Article pubs.acs.org/Langmuir
Using Flow to Switch the Valency of Bacterial Capture on Engineered Surfaces Containing Immobilized Nanoparticles Bing Fang,† Saugata Gon,‡ Myoung-Hwan Park,§ Kushi-Nidhi Kumar,∥ Vincent M. Rotello,§ Klaus Nüsslein,∥ and Maria M. Santore*,† †
Department of Polymer Science and Engineering, ‡Department of Chemical Engineering, §Department of Chemistry, and Department of Microbiology, University of Massachusetts, Amherst, Massachusetts 01003, United States
∥
S Supporting Information *
ABSTRACT: Toward an understanding of nanoparticle− bacterial interactions and the development of sensors and other substrates for controlled bacterial adhesion, this article describes the influence of flow on the initial stages of bacterial capture (Staphylococcus aureus) on surfaces containing cationic nanoparticles. A PEG (poly(ethylene glycol)) brush on the surface around the nanoparticles sterically repels the bacteria. Variations in ionic strength tune the Debye length from 1 to 4 nm, increasing the strength and range of the nanoparticle attractions toward the bacteria. At relatively high ionic strengths (physiological conditions), bacterial capture requires several nanoparticle−bacterial contacts, termed “multivalent capture”. At low ionic strength and gentle wall shear rates (on the order of 10 s−1), individual bacteria can be captured and held by single surface-immobilized nanoparticles. Increasing the flow rate to 50 s−1 causes a shift from monovalent to divalent capture. A comparison of experimental capture efficiencies with statistically determined capture probabilities reveals the initial area of bacteria−surface interaction, here about 50 nm in diameter for a Debye length κ−1 of 4 nm. Additionally, for κ−1 = 4 nm, the net per nanoparticle binding energies are strong but highly shear-sensitive, as is the case for biological ligand−receptor interactions. Although these results have been obtained for a specific system, they represent a regime of behavior that could be achieved with different bacteria and different materials, presenting an opportunity for further tuning of selective interactions. These finding suggest the use of surface elements to manipulate individual bacteria and nonfouling designs with precise but finite bacterial interactions.
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interactions typically range from 0 to 2 nN in strength.3,4 For instance, Busscher et al. report negligible nonspecific attractions between streptococci and laminin films, but these attractions were sometimes as attractive as 1.5 nN.5 Likewise, Liu et al. find about 0.1 nN of attraction between S. epidermidis and albuminsaturated self-assembled monolayers on gold.6 Contrast this with 0.8 nN of attractive force between the same bacteria and fibronectin coated on the same substrates. Greater specific forces, typically by a factor of 3−5, are reported throughout the literature for AFM measurements of bacterial adhesion.4 These AFM measurements are consistent with engineering studies, for instance, the capture of bacteria from controlled flow.7,8 On the basis of these measurements and separate studies of the strength of individual bonds, Busscher et al. estimate that 10− 50 specific bonds can form and must dissociate when bacteria are dislodged from a surface.3 This quantity represents an upper limit to the number of bonds that must engage during initial bacterial capture: the adhesion strength between a bacterium and a surface typically increases with residence time.9 The key to manipulating bacteria, then, would be to control the shorttime bacteria−surface interactions.
INTRODUCTION With the growing use of polymers in biomedical devices and the growing resistance of bacteria to antibiotics, the need for surfaces that execute a range of bacterial manipulation functions continues to grow. Applications span from implants that resist bacterial fouling and/or selectively kill bacteria (not harming mammalian cells) to sensor elements with selective adhesion and, in the best case, spontaneously regenerating (smokedetector-like) surfaces. There is a need not just to avoid bacterial adhesion but to control it. Toward this goal, we are interested in designing surfaces to exploit the interplay of interfacial and hydrodynamic forces during bacterial capture. This article focuses on a promising new class of biomimetic surfaces that localize attractive forces in nanoscale surface elements while the remaining surface is protein- and bacteriarepellant. This biomimetic surface architecture holds promise for the selective, switchable adhesion of proteins and cells. The forces associated with bacteria−surface interactions have become a topic of interest because both nonspecific and specific interactions can drive bacterial adhesion. Specific interactions are particularly important when proteins adsorb onto biomaterial surfaces because bacteria have known receptors for common proteins.1,2 Recent AFM measurements of bacteria−surface interactions have revealed distinctly different values for nonspecific and specific interactions. Nonspecific © 2012 American Chemical Society
Received: December 22, 2011 Revised: April 9, 2012 Published: May 7, 2012 7803
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Figure 1. Schematic of nanoparticle-containing surfaces with a brushy backfill.
