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Langmuir 2008, 24, 10988-10995
Coupled Electrostatic, Hydrodynamic, and Mechanical Properties of Bacterial Interfaces in Aqueous Media Fabien Gaboriaud,*,† Michelle L. Gee,§ Richard Strugnell,| and Je´roˆme F. L. Duval‡ Laboratory of Physical Chemistry and Microbiology for the EnVironment, Nancy-UniVersity, CNRS, 405 rue de VandoæeuVre, F-54600 Villers-le`s-Nancy, France, Laboratory of EnVironment and Mineral Processing, Nancy-UniVersity, CNRS, Box 40, F-54501 VandoeuVre-le`s-Nancy Cedex, France and School of Chemistry and Department of Microbiology and Immunology, UniVersity of Melbourne, Victoria 3010, Australia ReceiVed January 25, 2008. ReVised Manuscript ReceiVed March 12, 2008 The interactions of bacteria with their environment are governed by a complex interplay between biological and physicochemical phenomena. The main challenge is the joint determination of the intertwined interfacial characteristics of bacteria such as mechanical and hydrodynamic softness, interfacial heterogeneity, and electrostatic properties. In this study, we have combined electrokinetics and force spectroscopy to unravel this intricate coupling for two types of Shewanella bacterial strains that vary according to the nature of their outer, permeable, charged gel-like layers. The theoretical interpretation of the bacterial electrokinetic response allows for the estimation of the hydrodynamic permeability, degree of interfacial heterogeneity, and volume charge density for the soft layer that constitutes the outer permeable part of the bacteria. Additionally, the electrostatic interaction forces between an AFM probe and the bacteria were calculated on the basis of their interfacial properties obtained from advanced soft particle electrokinetic analysis. For both bacterial strains, excellent agreement between experimental and theoretical force curves is obtained, which highlights the necessity to account for the interfacial heterogeneity of the bioparticle to interpret AFM and electrokinetic data consistently. From the force profiles, we also derived the relevant mechanical parameters in relation to the turgor pressure within the cell and the nature of the bacterial outer surface layer. These results corroborate the heterogeneous representation of the bacterial interface and show that the decrease in the turgor pressure of the cell with increasing ionic strength is more pronounced for bacteria with a thin surface gel-like layer.
Introduction The physicochemical properties of bacterial surfaces in aqueous media govern, to a large degree, numerous interfacial phenomena involving bacteria (e.g., bacterial adhesion,1 biocorrosion,2 bacterial infection3 and biofilm formation4). Over the past decade, many attempts have been made to quantify the surface properties of bacterial cells. For example, the hydrophobic/hydrophilic character of cells has been inferred from the macroscopic measurements of water contact angles of bacterial lawns,5 the partitioning of bacteria between water and various nonpolar solvents,6 and the efficiency of cell adhesion in a parallel-plate flow chamber.7 The interfacial properties of bacterial cells are usually described in terms of a single parameter, the electrokinetic or zeta potential (ζ), which is evaluated from electrophoretic mobility measurements8 and subsequently used to estimate the charge density over the bacterial surface. Traditionally, these * To whom correspondence should be addressed. E-mail: gaboriaud@ lcpme.cnrs-nancy.fr. Tel: 33 3 83 68 52 39. Fax: 33 3 83 27 54 44 † Laboratory of Physical Chemistry and Microbiology for the Environment, Nancy-University. ‡ Laboratory Environment and Mineral Processing, Nancy-University. § School of Chemistry, University of Melbourne. | Department of Microbiology and Immunology, University of Melbourne. (1) Bos, R.; van der Mei, H. C.; Busscher, H. J. FEMS Microbiol. ReV. 1999, 23, 179–230. (2) Busalmen, J. P.; Valcarce, M. B.; de Sanchez, S. R. Corrosion ReV. 2004, 22, 277–305. (3) Bavington, C.; Page, C. Respiration 2005, 72, 335–344. (4) Hall-Stoodley, L.; Costerton, J. W.; Stoodley, P. Nat. ReV. Microbiol. 2004, 2, 95–108. (5) Van der Mei, H. C.; Bos, R.; Busscher, H. J. Colloids Surf., B 1998, 11, 213–221. (6) Bellon-Fontaine, M. N.; Rault, J.; van Oss, C. J. Colloids Surf., B 1996, 7, 47–53. (7) Busscher, H. J.; van der Mei, H. C. Clin. Microbiol. ReV. 2006, 19, 127– 141. (8) Poortinga, A. T.; Bos, R.; Norde, W.; Busscher, H. J. Surf. Sci. Rep. 2002, 47, 1–32.
types of data are used to predict the double-layer interaction force as evaluated from DLVO theory in its simplest or extended version.1 The DLVO theory, which dates back to the late 1940s, was originally developed to describe the interactions between impermeable and nondeformable colloids. Various theoretical analyses have pointed out the inadequacy of this formalism for soft colloidal particles such as bacteria, which are, in essence, heterogeneous, permeable, and deformable particles.9–12 The emergence of new experimental techniques such as AFM, which can probe interfacial phenomena on the nanometer length scale, enables bacterial organisms to be investigated in liquid media without the need to alter the bacterial envelope, as required by more traditional methods (e.g., freezing or cryoscopic manipulation). Of particular note are the recent advances in the measurement and identification of the mechanical characteristics of bacterial cells,13,14 single molecular recognition events on bacterial surfaces,15,16 and cell-solid and cell-cell interactions by using a cell as an AFM probe.17–19 Despite these advances, few studies have attempted to combine experimental and appropriate theoretical analyses of bacterial physico-chemical surface properties. Thus, the challenge remains to identify and (9) Duval, J. F. L.; Ohshima, H. Langmuir 2006, 22, 3533–3546. (10) Hill, R. J.; Saville, D. A.; Russel, W. B. J. Colloid Interface Sci. 2003, 258, 56–74. (11) Hill, R. J.; Saville, D. A. Colloids Surf., A 2005, 267, 31–49. (12) Lopez-Garcia, J. J.; Grosse, C.; Horno, J. J. Colloid Interface Sci. 2003, 265, 327–340. (13) Touhami, A.; Nysten, B.; Dufreˆne, Y. F. Langmuir 2003, 19, 4539–4543. (14) Gaboriaud, F.; Bailet, S.; Dague, E.; Jorand, F. J. Bacteriol. 2005, 187, 3864–3868. (15) Ahimou, F.; Denis, F. A.; Touhami, A.; Dufreˆne, Y. F. Langmuir 2002, 18, 9937–9941. (16) Hinterdorfer, P.; Dufreˆne, Y. F. Nat. Methods 2006, 3, 347–355. (17) Benoit, M.; Gaub, H. E. Cell Tissue Organs 2002, 172, 174–189. (18) Lower, S. K.; Hochella, M. F.; Beveridge, T. J. Science 2001, 292, 1360– 1363. (19) Wright, C.; Armstrong, I. Surf. Int. Anal. 2006, 38, 1419–1428.
