Correlation of macroscopic aggregation behavior and microscopic
Journal of Colloid and Interface Science 374 (2012) 70–76
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Correlation of macroscopic aggregation behavior and microscopic adhesion properties of bacteria strains using a dimensionless Tabor’s parameter Xin Wang a, Yueyun Li b, Annalisa Onnis-Hayden b, Ce Gao b, April Z. Gu b, Kai-tak Wan a,⇑ a b
Mechanical & Industrial Engineering, Northeastern University, Boston, MA 02115, USA Civil & Environmental Engineering, Northeastern University, Boston, MA 02115, USA
a r t i c l e
i n f o
Article history: Received 6 November 2011 Accepted 19 January 2012 Available online 31 January 2012 Keywords: Aggregation Adhesion Bacteria AFM Tabor’s parameter
a b s t r a c t Macroscopic adhesion–aggregation, floc formation, and subsequent transportation of microorganisms in porous media are closely related to the microscopic behavior and properties of individual cells. The classical Tabor’s parameter in colloidal science is modified to correlate the macroscopic aggregation and microscopic adhesion properties of microorganisms. Seven bacterial strains relevant to wastewater treatment and bioremediation were characterized in terms of their macroscopic aggregation index (AI) using an optical method, and their microscopic coupled adhesion and deformation properties using atomic force microscopy (AFM). Single cells were indented to measure the range and magnitude of the repulsive–attractive intersurface forces, elastic modulus, thickness and density of the cellular surface substances (CSS). The strong correlation suggests that cost and time effective microscopic AFM characterization is capable of making reliable prediction of macroscopic behavior. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Microbial adhesion–aggregation–transportation is of great importance to various environment processes such as in situ or enhanced subsurface bioremediation [1], filtration processes for water and wastewater treatments [2,3] and protection of drinking water supplies [4]. Metabolic activities of the microorganisms and their phenotypes are conventionally believed to hold the key to control the contaminants’ fate and mobility, as well as transformation and degradation, in changing geochemical conditions [5,6]. Equally important, but by and large ignored, is the mechanical aspects of bacteria aggregation behavior when flowing through a subsurface porous medium. There is an urgent need to understand the fundamental science and mechanics of microbial adhesion– aggregation. Colloid filtration theory (CFT) is a celebrated model for macroscale microbial transport in saturated porous media based on advection–dispersion [7–9], and is widely used to quantify microbial behavior in laboratory and field-scale studies [10–12]. Removal of microbes from the collector (e.g. sand grain) is assumed to be governed by either equilibrium adsorption or the kinetic rate-controlled bacteria attachment to and detachment from the aquifer materials [8,12,13]. Particle–collector interactions are assumed to be weakly attractive with a short range. Notwithstanding its success in many perspectives, CFT prediction often fails to a ⇑ Corresponding author. E-mail address: [email protected] (K.-t. Wan). 0021-9797/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2012.01.032
large extent to match with experimental observations in lab- and field-scales, especially in particle deposition rates [9,10,13–17]. Elimelech et al. shows the necessity of introducing full intersurface potential of the electrostatic double layers developed at the surfaces of both the particle and collector according to Derjaguin –Landau–Verwey–Overbeek (DLVO) theory [18–22]. Despite the improvement, the modified model still misses to factor in other essential features such as the elastic deformation of individual cells associated with adhesion contact. When microorganisms are influenced by strong surface forces, they inevitably deform into distorted shape. Compliant cells with small elastic modulus conform to one another, making the resulting multi-cell aggregate more streamlined to the flow and thus more resistant to segregation. Conversely, rigid cells are less likely to aggregate even in the presence of strong surface forces because of their mechanical resistance to deformation. In addition, the size of a single cell in comparison to the surface force range also plays a critical role. Cells smaller than the force range are fully immersed in the cohesive zone and the entire cell will sense the influence of the substrate, but large cells are only partially influenced by the surface forces. Cell geometry is another relevant quantity. While a spherical cell gives rise to a circular contact with a planar substrate, a cigar shape cell leads to a rectangular contact. In the presence of the same surface force, area of the circular contact is expected to be smaller than the rectangular counterpart because of geometrical constraints and rigorous solid mechanics calculation [23–25]. A comprehensive adhesion-detachment mechanics model capable of predicting bacteria aggregation and transportation must therefore fully account
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for the combined effects of cell wall stiffness, deformation mode, magnitude and range of surface forces, and cell size and geometry. Such model is not available in the literature. In this paper, we establish a new dimensionless parameter, l, based on the conventional Tabor’s parameter in classical adhesion and colloidal science [26,27], to relate the macroscopic cell aggregation to the microscopic mechanical properties of single cell and inter-particle and particle–collector interfacial adhesion energy. A positive correlation between the macro- and micro-behavior thus allows one to make reliable prediction of the macroscopic aggregation based on merely microscopic characterization of single cells that is both time and cost effective. As a demonstration, we chose seven representative bacterial strains commonly found in domestic wastewaters or polluted sites, which possessed a wide range of aggregation behavior. Macroscopic characterization of these strains was performed by an optical method and image analysis to assess their ability to adhere and aggregate. Microscopic mechanical properties are measured by nano-indentation of single cells using atomic force microscopy (AFM), which yields information of range and magnitude of repulsive–attractive surface forces, elastic modulus of cell, and thickness and density of the cell surface substance (CSS) molecules etc. 2. Methods and materials Seven vastly different bacteria strains were chosen for this study based on their relevance to environment and human health, and their natural differences. Some of these strains were isolates from activated sludge samples obtained from the aeration basin of Clemson Municipal Wastewater Treatment Plant [28], and others are relevant to subsurface bioremediation. Special features are listed as follows: (i) K: Comamonas testosteroni is aerobic and is capable of mineralization of the common pollutant 3-chloroaniline (3-CA) [29], (ii) Q: Aeromonas punctata is aerobic and is reported to be associated with human diseases including gastroenteritis, cellulitis and peritonitis [30]. (iii) A: Raoultella ornithinolytica is aerobic and is found to be a major cause of histamine fish poisoning [31]. (iv) H: Bacillus cereus is aerobic and is a common culprit in food poisoning, causing both intoxications and infections [32]. (v) SH2: Shewanella putrefaciens CN32 is an anaerobic strain belonging to DMRB (Dissimilatory metal reducing bacteria). It is capable of reducing various metals and radionuclides including Fe (III) and Mn (III/IV) abundant in sediment and U (VI), Cr (VI), Co (III), and Tc (VII) cations in aqueous environment [33]. (vi) SH1: Shewanella Oneidensis MR-1 is another anaerobic DMRB and is capable of reducing a wide range of organic compounds, metal ions, radionuclides and associated metal/ organic contaminants [34]. (vii) Des: Desulfovibrio vulgaris is an anaerobic strain. Its ability to reduce sulfate, sulfite, thiosulfate and nitrite in anaerobic subsurface environments puts it to the forefront of biological research [35].
