Anal. Chem. 1999, 71, 3622-3625
Ultrasonic Flexural-Plate-Wave Sensor for Detecting the Concentration of Settling E. coli W3110 Cells Stacie E. Cowan,†,‡ Justin Black,† J. D. Keasling,§ and Richard M. White*,†,‡
Berkeley Sensor & Actuator Center, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, 94720, Joint Bioengineering Graduate Program, Univesity of California, San Francisco and Berkeley, Berkeley, California 94720, and Department of Chemical Engineering, University of California, Berkeley, California 94720
The flexural-plate-wave (FPW) sensor, a type of ultrasonic sensor, can detect changes in E. coli W3110 concentration in solution as the cells settle onto the sensor under the influence of gravity. A model of the sensor’s response to cell settling has been developed and is in good agreement with the experimental data. The FPW technique improves on conventional methods for determining cell concentrations; this technique allows for on-line data collection, is nondestructive, and requires only small sample volumes. The FPW sensor has applications as a device to measure cell concentrations and growth rates in industrial fermentors, biofilms, and wastewater treatment facilities. A device that can measure cell concentrations has numerous applications in the biotechnology industry and in research centers. For example, the concentration of cells in liquid culture, such as in an industrial fermentor, is of great importance. The ability to measure the growth rate of immobilized cells and biofilms is also of great interest to both industry and research laboratories. Conventional methods for determining cell concentration include ATP measurements by bioluminescence or chemiluminescence, DNA analysis, measurements of enzymes and proteins by fluorescence, viable cell counts by microscopy, and other optical methods, such as turbidity measurements.1 Most conventional methods for measuring cell concentration are off-line systems2, which tend to be labor intensive and slow. On-line measurements of cell concentration would allow continuous measurement of cell concentration, which would be useful for fermentation control. The flexural-plate-wave (FPW) sensor3 a type of gravimetric ultrasonic sensor, can perform on-line measurements of cell concentration in real time. The FPW technique improves on the conventional methods for determining cell concentration; in addition to collecting data on-line, this technique is nondestructive and requires only small sample volumes. The FPW sensor can * Corresponding author: (e-mail)
[email protected], (fax) 510643-6637. † Berkeley Sensor & Actuator Center. ‡ Joint Bioengineering Graduate Program. § Department of Chemical Engineering. (1) Rhodes, P. M.; Stanbury, P. F. Applied Microbial Physiology; Oxford University Press: Oxford, England, 1997; pp 104-126. (2) Reference 1, p 104. (3) Wenzel, S. W.; White, R. M. IEEE Trans. Electron. Dev. 1988, ED-35, 735743.
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detect changes in Escherichia coli W3110 concentration in a solution as the cells settle onto the membrane of the sensor under the influence of gravity. In addition, a model of the sensor’s response to cell settling is developed and compared with experimental results. The FPW sensor is similar to, but much more sensitive than, the quartz crystal microbalance.4 FPW Sensor. As illustrated in Figure 1, the FPW device consists of a thin micromachined silicon nitride membrane produced by semiconductor fabrication techniques. The thickness of the membrane is much smaller than the wavelength of the ultrasonic waves that travel in the membrane; as a result, the ultrasonic waves travel at a velocity that is typically less than the speed of sound in water. Thus, the ultrasonic disturbance in the liquid has an evanescent character and the displacement of fluid particles varies as e-h/δ, where h is the distance between the center of the particle and the FPW membrane and δ is the evanescent decay length. δ is approximated by λ/2π, where λ is the ultrasonic wavelength. λ was 100 µm in these experiments.5 (A discussion of FPW theory is presented in ref 3.) Changes in the density of the liquid close to the membrane cause changes in the velocity of the ultrasonic wave and can be measured by the sensor. A change in mass near the surface of the membrane is determined by measuring the resonant frequency shift of a delayline oscillator, including an FPW. The response of the FPW to a change in mass per unit area, ∆m, is given by6
∆f/f ) Sm∆m
(1)
where f denotes resonant frequency, ∆f, shift in resonant frequency, and Sm, mass sensitivity of the sensor. When a fluid with spatially uniform density is placed in the sensor, Sm can be approximated as7
Sm ) -1/2(M + Fδ)
(2)
where M is the mass per unit area of the membrane and F is the liquid density (water). For the sensors used in the cell-settling (4) Ballantine, D. S.; Martin, S. J.; Ricco, A. J.; Frye, G. C.; Wohltjen, H.; White, R. M.; Zellers, E. T. Acoustic Wave SensorssTheory, Design, and PhysicoChemical Applications; Academic Press: San Diego, CA, 1997; pp 38-70. (5) Reference 4, p 124. (6) Reference 4, p 128. (7) Wenzel, S. W. Ph.D. Dissertation, UC Berkeley, 1992; p 91. 10.1021/ac9809884 CCC: $18.00
© 1999 American Chemical Society Published on Web 07/13/1999
well side of the sensor with 100% silicone aquarium sealant (Dow Corning). The settling chamber was then supported by a stainless steel housing and placed in a 37 °C air incubator (Boekel Industries, Inc., model 133730).