10.1021/la800258n CCC: $40.75 2008 American Chemical Society Published on Web 05/30/2008
Coupled Properties of Bacterial Interfaces
Figure 1. Schematic representation of the outer permeable charged gellike layer of thickness L for the two Shewanella strains used in this study. The sketches are based on electron micrographs by Korenevsky et al.41
quantitatively evaluate the molecular characteristics of the bacterial interface that govern the interactions of bacteria with their surrounding media. This avenue of inquiry should provide new insights toward a better understanding of bacterial interfaces and shed light on how these relate to bacterial behavior (e.g., in bioadhesion phenomena). To this end, we have combined force spectroscopy and advanced electrokinetic analysis to evaluate the physicochemical properties and molecular-level structure of the interface between rod-like Shewanella bacteria and KNO3 electrolytic medium. We investigate two types of bacterial strains with different outer permeable charged gel-like layers (Figure 1): one with a thick hydrated carbohydrate layer (Shewanella oneidensis MR-4) and another with a thin lipopolysaccharide ultrastructure (S. putrefaciens CN32). The theoretical interpretation of the electrokinetic data allows for the quantification of the electrohydrodynamic characteristics of both bacterial strains. On the basis of those, we evaluate the electrostatic interaction forces between the AFM tip and the bacteria by considering either a homogeneous or heterogeneous spatial distribution for the polymer segment density within the soft, permeable gel-like layer at the periphery of the bacteria. For both systems examined (MR-4 and CN32), the electrostatic contribution to the experimental force profiles obtained by force spectroscopy is in excellent agreement in magnitude and range with that estimated from the force expression based on a diffuse representation of the bacteria/electrolyte interface. We also investigate the nanomechanical features of the bacterial cell from the force profiles and demonstrate the possibility to derive from those the structure of the bacterial envelope.
Experimental Section Bacterial Culture and Preparation. Shewanella putrefaciens CN32 (ATCC BAA-453) and Shewanella oneidensis MR-4 were kindly provided by Professor T. J. Beveridge (University of Guelph, Ontario, Canada). Bacterial strains were twice successively revived from a stock suspension at -80 °C on a TSA medium (51044Biome´rieux, Marcy l’Etoile, France) for 48 h at 30 °C to remove glycerol. Cultures were then prepared in 250 mL Erlenmeyer flasks containing 20 mL of a bacterial suspension (NaCl 0.7%, optical density, OD600nm ) 0.5) and 200 mL of TSB (30 g/L, 51019BioMerieux) and then incubated for 14 h with shaking (150 rpm, 30 °C). Cells were then harvested, in a pseudostationary phase, by centrifugation (10 min, 10 000g), washed twice with adequate KNO3 solution (0.1 mol/L or 0.001 mol/L), and subsequently used for AFM experiments. For electrophoretic mobility measurements, which require a larger number of cells, bacteria were grown in a 750 mL batch reactor (300 rpm, 30 °C, 25 L/h air flux) over 24 h and harvested in a pseudostationary phase by centrifugation (10 min, 10 000g) and then washed twice in 0.001 mol/L KNO3 and resuspended to reach a final concentration ranging from 5 × 106 to 1 × 107 cells/mL. Electrophoretic Measurements. Electrophoretic mobilities were measured using a Zetaphoremeter IV (SEPHY-CAD instrumentations, Les Essarts le Roi, France) at room temperature. The bacterial suspensions were adjusted with respect to pH and ionic strength by using appropriate aliquots of KOH, HNO3, and KNO3 solutions of
Langmuir, Vol. 24, No. 19, 2008 10989 known concentrations and were subsequently injected into the electrophoresis chamber, which consists of a quartz suprasil cell where a constant electric field (800 V/m) is generated between two palladium-covered electrodes. The bacterial mobilities were calculated through laser reflection by bacteria via an optical image recorded at different times with a CCD camera. Different cycles were performed to record at least 100 bacteria trajectories for each condition. Force Spectroscopy Measurements. Force curves were obtained at room temperature using an MFP-3D instrument (Asylum Research, Santa Barbara, CA). Silicon nitride cantilevers were purchased from Veeco (MLCT-EXMT-BF, Santa Barbara, CA), and their respective spring constants were calibrated using the thermal calibration method with, as a result, an average value of 60 ( 5 pN/nm. Prior to experiment, the geometry of the tip was systematically controlled using a commercial grid for 3-D visualization (TGT1, NT-MTD Company, Moscow, Russia). All force experiments were carried out in 1 and 100 mM potassium nitrate solutions at neutral pH. Cells were immobilized by physical adsorption onto polyethyleneimine (PEI)-coated glass slides, as described elsewhere.20 Glass slides were freshly prepared by incubation in PEI solution (0.2%, 4 h), rigorously rinsed with Milli-Q water, and dried under sterile conditions. A droplet of bacterial suspension (OD600nm ) 1) of given ionic strength was deposited onto the PEI-prepared slide for a period of 1 h and subsequently rinsed before use in AFM experiments. First, cells were imaged in contact mode to locate the bacterium by minimization of the force applied so as to avoid the detachment of bacteria. Force volume data were then collected to locate accurately the apical surface of the cell using a 10 × 10 grid at scan rate of 1 µm s-1 (no impact of the loading rate between 0.01 and 5 µm s-1 on the force profiles) and with a 10 nN force trigger following the procedure described previously.21 It is emphasized here that experiments carried out at different loading rates (from 0.01 up to 5 µm s-1) did not reveal any significant loading-rate dependence for the force curves, which suggests no major energy dissipation during the measurements. These results further indicate that the dynamics of the outer/inner parts of the cells come into play for faster approaching/retracting rates of the tip than that chosen for our study and that our results essentially pertain to fully relaxed systems (i.e., at thermodynamic equilibrium).