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mented with a mixture of 10 mM sodium lactate as an electron donor and 10 mM sodium fumarate as an electron acceptor at 30 °C in a glove box (Coy Laboratory Products, Grass Lake, MI) with an atmosphere of 5% hydrogen/nitrogen balance. Strain Des was grown anaerobically in ATCC medium 1249, modified Baars’ medium for sulfate reducers. Cells were harvested by centrifugation during exponential growth phase, and growth curves were obtained to determine the sampling time. 10 ml of aliquot suspension was pipetted out of the bottles and into 15 ml tubes for optical and mechanical characterization. 2.2. Macroscopic aggregation: optical quantification and image analysis The macroscopic aggregation capacity of bacteria was characterized using a prescribed assay [36] and was measured in terms of the aggregation index, AI, which ranges from 0 to 1. Large AI corresponds to high aggregation tendency. 10 ml of sample cells were harvested in the exponential growth phase by centrifugation (11000g for 10 min), washed twice with buffer solution (3 mM NaCl containing 0.5 mM CaCl2), and suspended in the same solution. The sample was exposed to a beam of laser with wavelength k = 660 nm to measure the optical density OD using a plate reader (Synergy HT Multi-Mode, Biotech, Winooski, VT). By adjusting the cell concentration using the same buffer solution, the initial optical density, ODtot, of the suspension was adjusted to about 0.30. The sample was then immediately centrifuged at 650g for 2 min, and optical density of the carefully pipetted supernatant was measured as ODs. The aggregation Index (AI) is defined as:
AI ¼
ODtot ODs 100% ODtot
ð1Þ
Should the cells become resistant to aggregation, they remain scattered in colloidal form such that ODs ODtot and AI 0. Conversely, formation of flocs or multi-cell aggregates facilitates passage of optical beam and thus raises the optical transmission and AI. To estimate the average dimension of an aggregate, cell suspension was dispersed on a glass slide, and stained with 1 lg/ml 40 , 6-diamidino-2-phenylindole (DAPI) for 10 min. The settling multi-cell aggregates were observed in situ by fluorescent microscopy (Zeiss, Axio Imager M1-1). At least 20 micrographs were taken at different locations for each sample. Fig. 1a shows typical multi-cell aggregates of Strains Q and H. Based on DAPI signal, the analytical software AxioVision Rel4.8 was used to map the irregular shape of an aggregate. Diameter of a circle having the same area as the circumscribing region was taken as the nominal aggregate dimension. Fig. 1b shows a cumulative frequency plot of cell aggregates with diameter smaller than or equal to different nominal aggregate diameters. The equivalent aggregate diameter was determined as the value at cumulative frequency of 50%. Measurement was repeated for each strain. Number of single cells in each aggregation was estimated by dividing the average aggregation area by the mean single cell area. Note that the estimates here did not consider the 3-D geometry and dimension of the aggregates, though we believe the 2-D correspondence is sufficient for the purpose of evaluating the correlation of aggregation trends with cellular surface properties.
2.1. Sample preparation
2.3. Microscopic characterization of single cells: AFM indentation
The four aerobic strains K, Q, A, and H were cultured in Luria– Bertani (LB) media (Sigma-Aldrich, Inc., St. Louis, MO) in 500 ml bottles (Corning, Inc., Corning, NY) at 37 °C placed on shaker of 200 RPM until they reached stationary phase. The facultative anaerobic strains SH1 and SH2 were grown in LB medium supple-
A 15 ml strain suspension in a stationary phase culture was pelleted by centrifugation, washed in the same volume of nanopore deionized water, pelleted a second time, and promptly re-suspended in 5 ml deionized water. 3 ml of the solution was pipetted onto a gelatin treated cleaved mica surface (Sigma #G-6144). The
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(a)
(b)
Fig. 1. (a) Typical fluorescent optical images. Top micrograph shows Strain Q Aeromonas Punctata aggregates along with the circular envelop (dashed curve) to define the equivalent diameter d 8 lm. Bottom micrograph shows highly irregular Strain H Bacillus Cereus aggregate with d 20 lm. (b) Cumulative frequency plot for the nominal aggregate diameter of strain A, 4.9 ± 2.5 lm.
sample was then allowed to settle for 20 min, rinsed, and stored in deionized water, ready for AFM indentation in a liquid cell. To calibrate the spring constant, k, of the AFM cantilever, contact mode indentation on freshly cleaved mica surface in air was repeated 10 times with sweep duration of 1.04 s. From the average force curves, k was determined to be 0.205 ± 0.015 N/m by the Cleveland method [37]. The unloaded resonant frequency in air was calibrated using AFM (Agilent 5500) in tapping mode with frequency range suggested by the manufacturer. The length and width of the cantilever were measured using optical microscopy (Olympus, GX71). Force measurements were repeated on mica surfaces before and after probing the bacteria samples to ensure no contamination of the silicon nitride AFM tip during experiments. As will be seen in the next section, the AFM tip displacement was measured in the order of 100 nm and the maximum applied force was roughly 3–4 nN. Deflection of the stiff AFM cantilever in the 1–20 nm range was negligibly small and will be ignored hereafter. Distance of the piezoelectric cell driving the AFM tip is therefore taken to be the same as the vertical displacement travelled by the AFM tip. A typical cell was first identified by large scan size using low resolution MAC (Magnetic Acoustic Control) Mode. The AFM tip was repositioned approximately over the cell center, before switching from tapping to contact mode. Applied load, F, was measured as a function of the vertical displacement of AFM tip, w. The mechanical response, F(w), was obtained for loading (compression) followed by unloading (tension) of the tip. At least five loading– unloading cycles were performed at different locations close to the cell center to ensure repeatability, and at least some 10 typical cells were characterized in each batch. Measurements during loading were reproducible to a high precision, though unloading led to relatively random intermittent jumps (see later section for explanation). 3. Results and analysis 3.1. Macroscopic measurements of AI Fig. 1a shows two fluorescent microscopy pictures of aggregates of strain Q and strain H. For each bacterial strain, the aggregation