As discussed by Busscher et al.,3 the literature on cell adhesion has focused either on nonspecific forces (van der Waals, electrostatic, etc.) or on ligand−receptor interactions, as if the two were fundamentally different. These authors assert that the nonspecific and ligand−receptor interactions are fundamentally identical because ligand−receptor bonds are composed of electrostatic, van der Waals, and donor−acceptor interactions. As they explain, the primary difference is that ligands and receptors localize the forces to extremely small regions of the interface, usually of the same order of magnitude as the range of forces themselves. In our thinking, this distinction is critical. The localization of forces enables highly specific mating of ligands and receptors that usually occurs on time scales slightly longer than for nonspecific interactions: appropriate regions of the opposing surfaces (and the molecules themselves) must register correctly to facilitate ligand−receptor mating, which is typically not necessary for nonspecific forces. When interfacial interactions become discretized, as is the case for ligand−receptor pairs, it becomes possible to invoke the principles of valency. Biochemists say that binding is monovalent if engagement occurs at a single site whereas multivalent interactions involve the engagement of several sites. Then, sharp binding specificity can result from the power-law amplification of the more modestly selective single bonding events. This is a commonly exploited strategy in pharmaceutical targeting, as reviewed by Kiessling.10,11 These considerations motivated our development of synthetic surfaces containing nanoscale adhesive elements: Immobilized cationic polymer coils12−14 and nanoparticles15,16 localize electrostatic interactions whereas the rest of the surface is repulsive toward approaching objects. Some of our libraries have main surfaces that are electrostatically repulsive toward approaching particles,12,17 and other surface libraries employ a nonadhesive biocompatible polymer brush to produce steric repulsions against approaching molecules and cells.14,16 We have demonstrated that such “patchy” brushes can exhibit multivalent protein binding with size-based selectivity that is sufficiently sharp to discriminate proteins with 99% purity.18 Related libraries of brushy surfaces containing embedded cationic nanoparticles were shown to exhibit the multivalent capture of bacteria (Staphylococcus aureus, S. aureus), which could be tuned to a monovalent mechanism (one binding event per bacterium) when the ionic strength was decreased to strengthen the electrostatic attraction relative to a fixed steric background repulsion.16 The current study expands our work on bacterial capture to establish hydrodynamic switching of the bacterial capture valency. In this article, we demonstrate that surfaces that capture bacteria through many contacts (on the order of three to seven, determined by comparison with a statistical model) capture those same bacteria through a monovalent mechanism when the flow rate is decreased. On these surfaces under these conditions, single bacteria are captured and held by single surface-immobilized nanoparticles. Subsequent analysis reveals
the forces and binding strength of the nanoparticle−bacterium interface. The use of hydrodynamic forces to tune the bacteria capture valency constitutes a means of rapidly manipulating bacterial adhesion (compared to chemical means that are limited by diffusion when, for instance, pH-altering compounds are introduced), which is useful for sensor applications and diagnostics where bacteria are hydrodynamically and selectively directed to targeted surface regions. Also determined from this treatment is the initial area of bacteria−surface interaction, which turns out to be about 50 nm in diameter. To our knowledge, the area of interaction between a bacterium and a surface, especially in the initial stages of capture, has not been previously reported.