Theoretical Framework In a pioneering study by Ohshima, flow permeation has been explicitly included in electrokinetic models of bacteria for deriving their volume charge density and hydrodynamic permeability from raw electrophoretic mobility measurements.22 This formalism has been recently refined with including the diffuse (i.e., heterogeneous) character of soft bacterial interfaces as generally characterized by an interfacial region where the structural, electrostatic and hydrodynamic properties gradually change from bulk cytoplasm, peripheral membrane to bulk aqueous electrolyte.9 The formalism of diffuse soft interfaces enables -without any restriction on the bacterial size and magnitude of the electrostatic potential distribution at the interface bacteria/ electrolyte- the retrieval from electrophoretic bacterial mobility data of the volume charge density, hydrodynamic properties and diffuse character of the most external permeable charged soft layers. The model is particularly relevant for considering the dynamics of discreet surface structures (pili, polymeric capside, etc) that lead to highly diffuse bacterial interfaces that may evolve (swell or shrink) as a result of changes in physico- chemical conditions of the medium. A successful application of the above formalism has been performed for analyzing the interfacial (20) Burks, G. A.; Velegol, S. B.; Paramonova, E.; Lindenmuth, B. E.; Feick, J. D.; Logan, B. E. Langmuir 2003, 19, 2366–2371. (21) Gaboriaud, F.; Parcha, B. S.; Gee, M. L.; Holden, J. H.; Strugnell, R. A. Colloids Surf. B 2008, 62, 206–213. (22) Ohshima, H. AdV. Colloid Interface Sci. 1995, 62, 189–235.
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permeable charged gel-like layer may be described by a function of the form
f(r) )
{
(
r - (ac + L) n(r) 1 ) ω 1 - tanh no 2 R
)}
(1)
where no is the nominal segment density for a homogeneous segment distribution, n(r) is the spatial dependence of the polymer segment density within the permeable charged gel-like layer, r is the radial position according to the polar coordinate system taken at the center of the particle (Figure 2A), ac is the radius of the particle core, and L is the thickness of the permeable charged gel-like layer. The characteristic parameter R/L represents the degree of diffuseness of the interface with the limit R/L f 0 implying a step-like or homogeneous soft layer distribution,12,22,26–28 (Figure 2B). The dimensionless parameter ω depends on ac, R, and L according to the explicit expression in ref 29 and imposes the constraint that the total number of polymer segments is constant upon variation of the interfacial diffuseness as defined by the magnitude of the ratio R/L. Assuming that the local charges are homogeneously distributed along the polymer chains, the function f(r) introduced in eq 1 represents the radial distribution of the normalized volume density of fixed charges. For highly hydrated soft surface layers, f(r) further pertains to the distribution of the normalized local friction exerted by the polymer segments on water flow through the permeable polymer network. Therefore
f(r) ) Figure 2. (A) Schematic representations of the bacterium/solution interface showing both 3-D and cross-sectional views of the cylindrical bacterium. The bacterium is modeled as a soft particle composed of a hard core of radius ac and a permeable charged gel-like layer of thickness b in an electrolyte solution in response L, that is moving with a velocity U to an applied dc electric field b E. The polar coordinates (r, θ) are indicated. The electrophoretic mobility µ is defined as the ratio U/E. (B) Schematic diagram of the function f(r) that represents the normalized spatial distribution of the polymer segment density, the friction coefficient, and the fixed charges of the polymeric shell. The degree to which the interface is diffuse is subsumed in parameter R/L
features of two strains of Streptococcus saliVarius23 and four strains of Shewanella species.24,25 Modeling the Soft Rod-like Bacterium: Homogeneous versus Diffuse Representation. Bacteria of interest here may be assimilated to rod-like bioparticles on the micrometer length scale (typically between 3 and 4 µm). The presence of the thin lipopolysaccharide or thick hydrated carbohydrate layer at the periphery of the bacteria (Figure 1) confers upon them a hydrodynamic permeability or, said differently, a certain propensity for fluid flow penetration. For that reason, bacteria may be regarded as paradigms of so-called soft (bio)colloids.22 The bacteria are modeled as soft particles (Figure 2A) composed of (i) a hard-core, which is stricto sensu impermeable to water flow and corresponds to the cytoplasmic part of the bacterial cell that withstands the considerable inner turgor pressure and (ii) a permeable, charged gel-like layer located at the bacterial periphery. Without any detailed molecular information on the local distribution of the soft matter that surrounds the cytoplasm, as is generally the case for bacterial systems, the spatial density distribution, f(r), of polymer segments that constitute the (23) Duval, J. F. L.; Busscher, H. J.; van de Belt-Gritter, B.; van der Mei, H. C.; Norde, W. Langmuir 2005, 21, 11268–11282. (24) Dague, E.; Duval, J.; Jorand, F.; Thomas, F.; Gaboriaud, F. Biophys. J. 2006, 90, 2612–2621. (25) Gaboriaud, F.; Dague, E.; Bailet, S.; Jorand, F.; Duval, J.; Thomas, F. Colloids Surf., B 2006, 52, 108–116.
