Holographic microrheology of polysaccharides from Streptococcus mutans biofilms
We use three-dimensional holographic particle tracking to perform microrheological measurements of model gelled media, including the polysaccharide pellicle of dental biofilms created by the common cariogenic oral pathogen Streptococcus mutans. Nanometer-resolution video-rate holographic tracking of embedded colloidal spheres provides accurate measurements of the gels' complex viscoelastic moduli, including insights into these properties' heterogeneity. When applied to polysaccharides of S. mutans biofilms, these techniques promise quantitative microscopic assays for candidate therapeutic agents against cariogenic dental biofilms.
§ I. Introduction
The dental pathogen Streptococcus mutans exudes ectoenzymes known as glycosyltransferases that polymerize environmental sugars, mainly sucrose, into a robust polysaccharide gel also known as glucans. Glucans are one of the main components of the extracellular matrix in dental biofilms, providing them with bulk and structural integrity. In addition, glucans enable S. mutans and other oral bacteria to adhere to the tooth surface, resulting in the formation and establishment of a cariogenic dental biofilm. The presence of a cariogenic dental biofilm, together with some other specific factors, are implicated in tooth decay, the most prevalent infectious disease in humans. Although disrupting the polyglucan pellicle would greatly reduce the incidence of tooth decay, comparatively little is known regarding the physical properties of these biofilms, including the gel network's viscoelastic properties, the only previous studies having been performed on macroscopic model systems (31); (27); (9); (32). Consequently, few quantitative metrics have been available to gauge the efficacy of proposed treatments (31); (11); (10); (16).
As a step toward micromechanical screening for new therapeutic agents, this Article introduces holographic microrheology, which extends particle-tracking microrheology (23); (22); (21); (3) through the use of video holographic microscopy (28); (19); (20). After first demonstrating the efficacy of holographic microrheology through measurements on standard polyethylene oxide (PEO) samples (8), we use it to characterize model extracts of S. mutans biofilms. This proof-of-concept demonstration establishes microrheology as a viable tool for studying biofilms' viscoelastic properties and sets the stage for parallel and combinatorial studies of biofilms' physical responses to environmental challenges.
§ II. Holographic microrheology
Microrheology gauges a medium's viscoelastic properties by analyzing its thermally-driven fluctuations, either directly, or through their influence on embedded probe particles. The approach we adopt monitors a probe particle's mean-square fluctuations, , and uses a generalized Stokes-Einstein relation to extract the medium's frequency-dependent storage modulus, . This is related by the Kramer-Kronig relation to the frequency-dependent loss modulus, , which completes the micromechanical description.
Previous implementations of particle-tracking microrheology have used a variety of particle-tracking techniques including diffusing wave spectroscopy (25), dynamic light scattering (23); (22), interferometric particle tracking (23); (22); (13), and digital video microscopy (14); (24); (6); (3).
Light scattering approaches provide excellent resolution and bandwidth, but generally yield sample-averaged results, and so are not suitable for inhomogeneous samples. Interferometric methods have similarly high spatial and temporal resolution, and also resolve single-particle trajectories, but can only track one or two particles at a time, and often are limited to in-plane tracking. Conventional particle image velocimetry offers single-particle tracking for many independent probe particles, but at lower spatial and temporal resolution, and typically only for in-plane motions. Many of these issues can be addressed with the introduction of quantitative holographic microscopy (28); (19); (20), which can track multiple individual particles with nanometer-scale resolution in three dimensions (20).
Our holographic microrheology instrument, shown schematically in Fig. 1, consists of a standard inverted optical microscope (Zeiss Axiovert S100 2TV) outfitted with a NA 1.4 oil immersion objective. We implement holographic imaging by replacing the standard bright-field illuminator with a collimated He-Ne laser operating at a vacuum wavelength of . Laser light scattered by a probe particle interferes with the unscattered portion of the beam in the focal plane to create an in-line hologram (28); (19). This hologram is magnified by the objective and the video eyepiece onto the face of a video camera (NEC TI-324A II) to provide an effective magnification of 101 nm/pixel.
Our probe particles are charge-stabilized polystyrene spheres of nominal radius (Duke Scientific, Catalog #5153A, Lot #26621) that are dispersed at random into the sample by vortexing. The sample then is charged into a transparent container formed by bonding a no. 1 glass cover slip to the face of a microscope slide. The sealed sample is allowed to come to thermal and mechanical equilibrium on the microscope stage at .
Holographic images are recorded as an uncompressed digital video stream at 30 frames per second on a digital video recorder (Panasonic DMR-E100H). Each image then is analyzed to measure the probe particle's three-dimensional location relative to the center of the microscope's focal plane.
