when evaluating potential sources of error, it is important to focus on ways in which the amount of fluorescence detected at a point of contact between a cell and a surface may be nonzero. Cell Curvature. Figure 7 illustrates that a bacterium can be in contact with the surface but not over the entire area of a pixel because of the size of the cell and the curvature of its surface relative to the size of the pixel. Each pixel is actually a 2 × 2 matrix of subpixels that are binned during data collection and is 1/3 µm on a side as compared to our bacteria, which range from 1 µm in diameter and 2 µm long to 2 µm in diameter and 5 µm long depending on the mutant. Since the separation distance is determined by measuring the amount of fluorescence emanating from the volume of fluid located between the cell and the surface, any portion of the cell that is not in contact with the surface over the area of a pixel will contribute to the light intensity value measured for that pixel and will cause the determined separation distance to be greater than zero. In previous work, an analysis box 3 pixels wide was used for extracting light intensities from the images.8 In this work, 4 subpixels of a square are still binned into 1 pixel. These two layers of averaging could be removed to improve our image resolution parallel to the plane of the substratum and thus improve the resolution of our distance measurements vertical to the surface. The degree of improvement depends on the size of the cell and whether the cylindrical part or spherical part of the rod-shaped cell body is closest to the substratum. Cells in various stages of attachment observed with TIRAF microscopy appeared to be oriented with their long axes anywhere from perpendicular to the surface, for which a spherical model would be appropriate, to parallel to the surface, for which a cylindrical model would be appropriate. Many cells appeared to be somewhere between these two extremes. In their study of hydrodynamic forces on

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Figure 9. TIRAF image showing a large (31-70 µm2) nonreflecting lipid formation. Figure 8. Plot of the separation distance obtained from averaging over the area of one pixel, h (nm), versus the closest true separation distance between a cell and a surface, H (nm). Models or analysis methods that produce curves that are closer to the diagonal have less error caused by the curvature of the cell.

cells swimming near a surface, Vigeant et al.25 state that cells swimming 100 nm away from a surface are expected to be oriented with their long axis 30° relative to the surface. Furthermore, as cells approach a surface, they are expected to become more perpendicularly oriented. Calculations were performed to determine to what extent cell curvature causes the overestimation of separation distance. The volume of fluid between the substratum and the cell over one pixel was divided by the area of a pixel to obtain an area average height of the fluid volume. This approach is equivalent to assigning one light intensity value to the whole area covered by a pixel. Calculations were performed for different cell models and analysis methods to generate a plot of the measured separation distance versus the true closest separation distance as shown in Figure 8. A brief example calculation is shown in Appendix B. Notice that for the case with the larger analysis box the amount of overestimation associated with cell curvature, that is, how far away the data are from the diagonal in Figure 8, increases as the separation distance gets closer to zero. For all other cases the amount of overestimation remains nearly constant over a large distance range. Holding all other variables constant but reducing a cell to half of its size causes the cell to appear 10 nm farther away. Similarly, because the cylindrical part of the cell body has curvature in only one direction instead of two directions, cells that contact a surface in the middle of their bodies appear to be 5 nm closer than cells that contact a surface with their spherical ends. Using a 1 × 162 analysis box instead of a 3 × 162 analysis box had the greatest impact on the separation distance. It was estimated that removing this one layer of averaging for a cell that appeared to be 50 nm away from a surface would reduce the separation distance by about 36 nm. Even with this improvement, there is an estimated 9 nm difference between the actual closest distance and the closest distance determined with TIRAF. Experimental tests with one nonflagellated and five wild-type cells that appeared to be stuck to the substratum show that reducing the size of the analysis box reduced the separation distance by as much as 13 nm and as little as 2 nm. While this may explain a significant part of the nonzero distance, there (25) Vigeant, M. A.-S.; Ford, R. M.; Wagner, M.; Tamm, L. K. Appl. Environ. Microbiol., in press.