( )
Ffix(r) λ(r) ) Fo λo
2
(2)
where Fo and λo are the volume charge density and the hydrodynamic softness parameter within the homogeneously distributed soft gel-like structure (limit R/L f 0), respectively. The quantity 1/λo defines the characteristic penetration length of flow within the permeable gel-like layer. Ffix(r) and λ(r) denote the local volume charge density and hydrodynamic softness throughout the water-permeable part of the particle, respectively. Electrokinetic Model for a Rod-like, Diffuse Soft Particle. The electrophoretic mobility, µ, for a cylindrical or rod-like particle depends on the orientation of its long axis relative to the direction of the applied dc electric field (Figure 2A). As for hard cylinders, the mobility of a soft, cylindrical particle oriented at an arbitrary angle between its axis and an applied field is averaged over a random distribution of orientations as follows30
2 1 µ ) µ⊥ + µ| 3 3
(3)
where µ⊥ and µ| are the electrophoretic mobilities of the cylindrical particle with its axis perpendicular and parallel to the applied electric field, respectively. Following the strategy developed in ref 9 for the electrohydrodynamics of spherical diffuse soft particles and in ref 29 for the case of rod-like particle geometry, µ⊥ and µ| are obtained upon numerical resolution of the set of coupled Navier-Stokes, Poisson-Boltzmann, and continuitygoverning equations explicitly given in Supporting Information (SI) for a particle of cylindrical geometry in an electrolyte of dielectric permittivity εoεr composed of N different ionic species, i, with valency zi and bulk concentration ci∞. In particular, it is (26) Ohshima, H. J. Colloid Interface Sci. 1994, 163, 474–483. (27) Ohshima, H. Colloid Polym. Sci. 2005, 283, 819–825. (28) Lopez-Garcia, J. J.; Grosse, C.; Horno, J. J. Colloid Interface Sci. 2003, 265, 341–350. (29) Duval, J. F. L.; Slaveykova, V. I.; Hosse, M.; Buffle, J.; Wilkinson, K. J. Biomacromolecules 2006, 7, 2818–2826. (30) De Keizer, A.; Van Der Drift, W. P. J. T.; Overbeek, J. T. Biophys. Chem. 1975, 3, 107–108.
Coupled Properties of Bacterial Interfaces
Langmuir, Vol. 24, No. 19, 2008 10991
shown in ref 29 that the estimate of the perpendicular component involves the resolution of the following coupled differential equations:
∇2y(r) )
{
}
N
∑
F F z c∞ exp{-ziy(r)} + Fo f(r) RTεoεr i)1 i i
[
(4)
df(r) dh(r) )dr dr F 1 dy(r) c∞z 2 exp{-ziy(r)}χi(r) (5) η r dr i i i
]
Ξr{Ξrh(r)} - λo2 f(r)Ξrh(r) +
∑
and
i ) 1, ... , N:Ξrχi(r) )
{
dy dχi(r) λi h(r) z dr i dr e r
}
(6)
where y(r) in eqs 4 and 5 denotes the local dimensionless equilibrium potential (in the absence of an applied field) determined from the nonlinearized form of the Poisson-Boltzmann equation across the polymeric shell layer, R is the gas constant, F is the Faraday constant, T is the temperature, λji is the drag coefficient of the ith ion, η is the dynamic viscosity of water, and Ξr is the radial operator given by eq S9 in SI. Essentially, the function χi(r) in eqs 5 and 6 accounts for the local deviation of the electrochemical potential of the ith ion with respect to its equilibrium value. The determination of the radial function h(r), which enters the definition of the radial and azimuthal components of the flow velocity profile relative to the particle (eq S4 in SI) under appropriate boundary conditions (eqs S12 and S13 in SI) allows the evaluation of µ⊥ (eq S15 in SI). When the cylindrical particle is oriented parallel to the electric field b E, the Navier-Stokes equation is simply given by
(
)
1 d duz(r) EF r - λo2f(r) uz(r) r dr dr η
∑ zici∞exp(-ziy(r)) ) 0 i
(7) where the radial function uz(r) corresponds to the z component of the flow velocity. Once uz(r) is known, the component µ| may be obtained (eq S42 in SI). The electrostatic interaction force between a hard spherical AFM probe and a soft rod-like particle is determined theoretically. The electrostatic interaction force between a hard sphere (AFM tip of radius as) and a soft rod-like particle (bacterium of core radius ac and a permeable charged gel-like layer of thickness L, Figure 1) separated by a distance H, as defined in SI Figure S1A, is calculated upon differentiation with respect to H of the electrostatic contribution to the total Gibbs free energy of interaction, Usc, in the case of a 1:1 electrolyte of bulk concentration c∞. (Details of the calculation are available in SI.) As a first approximation, we chose to model rigorously the only electrostatic forces in the absence of surface layer deformation (upon decreasing the separation distance H) and van der Waals interaction. (See motivations and details in SI.) Using the Derjaguin approximation, Usc may be derived from the electrostatic component of the Gibbs free energy per unit surface area for the interaction between two parallel planar surfaces, Upp, according to31
Usc(H) ) 4ac
∫0π⁄2 ∫0a Upp(γ(H, z, θ)) dzdθ s
(8)
where the meanings of H, z, and θ are as indicated in SI Figure S1B. The function γ represents the distance between surface (31) Gu, Y. J. Colloid Interface Sci. 2000, 231, 199–203.
elements taken on both particles that face each other. (See SI Figure S1B.) The electrostatic interaction energy Upp may be calculated by integration of the disjoining pressure, Πpp, defined as the sum of an osmotic and electrical (i.e., Maxwell stress) component, that is,32
Πpp(H) ) 2c∞RT{cosh[y(H)] - 1} -
εoεr RT 2 F
( ) ( dy(H) dx ) 2
2
(9) where x is the dimension perpendicular to the bacterial interface and the function y(x) denotes the dimensionless electrostatic potential distribution in between the two parallel planar surfaces considered. For a potential distribution that exhibits a minimum at a position x ) xo, eq 9 simplifies to
Πpp(H) ) 2c∞RT{cosh[yx)xo(H)] - 1}
(10)
Using an iterative finite differences scheme according to a globally convergent Newton- Raphson method,33 the potential distribution is computed from the Poisson-Boltzmann equation under appropriate boundary conditions (Eqs S46-S47 in SI) for the interaction configuration depicted in SI Figure S1A. This allows the position xo, the corresponding (dimensionless) potential yx)xo, the disjoining pressure Πpp, the electrostatic component of the Gibbs energy Usc, and the associated electrostatic interaction force to be evaluated as a function of H. (Details of the calculation are available in SI.)