diameter were repeated with n = 20. Strain Q aggregates take on a roughly circular envelop (dashed curve) with an equivalent diameter d 8 lm, while Strain H aggregate shows an irregular envelop with d 20 lm. Fig. 1b is the example of mean nominal aggregation size determination for strain A, which obeys cumulative frequency distribution with d 4.9 ± 2.5 (51% error) lm. Table 1 summarizes the aggregation index, equivalent cell-aggregate diameter, and average number of cells within an aggregate for all strains. In our measurements, the strains are ranked as SH2 < SH1 < Des < K < Q < A < H in terms of the equivalent aggregate diameter, d, average number of cells per aggregate, N, and AI. 3.2. Microscopic: AFM measurements Fig. 2 shows AFM topographical scans of typical representative samples. All strains possess similar prolate geometry with circular cross-section. The long and short axes are denoted by b1 and b2 respectively. Fig. 3 shows representative mechanical responses of three selected strains. Fig. 3a shows F(w) of Strain K. Loading followed path ABCD. As the probe approached the cell surface from a distance along AB, no force was recorded until it touched the surface of the molecular brush of cellular surface substance (CSS) at B. It is not certain whether the AFM tip actually penetrates the CSS, or simply causes the long chain surface biomolecules to fold, stack and compress. In any case, an apparent repulsive force is felt resisting the AFM motion. The distance BC was taken roughly to be the CSS thickness, l. The work done for the tip to penetrate the CSS, or energy barrier, Upen, was given by the area under BC (c.f. Fig. 3b), and the average penetration or external compression was defined as Fpen = Upen/l. Further loading along CD led to the onset of elastic global deformation of the cell. The classical Hertz–Sneddon model is used to compute the cell elastic modulus, which is given by [38]
! 3 1 m2 @F E¼ 3=2 Þ 4 R1=2 @ðw AFM
ð2Þ
with RAFM = 10 nm the radius of curvature of the AFM tip, and m 0.50 the Poisson’s ratio for incompressible polymeric solid. Retraction of the AFM tip led to unloading path DCGH. Little or no
104 (22.1%) 12600 (22.2%) 2.16 (14.3%) 0.73 (8.2%) 39.3 (8.3%) 360 (3.7%) 1590 (18.2%) 0.88 (13.6%) 0.42 (16.6%) 0.18 (5.6%)
568 (4.4%) 2800 (4.6%) 1.15 (35.6%) 0.51 (13.7%) 0.68 (13.2%)
524 (9.5%) 9700 (13.4%) 1.28 (55.0%) 0.78 (19.2%) 1.19 (9.2%) 500 (6.8%) 3980 (30.1%) 2.06 (13.1%) 0.54 (27.8%) 0.94 (12.7%) 900 (3.2%) 2670 (14.9%) 1.47 (26.5%) 0.594 (16.8%) 0.92 (6.5%)
162 (24.7%) 9770 (29.6%) 1.58 (24.6%) 0.80 (11.3%) 11.4 (3.6%)
/ / 1.10 (21.8%) 578 (21.6%) 0.50 (8.0%) 249 (8.8%) 0.58 (5.8%) 209 (5.7%)
0.21 (9.5%) 116 (9.4%)
0.58 (3.4%) 522 (4.0%)
/ /
105 (3.8%) 300 (12.7%) 244 (16.8%) 40.4 (14.8%) 559 (12.9%) 4.4 (11.4%)
415 (9.2%) 41.9 (19.3%)
380 (8.4%) 112 (9.1%)
337 (20.5%) 43.9 (20.5%)
237 (17.7%) 197 (5.6%)
183 (15.8%)
Aggregation index, AI (%) Equivalent aggregate diameter, d (lm) Aggregation number estimation, N Elastic modulus, E (kPa) Adhesion energy, Uad (1018 J) Penetration force, Fpen (nN) Penetration energy barrier, Upen (1018 J) Thickness of CSS (nm) Density of CSS, C (mol/lm2) Length, b1 (lm) Width, b2 (lm) Tabor’s parameter, l
2.3 (26.1%)
6.2 (33.9%)
8.1 (33.3%)
13.7 (45.3%)
14.7 (25.8%)
H
11.3 (30.9%)
Raoultella ornithinolytica (Gram-negative) 72 (4.2%) 4.9 (51%)
A Q
Aeromonas punctata (Gram-negative) 60 (3.3%) 4.2 (47.6%)
K
Comamonas testosteroni (Gram-negative) 51 (3.9%) 4.01 (64.8%)
Des
Desulfovibrio Vulgaris (Gram-negative) 29 (24.0%) 3.0 (73.3%)
SH1
Species
S. Oneidensis MR-1 (Gram-negative) 21 (19.0%) 2.2 (50%)
SH2
S. Putrefaciens CN32 (Gram-negative) 12 (33.3%) 1.04 (42.3%)
Strain
Table 1 Summary of materials and surface properties. Percentage errors are shown in parentheses.
Bacillus cereus (Grampositive) 88 (13.6%) 19 (52.6%)
X. Wang et al. / Journal of Colloid and Interface Science 374 (2012) 70–76
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hysteresis was measured along DC, indicating the elastic recovery of the sample cell. At G, the cell resumed the undeformed geometry and the AFM was fully unloaded with F = 0. Tensile force was needed along GH to pull the tip out from the sample. The zigzagging F(w) showed multiple sudden jumps of the order of 100– 200 pN, corresponding to the detachment of individual or an entangled bundles of CSS (e.g. extracellular polymeric substance EPS) from the AFM tip. At H, the AFM tip ‘‘pulled-off’’ from the cell surface and the external load dropped to zero. The total work done needed to detach the AFM tip was given by the area enclosed, Uad (c.f. Fig. 3c). Fig. 3b shows the mechanical response of strain Q, which is quite different from that of strain K. Upon loading on the cellular surface substance (CSS), the AFM tip measured an increasing compressive load until global deformation of the cell occurred at C. The absence of a force plateau indicated a continual compaction of the cellular surface substance (e.g. EPS) rather than penetration. Elastic recovery was again observed for further loading– unloading. Upon tip retraction, a hysteresis was observed with a smaller repulsive load, and complete detachment occurred further away from the cellular surface due to adhesion. Fig. 3c shows behavior of Strain A. Here CSS was not detectable by AFM, but a significant adhesion was measured. Stepwise detachment was also observed. It is noted that a non-zero loading–unloading hysteresis occurred during the global deformation. In repeated loading–unloading measurements at various positions of the sample batch, the hysteretic loop showed an average of vanishingly small area in F(w). The AFM indentation at this stage is unable to identify whether the non-zero hysteresis is the result of viscoelasticity of the CSS or the cell or possible natural variation of the surface texture. To find the cellular surface substance (CSS) molecular brush density, we resorted to the de Gennes’ steric repulsion model [39,40]. The CSS was treated as a brush of polymer chains impregnated on the cell surface, while the AFM tip was taken to be a bare rigid surface. The total mechanical forces acting on the tip as it penetrated the CSS was given by
2ph F steric 50kB TRAFM C3=2 l exp l
ð3Þ
with kB is the Boltzmann constant, T the absolute temperature, C the effective number density of brush molecules on cell surface, l the equilibrium thickness of the CSS layer, and h is the distance between the bending probe and the deformed cell surface. Table 1 summarizes the measured parameters for all strains under investigation. 3.3. Tabor’s parameter In general, large and compliant cells are expected to be more prone to adhesion and aggregation, especially when the attractive intersurface force is sufficiently strong and the steric repulsion as a result of thick CCS is minimized. In quantitative terms, a higher propensity to aggregation with large AI is expected for large Fad, Uad, b1, and b2, and small Frep, Urep, l and E. For instance, Table 1 shows that strains K and Q are less aggregative (small AI) than A and H, but the four strains have different elastic moduli. It is ideal to derive a universal dimensionless parameter to collectively combine these measureable quantities. We attempt to modify the Tabor parameter [27,41], l, in classical adhesion and colloidal science to fit our needs. When two identical solid elastic spheres of radius Rs come into contact under an external compressive load, F, in the presence of intersurface forces with adhesion energy, c in J m2, a contact circle of radius, c, is formed at the interface. In case of strong but
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Fig. 2. AFM topological scans of four aerobic strains K, Q, A, and H, showing the cigar shape cells and morphological details.