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EXPERIMENTAL DETAIL
The surfaces in this study contain immobilized cationic nanoparticles, with the remaining area made adhesion-resistant by the subsequent adsorption of a PEG (poly(ethylene glycol)) polymer brush per Figure 1. The cationically functionalized nanoparticles were composed of 7 nm gold cores, each with a shell of ∼500 ligands. Approximately 200 of the ligands on each particle were N,N,N-trimethyl(11-mercaptoundecyl) ammonium chloride, and the other ∼300 were 1-mercaptoundecane molecules.19,20 The overall nanoparticle size was about ∼11 nm, as measured via TEM in the dry state. When exposed to silica, the nanoparticles adsorb randomly and irreversibly from solution at the diffusion-limited rate, allowing precise control of their surface density, from about 10 to 1000/μm2.17 This corresponds to average nanoparticle spacings of 25−350 nm. The immobilized nanoparticles are not removed from the substrate (nor is there evidence for their rearrangement or surface aggregation) during drying, exposure to organic solvents, or sonication, as a result of their combined van der Waals and electrostatic attractions with the silica substrate.17 The silica substrate area not covered with nanoparticles is functionalized with a protein-resistant biocompatible PEG brush. The exclusion of the PEG brush from the nanoparticles themselves is an important feature that we carefully established in prior studies.16 Our particular PEG brushes were chosen for their nearly complete resistance to protein adsorption21,22 and lack of bacterial adhesion,23 isolating all of the attractive functionality on the nanoparticles themselves. The brushes were composed of a PLL-PEG (poly Llysine-graft-co-poly(ethylene glycol)) copolymer, as developed by Kenausis et al.22 and Huang et al.24 These investigators produced libraries of PLL-PEG copolymers and established which copolymers, upon adsorption to negative surfaces by their PLL backbones, extended their PEG side chains into solution to produce the most protein-resistant PEG brushes. On the basis of their studies, we chose 2300 molecular weight PEG sides arms and a 20 000 molecular weight PLL backbone with a grafting ratio of 2.9 PLL units for each PEG side chain. This is equivalent to a PLL functionalization of 34%. Our modifications of Kenausis et al.22 and Huang et al.’s24 synthesis procedures, necessitated by the availability of slightly different starting materials, have been described by us elsewhere.14,16,21 Notably, anchoring of the PEG side chains by a cationic backbone avoids adsorption on previously deposited cationic nanoparticles. The characterization of these surfaces using AFM confirmed the random nanoparticle arrangement, their deposition in the targeted amounts, and their protrusion forward from the surface in the dry state by 7−9 nm. From reflectometry measurements of the adsorbed polymer amounts along with the application of the Alexander−de 7804
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Gennes treatment25,26 of the brush, we estimate brush thicknesses of 9 to 10 nm in water. We note that this widely accepted treatment of brushes approximates them as a step function in polymer concentration. More realistically, there is a concentration decay of PEG chains away from the surface, but 10 nm is a useful length scale for describing the brush in the wet state. Silica substrates were the surfaces of microscope slides, etched overnight in sulfuric acid to remove metal cations. After being rinsed in DI water, each slide was placed in a slit shear flow chamber and exposed to flowing buffer. Following a valve turnover, a 5 ppm nanoparticle solution in DI water was introduced. Nanoparticle deposition was linear in time as the solution continued to flow over the surface. After the desired time, the flow was switched back to DI water. After the introduction of phosphate buffer (pH 7.4, 0.008 M Na2HPO4 plus 0.002 M KH2PO4 having κ−1 = 2 nm), a 100 ppm PLL-PEG solution was allowed to flow to fill the remaining surface and buffer was reintroduced to flush away the remaining polymer. Additional changes were made to the buffer concentration to produce a Debye length of κ−1 = 1, 2, or 4 nm, and then bacteria were allowed to flow in the buffer of interest. Though the ionic strength during bacterial exposure was varied, the surfaces were always fabricated under the same ionic conditions. To determine the transport-limited bacteria capture rate, a substantially cationic surface was employed. This was an adsorbed layer of poly(L-lysine) (PLL). In this case, after an acid-etched slide was placed in the flow chamber, buffer was introduced, and then a 100 ppm solution of PLL in pH 7.4 phosphate buffer flowed over the surface for 10 min to allow saturation,14 prior to the reintroduction of buffer. At this point, changes were made to the buffer concentration to produce the desired Debye length, and then bacteria were introduced. In additional calibration studies, 1 μm silica spheres (GelTech, Orlando) were allowed to flow instead of bacteria. Near-Brewster reflectometry was employed, as necessary, to track nanoparticle or backfill deposition. This technique is similar to ellipsometry but allows small numbers of interfacial species to be quantified on optically clear surfaces such as microscope slides. With a calibration for the deposition time needed to produce a targeted surface density of nanoparticles, as produced by reflectometry and confirmed via atomic force microscopy,16 most deposition runs used to prepare surfaces were conducted “blind” in a lateral microscope that enabled the subsequent bacterial capture processes to be monitored. The key feature of the lateral microscope used to monitor bacterial deposition is the orientation of the flow chamber so that the engineered surface is perpendicular to the floor. In this way, gravity does not compete with interfacial forces in determining bacterial capture. Bacteria deposition experiments, in the same slit flow chambers used to create the surfaces, were recorded on video and analyzed using ImageJ software. The bacterium chosen was S. aureus (ATCC 25923), grown according to a standard procedure in Luria−Bertani (LB) medium. The strain itself was originally a clinical isolate and today is widely used in standardized tests of bacterial antibiotic susceptibility. This particular strain was chosen for its nonpathogenic behavior while still closely resembling strains found in hospital infections. Cultures were incubated aerobically overnight at 37 °C, during which time they were shaken at 200 rpm. They were harvested after a total of 24 h during logarithmic growth. Centrifugation at 100g and resuspension in phosphate buffer was conducted twice to remove protein and other molecules that might potentially contaminate the surfaces. All bacteria were studied within 24 h of preparation and stored in a refrigerator near 4 °C. The nominal target bacterial concentration was 5 × 105/mL during the runs themselves. The zeta potentials of these bacteria were ζ = −12, −25, and −24 mV at ionic strengths corresponding to κ−1 = 1, 2, and 4 nm, respectively.