Results Soft Particle Analysis of the Electrokinetic Data. Quantitative evaluation of the electrophoretic mobilities for the two Shewanella strains MR-4 and CN32 is carried out on the basis of the electrokinetic theory for diffuse soft rod-like particles described above and relies on the determination of three relevant parameters: the flow penetration length 1/λo, the volume charge density Fo, and the decay length R for the material density distribution within the outer permeable charged gel-like layer of the particle. To scrutinize the effect of interfacial diffuseness on the electrohydrodynamic properties of the bacteria, the quantitative interpretation of electrokinetic data is performed according to a procedure that we now explain. First, the volume charge density and the hydrodynamic permeability of the soft bacterial gel-like layer are determined, using a least-squares method, from the merging between theoretical and experimental data for sufficiently high ionic strengths (i.e., where an approximately mobility plateau value is reached). A step-function representation of the interface between the bacterium and the aqueous solution (R/L f 0) is assumed for that purpose. At such ionic strengths, the diffuseness of the interface does not play a role in determining the electrophoretic mobility of the particle.9 From the set of parameters obtained, the electrophoretic mobilities are then computed over the whole range of electrolyte concentrations. Any deviation from the experimental data at low ionic strength is then quantitatively adjusted via either the volume charge density within the permeable charged gel-like layer (i.e., decrease in |Fo|) or the diffuseness of the interface (i.e., increase in R/L). The former case is the result of the decrease in the number of charges within the gellike layer with decreasing ionic strength without volume change. It may also be attributed to homogeneous swelling of the gel(32) Lyklema, J. Fundamental of Interfaces and Colloid Science:Particulate Colloids; Elsevier: Amsterdam, 2005; Vol. 4. (33) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannerty, B. P. Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1986.
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Figure 4. Theoretically predicted and experimental surface force profiles for the interaction between the AFM tip and two different bacterial strains, MR-4 and CN32. The predicted data were computed for MR-4 (left side) using the homogeneous layer model (dotted curve, R/L ) 0) with Fo ) -7 mM and the diffuse layer model (solid curve) with Fo ) -10 mM and R/L ) 0.06. This was done similarly for CN32 (right side) using the homogeneous model (dotted curve, R/L ) 0) with Fo ) -15 mM and the diffuse model (solid curve) with Fo ) -35 mM and R/L ) 1.
Figure 3. Experimental (filled circles) and theoretical (curves) electrophoretic mobilities (expressed in dimensionless form) as a function of ionic strength at neutral pH for S. oneidensis strain MR-4 (left side) and S. putrefaciens strain CN32 (right side). The experimental data were first analyzed at high ionic strengths, assuming a homogeneous distribution of polymer segments within the permeable charged gel-like layer. From the fits (dotted lines), we quantified the hydrodynamic softness λ0-1 and the volume charge density Fo as λ0-1 ) 3.5 nm Fo ) -10 mM for MR-4 and λ0-1 ) 2.0 nm Fo ) -35 mM for CN32. Below a critical concentration cc∞ (indicated by arrows) defined as the ionic strength at which these theoretical fits deviate from measurements, the experimental data were fitted by either (A) tuning the volume charge density, still assuming a homogeneous distribution of polymer segments in the permeable gel-like layer (R/L ) 0) or (B) increasing the diffuseness of the bacterial interfaces (i.e.. R/L).
layer due to an increase in the range of segment-segment electrostatic repulsion with decreasing electrolyte concentration without changing the number of charges. The latter situation evoked above (increase in the interfacial diffuseness) arises when swelling of the permeable gel-like layer around the bacteria is heterogeneous, implying a diffuse spatial gradient of soft material density at the interface. The computations performed under the assumption of a homogeneous distribution of the permeable charged gel-like layer at the periphery of bacteria MR-4 and CN32 are displayed in Figure 3A. For both the MR-4 and CN32 strains, the theory provides a very good fit to the experimental data with Fo ) -10 mM for MR-4 and Fo ) -35 mM for CN32 (Figure 3A, dotted lines). However, increasing deviations between experiment and theory are observed as the electrolyte concentration is decreased. This deviation is particularly marked for the CN32 strain. As stated above, such a deviation may arise from the assumption that the permeable, charged gel-like layer remains homogeneous and the volume charge density is fixed over the entire range of electrolyte concentration. However, it is likely that with decreasing ionic strength the magnitude of the volume charge density decreases as a result of changes in the number of charges within the gel-like layer (polyelectrolyte effect) or as a result of homogeneous swelling. Supporting this interpretation is that decreasing the magnitude of Fo when lowering the electrolyte concentration (Figure 3A, dashed lines) improves the quality of the fit to the experimental data at low ionic strengths. Interestingly, only minor adjustment of Fo from -10 to -7 mM is required for the MR-4 strain. However, for the CN32 cells, the adjustment
of Fo for recovering data at low ionic strengths is considerable (-35 to -15 mM). Another explanation for the deviation between the electrokinetic data at low ionic strengths and the theoretical prediction is that the diffuseness of the interface increases due to heterogeneous swelling of the permeable charged gel-like layer. This is consistent with the fact that the experimental data at low ionic strength can be fitted by adjustment, at fixed Fo, of parameter R representing the decay length of the segment density distribution at the gel-like layer/aqueous solution interface (Figure 3B for MR-4 and CN32). An increase in the dimensionless parameter R/L corresponds to an increase in the local concentration of charged segments at the onset of the gel-like layer of the particle where the electro-osmotic flow is most significant. Consequently, the friction exerted on the flow of water through the polymer network increases, resulting in a decrease in the magnitude of the electrophoretic mobility.9 Note that the increase in the diffuseness of the bacterium interface at low ionic strength is more pronounced for the CN32 strain, as indicated by the relatively large value of R/L (e.g., R/L ) 1 at 1 mM KNO3). For the MR-4 strain, the values obtained for R/L are significantly smaller (e.g., R/L ) 0.06 at 1 mM KNO3). Theoretical Evaluation of the Electrostatic Interaction Forces between the AFM tip and the Bacteria. On the basis of the electrohydrodynamic characteristics of the bacterial interfaces obtained from the analysis of the electrophoretic mobility data, we have estimated the electrostatic interaction force between the bacteria and the AFM tip. As recently reported,34 the quantitative evaluation of the electrostatic contribution to the net force profile for microbial cells is generally based on the solution of the Poisson-Boltzmann equation (either in linear or nonlinear form) for two interacting hard surfaces. This approach disregards the presence of permeable, soft, charged gel-like layers at the bacterial interfaces and the charge distribution within such a layer. Following the interpretations of the electrophoretic data, we estimated the double-layer (electrostatic) interaction between the soft bacteria and the hard AFM tip for the two distinct cases of either a homogeneous or diffuse soft layer representation. For both cases, the required interfacial parameters R/L and/or Fo are directly inferred from the electrohydrodynamic analysis detailed above. The results are reported at 1 mM ionic strength in Figure 4 and compared to the experimental force profiles as measured by force spectroscopy. Note that we have assumed the contact between the AFM tip and (34) Gaboriaud, F.; Dufreˆne, Y. F. Colloids Surf., B 2007, 54, 10–19.