short-range forces between two large and compliant spheres in the Johnson–Kendall–Roberts (JKR) limit, the spheres deform locally at the circular contact edge known as the ‘‘neck’’, and a critical tensile load, F = (3/2)pRsc is needed to detach the adhering spheres at ‘‘pull-off’’. In case of weak but long-range adhesion between two small and hard spheres in the Derjaguin–Muller–Toporov (DMT) limit, the local deformation ‘‘neck’’ vanishes and the ‘‘pull-off’’ force becomes F = 2pRsc. Tabor and then Maugis [27] derived a dimensionless Tabor’s parameter, l = (4Rsc2/9E2y3)1/3, to encompass geometry (Rs), interfacial properties (c), intersurface force range (y), and materials properties of the solid (E). A large l > 2 leads to the JKR limit and a small l < 0.50 corresponds to the DMT limit and the ‘‘pull-off’’ force is bounded between the upper and lower limits of 3/2 6 F/pRsc 6 2. In physical terms, l governs the size of the ‘‘neck’’ and the contact area at adhesion interface as well as the deformability due to adhesion. In the present context, a large l facilitates the large and compliant cells to deform and aggregate, to an extent that the resulting multi-cell aggregates conform to a better hydrodynamic streamlined geometry to resist liquid flow. It is therefore logically expected that a large l leads to large AI and vice versa. Several limitations of the classical l description are noted nonetheless. For instance, bacteria strains comprise glycoprotein shells instead of being homogeneous solids, and they always take on cylindrical geometry instead of being spherical. To circumvent the fine mathematical details to deal with exact geometry and micro-structure, a modified Tabor’s parameter capturing the essential features of the system is defined as
2
l¼
4 2b2 3
l E2
U ad
pR2AFM
31=3
!2
2 25
ð1 v Þ
ð4Þ
Here the cell is taken to be an ellipsoid with the smallest principal radius to be (b2/2), replacing Rs. The adhesion energy c is substituted by the effective adhesion energy Uad divided by the contact area with the AFM tip or pR2AFM . Surface force range is taken to be
roughly the cellular surface substance thickness, l, in that, from where the AFM tip first senses the presence of intersurface forces to AFM tip touching cell surface during loading. The elastic modulus is taken to be some average of the cell wall and cytoplasm of an ideal homogeneous cell. Fig. 4 shows a strong correlation between AI and l. The linear relation justifies l to be a reasonable parameter to correlate the macro- to micro-scale behavior. Simple curve fit yields
AIð%Þ ¼ c1 log10 l þ c2
ð5Þ
with the numerical constants c1 = 33.03 ± 2.24 and c2 = 37.79 ± 2.65. Should l of an arbitrary strain be determined by AFM measurement, the macroscopic aggregation index can be estimated by Eq. (5). A large Tabor’s parameter corresponds to a high propensity to aggregate. 4. Discussion Microscopic characterization of single cells using AFM is attractive in the environmental engineering community. Conventional macroscopic measurements using optical transmission and packed columns are both expensive and time consuming for the virtually millions of different bacterial strains in the contaminated sites around the globe. The cost and time effective AFM indentation thus presents a promising method to make sensible and reliable prediction of the macroscopic behavior of aggregation–transportation of microbes. In spite of the fair correlation between the micro- and macroproperties via the modified Tabor’s parameter, some cautions should be taken. For instance, the intersurface potential at the cell–cell and cell–substrate interfaces are loosely defined as the attractive force measured by AFM, rather than resorting to the well established DLVO theory [42]. Spontaneous build-up of electrostatic double layers on surface of cell and colloidal particles in the presence of an electrolyte possesses intrinsic primary and
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Fig. 3. Typical mechanical response of representative strains measured by AFM indentation. Loading is shown as dark curve and unloading gray. (a) Strain K. Loading followed ABCD and unloading DCGH. Presence of CSS led to repulsive barrier BC. Global deformation of cell along CD showed full elastic recovery. (b) Strain Q. Energy barrier, Upen, was defined as the shaded area. An extrapolating tangent was defined to exclude energy stored in form of elastic deformation during indentation of CSS. (c) Strain A. The adhesion energy, Uad, was defined as the shaded area.
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microorganisms on silica collector. In case of a high energy barrier, the particles are trapped only by the secondary minimum. Depending on the degree of thermal agitation in terms of kBT, the particle may only stay on the collector surface temporarily, and deposition becomes unfavorable. By adjusting the ionic strength of the solution, the energy barrier can be lowered to an extent that the particle can overcome and reach the primary potential minimum. Since the energy well is deep, the particle with limited thermal energy is permanently trapped and thus raises the macroscopic deposition rate. Elastic deformation of the particle or cell therefore relies on the full surface potential, rather than the simple description portrayed by the new Tabor’s parameter. The above description is also correct for cell–cell adhesion–aggregation, since the electrostatic double layers are also present on the cell surface. Another comment is the presence of surface biomolecules such as polysaccharide. When two apposing cells approach each other in the presence of electrolyte, the molecular brush on each side interact leading to either surface adhesion or repulsion [42], depending on (i) the surface potentials, (ii) the number of entropic configurations available for each chain, (iii) apparent thickness of CSS or mean length of the surface molecules, and (iv) density of the CSS molecules. These factors should ultimately be fully incorporated into a comprehensive Tabor’s parameter to be derived in the future. As a last remark, the adhesion energy in Eq. (4) should strictly represent direct cell–cell adhesion. But since it is difficult to get the direct adhesion measurement, we take it as the adhesion between silicon nitride AFM tip and cell surface which is a closely related quantity as c = (cSiN ccell)1/2 [42]. By adopting such simple model, the new Tabor’s parameter is useful not only in aggregation of homogenous bacterial strains, but is also applicable to dissimilar and heterogeneous strains, as well as collectors such as sand and mica. 5. Conclusion A new dimensionless Tabor’s parameter is derived to account for the combined microscopic mechanical and adhesion properties of single bacteria strain. It bears a strong correlation with the macroscopic cell aggregation behavior for seven vastly different strains of environmental relevance. The work presents an important preliminary step to incorporate fundamental surface science and solid mechanics into the subject of bacteria adhesion-aggregation–transportation, improving the conventional empirically driven approach for predicting microbial attachment and transport in porous media. Acknowledgments
Fig. 4. Linear correlation between Tabor’s parameter, l, and aggregation index, AI, for the 7 bacteria strains. Once l is obtained by AFM, AI can be deduced from the fitted curve.
secondary potential energy minima separated by a repulsive energy barrier. Tufenkji and Elimelech [43] showed how such surface potential influences the favorable and unfavorable deposition of
The authors acknowledge the support from Department of Energy’s Environmental Remediation Science Program (DOE-SBR Grant # DE-SC0005249). XW and KTW are partially supported by National Science Foundation (NSF-CMMI Grant #0757140). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We are grateful to Dr. Christopher Schadt at U.S. DOE for providing the Shewanella and Desulfovibrio strains, and Dr. YanRu Yang for providing all the isolated strains. References [1] R.J. Steffan, K.L. Sperry, M.T. Walsh, S. Vainberg, C.W. Condee, Environ. Sci. Technol. 33 (16) (1999) 2771–2781. [2] N. Tufenkji, J.N. Ryan, M. Elimelech, Environ. Sci. Technol. 36 (21) (2002) 422a– 428a. [3] J.E. Tobiason, C.R. Omelia, J. Am. Water Works Assn. 80 (12) (1988) 54–64.