must be other contributing factors as well. Unless specified otherwise, a 1 × 162 analysis box was used to generate the distance results presented in this paper. Improving the resolution of TIRAF images by changing the binning from 2 × 2 to 1 × 1 was expected to improve our results by minimizing the effect of cell curvature within each image pixel. For the spherical part of the cell body, it was estimated that eliminating binning would decrease the separation distance by 7 nm and reduce the difference between the actual closest distance and the closest distance determined with TIRAF to 2 nm. Experimental tests with attached nonflagellated cells show a reduction in separation distance of about 6 nm. Despite this improvement, the data for this paper were collected with 2 × 2 binning because memory limitations of the computer made it difficult to collect movies with 1 × 1 binning. Liposomes. Giant unilamellar liposomes were constructed to serve as model cells in a control experiment. The purpose was to test the experimental method with a simple system for which we expected artifacts in the method to be minimized. Using liposomes instead of bacterial cells simplified the system by reducing the uncertainty in the parameters used in Gingell’s equations for determining the separation distance. Also, the larger radius of giant liposomes and flexibility of lipid membranes minimized curvature effects. The larger the colloid, the less the effect of surface curvature on the calculated separation distance. Because lipid bilayers are much more flexible than the cell envelope of gram negative bacteria, they become flat when pressed against a surface. Polymeric microspheres also were considered for these studies but were rejected because their refractive index is higher than that of quartz, which precludes the application of Gingell’s equations. The closest distance obtained at a single point in time was for a large liposome without any reflection at 22 nm, which is almost 10 nm closer than that obtained for a bacterium but still not equal to the 3 nm predicted by DLVO theory. Figure 9 shows a TIRAF image of a large nonreflecting lipid formation assumed to be a giant unilamellar liposome. These formations were found to be on average 28 nm from the surface. A sensitivity analysis was also performed for parameters describing the experimental system with liposomes. The normal parameter values are listed in Table 1. Although the calculated separation distance is quite sensitive to the refractive indices of the internal and external fluid media, these parameters are well characterized. It is not very sensitive to the parameters describing the lipid bilayer. The discussion of combined sources of error in a later section compares the results for bacteria with those for liposomes.

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In addition to giant unilamellar liposomes, this preparation method produces small vesicles, large multilamellar liposomes, aggregates of vesicles, and lipid debris. Under a phase-contrast microscope, the giant unilamellar liposomes appeared to be circular and had thin membranes, but in the TIRAF apparatus it was not easy to distinguish between the different lipid formations. However, we did observe with TIRAF that the peripheries of the large formations were clearly undulating, which Akashi et al.21 attributed to thermal fluctuations and took as one sign that the liposomes were unilamellar. Most of the lipid formations lacked a reflection like that caused by the laser photons scattering off the surface of a bacterium. Because light that is reflected at one location can be detected by pixels that are nearby (see discussion that follows on stray light as a source of error), measurements for colloids without a reflection are more accurate than those for colloids with a reflection. Therefore, results for large formations without any reflection were assumed to be the best estimate of the true separation distance between giant unilamellar liposomes and a quartz surface. Stray Light as a Source of Error. In their evaluation of the effects of stray light in TIRAF measurements, Gingell and Heavens13 concluded that compensation should be made in order to avoid significant error in distance measurements. Because the magnitudes of these effects are dependent on the experimental apparatus, we have examined light scattering in our system. Following the nomenclature of Gingell and Heavens, the fraction of light scattered off an object such as a bacterial cell or the microscope slide itself can be estimated with the equation

P)

K[CM(1) - CM(2)] CM(3)

