Modeling and Measuring the Elastic Properties of an Archaeal Surface

JOURNAL OF BACTERIOLOGY, June 1996, p. 3106–3112 0021-9193/96/$04.0010 Copyright q 1996, American Society for Microbiology

Vol. 178, No. 11

Modeling and Measuring the Elastic Properties of an Archaeal Surface, the Sheath of Methanospirillum hungatei, and the Implication for Methane Production† W. XU,1 P. J. MULHERN,1 B. L. BLACKFORD,1 M. H. JERICHO,1 M. FIRTEL,2

AND

T. J. BEVERIDGE2*

1

Physics Department, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 and Department of Microbiology, College of Biological Science, University of Guelph, Guelph, Ontario, Canada N1G 2W12 Received 20 November 1995/Accepted 8 March 1996

We describe a technique for probing the elastic properties of biological membranes by using an atomic force microscope (AFM) tip to press the biological material into a groove in a solid surface. A simple model is developed to relate the applied force and observed depression distance to the elastic modulus of the material. A measurement on the proteinaceous sheath of the archaebacterium Methanospirillum hungatei GP1 gave a Young’s modulus of 2 3 1010 to 4 3 1010 N/m2. The measurements suggested that the maximum sustainable tension in the sheath was 3.5 to 5 N/m. This finding implied a maximum possible internal pressure for the bacterium of between 300 and 400 atm. Since the cell membrane and S-layer (wall) which surround each cell should be freely permeable to methane and since we demonstrate that the sheath undergoes creep (expansion) with pressure increase, it is possible that the sheath acts as a pressure regulator by stretching, allowing the gas to escape only after a certain pressure is reached. This creep would increase the permeability of the sheath to diffusible substances. lecular bonding (3, 8). However, thus far it has been impossible to extrapolate these data to a more complete understanding of how these features fit together and are physically expressed in the complete structure. One way to understand this complexity is to determine the elastic properties of such a surface. The degree of elasticity will be a function of chemical makeup and bonding and of the combination of the various structural components with one another. Furthermore, because the walls of bacteria can be easily isolated and purified, they are convenient biological structures for elasticity measurements with an atomic force microscope (AFM). Such measurements can then be extrapolated to other macromolecular assemblies. An analysis of a single-layered structure is a necessary precursor to understanding more complex measurements on multilayered bacterial surfaces and intact bacterial cells. For this reason, we have chosen to initiate such a study on the sheath of Methanospirillum hungatei GP1 since it is a proteinaceous single-layered structure of unusual strength (6, 15, 16). It has high cross-beta structure (20), which maximizes protein bonding, it is paracrystalline, and it has oblique symmetry (Fig. 1); all of these attributes make the elastophysical properties easier to interpret and understand. In addition, the sheath has already been characterized by scanning probe microscopy (5, 7, 17) and is one of the few microbial surfaces that has been so studied (9). It is therefore a good starting point before more complex bacterial surfaces (such as those of gram-positive and gram-negative organisms) are attempted. M. hungatei possesses a complex surface architecture. The cell wall consists of a simple S-layer with hexagonally arranged subunits 15.1 nm apart (10). At the ends of each cell there reside multilamellar spacer or terminal plugs with the various layers so interdigitated that a complex moire´ pattern is produced (4, 11). The cells are arranged end to end and are held in place by an encompassing layer, the sheath, which forms a hollow cylinder in which the cells reside. The sheath is the outer most surface layer through which all nutrients (e.g., H2 and CO2) and wastes (e.g., CH4) must pass.