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Contents lists available at SciVerse ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Correlation of macroscopic aggregation behavior and microscopic adhesion properties of bacteria strains using a dimensionless Tabor’s parameter Xin Wang a, Yueyun Li b, Annalisa Onnis-Hayden b, Ce Gao b, April Z. Gu b, Kai-tak Wan a,⇑ a b
Mechanical & Industrial Engineering, Northeastern University, Boston, MA 02115, USA Civil & Environmental Engineering, Northeastern University, Boston, MA 02115, USA
a r t i c l e
i n f o
Article history: Received 6 November 2011 Accepted 19 January 2012 Available online 31 January 2012 Keywords: Aggregation Adhesion Bacteria AFM Tabor’s parameter
a b s t r a c t Macroscopic adhesion–aggregation, floc formation, and subsequent transportation of microorganisms in porous media are closely related to the microscopic behavior and properties of individual cells. The classical Tabor’s parameter in colloidal science is modified to correlate the macroscopic aggregation and microscopic adhesion properties of microorganisms. Seven bacterial strains relevant to wastewater treatment and bioremediation were characterized in terms of their macroscopic aggregation index (AI) using an optical method, and their microscopic coupled adhesion and deformation properties using atomic force microscopy (AFM). Single cells were indented to measure the range and magnitude of the repulsive–attractive intersurface forces, elastic modulus, thickness and density of the cellular surface substances (CSS). The strong correlation suggests that cost and time effective microscopic AFM characterization is capable of making reliable prediction of macroscopic behavior. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Microbial adhesion–aggregation–transportation is of great importance to various environment processes such as in situ or enhanced subsurface bioremediation [1], filtration processes for water and wastewater treatments [2,3] and protection of drinking water supplies [4]. Metabolic activities of the microorganisms and their phenotypes are conventionally believed to hold the key to control the contaminants’ fate and mobility, as well as transformation and degradation, in changing geochemical conditions [5,6]. Equally important, but by and large ignored, is the mechanical aspects of bacteria aggregation behavior when flowing through a subsurface porous medium. There is an urgent need to understand the fundamental science and mechanics of microbial adhesion– aggregation. Colloid filtration theory (CFT) is a celebrated model for macroscale microbial transport in saturated porous media based on advection–dispersion [7–9], and is widely used to quantify microbial behavior in laboratory and field-scale studies [10–12]. Removal of microbes from the collector (e.g. sand grain) is assumed to be governed by either equilibrium adsorption or the kinetic rate-controlled bacteria attachment to and detachment from the aquifer materials [8,12,13]. Particle–collector interactions are assumed to be weakly attractive with a short range. Notwithstanding its success in many perspectives, CFT prediction often fails to a ⇑ Corresponding author. E-mail address: [email protected] (K.-t. Wan). 0021-9797/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2012.01.032
large extent to match with experimental observations in lab- and field-scales, especially in particle deposition rates [9,10,13–17]. Elimelech et al. shows the necessity of introducing full intersurface potential of the electrostatic double layers developed at the surfaces of both the particle and collector according to Derjaguin –Landau–Verwey–Overbeek (DLVO) theory [18–22]. Despite the improvement, the modified model still misses to factor in other essential features such as the elastic deformation of individual cells associated with adhesion contact. When microorganisms are influenced by strong surface forces, they inevitably deform into distorted shape. Compliant cells with small elastic modulus conform to one another, making the resulting multi-cell aggregate more streamlined to the flow and thus more resistant to segregation. Conversely, rigid cells are less likely to aggregate even in the presence of strong surface forces because of their mechanical resistance to deformation. In addition, the size of a single cell in comparison to the surface force range also plays a critical role. Cells smaller than the force range are fully immersed in the cohesive zone and the entire cell will sense the influence of the substrate, but large cells are only partially influenced by the surface forces. Cell geometry is another relevant quantity. While a spherical cell gives rise to a circular contact with a planar substrate, a cigar shape cell leads to a rectangular contact. In the presence of the same surface force, area of the circular contact is expected to be smaller than the rectangular counterpart because of geometrical constraints and rigorous solid mechanics calculation [23–25]. A comprehensive adhesion-detachment mechanics model capable of predicting bacteria aggregation and transportation must therefore fully account
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for the combined effects of cell wall stiffness, deformation mode, magnitude and range of surface forces, and cell size and geometry. Such model is not available in the literature. In this paper, we establish a new dimensionless parameter, l, based on the conventional Tabor’s parameter in classical adhesion and colloidal science [26,27], to relate the macroscopic cell aggregation to the microscopic mechanical properties of single cell and inter-particle and particle–collector interfacial adhesion energy. A positive correlation between the macro- and micro-behavior thus allows one to make reliable prediction of the macroscopic aggregation based on merely microscopic characterization of single cells that is both time and cost effective. As a demonstration, we chose seven representative bacterial strains commonly found in domestic wastewaters or polluted sites, which possessed a wide range of aggregation behavior. Macroscopic characterization of these strains was performed by an optical method and image analysis to assess their ability to adhere and aggregate. Microscopic mechanical properties are measured by nano-indentation of single cells using atomic force microscopy (AFM), which yields information of range and magnitude of repulsive–attractive surface forces, elastic modulus of cell, and thickness and density of the cell surface substance (CSS) molecules etc. 2. Methods and materials Seven vastly different bacteria strains were chosen for this study based on their relevance to environment and human health, and their natural differences. Some of these strains were isolates from activated sludge samples obtained from the aeration basin of Clemson Municipal Wastewater Treatment Plant [28], and others are relevant to subsurface bioremediation. Special features are listed as follows: (i) K: Comamonas testosteroni is aerobic and is capable of mineralization of the common pollutant 3-chloroaniline (3-CA) [29], (ii) Q: Aeromonas punctata is aerobic and is reported to be associated with human diseases including gastroenteritis, cellulitis and peritonitis [30]. (iii) A: Raoultella ornithinolytica is aerobic and is found to be a major cause of histamine fish poisoning [31]. (iv) H: Bacillus cereus is aerobic and is a common culprit in food poisoning, causing both intoxications and infections [32]. (v) SH2: Shewanella putrefaciens CN32 is an anaerobic strain belonging to DMRB (Dissimilatory metal reducing bacteria). It is capable of reducing various metals and radionuclides including Fe (III) and Mn (III/IV) abundant in sediment and U (VI), Cr (VI), Co (III), and Tc (VII) cations in aqueous environment [33]. (vi) SH1: Shewanella Oneidensis MR-1 is another anaerobic DMRB and is capable of reducing a wide range of organic compounds, metal ions, radionuclides and associated metal/ organic contaminants [34]. (vii) Des: Desulfovibrio vulgaris is an anaerobic strain. Its ability to reduce sulfate, sulfite, thiosulfate and nitrite in anaerobic subsurface environments puts it to the forefront of biological research [35].