Coupled Properties of Bacterial Interfaces
Figure 5. Sample interpretations of loading force profiles of S. oneidensis strain MR-4 (left side) and S. putrefaciens strain CN32 (right side) in neutral pH solution at different potassium nitrate concentrations: (A) 100 mM and (B) 1 mM.
the bacterium at the point where the measured force profile deviates from exponential behavior (details in SI). It is important to point out that no fitting procedure has been carried out to adjust the electrostatic force calculations, which were performed on the basis of the independently determined electrokinetic characteristics of the microbial cells investigated. In both cases (MR-4 and CN32), the diffuse representation of the bacterial interface describes more satisfactorily the experimental force profiles in terms of magnitude and range. Whereas the agreement is excellent for CN32, there is a slight deviation between theory and experiment in the case of MR-4 at surface separations higher than 10 nm, with the range of the experimental interaction forces being larger than predicted. Such an effect may arise from the deformation of the bacteria while the AFM tip is not in contact with the cell but still under significant pressure that originates from the repulsive electrostatic force between the AFM tip and the bacterial interface. As a whole, the agreement between theory and experiment for the electrostatic interactions the bacteria and AFM tip demonstrates the strength of using electrokinetics to predict the interaction forces measured by AFM. For the bacterial strains investigated here, the analysis leads us to suggest the diffuse representation of the bacterial interfaces as the appropriate physical picture at a low salt level. For the sake of completeness, we have evaluated the doublelayer interaction between the AFM tip and the CN32 and MR-4 bacterial strains at 100 mM. As expected, very weak doublelayer interactions were obtained and were well below the detection limit of the AFM instrument (SI Figure S2). This quantitatively justifies the assumption that the interaction forces at high ionic strength do not interfere with the measurement of the nanomechanical properties of soft, deformable interfaces.14,25 Below, we tackle such an analysis for MR-4 and CN32 at 1 and 100 mM salt levels. Quantitative Analysis of the Nanomechanical Properties of Bacterial Interfaces by Force Spectroscopy. Force profiles were measured for the interaction between bacterial strains MR-4 and CN32 and the AFM tip at low and high ionic strengths (1 and 100 mM KNO3; see SI Figure S3 for typical force curves). Shown in Figure 5 are the force versus tip-to-sample distance plots corresponding to the loading force measured upon approach of the bacterium to the tip. Note that at low electrolyte
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concentration (1 mM) the force profiles for both bacterial strains exhibit a measurable force at positive tip-to-sample values corresponding to the double-layer interaction between bacteria and the AFM tip as commented on and analyzed in the preceding section. At high electrolyte concentration (100 mM), doublelayer repulsion is considerably minimized so that no net force is detected until contact (i.e., at zero tip-to-sample distance) between the AFM tip and the bacterial surface is achieved. At negative tip-to-sample values, the measured force corresponds to the deformation or indentation, δ, of the bacterium under compression by the AFM tip. It is from this compressive part of the force profile that the nanomechanical properties of the deformable soft bacterial layer can be extracted, upon application of the appropriate formalism. Generally, the compressive part of the force profiles exhibits two regimes: a nonlinear regime for small applied loading forces and resulting small indentations and a linear regime upon further increase in the loading force applied by the AFM tip (SI Figure S3). It is well established that the gradient of the linear regime of the load-indentation curve is related to the turgor pressure that counteracts the compression of the bacterium’s cytoplasm by the AFM tip.35,36 This gradient is directly related to the bacterial spring constant, Kbacterium, expressed by Hooke’s law as
Floading ) Kbacteriumδ
(11)
where Floading is the loading force and δ is the indentation (i.e., the negative tip-to-sample distances). We denote the characteristic indentation value at the onset of linear compliance as δL0 (SI Figure S4). The distance between the indentation at the force trigger value and δL0 defines the spatial range over which eq 11 is obeyed. δL0 is expected to correspond to the inner membrane of the bacterium that withstands the turgor pressure of the cytoplasm. (See Figure 1 for a schematic representation of the bacterial envelope.) Therefore, the nonlinear regime, which ranges from the zero tip-to-sample distance to δL0, corresponds a priori to the compression of the permeable charged polymeric gel-like layer of thickness L at the bacterium’s periphery (Figure 1). To interpret this nonlinear part of the load-indentation curve, we have used the theory originally developed by Pincus for the compression of a polyelectrolyte brush layer.37 His formalism applies to the evaluation of the interfacial disjoining pressure between two similar polyelectrolyte brushes both end-grafted to a solid surface. (See SI for details.) However, any attempt to interpret the force profiles on the basis of the Pincus theory requires a knowledge of the absolute separation distance between the nondeformable substrates bearing the polymer. As a first approximation, we consider the onset of linear compliance, δL0, to be the origin of the apparent nondeformable surface, which in our case corresponds to the inner membrane of the bacteria. We also assume that the charged gel-like layer is located entirely on the bacteria and that there is no adsorption of polymer onto the AFM tip. Note that the various terms that enter the definition of the force involved in the compressive regime (eq S64 in SI) remain unknown and difficult to access for complex heterogeneous bacterial interfaces. We therefore simplify the equation by Pincus using a numerical prefactor, AP:
Floading ) Ap ln
[ ] -δL0 δ
(12)
It is observed that eq 12 does not reproduce the force profiles over the entire nonlinear regime. This is attributed to the inherent (35) Arnoldi, M.; Kacher, C. M.; Ba¨uerlein, E.; Radmacher, M.; Fritz, M. Appl. Phys. A 1998, 66, S613–S617. (36) Arnoldi, M.; Fritz, M.; Ba¨uerlein, E.; Radmacher, M.; Sackmann, E.; Boulbitch, A. Phys. ReV. E 2000, 62, 1034–1044.