The physical properties of biological material at the cellular and subcellular level have traditionally been difficult to explore at the level of a single cell, especially for such small cells as bacteria. Bacteria, unlike eucaryotic cells, depend entirely on the diffusion of soluble nutrients and wastes into and out of their cell substance for their livelihood (2). Bacterial cytoplasms contain an impressive array of electrolytes and organics and ;80% water (2). Their boundary protein-lipid bilayer, the plasma or cytoplasmic membrane, is energized and is responsible for the maintenance of cytoplasmic concentrations. Since water concentration is kept low compared with that in the external milieu, a substantial turgor pressure can be developed against the cytoplasmic side of the membrane (2, 12, 13). Yet the membrane must remain fluid and malleable to retain its vital functions and is therefore not a good pressure containment vessel for the cell. Because of this, bacteria possess external layers above the plasma membrane to help buoy up the membrane as it resists turgor pressure. This additional structure, usually the cell wall, is firmly knit together by a combination of strong (e.g., covalent and H-bonding) and weak (e.g., ionic, van der Waals, and hydrophobic) interactions. Bacterial walls can consist of a variety of polymeric substances, and their structural and biochemical format depend on the taxonomic group to which they belong (1). Almost without exception, one of the prime duties of walls is to resist turgor pressure and therefore stop osmotic lysis (12). Interestingly, it is precisely this osmotic problem which b-lactam antibiotics (e.g., penicillin) take advantage of. They inhibit the incorporation of new material (peptidoglycan) into the wall, thereby stopping growth and initiating lysis (8). It is therefore important to better understand the physical properties of bacterial surfaces. We often know their chemical makeup and their physical ultrastructure, and we can even estimate macromolecular intra- and intermo* Corresponding author. Phone: (519) 824-4120, ext. 3366. Fax: (519) 837-1802. Electronic mail address: [email protected]. † This article is dedicated to Max Firtel, who died suddenly of intestinal cancer on July 6, 1995, near the completion of this research. 3106

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FIG. 1. A transmission electron microscope image of a negatively stained surface of the M. hungatei sheath. The longitudinal axis of the sheath is at right angles to the hoop boundaries, which are indicated by the arrowheads. For our elasticity calculations, we assumed that the sheath was most flexible along the longitudinal axis and would stretch in the directions of the arrow.

MATERIALS AND METHODS The general aspects of the method have been presented previously (24). The essential element of the method is the use of a hard substratum that contains grooves that are narrow compared with the width or the length of the material to be investigated. In our experiments, the substrate was a Ga-As plate which contained an array of 300-nm deep grooves that were 700, 500, and 300 nm wide. Sheaths of M. hungatei GP1 were isolated as previously outlined by Sprott and McKellar (19) and suspended in deionized water, and a small drop was placed on the Ga-As plate. This drop was partially dried with filter paper and then air dried. This resulted in many intact sheaths being suspended over the grooves. An example of such a sheath bridge is shown in Fig. 2a. In an experiment, an area of the grating was scanned with minimum force to locate a suitable sheath bridge and to measure its width and thickness. One method of measuring the elastic properties of the sheath involved placing the AFM tip on a suspended section of a sheath near the middle of a groove. Deflection of this region was then measured as the tip force was varied. Most measurements of the sheath deflection, however, were made by collecting images of the sheath bridge and the neighboring support areas under progressively increasing tip forces. The net depression of the center of the sheath relative to the supports was obtained from computer-generated cross sections through these images. The general arrangement for the force measurement is shown schematically in Fig. 2b. Increasing the loading force, F, by the tip increased the depression, d, of the sheath relative to the grating supports. Our AFM cantilevers had force constants of 0.16 to 0.76 N/m. If the response of the material to the applied force is elastic and if the sheath does not slip on the grating supports, then the cantilever deflection as a function of the applied force can give information about the elastic properties of the suspended material. To confirm elastic behavior, the loading force was cycled from small to large and back to small, and only results on those sheath bridges where the deflection returned close to the original deflection under small loads were evaluated.

RESULTS General considerations and modeling. The sheath of M. hungatei resembles a long, hollow tube that collapses when dried onto a surface. It consists of a number of hoop-like structures that are stacked on to one another to form the hollow tube. The hoops and their crystalline appearance can readily be seen by transmission electron microscopy of negatively stained specimens (Fig. 1). When deposited on a surface such as the Ga-As grating, the sheath is collapsed, and it must be treated as a double layer 18 nm thick and 650 nm wide (17).

FIG. 2. (a) A scanning tunneling microscope image (2,100 by 3,000 nm) of a sheath suspended over a 300-nm-wide gap in a Ga-As substrate. (b) Schematic arrangement for the force measurement on the sheath. The AFM tip applied a loading force, F, near the center of the span and causes a deflection, d, of the membrane relative to the Ga-As grating. The measured tip forces and corresponding sheath depressions allow a determination of the elastic modulus with the help of equation 9.

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FIG. 3. (a) Sketch of a sheath bridge of wideth w0 that is stretched over two grating support ridges at a distance of 2L0 apart. The tip loading force at the center results in a tip contact radius rt. Most of the strain from the tip loading is taken by the two trapezoidally shaped regions shown in light gray shading. The unshaded regions were assumed to remain essentially unstrained. (b) Diagram illustrating the straining of an elemental wedge for which w0/L0 ,, 1.