71
mented with a mixture of 10 mM sodium lactate as an electron donor and 10 mM sodium fumarate as an electron acceptor at 30 °C in a glove box (Coy Laboratory Products, Grass Lake, MI) with an atmosphere of 5% hydrogen/nitrogen balance. Strain Des was grown anaerobically in ATCC medium 1249, modified Baars’ medium for sulfate reducers. Cells were harvested by centrifugation during exponential growth phase, and growth curves were obtained to determine the sampling time. 10 ml of aliquot suspension was pipetted out of the bottles and into 15 ml tubes for optical and mechanical characterization. 2.2. Macroscopic aggregation: optical quantification and image analysis The macroscopic aggregation capacity of bacteria was characterized using a prescribed assay [36] and was measured in terms of the aggregation index, AI, which ranges from 0 to 1. Large AI corresponds to high aggregation tendency. 10 ml of sample cells were harvested in the exponential growth phase by centrifugation (11000g for 10 min), washed twice with buffer solution (3 mM NaCl containing 0.5 mM CaCl2), and suspended in the same solution. The sample was exposed to a beam of laser with wavelength k = 660 nm to measure the optical density OD using a plate reader (Synergy HT Multi-Mode, Biotech, Winooski, VT). By adjusting the cell concentration using the same buffer solution, the initial optical density, ODtot, of the suspension was adjusted to about 0.30. The sample was then immediately centrifuged at 650g for 2 min, and optical density of the carefully pipetted supernatant was measured as ODs. The aggregation Index (AI) is defined as:
AI ¼
ODtot ODs 100% ODtot
ð1Þ
Should the cells become resistant to aggregation, they remain scattered in colloidal form such that ODs ODtot and AI 0. Conversely, formation of flocs or multi-cell aggregates facilitates passage of optical beam and thus raises the optical transmission and AI. To estimate the average dimension of an aggregate, cell suspension was dispersed on a glass slide, and stained with 1 lg/ml 40 , 6-diamidino-2-phenylindole (DAPI) for 10 min. The settling multi-cell aggregates were observed in situ by fluorescent microscopy (Zeiss, Axio Imager M1-1). At least 20 micrographs were taken at different locations for each sample. Fig. 1a shows typical multi-cell aggregates of Strains Q and H. Based on DAPI signal, the analytical software AxioVision Rel4.8 was used to map the irregular shape of an aggregate. Diameter of a circle having the same area as the circumscribing region was taken as the nominal aggregate dimension. Fig. 1b shows a cumulative frequency plot of cell aggregates with diameter smaller than or equal to different nominal aggregate diameters. The equivalent aggregate diameter was determined as the value at cumulative frequency of 50%. Measurement was repeated for each strain. Number of single cells in each aggregation was estimated by dividing the average aggregation area by the mean single cell area. Note that the estimates here did not consider the 3-D geometry and dimension of the aggregates, though we believe the 2-D correspondence is sufficient for the purpose of evaluating the correlation of aggregation trends with cellular surface properties.
2.1. Sample preparation
2.3. Microscopic characterization of single cells: AFM indentation
The four aerobic strains K, Q, A, and H were cultured in Luria– Bertani (LB) media (Sigma-Aldrich, Inc., St. Louis, MO) in 500 ml bottles (Corning, Inc., Corning, NY) at 37 °C placed on shaker of 200 RPM until they reached stationary phase. The facultative anaerobic strains SH1 and SH2 were grown in LB medium supple-
A 15 ml strain suspension in a stationary phase culture was pelleted by centrifugation, washed in the same volume of nanopore deionized water, pelleted a second time, and promptly re-suspended in 5 ml deionized water. 3 ml of the solution was pipetted onto a gelatin treated cleaved mica surface (Sigma #G-6144). The
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(a)
(b)
Fig. 1. (a) Typical fluorescent optical images. Top micrograph shows Strain Q Aeromonas Punctata aggregates along with the circular envelop (dashed curve) to define the equivalent diameter d 8 lm. Bottom micrograph shows highly irregular Strain H Bacillus Cereus aggregate with d 20 lm. (b) Cumulative frequency plot for the nominal aggregate diameter of strain A, 4.9 ± 2.5 lm.
sample was then allowed to settle for 20 min, rinsed, and stored in deionized water, ready for AFM indentation in a liquid cell. To calibrate the spring constant, k, of the AFM cantilever, contact mode indentation on freshly cleaved mica surface in air was repeated 10 times with sweep duration of 1.04 s. From the average force curves, k was determined to be 0.205 ± 0.015 N/m by the Cleveland method [37]. The unloaded resonant frequency in air was calibrated using AFM (Agilent 5500) in tapping mode with frequency range suggested by the manufacturer. The length and width of the cantilever were measured using optical microscopy (Olympus, GX71). Force measurements were repeated on mica surfaces before and after probing the bacteria samples to ensure no contamination of the silicon nitride AFM tip during experiments. As will be seen in the next section, the AFM tip displacement was measured in the order of 100 nm and the maximum applied force was roughly 3–4 nN. Deflection of the stiff AFM cantilever in the 1–20 nm range was negligibly small and will be ignored hereafter. Distance of the piezoelectric cell driving the AFM tip is therefore taken to be the same as the vertical displacement travelled by the AFM tip. A typical cell was first identified by large scan size using low resolution MAC (Magnetic Acoustic Control) Mode. The AFM tip was repositioned approximately over the cell center, before switching from tapping to contact mode. Applied load, F, was measured as a function of the vertical displacement of AFM tip, w. The mechanical response, F(w), was obtained for loading (compression) followed by unloading (tension) of the tip. At least five loading– unloading cycles were performed at different locations close to the cell center to ensure repeatability, and at least some 10 typical cells were characterized in each batch. Measurements during loading were reproducible to a high precision, though unloading led to relatively random intermittent jumps (see later section for explanation). 3. Results and analysis 3.1. Macroscopic measurements of AI Fig. 1a shows two fluorescent microscopy pictures of aggregates of strain Q and strain H. For each bacterial strain, the aggregation