(1)

where CM(3) is the detected fluorescent light intensity and CM(2) and CM(1) are the detected laser light intensities with and without a fluorescent marker in the suspension medium. CM(3) measurements were collected with the normal set of filters, which block laser light, while CM(1) and CM(2) measurements were taken with the alternative set of filters described in the methods section, which allow only laser light to reach the camera. K is a factor that accounts for the transmissivity of the filters used in the TIRAF apparatus as well as the sensitivity of the CCD camera and the quantum yield of the fluorescent marker. For our system K also includes a factor that accounts for the fact that CM(1) and CM(2) were measured at a different laser power than that used for CM(3). K for a particular experimental system can be determined from eq 1 when there is a broad scratch on the surface of the microscope slide because nearly all of the light intensity detected is due to light scattering and P is equal to 1.The average value for K from 10 measurements each of CM(1), CM(2), and CM(3) along a scratch was 0.12, and using this value, the average amount of detected light that was scattered off immobilized nonflagellated E. coli mutants was determined to be 20%. Gingell and Heavens13 found similar results for their experimental system: the scattering of laser light off cells in TIRAF measurements can increase the detected fluorescence by about 25%. Even though the results presented in this section are rough estimates and may depend on the severity of the scratch, they are sufficient to give us an indication of how significant this effect is. It is the ratio, R, of the signal light intensity, CMO(3), to the background light intensity, CMB(3), that is normally used to calculate the separation distance between a cell

and a surface. The O superscript indicates that the measurement was taken in the presence of an object such as a bacterium near the substratum. The B superscript stands for the background of the surface or the substratum itself. CB measurements were obtained for the same locations as those for the CO measurements by fitting a curve to the background light intensity profile. Correcting this ratio to account for the scattering of light off a cell as well as field scattering caused by imperfections in the microscope slide produces the expression

R)

CMO(3) - K[CMO(1) - CMO(2)] CMB(3) - K[CMB(1) - CMB(2)]

(2)

The second term in the numerator accounts for the effect of light scattering off a cell while the second term in the denominator accounts for the effect of light scattering off the microscope slide. Either term can be omitted in order to examine one effect at a time. Average measurements from 10 cells were determined, and the separation distance was found to decrease by 24% from 46 to 35 nm when corrected for the effects of cell scattering. The fraction of light caused by field scattering for our experimental system (0.09) was larger than that determined by Gingell and Heavens (0.003), and accounting for field scattering would increase the observed separation distance by 6 nm. The deflection of photons off path within the microscope itself, otherwise known as glare, also was found to be significant in Gingell and Heavens’ system. Parameters used to account for glare, one associated with fluorescent photons arising from the evanescent zone and the other associated with fluorescent photons generated by scattered light, have not been evaluated for our system yet. Because glare may be partially responsible for the nonzero separation distances that we obtain for colloids using TIRAF, it will be investigated further using the procedures for evaluating glare parameters described in ref 13. Surface Roughness of Bacteria and Quartz. Roughness on both the colloid surface and the quartz surface influences the value of the separation distance determined with TIRAF. Since each value obtained with this method applies to a discrete area, points of contact that are smaller than the size of a pixel (0.1 µm2 for 2 × 2 binning) will be lost within the averaging process. Furthermore, smallscale surface roughness has the potential to cause separation distances determined with TIRAF to be larger than they really are. The root-mean-square (RMS) average of the surface roughness of Burkholderia cepacia G4 and Pseudomonas stutzeri KC in the biological growth buffer MOPS has been determined to be 5.2 ( 0.5 nm and 4.6 ( 0.4 nm, respectively, via tapping mode atomic force microscopy.26 The ten-point mean roughness of the quartz substratum was measured to be 1.4 nm with AFM as described in the methods section. This amount of substratum surface roughness is too small to either influence the adsorption of cells27 or significantly obscure contact points between cells and the surface. Combination of Errors for Bacteria and Liposomes. From all the possible sources of error described in the previous sections, the ones that seem to be reasonable and relevant to bacteria are shown in Table 2. The quartz and bacterial surface roughness and cell curvature adjustments were made first because they do not depend on the separation distance. Also, since we are (26) Camesano, T. A.; Natan, M. J.; Logan, B. E. Langmuir 2000, 16, 4563-4572. (27) Mueller, R. F.; Characklis, W. G.; Jones, W. L.; Sears, J. T. Biotechnol. Bioeng. 1992, 39, 1161-1170.