This particular sheath (and others) were sufficiently long that they followed the contours of neighboring grooves and appeared well anchored to the substratum. Forces up to 1027 nN were applied and gave depression distances d up to 20 nm. For tip forces of this magnitude and for a tip radius of 20 nm, the tip can form a small depression in the substratum at the location of the tip. This indentation of the Ga-As substrate was calculated, and a small correction was applied to the measured deflections of the sheath (for the appropriate formula for a spherical indentor, see reference 22). The larger the elastic modulus is, the smaller is the indentation. The measured modulus of the sheath was significantly larger than that of Ga-As, and indentation correction for the sheath was therefore neglected. Determination of the elastic properties for simple materials such as those in the shape of a fiber is more straightforward than for the case of a biological membrane such as the M. hungatei sheath. A fiber that possesses rigidity can, when suspended over a groove, be modeled as a beam supported at both ends, and the elastic properties of b-chitin fibers with cross sections down to 20 3 40 nm2 have been determined by this beam deflection method (24). For samples in the shape of a membrane such as the sheath, interpretation of the elastic properties from the deflection measurements is more complicated. Before such measurements could be made, we felt it appropriate to test a simpler system that could be scaled up to centimeter dimensions. The test system used was a plastic film that was clamped between two supports. The dimensions of film width, gap width, and indentor radius were scaled to the corresponding quantities used for the measurements on the bacterial sheath. The sheath, however, was proportionately thicker than the plastic film. The model developed below agreed well with the measurements on the plastic films and suggested that application of the model to an actual membrane was reasonable. Relationship between sheath depression and applied force. Biological membranes, such as the sheath, readily conform to the underlying substratum; thus, they appear to have negligible rigidity, and so only tensile forces should be of importance.

The simplest way to characterize the elastic behavior of such a system is through the extensional or Young’s modulus, E. If the material is in the form of a thin strip of length L, uniform width w, and thickness t, and one end is fixed to a support while a loading force, T, is applied to the other end, then the applied stress s [ T/wt is related to the resulting strain h [ (ε/L) by the relation s 5 Eh. A measurement of the net stretch, ε, of the strip for an applied force along the strip thus allows one to calculate its elastic modulus, E, if the dimensions of the strip are known. The suspended sheath has two sides fixed and two sides free, and the description of the elastic behavior for a membrane supported in this way is considerably more complicated than for the strip of uniform width discussed above. The problem can be simplified if it is noticed that for a load applied over a small region near the geometric center of the membrane bridge, the two triangularly shaped regions that are bounded by the free sides are essentially unstrained. Most of the strain is therefore taken by the two trapezoidally shaped regions shown shaded in Fig. 3a. This can be demonstrated simply by clamping a stretched piece of plastic wrap between two supports and putting a small weight on the center. The problem then reduces to a calculation of the strains in a trapezoidally shaped membrane when a force, T, is applied at the narrow end (Fig. 3b). If the ratio of the width of the wide end, W0, to the length of the trapezoid, L0, is much less than unity, then the tension or the force per unit length is approximately constant in the direction perpendicular to the direction of the applied force. In that case, the total extension (ε) of the trapezoid is given by ε 5 T L0/(weffE t)

(1)

where the effective width weff is weff 5 (w0 2 w1)/[ln(w0/w1)]

(2)

On the other hand, if w0 . L0, then the tension is no longer uniform across the membrane but is largest near the central region. To obtain an estimate of the total stretch of the membrane for an applied load at the center and hence an estimate

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FIG. 4. Diagram illustrating how the strain-carrying section of the sheath is divided into wedge-shaped sections for the purpose of calculating the sheath depression as function of the loading force. The dashed circle at the center represents the tip contact circle.

for the deflection of the AFM cantilever, we divided the principal trapezoidal regions into sections each of angular width du as shown in Fig. 4. Each section is bounded by the groove edge on one end and by a circular arc that represents the contact circle of the AFM tip on the other end. Each angular section is now treated as an independent trapezoid of mean length Li 5 L0/cos(u). The effects of shear distortions in the membrane are therefore neglected. An applied load that stretches the central trapezoid by an amount Dlc will stretch the trapezoid at the angular position u by an amount Dli 5 Dlccos(u). The loaded membrane is therefore assumed to remain flat. If the membrane is treated as an elastically isotropic sheet characterized by a single modulus (Young’s modulus), then the strain for the ith section is Dli/Li 5 (Ti/E Sieff t) du