diameter were repeated with n = 20. Strain Q aggregates take on a roughly circular envelop (dashed curve) with an equivalent diameter d 8 lm, while Strain H aggregate shows an irregular envelop with d 20 lm. Fig. 1b is the example of mean nominal aggregation size determination for strain A, which obeys cumulative frequency distribution with d 4.9 ± 2.5 (51% error) lm. Table 1 summarizes the aggregation index, equivalent cell-aggregate diameter, and average number of cells within an aggregate for all strains. In our measurements, the strains are ranked as SH2 < SH1 < Des < K < Q < A < H in terms of the equivalent aggregate diameter, d, average number of cells per aggregate, N, and AI. 3.2. Microscopic: AFM measurements Fig. 2 shows AFM topographical scans of typical representative samples. All strains possess similar prolate geometry with circular cross-section. The long and short axes are denoted by b1 and b2 respectively. Fig. 3 shows representative mechanical responses of three selected strains. Fig. 3a shows F(w) of Strain K. Loading followed path ABCD. As the probe approached the cell surface from a distance along AB, no force was recorded until it touched the surface of the molecular brush of cellular surface substance (CSS) at B. It is not certain whether the AFM tip actually penetrates the CSS, or simply causes the long chain surface biomolecules to fold, stack and compress. In any case, an apparent repulsive force is felt resisting the AFM motion. The distance BC was taken roughly to be the CSS thickness, l. The work done for the tip to penetrate the CSS, or energy barrier, Upen, was given by the area under BC (c.f. Fig. 3b), and the average penetration or external compression was defined as Fpen = Upen/l. Further loading along CD led to the onset of elastic global deformation of the cell. The classical Hertz–Sneddon model is used to compute the cell elastic modulus, which is given by [38]
! 3 1 m2 @F E¼ 3=2 Þ 4 R1=2 @ðw AFM
ð2Þ
with RAFM = 10 nm the radius of curvature of the AFM tip, and m 0.50 the Poisson’s ratio for incompressible polymeric solid. Retraction of the AFM tip led to unloading path DCGH. Little or no
104 (22.1%) 12600 (22.2%) 2.16 (14.3%) 0.73 (8.2%) 39.3 (8.3%) 360 (3.7%) 1590 (18.2%) 0.88 (13.6%) 0.42 (16.6%) 0.18 (5.6%)
568 (4.4%) 2800 (4.6%) 1.15 (35.6%) 0.51 (13.7%) 0.68 (13.2%)
524 (9.5%) 9700 (13.4%) 1.28 (55.0%) 0.78 (19.2%) 1.19 (9.2%) 500 (6.8%) 3980 (30.1%) 2.06 (13.1%) 0.54 (27.8%) 0.94 (12.7%) 900 (3.2%) 2670 (14.9%) 1.47 (26.5%) 0.594 (16.8%) 0.92 (6.5%)
162 (24.7%) 9770 (29.6%) 1.58 (24.6%) 0.80 (11.3%) 11.4 (3.6%)
/ / 1.10 (21.8%) 578 (21.6%) 0.50 (8.0%) 249 (8.8%) 0.58 (5.8%) 209 (5.7%)
0.21 (9.5%) 116 (9.4%)
0.58 (3.4%) 522 (4.0%)
/ /
105 (3.8%) 300 (12.7%) 244 (16.8%) 40.4 (14.8%) 559 (12.9%) 4.4 (11.4%)
415 (9.2%) 41.9 (19.3%)
380 (8.4%) 112 (9.1%)
337 (20.5%) 43.9 (20.5%)
237 (17.7%) 197 (5.6%)
183 (15.8%)
Aggregation index, AI (%) Equivalent aggregate diameter, d (lm) Aggregation number estimation, N Elastic modulus, E (kPa) Adhesion energy, Uad (1018 J) Penetration force, Fpen (nN) Penetration energy barrier, Upen (1018 J) Thickness of CSS (nm) Density of CSS, C (mol/lm2) Length, b1 (lm) Width, b2 (lm) Tabor’s parameter, l
2.3 (26.1%)
6.2 (33.9%)
8.1 (33.3%)
13.7 (45.3%)
14.7 (25.8%)
H
11.3 (30.9%)
Raoultella ornithinolytica (Gram-negative) 72 (4.2%) 4.9 (51%)
A Q
Aeromonas punctata (Gram-negative) 60 (3.3%) 4.2 (47.6%)
K
Comamonas testosteroni (Gram-negative) 51 (3.9%) 4.01 (64.8%)
Des
Desulfovibrio Vulgaris (Gram-negative) 29 (24.0%) 3.0 (73.3%)
SH1
Species
S. Oneidensis MR-1 (Gram-negative) 21 (19.0%) 2.2 (50%)
SH2
S. Putrefaciens CN32 (Gram-negative) 12 (33.3%) 1.04 (42.3%)
Strain
Table 1 Summary of materials and surface properties. Percentage errors are shown in parentheses.
Bacillus cereus (Grampositive) 88 (13.6%) 19 (52.6%)
X. Wang et al. / Journal of Colloid and Interface Science 374 (2012) 70–76
73
hysteresis was measured along DC, indicating the elastic recovery of the sample cell. At G, the cell resumed the undeformed geometry and the AFM was fully unloaded with F = 0. Tensile force was needed along GH to pull the tip out from the sample. The zigzagging F(w) showed multiple sudden jumps of the order of 100– 200 pN, corresponding to the detachment of individual or an entangled bundles of CSS (e.g. extracellular polymeric substance EPS) from the AFM tip. At H, the AFM tip ‘‘pulled-off’’ from the cell surface and the external load dropped to zero. The total work done needed to detach the AFM tip was given by the area enclosed, Uad (c.f. Fig. 3c). Fig. 3b shows the mechanical response of strain Q, which is quite different from that of strain K. Upon loading on the cellular surface substance (CSS), the AFM tip measured an increasing compressive load until global deformation of the cell occurred at C. The absence of a force plateau indicated a continual compaction of the cellular surface substance (e.g. EPS) rather than penetration. Elastic recovery was again observed for further loading– unloading. Upon tip retraction, a hysteresis was observed with a smaller repulsive load, and complete detachment occurred further away from the cellular surface due to adhesion. Fig. 3c shows behavior of Strain A. Here CSS was not detectable by AFM, but a significant adhesion was measured. Stepwise detachment was also observed. It is noted that a non-zero loading–unloading hysteresis occurred during the global deformation. In repeated loading–unloading measurements at various positions of the sample batch, the hysteretic loop showed an average of vanishingly small area in F(w). The AFM indentation at this stage is unable to identify whether the non-zero hysteresis is the result of viscoelasticity of the CSS or the cell or possible natural variation of the surface texture. To find the cellular surface substance (CSS) molecular brush density, we resorted to the de Gennes’ steric repulsion model [39,40]. The CSS was treated as a brush of polymer chains impregnated on the cell surface, while the AFM tip was taken to be a bare rigid surface. The total mechanical forces acting on the tip as it penetrated the CSS was given by
2ph F steric 50kB TRAFM C3=2 l exp l
ð3Þ
with kB is the Boltzmann constant, T the absolute temperature, C the effective number density of brush molecules on cell surface, l the equilibrium thickness of the CSS layer, and h is the distance between the bending probe and the deformed cell surface. Table 1 summarizes the measured parameters for all strains under investigation. 3.3. Tabor’s parameter In general, large and compliant cells are expected to be more prone to adhesion and aggregation, especially when the attractive intersurface force is sufficiently strong and the steric repulsion as a result of thick CCS is minimized. In quantitative terms, a higher propensity to aggregation with large AI is expected for large Fad, Uad, b1, and b2, and small Frep, Urep, l and E. For instance, Table 1 shows that strains K and Q are less aggregative (small AI) than A and H, but the four strains have different elastic moduli. It is ideal to derive a universal dimensionless parameter to collectively combine these measureable quantities. We attempt to modify the Tabor parameter [27,41], l, in classical adhesion and colloidal science to fit our needs. When two identical solid elastic spheres of radius Rs come into contact under an external compressive load, F, in the presence of intersurface forces with adhesion energy, c in J m2, a contact circle of radius, c, is formed at the interface. In case of strong but
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X. Wang et al. / Journal of Colloid and Interface Science 374 (2012) 70–76
Fig. 2. AFM topological scans of four aerobic strains K, Q, A, and H, showing the cigar shape cells and morphological details.