Figure 2. Raw data for the capture of S. aureus on nanoparticlecontaining surfaces at pH 7.4 with κ−1 = 4 nm and γ = 22 s−1. The calibration run on PLL is included for this batch of bacteria.
first few minutes so that the initial capture rate is well-defined. The bacterial capture rates increase with the nanoparticle surface loading, here and in general. The curvature of individual runs at relatively low bacterial surface coverage (3 × 109/m2 or a few percent of the areal fraction) is strongly flow-dependent, as also seen for silica particles and bacteria on entirely cationic surfaces (Supporting Information). This hydrodynamic shadowing effect, documented previously in the literature and understood to be important at these low coverages,27−29 is beyond the current scope. Here we focus on bacterial coverages that are sufficiently low to avoid even the long-range hydrodynamic bacteria−bacteria interactions on the surface. The initial linear capture kinetics studied in this work emphasizes single bacteria−surface interactions. The data in Figure 2 were obtained with a single batch of bacteria. Because the bacterial concentration was fixed, the bacterial capture rates and amounts could be quantitatively compared within Figure 2. The comprehensive study in this article, however, required different bacterial batches, which varied in their solution concentrations sufficiently to confound quantitative batch-to-batch comparison. Data are therefore reported in terms of the capture efficiency relative to the transport-limited capture rate on a strongly cationic surface, an adsorbed PLL layer. For each batch of bacteria, the initial capture rate on PLL at 22 s−1 (and sometimes at other flow rates as well) was measured independently and used for the normalization of the initial capture rates on nanoparticle surfaces, such as in Figure 2. Details are described in the Supporting Information. The bacterial capture efficiencies are summarized in Figure 3 as a function of flow and the nanoparticle loading of the collector surfaces for different ionic strengths. Instead of a limiting proportionality between nanoparticle loading and bacterial capture (which one might expect on the basis of free solution behavior), Figure 3 shows that surfaces containing immobilized nanoparticles generally do not capture bacteria at low nanoparticle loadings. With one exception (for κ−1 = 4 nm and a shear rate of 22 s−1), bacterial capture occurs only above a distinct x intercept or nanoparticle loading on the surface. This adhesion threshold is an earmark of multivalent bacterial capture: a flowing bacterium must be engaged by several nanoparticles at once in order to be captured. (Surfaces with sparse nanoparticle loadings cannot capture bacteria, indicating that single nanoparticles are not sufficiently strongly binding.) At high surface loadings of nanoparticles, the data approach an
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RESULTS Particle Capture on Surface-Immobilized Nanoparticles. Typical data for the capture of S. aureus on nanoparticlecontaining brushy surfaces (Figure 2) are linear in time for the 7805
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Figure 4. (A) Adhesion thresholds as a function of the wall shear rate at different Debye lengths (1, 2, and 4 nm). (B) Adhesion thresholds as a function of the Debye length at different wall shear rates (22, 110, and 795 s−1). The error bars shown are characteristic of the data and represent two to three datum points at each point.