(3)

The tension per unit angle in the ith section in terms of the tension in the central section is then given by Ti 5 Tc(Sieff/Sceff) cos2(u)

(4)

Following equation 2, the effective width of the ith section Sieff in equations 3 and 4 is given by Sieff 5 (L0/cos(u) 2 rt)du/{ln[L0/rtcos(u)]}

(5)

where rt is the tip contact radius. The component of Ti that is in the plane of the membrane and perpendicular to the groove edge, Tiv, is Tiv 5 Tc cos2(u)/{1 2 ln[cos(u)]/ln(L0/rt)} for L0/rt .. 1

(6)

The total tensile force, T, perpendicular to the groove edge is T 5 2 *0um Tivdu

(7)

where um is the maximum angular width for the membrane. The logarithmic term in equation 6 is zero when u 5 0 and makes a contribution for exceptionally wide membranes only when um is near 908. The logarithmic term in equation 6 was therefore neglected in the integration. We then obtain the following approximate expression for the tension per unit angle:

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FIG. 5. Plot of the ratio of loading force, F, to depression distance, d, versus the square of the depression distance for the simulation experiments with plastic films. h, film with the unstrained regions cut out; ■, whole film.

Tiv 5 T cos2(u)/f(um)

(8)

where f(um) 5 um 1 1/2 sin(2um). If the principal trapezoidal regions remain plane after a load is applied, then the extension Dlc of the central section can be related to the total membrane depression relative to the substrate, d, by simple geometry and Dlc 5 (d2 2 d02) 2L0, where d0 is the initial sag of the membrane under zero load. The loading force, F, equals 2Td/L0, and applying equations 3 and 8 to the central section suggests the following relationship between applied force and membrane depression: F/d 5 f(um)E t(d2 2 d02)/[L02ln(L02ln(L0/rt)]

(9)

As stated before, to test the validity of equation 9, we performed loading experiments on suspended plastic films. The widths of the suspended film and of the gap, as well as the radius of a spherical loading device, were scaled to the dimensions of the sheath, to the groove width in the Ga-As substrate, and to the AFM tip radius. Two types of experiments were performed. In the first type, a complete film spanned the gap. In the second type of experiment, the weakly strained triangular regions (the unshaded regions in Fig. 3a) were cut out of the film so that at the center, a 2-cm-wide region equal to the diameter of the spherical indentor remained. For both types of sample films, the depression depth at the center (as function of an applied load) was measured. The results are plotted in Fig. 5 in the form suggested by equation 9. For both types of sample, the data were well represented by equation 9, and the results supported the various assumptions made in the derivation of equation 9. The slope of the lines in Fig. 5 permit a determination of the Young’s modulus of the plastic films. The values obtained for the intact and cut films were 1.0 (6 0.1) 3 108 N/m2. A direct modulus measurement on a narrow and uniformly wide strip of the film suspended vertically and loaded at one end gave a value of 1.18 (6 0.2) 3 108 N/m2, in good agreement with the value presented above. For the simulation, the contact radius of the spherical indentor could be determined directly by viewing the indentor through the transparent film. Elasticity measurement of the M. hungatei sheath. The agreement between equation 9 and the data of the simulation

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FIG. 6. Plot of F/d versus d2 for the experimental data on a sheath bridge.