short-range forces between two large and compliant spheres in the Johnson–Kendall–Roberts (JKR) limit, the spheres deform locally at the circular contact edge known as the ‘‘neck’’, and a critical tensile load, F = (3/2)pRsc is needed to detach the adhering spheres at ‘‘pull-off’’. In case of weak but long-range adhesion between two small and hard spheres in the Derjaguin–Muller–Toporov (DMT) limit, the local deformation ‘‘neck’’ vanishes and the ‘‘pull-off’’ force becomes F = 2pRsc. Tabor and then Maugis [27] derived a dimensionless Tabor’s parameter, l = (4Rsc2/9E2y3)1/3, to encompass geometry (Rs), interfacial properties (c), intersurface force range (y), and materials properties of the solid (E). A large l > 2 leads to the JKR limit and a small l < 0.50 corresponds to the DMT limit and the ‘‘pull-off’’ force is bounded between the upper and lower limits of 3/2 6 F/pRsc 6 2. In physical terms, l governs the size of the ‘‘neck’’ and the contact area at adhesion interface as well as the deformability due to adhesion. In the present context, a large l facilitates the large and compliant cells to deform and aggregate, to an extent that the resulting multi-cell aggregates conform to a better hydrodynamic streamlined geometry to resist liquid flow. It is therefore logically expected that a large l leads to large AI and vice versa. Several limitations of the classical l description are noted nonetheless. For instance, bacteria strains comprise glycoprotein shells instead of being homogeneous solids, and they always take on cylindrical geometry instead of being spherical. To circumvent the fine mathematical details to deal with exact geometry and micro-structure, a modified Tabor’s parameter capturing the essential features of the system is defined as
2
l¼
4 2b2 3
l E2
U ad
pR2AFM
31=3
!2
2 25
ð1 v Þ
ð4Þ
Here the cell is taken to be an ellipsoid with the smallest principal radius to be (b2/2), replacing Rs. The adhesion energy c is substituted by the effective adhesion energy Uad divided by the contact area with the AFM tip or pR2AFM . Surface force range is taken to be
roughly the cellular surface substance thickness, l, in that, from where the AFM tip first senses the presence of intersurface forces to AFM tip touching cell surface during loading. The elastic modulus is taken to be some average of the cell wall and cytoplasm of an ideal homogeneous cell. Fig. 4 shows a strong correlation between AI and l. The linear relation justifies l to be a reasonable parameter to correlate the macro- to micro-scale behavior. Simple curve fit yields
AIð%Þ ¼ c1 log10 l þ c2
ð5Þ
with the numerical constants c1 = 33.03 ± 2.24 and c2 = 37.79 ± 2.65. Should l of an arbitrary strain be determined by AFM measurement, the macroscopic aggregation index can be estimated by Eq. (5). A large Tabor’s parameter corresponds to a high propensity to aggregate. 4. Discussion Microscopic characterization of single cells using AFM is attractive in the environmental engineering community. Conventional macroscopic measurements using optical transmission and packed columns are both expensive and time consuming for the virtually millions of different bacterial strains in the contaminated sites around the globe. The cost and time effective AFM indentation thus presents a promising method to make sensible and reliable prediction of the macroscopic behavior of aggregation–transportation of microbes. In spite of the fair correlation between the micro- and macroproperties via the modified Tabor’s parameter, some cautions should be taken. For instance, the intersurface potential at the cell–cell and cell–substrate interfaces are loosely defined as the attractive force measured by AFM, rather than resorting to the well established DLVO theory [42]. Spontaneous build-up of electrostatic double layers on surface of cell and colloidal particles in the presence of an electrolyte possesses intrinsic primary and
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Fig. 3. Typical mechanical response of representative strains measured by AFM indentation. Loading is shown as dark curve and unloading gray. (a) Strain K. Loading followed ABCD and unloading DCGH. Presence of CSS led to repulsive barrier BC. Global deformation of cell along CD showed full elastic recovery. (b) Strain Q. Energy barrier, Upen, was defined as the shaded area. An extrapolating tangent was defined to exclude energy stored in form of elastic deformation during indentation of CSS. (c) Strain A. The adhesion energy, Uad, was defined as the shaded area.
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microorganisms on silica collector. In case of a high energy barrier, the particles are trapped only by the secondary minimum. Depending on the degree of thermal agitation in terms of kBT, the particle may only stay on the collector surface temporarily, and deposition becomes unfavorable. By adjusting the ionic strength of the solution, the energy barrier can be lowered to an extent that the particle can overcome and reach the primary potential minimum. Since the energy well is deep, the particle with limited thermal energy is permanently trapped and thus raises the macroscopic deposition rate. Elastic deformation of the particle or cell therefore relies on the full surface potential, rather than the simple description portrayed by the new Tabor’s parameter. The above description is also correct for cell–cell adhesion–aggregation, since the electrostatic double layers are also present on the cell surface. Another comment is the presence of surface biomolecules such as polysaccharide. When two apposing cells approach each other in the presence of electrolyte, the molecular brush on each side interact leading to either surface adhesion or repulsion [42], depending on (i) the surface potentials, (ii) the number of entropic configurations available for each chain, (iii) apparent thickness of CSS or mean length of the surface molecules, and (iv) density of the CSS molecules. These factors should ultimately be fully incorporated into a comprehensive Tabor’s parameter to be derived in the future. As a last remark, the adhesion energy in Eq. (4) should strictly represent direct cell–cell adhesion. But since it is difficult to get the direct adhesion measurement, we take it as the adhesion between silicon nitride AFM tip and cell surface which is a closely related quantity as c = (cSiN ccell)1/2 [42]. By adopting such simple model, the new Tabor’s parameter is useful not only in aggregation of homogenous bacterial strains, but is also applicable to dissimilar and heterogeneous strains, as well as collectors such as sand and mica. 5. Conclusion A new dimensionless Tabor’s parameter is derived to account for the combined microscopic mechanical and adhesion properties of single bacteria strain. It bears a strong correlation with the macroscopic cell aggregation behavior for seven vastly different strains of environmental relevance. The work presents an important preliminary step to incorporate fundamental surface science and solid mechanics into the subject of bacteria adhesion-aggregation–transportation, improving the conventional empirically driven approach for predicting microbial attachment and transport in porous media. Acknowledgments
Fig. 4. Linear correlation between Tabor’s parameter, l, and aggregation index, AI, for the 7 bacteria strains. Once l is obtained by AFM, AI can be deduced from the fitted curve.
secondary potential energy minima separated by a repulsive energy barrier. Tufenkji and Elimelech [43] showed how such surface potential influences the favorable and unfavorable deposition of
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