Attached Bacteria-Surface Separation Distances

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Table 2. Combination of Errors Expressed as Additional Deviation from the Measured Value additional deviation source of error

bacteria

quartz surface roughness -1 nm surface roughness of colloid -5 nm curvature of the colloidal surface -19 nm to -10 nm field scattering +1 nm to +2 nm object scattering -2 nm to -4 nm sensitivity of the calculations to 0 nm to +4 nm colloid parameters sum of the errors -26 nm to -14 nm

liposomes -1 nm +2 nm

+1 nm

applying these corrections to results for the nonflagellated strain, the effect of cell curvature for smaller bacteria (1 µm × 2 µm) was used. The field and object scattering adjustments were made to this corrected distance assuming that P remains constant at all separation distances. Finally, corrections to account for the sensitivity of Gingell’s equations to the cell parameters were made. When the closest distance measured for a bacterium (31 nm) was adjusted to account for all these sources of error, the resulting range was between 5 and 17 nm. Since the parameters for Gingell’s equations are much better known for the liposomes than for the bacteria, their uncertainty was not considered significant in our analysis. The curvature of the surface of the liposomes is not expected to play a role in the determination of the distance because the pixel from which the light intensity values were extracted was far from the edge of the liposome and the liposomes were large enough and flexible enough to cover many pixels completely. The surface of liposomes was assumed to be smooth relative to that of bacteria because it is composed only of lipids and thus did not contribute to the error. Furthermore, because measurements were taken far from the edge of large liposomes that lacked a visible reflection and because we did not perform experiments to estimate the amount of light that scatters off lipid surfaces, the influence of object scattering was not included in the combined error estimate for liposomes. The effect of field scattering was applied using P after an adjustment for the quartz surface roughness was made. The sources of error that remain for liposomes were combined in such a way that produced a closest corrected distance for liposomes of 23 nm. So that a comparison can be made between liposomes and bacteria, the results were adjusted to account for the difference in ionic strength of the suspension fluids. On the basis of estimates made with DLVO theory, if the bacteria had been suspended in a buffer of ionic strength 0.056 M like that of the liposome suspension instead of in a buffer of ionic strength 0.2 M, we would expect them to be 5 nm farther away from the surface than was determined experimentally in this study. Therefore, the most probable separation distance for the closest observed bacterium in low ionic strength solution would be between 10 and 22 nm. The corrected separation distances for bacteria and liposomes are the same order of magnitude as those presented in the literature and are closer to DLVO predictions for bacteria than the uncorrected distances are. In fact, we assume that the bacteria and liposomes are in contact with the surface. We have accounted for artifacts of the method, which influence them in different ways such that their corrected separation distances are very similar. However, since their corrected separation distances are nonzero, we may not have accounted for all the sources of error. For example, the most probable locations for both colloids would be closer to the surface if parameters for glare were known.

Figure 10. Plot of the uncorrected separation distance between a small cell and the surface versus the corrected distance. Error bars indicate the most probable distance range for a given uncorrected distance, and the dots are the median values of each range. Comparing the dotted line with the solid line illustrates the extent that the values have been corrected.