experiments gave us confidence to apply the model to the sheath suspended over a groove in the Ga-As substratum. Figure 6 shows a plot of F/d versus d2 for a sheath bridge. The deflection of the sheath bridge was measured relative to the grating substratum, and the loading force was calculated with the help of the experimentally determined cantilever force constant. In this type of experiment, the elastic modulus of the substratum is generally assumed to be high, and so substratum indentation by the tip can be neglected. The Young’s modulus of Ga-As was 7 3 109 N/m2, and substratum indentation effects were significant for the higher forces used in this experiment. The sheath deflections were therefore corrected for the indentation of the Ga-As reference surface with the help of standard indentation formulas (22). Although the scatter in the data is larger than in the simulation, a definite linear relationship is nevertheless evident. Results such as those shown in Fig. 6 on a number of sheath bridges suggested that the initial sag of the sheath was around 6 to 11 nm, while the slope ranged from 1.3 3 1016 to 2.4 3 1016 N/m3. DISCUSSION Limitations and advantages of the AFM depression technique for measuring elasticity of bacterial systems. These are the first AFM elasticity measurements of a procaryotic surface, and they show that the depression technique described here is a complement to the indentation method (21, 22). The depression technique should be particularly helpful for the study of elastically and compositionally anisotropic systems such as bacterial walls. For example, gram-positive walls are not isotropic and consist of several components such as peptidoglycan, teichoic and teichuronic acids, and (commonly) additional layers such as S-layers or capsules (1, 3). Gram-negative walls are even more complex possessing a bilayered outer membrane and thin peptidoglycan layer (1, 3). Even more simple isolated structures, such as the M. hungatei sheath, are not of a uniform composition since small amounts of specialized proteins are required for rigidity and as a cementing matrix for the hooplike regions of S-protein (15, 16, 18). Our depression technique can be used for such anisotropic systems; it can even be used to estimate bond strength in anisotropic systems and to investigate the yield of materials at the elastic limit. The modulation technique as devised by Radmacher et al. (14) that measures

the amplitude and phase of the cantilever in response to a vibrating sample also works best with soft samples. The specific case of the M. hungatei sheath. The calculations of the elastic modulus from those slopes generated by our study (Fig. 6) required a knowledge of the AFM tip contact radius on the sheath. Unlike the simulation case, determination of the contact radius on the sheath could have been a difficult problem. We overcame the problem by examining the shape of the scan lines at the edges of the grooves. These edges were sufficiently steep that the broadening of the image of the edge was presumably due to the tip shape. For the data in Fig. 6, the tip had a radius of curvature of 20 nm. The contact radius can be affected by the tilt angle of the sheath relative to the horizontal, by the elastic tip indentation depth into the sheath, by surface roughness of the sheath, and possibly by inelastic effects that may produce a deep local sheath depression at the location of the tip. For small loading forces and those cases in which the membrane depression approximately follows equation 9, the inelastic effects will be unimportant. We estimate that the contact radius for membrane (sheath) tilt and for elastic indentation was at most 4 nm. Our AFM and (previous) scanning tunneling microscope images of the sheath surface showed surface undulations with a period comparable to the tip diameter and with an amplitude of up to 3 nm (5, 7, 17, 23). With the tip located in such a surface depression, the average contact radius would be ;12 nm and could be no more than 20 nm. For the center of an intact sheath which is double layered (i.e., one layer of the cylinder has collapsed over top of the other), the contact radius would be 21 to 29 nm and f(um) would be '1.5. Using these values, Fig. 6 gives a Young’s modulus range of 3.3 3 1010 to 3.9 3 1010 N/m2 for the Methanospirillum sheath. The foregoing analysis assumes that the sheath could be treated as being elastically isotopic. However, there is evidence that considerable anisotropy may exist. For example, the sheath consists of a number of hoop-like structures (Fig. 1) which are cemented together by distinct adhesive polypeptides; the sheath can be decomposed into its constituent hoops by appropriate chemical treatment (15, 16, 18). These individual hoops resist further chemical dissolution unless harsh covalent bond-breaking agents are used (6, 15, 16). Furthermore, many transmission electron microscope, scanning tunneling microscope, and AFM images of collapsed sheath tubes clearly show that the sheath tends to fracture along hoop boundaries and only infrequently across the hoops. This finding suggests that the internal bonding between the particles within each hoop is stronger than the bonding between hoops. In that case, one might expect most of the stretch in the sheath under an applied load to come from the bonding elements that bind hoops to each other. To estimate the magnitude of the dilation of the gaps between hoops, we assumed that the sheath was most flexible along the tube’s longitudinal axis but essentially unstretchable in the direction perpendicular to the hoops (Fig. 1). The hoops were assumed to be coupled together by springs of spring constant, k, that are spaced at a distance, s, apart and that undergo extension when a tensile force is applied (23). The average hoop width is 15 nm (15, 16), and then ;10 hoops can be accommodated between the groove wall of the Ga-As substratum and the groove center (Fig. 2). A modified version of the trapezoidal model together with the experimentally determined net stretch of the sheath of 1.6 nm for an applied force of 1027 N gave hoop separations of '0.04 nm for the hoop gap nearest to the groove wall and '0.3 nm for the gap nearest to the tip (in the estimate, it was assumed that the tip was located at the center of a hoop). The analysis further gave k/s ' 1.4 3 1010 N/m2 for the hoop coupling region. The results