nanoparticle is potentially able to capture and hold an individual bacterium. (If the surface is relatively densely loaded with nanoparticles, then greater numbers of nanoparticles could still engage during bacterial capture. The capture of bacteria by single nanoparticles will occur only with the sparsest nanoparticle loadings.) With the possibility of monovalent capture, all surfaces, no matter how sparsely decorated with nanoparticles, are capable of capturing bacteria (albeit very slowly in some cases). With each nanoparticle capable of bacterial capture, the rate-limiting process becomes the diffusion of bacteria to sparsely situated individual nanoparticles. The second x axis in Figure 3, applicable to all parts of the figure, shows the average nanoparticle spacing for the different nanoparticle loadings. This average spacing is calculated from the inverse square root of the nanoparticle surface density with the appropriate unit conversion factors. For conditions producing large thresholds (e.g., γ = 795 s−1), the average nanoparticle spacing at the threshold is 40−50 nm. When the nanoparticle−bacterium attractions are strong, the average nanoparticle spacing at the threshold increases, and when monovalent capture is achieved, the spacing can be infinite because only single nanoparticles are involved. Given these average nanoparticle spacings, the number of nanoparticles actually engaging bacteria will depend on the area of bacteria− surface interaction and the statistical arrangement of the nanoparticles themselves. Quantifying the Bacteria−Surface Interaction Area and Valency from a Statistical Model. The observation in Figure 3 of hydrodynamic switching between monovalent and
Figure 3. Bacterial capture efficiencies at different shear rates, summarized for Debye lengths of 1, 2, and 4 nm on nanoparticlecontaining surfaces. Characteristic error bars are shown in B. Also, the precision on the x axis is about 350 PLL/μm2.
efficiency of unity, corresponding to fast bacterial capture, at the transport-limited rate. In Figure 3A,B, for Debye lengths of 1 and 2 nm, respectively, substantial adhesion thresholds are observed and grow roughly linearly, as summarized in Figure 4, in the wall shear rate, γ. When bacteria are flowing quickly and subject to strong hydrodynamic forces, greater surface adhesion is needed for their capture. This involves simultaneous engagement with greater numbers of nanoparticles, which are responsible for the shifting threshold. For a Debye length of 4 nm in Figure 3C, the electrostatic attractions between each nanoparticle and the bacteria exceed those at smaller Debye lengths. For κ−1 = 4 nm and a wall shear rate of 22 s−1, the capture data extend to the origin: there is no adhesion threshold. This lack of an adhesion threshold indicates monovalent bacterial capture, meaning that each 7806
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Figure 5. Illustration of bacteria−surface contact for (A) electrostatic interactions and (B) steric interactions with the brush on the engineered surface. The particle radius is a. The electrostatic contact radius, rc, can be found from a2 + rc2 = (a + κ−1)2 or rc ≅ (2aκ−1)1/2. The steric contact depends on the brush thickness h or, more precisely, the brush compression length, δ, which can approach h. Here, rc2 + (a − δ)2 = a2 or rc ≅ (2aδ)1/2.
therefore provides a lower bound to the interaction area. For electrostatic attractions between immobilized nanoparticles and the negative bacteria surface, geometrical arguments (a2 + rc2 = (a + κ−1)2 or rc ≅ √(2aκ−1)) suggest an interaction radius, rc, on the order of 50−60 nm. Smaller electrostatic interaction areas occur at higher ionic strengths and smaller Debye lengths. Real materials, especially soft ones such as bacteria and grafted polymer brushes, will deform. At short times and given the viscoelastic nature of the interfaces, one might expect that subsecond deformations, relevant to the initial moments of capture, would be restricted to the outermost portions of the bacteria and the engineered surface, which are polymer brushes. Indeed, the surfaces of some bacteria have been likened to a polymer brush.4 From the geometric arguments in Figure 5B, the compression of the bacterial lipopolysaccharide layer by just a few nanometers or an equivalent compression of the PEG brush on the substrate would produce a steric interaction area similar to the electrostatic interaction area in Figure 5A. The assessment of a 2500 nm2 contact area from the statistical model is therefore reasonable. An interaction diameter of about 50 nm is consistent with the range of nanoparticle spacings, observed in Figure 3, where the thresholds occur. When the two length scales, the interaction diameter, and the average spacing between nanoparticles become similar in magnitude, spatial fluctuations in the arrangement of the nanoparticles will become important and multivalent adhesion, based on a handful rather than hundreds of nanoparticle contacts per bacterium, can occur. To assess the valency of capture, Figure 6 presents the calculated bacterial capture rates for different valence numbers and two contact areas (5000 and 1000 nm2 to show the largest possible range of uncertainty), for