To use the information obtained in our examination of combined error to correct separation distances determined in future experiments, the calculation was repeated for several uncorrected separation distances. Figure 10 shows the results of this process for small bacteria. The uncorrected distance is plotted on the abscissa, and the corrected distance ranges are plotted as a mean with error bars on the ordinate. Comparing the dotted line through the means of the probable location ranges with the solid line illustrates the extent to which the values have been corrected. The amount to which the measured distance is overestimated is nearly constant for values from 31 to 100 nm; the difference between the two lines only changes from 20 to 21 nm, respectively. Therefore, we can compare relative separation distances determined with TIRAF. As illustrated by the decreasing size of the error bars with decreasing gap width, the closer a cell is to the surface, the easer it is to predict its true location. For cells that are very close to the surface, for example at an uncorrected separation distance of 31 nm, we can state that they are most likely located within a 12 nm range between 5 and 17 nm. But for cells that are far away from the surface in terms of TIRAF measurements, for example at an uncorrected separation distance of 100 nm, we can say only that they are located within a 38 nm range between 60 and 98 nm. Therefore, the differences that we observe in the separation distances for various samples of bacteria may have to be large in order to conclude that the difference is significant. Conclusions To relate separation distances between bacteria and surfaces to the forces governing adhesion, we need to have confidence that the measurements are accurate as well as precise. We have demonstrated that TIRAF can be used to determine relative separation distances between bacteria and surfaces with an error of approximately 12 nm due to the sensitivity of the parameters used in the calculations and the uncertainty in the orientation of the cells as they interact with the surface. The curvature of cells is the main contributing factor in the overestimation of distances determined with TIRAF. The cells are expected to be 14-26 nm closer to the surface than the uncorrected values indicate. However, it should be noted that, for larger cells, the importance of cell curvature

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Smith et al.

Figure 11. Areas under which the volume integral expressions were written as the cell gets closer to the surface: (a) eq b1; (b) eq b5; (c) eq b9.

effects is reduced relative to that of the effects of stray light and the roughness of the bacterial surface. Furthermore, the uncertainty associated with a measurement increases as a cell moves farther from the surface. Better understanding of the sources of error is the first step in making improvements to achieve more reliable results. In this paper we have identified which sources of error are most problematic and should be addressed. For example, cell curvature effects can be minimized by improving the horizontal resolution of the images collected and by subtraction of geometrically determined constants from the experimental distances as described in Appendix B. Switching from quartz to another transparent material with a higher refractive index will reduce field scattering as well as reduce the sensitivity of the results to cell parameters. Finally, on the basis of the work of Gingell and Heavens,13 the effects of glare for this particular experimental system should be evaluated. Acknowledgment. All Escherichia coli strains referred to in this study were generously provided by the laboratory of H. C. Berg (Harvard University). We thank the following people at the University of Virginia: Andrew Hillier for allowing us to use his atomic force microscope and assisting with measurements of surface roughness; Michael Wagner and Volker Kiessling for assistance with TIRAF microscopy; Attila Szabo and Gabor Szabo for assistance in constructing giant liposomes. This research was supported by grants from the National Science Foundation through the graduate traineeship in the Program for Interdisciplinary Research in Contaminant Hydrogeology, the Academic Enhancement Program at the University of Virginia, and the Jeffress Memorial Trust. Appendix A The equation describing the separation distance between a cell and a glass surface as shown in a previous publication8 contains a sign error. The correct expression for the definition of b2 is

b2 ) (γ32 + β2β4) sin δ1 + γ3(β2 - β4) cos δ1 Appendix B Imagine that the volume of fluorescing fluid that contributes to the light intensity captured by one pixel in an image can be represented by a box 335 nm square and 100 nm tall. When the cell is too far away to be detected, fluorescence is generated only to a distance equal to the penetration depth of the evanescent wave, and this value is used as the height of the fluid volume. When a bacterial cell comes just close enough to the surface that it is barely

visible with TIRAF microscopy, the volume of fluid that contributes to the light intensity is reduced and the representative box has a hemispherical depression because the cell has displaced fluid containing fluorescein-dextran molecules. To estimate the effect of cell surface curvature on the determination of separation distance, we calculated the volume of the box and divided it by the cross-sectional area to obtain an average height for one pixel. Figure 11 shows the outline of the spherical part of a cell (outer circle), the outline of one pixel (square), and the outline of the cell at the penetration depth (inner circle). The box that represents the fluorescing fluid has a hemispherical depression inside the inner circle and is flat outside the inner circle. Parts a-c show a progression as the cell gets closer to the substratum and displaces more fluid. In eq b1, written for the case depicted in Figure 11a when the cell is just barely visible, the height is averaged over the area of one pixel and the integrals can be divided into volumes of different shape that add up to the volume of fluorescing fluid within the pixel.