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Table 1. Relevant Parameters Extracted from the Analyses of Force Profiles for CN32 and MR-4 Bacterial Strainsa CN32 ionic strength -1
Kbacterium (mN m ) -δL0 (nm) Lp (nm) L + 2.3R (nm)
MR-4
1 mM
100 mM
1 mM
100 mM
129 ( 42 50 ( 11 30 ( 7 16.5
64 ( 25 214 ( 100 109 ( 56 5
88 ( 43 279 ( 74 173 ( 60 102
61 ( 9 191 ( 39 81 ( 22 90
a The data are obtained from an analysis of n ) 50 experimental force curves and from the advanced soft particle electrokinetic analysis detailed in the article.
(ionic strength-dependent) deformable character of the cytoplasm that becomes significant when the load exceeds a given threshold value, thus leading to the coupled deformation of both the gellike layer and the inner bacterial cytoplasm. This constitutes a major limitation in applying the Pincus equation at large loading forces, the derivation of which implies that the surface supporting the deformable layer is hard and incompressible. We therefore define the thickness of the polyelectrolyte layer, Lp, as the absolute indentation value from which the Pincus prediction deviates from the experimental data (SI Figure S4). Sample force curve analyses are shown in Figure 5, and the relevant parameters extracted from the analysis of the data are collected in Table 1. The values of the bacterial spring constant are strongly dependent on the electrolyte concentration for the CN32 strain whereas for MR-4 no significant variation is observed. In the case of CN32, the value of Kbacterium at 100 mM is about 50% of that determined at 1 mM. Interestingly, the mean bacterial spring constant for CN32 at high salt content is similar, within experimental error, to that for MR-4. Similar trends are observed for the characteristic δL0 distances (onset of linear behavior): at high salt concentration, the mean value of δL0 for CN32 is significantly larger than at 1 mM and is of the same order of magnitude as that obtained for MR-4 at 1 and 100 mM. The thickness of the polyelectrolyte brush (LP, Table 1), estimated from the quantitative interpretation of the nonlinear regime, depends on the bacterial strain and the electrolyte concentration. In the case of CN32, the mean thickness at 1 mM is about 4 times lower than that determined at 100 mM. In contrast, a slight decrease in the mean thickness is observed for MR-4 with increasing ionic strength. Finally, the difference between δL0 and LP highlights the discrepancy between the Pincus description and the onset of the linear compliance regime. It clearly appears that such a difference is most pronounced for the data obtained at 100 mM KNO3. We comment on these observations in the following section.
Discussion In this work, the mechanical and electrohydrodynamic properties of bacterial surfaces are determined by combined electrokinetic and force spectroscopy analyses and interpreted on the basis of a soft, diffuse spatial representation for the interface between bacterium and surrounding aqueous electrolyte solution. Such a representation allows us to consider the diffuse nature of the bacterial envelope’s structure and analyze how this responds to variations of the physicochemical composition of the medium. Upon changing the ionic strength of the solution, as was done in this study, the native 3D soft, deformable structure at the periphery of the bacteria might swell or shrink. When modeling the electrokinetic behavior of the bacteria, it is necessary to account for the effects of electrolyte on the local distribution of the soft material density within the bacterial envelope. This can (37) Pincus, P. A. Macromolecules 1991, 24, 2912–2919.
be achieved by necessarily abandoning the conventional picture of the bacterial interface as homogeneously (step-like) hard and impermeable. Instead, we represent the bacterial interface as a soft polyelectrolyte layer with electrohydrodynamic properties expressed in terms of the hydrodynamic softness, 1/λ, and volume charge density, Ffix, both of which gradually decay from their respective maximum values within the bulk gel-like layer to zero in the electrolyte solution. For sufficiently large electrolyte concentrations, the repulsive electrostatic interactions between neighboring charged sites along thepolyelectrolytechainsarescreened.Attractivesegment-segment interactions therefore lead to the collapse of the polyelectrolyte layer. Under these conditions, the electrokinetic signature of the bacteria can be satisfactorily interpreted by considering the soft surface layer to be homogeneous (R f 0 in eq 1) with a fixed volume charge density. However, on lowering the electrolyte concentration, the electrokinetic data (Figure 3) are consistent with (i) a soft interface, the diffuseness of which increases with decreasing salt concentration (heterogeneous swelling) or (ii) a soft homogeneous interface with a volume charge density that decreases as a result of homogeneous swelling or a charge effect as the salt concentration is decreased. Quantitative analysis of the electrostatic interaction as measured by force spectroscopy between a bacterium and an AFM tip demonstrates that the diffuse interfacial representation most accurately and consistently describes both electrophoretic and AFM measurements at low salt concentration (Figure 4). The diffuse character of the CN32 strain is more pronounced than that of MR-4, as evidenced by the magnitude of R/L (e.g., at 1 mM (Figure 3B) R/L ) 1 for the CN32 strain whereas for the MR-4 strain R/L ) 0.06). The effect arises from the swelling of the permeable soft bacterial envelop due to the increase in osmotic pressure.38,39 A close inspection of Figure 3 also suggests that the interfacial diffuseness of the bacteria starts to have a significant impact on the electrokinetic characteristics at ionic strengths lower than 15 mM in the case of CN32 and at 4 mM for MR-4 (denoted by cc∞ in Figure 3). This is in line with the respective magnitudes of the (nominal) volume charge densities Fo as determined for these two bacterial strains at high salt concentrations (i.e., for CN32, Fo ) -35 mM and for MR-4, Fo ) -15 mM). Indeed, the extent of swelling is determined by the thermodynamic condition of zero net interfacial osmotic pressure. Whereas the elastic and polymer-solvent mixing contributions remain, to first approximation, independent of the electrolyte concentration, the electrostatic component is strongly determined by the volume charge density within the deformable layer and the salt concentration of the medium. Consequently, the larger the Fo (in absolute terms), the larger the segment-segment repulsive forces at fixed electrolyte concentration and the earlier the swelling upon decreasing the solution ionic strength. We also used the compressive regime of the force-separation distance profiles to obtain a measure of the mechanical properties of the MR-4 and CN32 bacterial envelopes (Table 1). First, the bacterial spring constant, which is related to the inner turgor pressure of the cell, increases significantly for the CN32 bacteria (presence of a thin, outer permeable charged gel-like layer) when decreasing the electrolyte concentration from 100 to 1 mM. In contrast, the turgor pressure remains roughly the same for the MR-4 strain with the thick permeable charged gel-like layer. It is well known that bacteria respond to changes in the osmolarity of their environment by modulating their turgor pressure through (38) Rotureau, E.; Thomas, F.; Duval, J. F. L. Langmuir 2007, 23, 8460–8473. (39) Yezek, L. P.; Duval, J. F. L.; van Leeuwen, H. P. Langmuir 2005, 21, 6220–6227.