comparison with Figure 3. Also included in Figure 6 is a reasonable estimate of the maximum probability of capture that can be observed before bacterial diffusion obscures the surface kinetics. The resulting capture efficiencies are represented on the right-side y axis. Although the interaction area affects the slopes of the curves, the thresholds (apparent x intercepts) are only modestly affected, making a semiquantitative comparison quite powerful. Even with the uncertainty in the interaction area (with A = 2500 nm2 being the best estimate for κ−1 = 4 nm), it is clear that in the multivalent regime only a handful of nanoparticles are involved in bacterial capture. In Figure 3C, as the wall shear is increased from 22 to 55 s−1, producing the shift from monovalent to multivalent capture, the corresponding predictions in Figure 6 show a shift from one to two nanoparticles needed for bacterial capture. At higher shear rates, depending on the ionic strength, up to about six nanoparticles constitute the minimum needed to capture bacteria. The model does not account for the size of the
multivalent bacterial capture raises important fundamental issues concerning the number of nanoparticles engaged in the multivalent regime and the area of the initial bacteria−surface interaction or effective contact area. These structural features of bacterial capture are addressed via a statistical model that was developed previously to interpret silica particle capture on heterogeneous surfaces30 and are modified here (in the Supporting Information) for the study of bacteria. Key features of the model include (1) the use of a Poisson distribution to describe the random arrangement of adhesive nanoparticles on the surface (previously established in experiments17), (2) the incorporation of a minimum number of engaging nanoparticles needed to capture bacteria, and (3) the specification of the bacteria−surface interaction area. The latter is defined as the area over which steric or electrostatic forces act. Outside this effective contact area, the bacteria do not experience surface forces. The minimum number of nanoparticles for bacteria capture is, in fact, the valency number, which is the object of the modeling exercise. The interaction area is an equally important parameter that was not previously addressed in the literature, to our knowledge. For a particular interaction area, bacterial capture valency, and surface loading of nanoparticles, the model predicts the probability of bacterial capture. This probability, plotted as a function of the nanoparticle loading, resembles Figure 3, with the probability of capture proportional to the capture efficiency. As the capture probability approaches unity, the experimental capture rates become limited by the transport of bacteria to the interface (equivalent to an efficiency of unity.) Assigning the maximum observable probability introduces uncertainty into the comparison of modeled and observed data (also in the Supporting Information); however, the uncertainty turns out not to alter conclusions except at the most quantitatively precise levels (with an error of two nanoparticles or fewer). The Supporting Information describes the model itself and the analysis, in the monovalent capture regime, of the bacteria− surface interaction area. Although both the valency and the interaction area are independent fitting parameters, determining the interaction area in the regime of monovalent capture (for data passing through the origin) for the single data set of γ = 22 s−1 and κ−1 = 4 nm independently produces an estimated interaction area of about 2500 nm2, but the actual number could reasonably be in the range of 1000−5000 nm2. This corresponds to a diameter of about 50 ± 20 nm. That such a result is reasonable follows from the geometry in Figure 5. A perfect sphere−plate contact occurs at a single point; however, regions of the surface within electrostatic or steric range of the bacteria exert force on it and are therefore part of the interaction zone. Approximating an S. aureus bacterium (radius a = 500 nm) as a rigid 1-μm-diameter sphere 7807
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the bacteria−nanoparticle binding strength and potentially also by the influence of electrostatics on the bacteria−surface contact area. Larger electrostatic interaction areas make it easier for approaching bacteria to encounter the requisite number of nanoparticles. The interaction area, if electrostatically controlled rather than sterically, scales as κ−1/2.13,30 At the same time, the electrostatic binding energy per nanoparticle should be linear in κ for small potentials, obscuring the overall expected scaling. The perspective on bacteria−nanoparticle binding, on a per nanoparticle basis, follows from a consideration of the hydrodynamic forces on a 1-μm-diameter sphere. The shear force on a sphere adhering to the wall of the chamber is Fs = 0.03205γ(a2), with Fs in Newtons when a is in meters.31,32 For 1 μm spheres, this shear force increases from 0.18 to 6.4 pN as γ varies from 22 to 795 s−1. For a captured bacterium to be held at the surface by a single nanoparticle, the binding force, which is primarily electrostatic, as evidenced by the influence of ionic strength, must