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suggested that hoops may separate by several angstroms (1 Å 5 0.1 nm) before fracture of interhoop bonds occurs. Biological significance of elasticity measurements. This is the first time that an elasticity measurement has been made on a bacterial surface by AFM, and it represents a starting point for similar studies on more complex microbial surfaces, including those on living cells. It is one of the very few pressuremeasuring techniques that can be used on such minute individual cells and (as this study shows) on their isolated boundary layers. M. hungatei is a bacterial cell which possesses a remarkable number of external layers above the plasma membrane (10, 11, 18–20). The sheath is the outermost boundary layer, and it is the most resilient; the sheath is responsible for maintaining the rod shape of each cell (4, 10) as well as, by its innate porosity, for dictating what compounds can diffuse to and from the cell (4). Carbon metabolism for this methanogen requires small, simple substrates (H2 and CO2; although, through laboratory adaptation, strain GP1 can now also use acetate) which develop an equally small, simple waste product (CH4). The lattice constant of the subunits that compose the sheath is 2.81 nm (a 5 5.66 nm, b 5 2.81 nm, and g 5 85.6 [20]) so that a relatively impermeable protein meshwork is produced. The size of diffusible compounds is thought to be limited by the diameter of the pores that exist between the subunits (4), a diameter that just approaches the molecular size of H2, CO2, and CH4 (4, 20). It is possible that the sheath acts as a pressure vessel which regulates pressure for the bacterium. The concentration of intracellular CH4 could build up at this boundary layer during carbon metabolism until a threshold pressure level was attained, at which point the sheath would be subjected to creep, or expansion. This would stretch the size of the pores in the sheath, making it more permeable for the exit of CH4 and the entry of H2 and CO2. Previous experiments showed that for an AFM tip with a tip radius of 20 nm, the sheath was punctured when the tip force exceeded 1027 N (24). From this value and our calculated range of tip contact radii, we estimate a limiting boundary layer tension of between 3.5 and 5.0 N/m. Since the diameter of the bacterium is ;440 nm, this value for the tension implies a maximum sustainable internal pressure for the sheath of 300 to 400 atm. The sheath, therefore, appears to have more than adequate structural strength to resist those internal turgor pressures that have been determined for both gram-positive (20 to 50 atm) and gram-negative (3 to 5 atm) eubacteria (2, 12, 13). Although the tensile strength of the sheath may be different in a fully hydrated environment, we nevertheless suggest that M. hungatei may be capable of developing internal pressures approaching hundreds of atmospheres which are sustained by its boundary sheath. As these pressures develop, the sheath would have a limited capacity to expand, thereby making it easier for molecules to pass through. It may be too simplistic to envision overall sheath expansion since the hoop boundaries could be the most expandable regions. If these junctions are more prone to expansion, then the sheath would stretch only along the longitudinal axis (Fig. 1). Our value of 1.4 3 1010 N/m2 for k/s implies that an internal pressure increase of 10 atm would expand each hoop juncture by 0.01 nm. Higher pressures would increase the separation much more (i.e., 400 atm 5 0.4 nm). It must also be recognized that for the entire cellular filament to act as a pressure vessel which is regulated by the sheath, we must also explain the function of the terminal and spacer plugs that separate the individual cells along the sheath tube. These plugs are lamellar and contain a number of different layers of different permeabilities (11). Although they are more permeable than the sheath, small molecules, such as