More specifically, the collimated laser illuminates the probe particle at position with a plane-wave incident electric field, , where is the wavenumber of the light in a medium of refractive index . The field scattered by the particle, , propagates to the focal plane at , where it interferes with the incident beam. The distribution of scattered light is described by the Lorenz-Mie scattering function (1), , which depends on the particle's position , its radius, , and its refractive index, .
In practice, the incident illumination varies with position, so that we normalize the measured interference pattern, , by a measurement of the incident illumination to obtain
where accounts for variations in . Equation (1) can be fit to normalized images such as the example in Fig. 1, with the particle's position, radius, and refractive index as free parameters. Whereas conventional bright-field particle tracking on the same instrument offers 10 nm in-plane resolution and 100 nm axial resolution (5), holographic particle tracking performs at least one order of magnitude better (20). Unlike conventional particle tracking, moreover, holographic tracking does not require separate calibrations for axial measurements.
We assess the measurement error in the particles' positions by tracking probe particles freely diffusing in Newtonian fluids such as water. Provided the particle is far enough from bounding surfaces, its mean-square displacement in each of the three Cartesian directions should evolve according to the Stokes-Einstein relation
where is the diffusion coefficient for a sphere in a fluid of viscosity at absolute temperature . The angle brackets in Eq. (2) denote an ensemble average over starting times. Restricting the average to starting times that are separated by the interval ensures that contributions to are statistically independent. When analyzing a single discretely sampled trajectory, however, this choice yields disproportionately large statistical errors at longer lag times, . Averaging over all starting times improves the estimate for and is justified if the trajectory may be treated as a Markov process. This is the case for the thermally driven trajectories we consider, and such exhaustive sampling enables us to estimate the mean-squared displacement from a single trajectory measured over a few thousand time steps. Statistical errors in must be corrected for covariances among correlated measurements over the interval .
Measurements of also suffer from random errors whose mean value, , establishes the tracking resolution. These errors increase the particle's apparent mean-square displacement by (5); (26), independent of . A complementary error due to motional blurring during the camera's shutter period, , reduces the apparent mean-square displacement. The result (26),
accounts for both effects, and enables us to measure .
where is the gamma function and
From this, we obtain
measures the medium's elastic response to shear forces, and measures its viscosity. They are natural probes of biofilms' responses to potential therapeutic agents. Similarly, the dynamic viscosity,
provides an overall impression of a biofilm's ability to exchange material with its surroundings.
§ III. Results
§ III.1. Newtonian fluid
To establish the accuracy of our holographic microrheology system, we first analyze the motions of a probe particle diffusing in a Newtonian fluid. The five-minute trajectory plotted in Fig. 2 was obtained for a single polystyrene sphere of nominal radius suspended in a density matched solution of 25% (w/w) glycerol in water whose viscosity is expected to be 1.7 mPa s. The particle was positioned with an optical tweezer at the midplane of a 50 thick sample volume to minimize hydrodynamic coupling to the glass walls (12) and then was released to acquire data.
Fitting images to the Lorenz-Mie scattering formula yields an estimated single-image precision of and (20). The mean-square displacement for each coordinate is plotted in Fig. 2 together with a fit to Eq. (3). All three traces are consistent with . When combined with the trajectory average of the particle's measured radius, , this suggests an overall viscosity of . Given the shutter period of , the extrapolated offsets yield and . These values are consistent with the estimated single-frame resolution and suggest that the accuracy of the position measurement is comparable to its precision.
The availability of high-resolution axial tracking data is one of the principal benefits of holographic particle tracking for microrheology. Consistency among the three data sets in this case confirms the measurements' freedom from hydrodynamic coupling to the surfaces. More generally such comparisons are useful for gauging a sample's isotropy and homogeneity.
Because results from the three coordinates are in agreement, we analyze the three-dimensional mean-squared displacement, , with Eqs. (4), (6) and (8) to obtain the loss modulus, , plotted in Fig. 3(a) and the dynamic viscosity, , plotted in Fig. 3(b). As expected, the glycerol-water solution acts as a Newtonian fluid whose storage modulus, , is too small to resolve over the range of frequencies probed. Its viscosity, is therefore independent of frequency and agrees with values obtained from bulk measurements.
§ III.2. Non-Newtonian Fluid
Having established the accuracy of our three-dimensional particle tracking method and the mechanical stability of our instrument, we next demonstrate its efficacy for particle-tracking microrheology by applying it to a standard non-Newtonian sample, an aqueous solution of high-molecular-weight PEO. Figure 3(c) shows and obtained from a single sphere dispersed in a 17 wt % solution of 200 kDa PEO in deionized water. As for the Newtonian fluid, consistent results are obtained in all three coordinates, so that combined results are presented in Figs. 3(c) and (d).