h (nm) )

1 A

0.335/2 0.335/2 h(x, z) dx dz ) ∫-0.335/2 ∫-0.335/2

2‚2‚1000 [V + VF1 + VF2] (b1) 0.335‚0.335 S1 Figure 11a shows the areas corresponding to each integral expression: VS1 represents the volume underneath the spherical depression; VF1 and VF2 each represent the volume under a portion of the flat part. The factors of 2 in the numerator of eq b1 take into account that the volume expressions were written for only a quarter of the volume, and the 1000 is a unit conversion from microns to nanometers. In eqs b2-b4, H is the smallest true separation distance between the cell and the surface and is expressed in nanometers and r is the radius of the cell. The argument of the integral in eq b2 is an expression for the spherical surface at the end of the cell at some height H, and the argument of the integrals in eqs b3 and b4 is the characteristic penetration depth of the evanescent wave.

VS1 )

∫0{r -(0.1017-r-H/1000) } ∫0{r -(0.1017-r-H/1000) -x } 2

2 1/2

{-(r - x - z ) 2

VF1 )

2

2 1/2

2

2

2 1/2

+ r + H/1000} dz dx (b2)

0.335/2 (0.1017) dz dx ∫{r0.335/2 -(0.1017-r-H/1000) } ∫0 2

×

2 1/2

(b3)

Attached Bacteria-Surface Separation Distances

VF2 )

∫0

∫{r -(0.1017-r-H/1000) -x }

{r2-(0.1017-r-H/1000)2}1/2

0.335/2 2

2

2 1/2

Langmuir, Vol. 18, No. 13, 2002 5255

×

(0.1017) dz dx (b4) When the cell gets a little closer to the surface, the above expressions no longer hold because the hemispherical depression extends beyond the bounds of the pixel area (see Figure 11b). Equations b1-b4 can be used for 88 nm e H < 102 nm; equations b5-b8 can be used for 73 nm e H < 88 nm.

h (nm) ) VS2 )

2‚2‚1000 [V + VS3 + VF3] 0.335‚0.335 S2

× ∫{r0.335/2 -(0.1017-r-H/1000) -(0.335/2) } ∫0{r -(0.1017-r-H/1000) -z } 2

2

2 1/2

2

2

{-(r - x - z ) 2

VS3 )

2

2 1/2

(b5)

2 1/2

×

+ r + H/1000} dx dz (b6)

∫0

{r2-(0.1017-r-H/1000)2-(0.335/2)2}1/2

∫00.335/2 ×

{-(r2 - x2 - z2)1/2 + r + H/1000} dx dz (b7) VF3 )

∫{r0.335/2 -(0.1017-r-H/1000) -(0.335/2) } ∫{r0.335/2 -(0.1017-r-H/1000) -z } 2

2

2

2 1/2

2

2 1/2

×

(0.1017) dx dz (b8)

When the cell gets even closer to the surface, the pixel is smaller than the hemispherical depression so that the entire top of the box is a curved surface (see Figure 11c). Equations b9 and b10 can be used for H < 73 nm.

h (nm) ) VS4 )

2‚2‚1000 [V ] 0.335‚0.335 S4

(b9)

∫00.335/2∫00.335/2{-(r2 - x2 - z2)1/2 + r + H/1000} dz dx (b10)

These expressions combine to form the base case curve that was shown in Figure 8. Note Added in Proof. In our analysis of the sensitivity of separation distances determined with TIRAF to cell parameters, we were incorrect in assuming that the refractive index of the cell envelope could not be greater than that for the quartz substratum. Using a wider range for this parameter changes the numerical results presented in the Sensitivity Analysis section and Combination of Errors for Bacteria and Liposomes section of this paper by about 10% or less (some numbers increase and others decrease). However, these changes do not affect the conclusions drawn. LA0117855