exceed the hydrodynamic pull-off force. At the point where pull-off is just about to occur, the energy barrier opposing pull-off is reduced by the pull-off force times a characteristic bond distance.33 As pull-off conditions are approached (or, equivalently, during the moment of initial capture), the binding and hydrodynamic pull-off forces approach each other but need not be equal, Fbind ≥ Fhydro. Multiplying the binding force by a characteristic capture length provides a lower bound on the binding energy when the equality is used. Using the Debye length as the bond length and a force of 0.18 pN, corresponding to capture at γ = 22 s−1, one obtains 0.18kT as the lower limit of the bond energy. As we observed, for the removal of most bacteria within a minute of increasing the flow to γ = 50 s−1 (shortly after the initial capture), one might use a force of 0.36 pN, giving 0.36kT for the minimum per nanoparticle bond energy. As explained by Evans, however, even bonds on the order of 40kT can fail under “miniscule forces.”33 Although the energy barrier to dissociation is reduced by external forces, the thermally activated nature of the bacteria−nanoparticle bonds allows dissociation across the remaining energy barrier. As a result, the slow application of the external force tends to favor long bond lifetimes and failure under relatively weak forces. Conversely, the fast application of external force gives more immediate bond failure but higher apparent pull-off forces. In our case, an increase in the hydrodynamic force from the monovalent capture conditions at 0.18 pN (22 s−1 and κ−1=4 nm) to a level favoring the relatively rapid removal of most bacteria (0.36 pN) over about a second (the time needed to adjust the pump) gives a force loading rate of about 0.2 pN/s (within about an order of magnitude). The observed bond failure of 0.36 pN at this higher flow rate, while giving the initial appearance of a very weak bond, is actually consistent with the possibility of strong bonding. For instance, avidin−biotin bonds, which are established to be among the strongest, have been shown to fail with pull-off forces of less than 5 pN when the force is applied slowly, for instance, 0.05 pN/s.33 The observed capture and release behavior of bacteria in the monovalent regime is therefore consistent with strong binding and also with the natural consequences of the coupling of hydrodynamic interactions to localized adhesive interactions between a surface and a larger target.
Figure 6. Calculated bacterial capture probabilities as a function of nanoparticle loading for bacteria−surface contact areas of 5000 () and 1000 nm2 (---). The annotation on the curves indicates the minimum number of nanoparticles involved in capture. The dashed boxes around the annotation correspond to the dashed curves. The right y axis shows an example translation to capture efficiency for a reasonable choice of the transport-limited rate relative to the probability.
nanoparticles. Additionally, it seems reasonable that six nanoparticles (10 nm each) could fit into a 2500 nm2 interaction area, consistent with the emerging structural picture of the interaction zone at high shear. This relatively dense local concentration of nanoparticles is physically realizable but unlikely, consistent with the observed small bacterial capture efficiencies under high-shear conditions (γ = 795 s−1). Table 1 summarizes the best-fit valencies for the conditions studied. We note that the 2500 nm2 contact area is reported Table 1. Summary of the Valency of Nanoparticle Capture wall shear rate, s−1 Debye length, nm
22
1 2 4
3 2 1
55
110
795
2
5 3 3
7 5 4
here for the particular conditions corresponding to κ−1 = 4 nm. To the extent that the contact is dominated by electrostatics, smaller areas would apply at smaller Debye lengths, following the geometrical formula above. These different contact areas, then, potentially influence the valency analysis in which Figure 6 is compared with Figure 3A,B. Even with smaller contact areas, tending toward 1000 nm2, the qualitative conclusions are not altered. The number of nanoparticles involved in bacterial capture is small, on the order of three to five, when the wall shear is high, approaching 800 s−1. Scaling with Flow and Ionic Strength. In Figure 4A, the thresholds increase approximately linearly in shear rate. A roughly linear dependence of the thresholds on flow makes sense because for capture to occur greater numbers of nanoparticles are needed to oppose the increasing hydrodynamic force. Also needed to explain the near linearity of Figure 4A is the fact that for a random distribution of elements the threshold in the average surface loading turns out to grow in proportion to the target number (or valency) itself, at least when the valency is small. In Figure 4B, the observed nearly linear decrease in the adhesion thresholds with increased Debye length suggests that the adhesion threshold is dominated by the influence of salt on 7808