The viscoelastic moduli, plotted in Fig. 3(c), agree quantitatively with results reported for similar samples under comparable conditions (8). The loss modulus, , exceeds the storage modulus, , over the entire frequency range, which identifies this sample as a fluid, rather than a gel. The associated dynamic viscosity, plotted in Fig. 3(d), decreases monotonically with increasing frequency, which is the signature of a shear-thinning fluid.
§ III.3. S. mutans biofilm
The data in Fig. 4 show comparable results for biofilm polysaccharides. Pioneering studies of biofilm's structure (18); (4) have revealed a degree of heterogeneity at the sub-millimeter scale that might seem unamenable to systematic physical analysis. Indeed, measurements of model biofilms' macroscopic rheological properties (29); (17); (30); (27); (31); (2) have yielded viscoelastic moduli differing by more than three orders of magnitude, even for nominally similar samples. These differences have been attributed to loading, strain rate, total strain and sample preparation (2).
Microrheology addresses many of these concerns by probing the local-scale properties of unloaded samples in equilibrium. Although particle-tracking microrheology has been applied to a wide range of industrially and biologically relevant materials, its application to biofilms appears to be novel. Model biofilms can be prepared without the complication of swimming bacteria, and so lend themselves to this kind of analysis.
Streptococcus mutans polysaccharide samples were extracted from 5-day-old biofilms of S. mutans UA159 (ATCC 700610) that were grown on glass slides in the presence of 10% sucrose (16). Water-soluble (S) polysaccharides were extracted with MilliQ water at room temperature. The insoluble (N) polysaccharide fraction then was extracted in 1N NaOH. Both extracts were neutralized to pH and precipitated with cold ethanol (75% v/v) at for at least 24 h. The resulting polysaccharide samples have a mean molecular weight of about 10 kDa with a polydispersity of at least 50 percent, and contain trace amounts of protein (7). After precipitation, the samples were washed several times with 75% (v/v) ethanol, blot-dried and and dissolved in water (S) or 1N NaOH (N), at 20% (w/v) to form the gels used in the microrheological measurements. Polystyrene probe particles were dispersed at random in the polysaccharide at this time, and particles near the mid-plane of the sealed sample chamber were selected for measurement.
Results for the S fraction, plotted in Figs. 4(a) and (b), resemble those for the PEO solution in Figs. 3(c) and (d). The biofilm's water-soluble polysaccharides form a shear-thinning fluid roughly ten times more viscous than water.
The data in Fig. 4(c), by contrast, show that the N-type fraction forms an elastic gel with a typical storage modulus of 10 Pa. This is several hundred times smaller than the mean value reported for bulk samples of S. mutans polysaccharides in Ref. (31). It is consistent, however, with values reported at the lowest loadings when the substantial measurement error is taken into account (31). Accurate measurements at low loading are one of the strengths of microrheology, so that the results in Figs. 4(c) and (d) are more likely to reflect the biofilm's properties in vivo. Even at low loading, the N-type gel is strongly shear-thinning, as indicated by its dynamic viscosity in Fig. 4(d). This is a desirable trait for dental biofilms because it facilitates removal by brushing.
These observations suggest complementary roles of the two fractions in establishing the biofilm's mechanical and biological properties in vivo. The N-type material appears better suited to play the role of the mechanical scaffold within which the biofilm's bacterial colony establishes its ecosystem. Ability to disrupt the N-type gel, therefore, might be considered a promising characteristic for therapeutic agents. Microrheological assays of such agents' influence on N-type extracts should provide a simple and cost-effective screening technique. The ability of holographic microrheology to track multiple probe particles simultaneously furthermore creates opportunities for screening multiple therapeutic agents individually and in combination as a function of concentration.
§ IV. Discussion
We have demonstrated that precise measurements of probe particles' three-dimensional trajectories made possible by video holographic microscopy lend themselves naturally to applications in particle-imaging microrheology. Applying this technique to biofilms, in particular, shows promise for high-throughput combinatorial screening of candidate therapeutic or remedial agents. Rather than assessing their biological or biochemical influence, holographic microrheology offers direct insight into these agents' influence on biofilms' physical properties. In the case of dental biofilms, the availability of model polysaccharide gels will greatly simplify the development of standard assays for therapeutic agents. Because microrheological measurements require only micrometer-scale samples, very large arrays of independent assays should be possible in centimeter-scale systems, with each assay requiring just a few minutes of holographic recording.
§ V. Acknowledgments
This work was supported by the National Science Foundation under Grant Number DMR-0606415.
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