Coupled Properties of Bacterial Interfaces
water flux.40 Our results show clearly that the thick gel-like layer around the bacteria acts as a protective barrier, attenuating the impact of changes in the extracellular ionic strength. This change is probably due to chemical and ionic gradients within the thick gel-like layer that tend to cancel the osmotic stress within the cytoplasm. Although this process is osmotically driven, the presence of the thick gel-like layer may also screen the role of the bacterial osmosensors that are usually located in the outer membrane. Using the theory of Pincus to fit the nonlinear regime of the compressive part of the force profiles, we can estimate the thickness of the soft layer from the mean Pincus length Lp (Table 1). For the sake of comparison, we independently evaluated that thickness from the diffuse parameter R/L as obtained from the electrokinetic data at 1 mM. Indeed, it may be shown from eq 1 that the thickness of the soft layer with diffuseness R/L is about L + 2.3R. (See Figure 2. For details, see ref 9.) In the case of CN32 at 1 mM, we obtained a thickness of 16.5 nm, which is about half the value derived from the analyses with Pincus theory (〈LP〉 ) 30 ( 7 nm). This discrepancy may be explained from the scheme depicted in SI Figure S5. Once the bacterium and the AFM tip are in intimate contact, an increase in the loading force results in a compression of the upper deformable part of the bacterium but also leads to a deformation of the other extremity of the bacteria supported by the substrate (polyethyleneiminecovered glass material). The latter deformation is possible because of momentum transfer via the cytoplasm of the bacteria. Similar conclusions may be drawn for MR-4 at low electrolyte concentration (1 mM), where we evaluated a mean Pincus length of 〈LP〉 ) 173 ( 60 nm that is also in agreement with twice the value obtained from the electrokinetic formalism for soft diffuse particles (102 nm). When comparing the thicknesses of the soft layer as determined from electrokinetics and AFM data collected at high salt concentration (100 mM), the 1:2 ratio discussed above is no longer met (Table 1). This is due to the decrease in the turgor pressure that leads to a misleading interpretation when attributing the nonlinear mechanical behavior to the compression of only the permeable charged gel-like layer. Obviously, the mismatch is more pronounced for the CN32 strain as compared to that for MR-4.
Conclusions In summary, this study presents a powerful approach that consists of combining electrokinetics and force spectroscopy to describe quantitatively the electrostatic, hydrodynamic, and mechanical features of soft diffuse bacterial interfaces. Figure 6 summarizes schematically the important findings in terms of the spatial distribution of the electrohydrodynamic parameters, volume charge density, and hydrodynamic softness and further illustrates the impact of the turgor pressure of the cell on the (40) Wood, J. M. Microbiol. Mol. Biol. ReV. 1999, 63, 230–262. (41) Korenevsky, A. A.; Vinogradov, E.; Gorby, Y.; Beveridge, T. J. Appl. EnViron. Microbiol. 2002, 68, 4653–4657.
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Figure 6. Schematic illustration of the impact of ionic strength on the structure and physical properties of the bacterial envelope, from the external permeable charged gel-like layer to the cytoplasm. The number of arrows represents the magnitude of the turgor pressure of the cell as inferred from the bacterial spring constant. The dotted red lines correspond to the spatial distribution (f(r) in Eq. 1) of the soft-permeable layer as derived from electrokinetic analysis.
mechanical characteristics of the interface. Whereas the physicochemical properties of the CN32 bacteria surrounded by a thin charged envelope are significantly modulated by changes in ionic strength, the presence of a thick gel layer, such as that surrounding the MR-4 strain, acts as a protective barrier against changes under extracellular conditions. We anticipate that such approaches will provide broadly applicable methods for investigating the interactions between bacteria and various substrates and molecules with antibiotic or nonadhesive properties and biological surfaces such as viruses or mamalian cells that can be used to probe pathogenic infections. Acknowledgment. We thank Etienne Dague for measuring the electrokinetic data, James A. Holden and Vincent Spiehler for assistance with growing the cells, and the CNRS communication service in Nancy (Nathalie Nevez, Ce´line Delalex, DR6). F.G. thanks M. L. Gee for accommodating him in her group during an 8 month sabbatical. This publication was also made possible in part by a grant from the CNRS program (CNRS cooperation 17990). F.G. also acknowledges the Particulate Fluids Processing Centre, the School of Chemistry (Melbourne University), and Asylum Research (Santa Barbara, CA) for providing some of the experimental and technical facilities. R.S. is supported by the National Health and Medical Research Council and are members of the Bacterial Pathogenesis Research Program. Supporting Information Available: Detailed steps of the theoretical framework and additional information concerning force curve analyses. This material is available free of charge via the Internet at http://pubs.acs.org. LA800258N