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those used in the Gram stain, can penetrate only into the terminal cells of each filament (4). The spacer plugs and the tight fit of subsequent cells inhibit additional diffusion down the length of the filament. Therefore, all interior cells must be in a diffusion-restricted environment that is mediated by the porosity of the sheath. It is possible that interior pressure buildup by methane and subsequent sheath expansion alleviate this problem for all necessary diffusible compounds. ACKNOWLEDGMENTS We thank Avila Cox for performing the elastic measurements on the plastic films. This work was supported by a grant from the National Science and Engineering Research Council of Canada to M. H. Jericho and B. L. Blackford and by a grant from the Medical Research Council of Canada to T. J. Beveridge. During part of this research, T. J. Beveridge was supported by the Canada Council as a Killam Research Fellow, and travel was made possible by a B. C. Matthews Alumni Fellowship from the University of Guelph. REFERENCES 1. Beveridge, T. J. 1981. Ultrastructure, chemistry and function of the bacterial wall. Int. Rev. Cytol. 72:229–317. 2. Beveridge, T. J. 1988. The bacterial surface: general considerations towards design and function. Can. J. Microbiol. 34:363–372. 3. Beveridge, T. J., and L. L. Graham. 1991. Surface layers of bacteria. Microbiol. Rev. 55:684–705. 4. Beveridge, T. J., G. D. Sprott, and P. Whippey. 1991. Ultrastructure, inferred porosity, and Gram-staining character of Methanospirillum hungatei termini describe a unique permeability for this archaeobacterium. J. Bacteriol. 173: 130–140. 5. Beveridge, T. J., G. Southam, M. H. Jericho, and B. L. Blackford. 1990. High-resolution topography of the S-layer sheath of the archaebacterium Methanospirillum hungatei provided by scanning tunneling microscopy. J. Bacteriol. 172:6589–6595. 6. Beveridge, T. J., M. Stewart, R. J. Doyle, and G. D. Sprott. 1985. Unusual stability of the Methanospirillum hungatei sheath. J. Bacteriol. 162:728–737. 7. Blackford, B. L., W. Xu, M. H. Jericho, P. J. Mulhern, M. Firtel, and T. J. Beveridge. 1994. Direct observation by scanning tunneling microscopy of the two-dimensional lattice structure of the S-layer sheath of the archaeobacterium Methanospirillum hungatei GP1. Scanning Microsc. 8:507–512. 8. de Pedro, M. A., J. V. Ho¨ltje, and W. Loffelhardt. 1993. Bacterial growth and lysis: metabolism and structure of the bacterial sacculus. Plenum Press, New York. 9. Firtel, M., and T. J. Beveridge. 1995. Scanning probe microscopy in microbiology. Micron 26:347–362. 10. Firtel, M., G. Southam, G. Harauz, and T. J. Beveridge. 1993. Characterization of the cell wall of the sheathed methanogen Methanospirillum hungatei GP1 as an S-layer. J. Bacteriol. 175:7550–7560. 11. Firtel, M., G. Southam, G. Harauz, and T. J. Beveridge. 1994. The organization of the paracrystalline multilayered spacer-plugs of Methanospirillum hungatei. J. Struct. Biol. 112:160–171. 12. Koch, A. 1983. The surfaces stress theory of microbial morphogenesis. Adv. Microbial Physiol. 24:301–367. 13. Koch, A. L., and M. F. S. Pinette. 1987. Nephelometric determination of osmotic pressure in growing gram-negative bacteria. J. Bacteriol. 169:3654– 3663. 14. Radmacher, M., R. W. Tillman, M. Fritz, and H. E. Gaub. 1992. From molecules to cells: imaging soft samples with the atomic force microscope. Science 257:1900–1905. 15. Southam, G., and T. J. Beveridge. 1991. Dissolution and immunochemical analysis of the sheath of the archaeobacterium Methanospirillum hungatei GP1. J. Bacteriol. 173:6213–6222. 16. Southam, G., and T. J. Beveridge. 1992. Characterization of novel, phenolsoluble polypeptides which confer rigidity to the sheath of Methanospirillum hungatei GP1. J. Bacteriol. 174:935–946. 17. Southam, G., M. Firtel, B. L. Blackford, M. H. Jericho, W. Xu, P. J. Mulhern, and T. J. Beveridge. 1993. Transmission electron microscopy, scanning tunneling microscopy, and atomic force microscopy of the cell envelope layers of the archaeobacterium Methanospirillum hungatei GP1. J. Bacteriol. 175:1946–1955. 18. Sprott, G. D., T. J. Beveridge, G. B. Patel, and G. Ferrante. 1986. Sheath disassembly in Methanospirillum hungatei strain GP1. Can. J. Microbiol. 32:847–854. 19. Sprott, G. D., and R. C. McKellar. 1980. Composition and properties of the cell wall of Methanospirillum hungatei. Can. J. Microbiol. 26:115–120. 20. Stewart, M., T. J. Beveridge, and G. D. Sprott. 1985. Crystalline order to high resolution in the sheath of Methanospirillum hungatei: a cross-beta structure.

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