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CONCLUSIONS AND SIGNIFICANCE This study demonstrated that when cationic nanoparticles are immobilized on an otherwise nonadhesive surface their capture of S. aureus bacteria is generally multivalent. This bacterial capture occurs at surface positions that randomly contain above-average densities of nanoparticles. Because bacteria− nanoparticle attractions are electrostatic, the ionic strength influences the per nanoparticle binding energy. More interesting, however, is that variations in flow tune the capture valency and, in the limit of gentle flow, it is possible to capture individual bacteria with single surface-immobilized nanoparticles. This hydrodynamic switching of the bacteria capture valency represents a rapidly tunable, highly precise means to manipulate bacterial adhesion. For instance, increasing the flow from 22 to 55 s−1 can produce a switch from monovalent to divalent bacterial capture. Changing the flow rate also provides a means to direct bacteria to specific surface regions having different local concentrations of nanoparticles. A comparison of the experimental capture efficiencies to the statistical probabilities of bacteria capture revealed both the effective bacteria−surface contact area and the numbers of nanoparticles needed for bacteria capture. Despite the uncertainty introduced by the maximum probability that could be measured for transport-limited bacteria capture and by error on the bacteria−surface interaction area, the error in the valency was small: the numbers of nanoparticles engaging bacteria was shown to be small (less than seven) with an error of only one or two nanoparticles under the conditions studied. At the monovalent−divalent transition, the error vanished. The experimentally determined interaction area inferred here, about 2500 nm2 (but in the range of 1000−5000 nm2), is the first report of an adhesive area for bacteria interactions to our knowledge. It was determined in the regime of monovalent capture (specifically for conditions of γ = 22 s−1 and κ−1 = 4 nm) and represents the range of steric and/or electrostatic interactions between bacteria and the surface. Its small size reflects that it corresponds only to initial bacteria capture. Once bacteria start to adhere, further bacterial deformations or compression of the polymer brush on the substrate occurs as the bacteria adhere more strongly.9 Our results suggest that such increases in binding strength happen even in the first few minutes of contact. Therefore, the interaction area revealed in this study pertains to the area of collecting surfaces that can be felt by a flowing bacterium, close to the surface, at the instant before it engages. We expect, with continued scientific interest in bacteria−biomaterial interactions, other estimates of the contact area to emerge in the literature. Notably, measurements even a few minutes after initial contact, for instance, by microscopy methods, would be expected to reveal larger areas. Geometrical arguments suggest that even nanoscale deformations of the bacterial lipopolysaccharide layer or the polymer brush on the substrate will increase the contact zone by tens of nanometers. This article documents bacteria−nanoparticle capture/pulloff forces in the range of 0.2−6 pN, depending on the ionic strength. This range concurs with previous reports of nonspecific bacterial binding forces.3−5 The observations of bacterial removal at a wall shear rate of 50 s−1 for bacteria captured by single nanoparticles suggest weak pull-off forces, consistent with the shear sensitivity of biological ligand− receptor pairs. An important issue is the significance of these results to other biological and materials systems. Although we
have produced these results with only a single bacterial type, S. aureus, we expect that other round, capsular bacteria will exhibit qualitatively similar contact areas and valencies to those seen here. Variations in the bacterial surface charge, the distribution of charge over bacterial surfaces, and the softness and thickness of the lipopolysaccharide layer are expected to affect the contact area and, ultimately, the valency. Finally, it is worth commenting that the richness of using shear to tune the bacterial capture valency includes the rapid manipulation of nanoscale interactions (compared to tuning adhesion through the introduction of salt or chemical agents, which add a diffusion time) and also the directing of particles to particular surface features. At high shear, bacteria can adhere only on relatively rare “hot spots”, for instance, a 2500 nm2 region containing six nanoparticles. Because such regions on the surface are few, the accumulation rate of bacteria on these hot spots is small but adhesively selective. By contrast, at gentle flow, a greater area of the surface will be sufficiently loaded with nanoparticles to capture bacteria. In this way, bacterial adhesion to the stickiest surface regions is most selective at high shear.
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ASSOCIATED CONTENT
S Supporting Information *
Transport-limited bacterial capture on a substantially cationic surface. Statistical model for bacterial capture. Monovalent capture and the initial bacteria−surface interaction area. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work was supported by NSF DMR-0805061 and the UMass NSF NSEC, the Center for Hierarchical Manufacturing (CMMI-1025020).
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