Figure 1. Top view of the flexural-plate-wave sensor and cross section of the settling chamber.
experiments, the mass sensitivity was ∼-180 cm2/g and δ was ∼16 µm. In the cell-settling experiments, the fluid density varied with position above the sensing surface. EXPERIMENTAL SECTION Sensor Fabrication. The FPW sensor shown in Figure 1 has two sides: (1) the “well” side, which serves as the sensing surface, and (2) the top side, which contains the transducers and electrical contacts. The sensor is fabricated by first depositing silicon nitride on a bare silicon wafer. The wafer is then patterned and etched in KOH to form a well. The dimensions of the well are 8 mm × 3 mm × 500 µm. Aluminum and piezoelectric zinc oxide are deposited on the wafer and patterned to form transducers, which send and receive the ultrasonic waves. A detailed account of the fabrication process can be found in ref 3. Cell Suspension Preparation. E. coli W3110 was grown in Luria broth8 (LB) medium at 37 °C to midexponential phase, harvested by centrifugation at 18900g, and washed twice in C minimal medium devoid of a carbon source.9 The concentration of bacteria in each suspension was measured by reading the optical density at a wavelength of 600 nm (OD600) with a Beckman DU 640 spectrophotometer. The correlation between cell number and optical density was determined by spreading a known volume of culture on LB agar plates and counting colonies after incubation at 37 °C overnight.10 An OD600 of 1 corresponded to 3.9 × 108 E. coli W3110 cells per milliliter of culture. Settling Chamber. The settling chamber, shown in Figure 1, was constructed by attaching a 1-cm-diameter glass tube to the (8) Atlas, R. M. Handbook of Microbiological Media; CRC Press: Boca Raton, FL, 1993; pp 491-492. (9) Helmstetter, C. E.; Cooper, S. J. Mol. Biol. 1968, 147, 507-510.
EXPERIMENTAL PROCEDURE Cell Settling Experiments. One milliliter of cell suspension was placed in the settling chamber and allowed to settle under the force of gravity. The top (open end) of the settling chamber was covered with Parafilm to prevent evaporation of liquid from the cell suspension during the experiment. Cell settling was monitored by recording the change in the sensor’s resonant frequency. The temperature of the liquid was also recorded using a thermocouple (Omega, type K) connected to a module (Fluke, model 80TK) that converted the thermocouple potential to degrees centigrade. Temperature and resonant frequency measurements were made and recorded by Labview data acquisition software (National Instruments, v. 4.0.1) at 30-s intervals for a total of 10 h. The temperature of the liquid in the settling chamber was 37 ( 0.5 °C. The settling experiments were performed using cell suspensions having OD600 of 0.2, 0.3, and 0.4. All experiments were performed within 24 h of sample preparation to reduce the probability of cell lysis. Control experiments were also performed in which 1 mL of C medium without cells was placed in the well. Analysis. To determine the diameter of an E. coli bacterium, the specific growth rate, µ, of E. coli W3110 in LB medium at 37 °C was measured and determined to be 1.8/h. The average length, Lh µ, and the average volume, V h µ, of a single E. coli cell have been 11 found to be functions of µ:
L h µ ) 2(2µ/3)
(µm)
(3)
V h µ ) 0.4(2µ)
(µm3)
(4)
Lh µ and V h µ were estimated to be 3 µm and 1.39 µm3, respectively. Using Lh µ and V h µ and assuming that a single E. coli is shaped like a cylinder with hemispherical caps, the average diameter, D h µ, was found to be 0.8 µm. Even though the E. coli are rod-shaped, the settling bacteria were modeled as spheres settling in the Stokes’ regime (Reynolds number less than 1).12 In this regime, the terminal settling velocity of a spherical particle is given by13
Vs ) gDp2(Fp - F)/18η
(5)
where Vs denotes the terminal settling velocity, g, gravitational constant, Dp, particle diameter, Fp, particle density, and η, fluid viscosity (water). The density of an E. coli bacterium, Fp, is 1.105 g/cm3.14 (10) Rhodes, P. M.; Stanbury, P. F. Applied Microbial Physiology; Oxford University Press: Oxford, England, 1997; pp 112-113. (11) Neidhardt, F. C., et al., Eds. Escherichia coli and Salmonella: Cellular and Molecular Biology; ASM Press: Washington, DC, 1987; Vol. 2, p 1580. (12) Denn, M. M. Process Fluid Mechanics; PTR Prentice Hall: Englewood Cliffs, NJ, 1980; p 54. (13) Reference 12, p 56.
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Figure 2. Sketch of E. coli W3110 cells settling onto the FPW membrane and packing into cell layers.
As mentioned, the E. coli cells are not spherical. A curve was fit to the initial data points, which corresponded to the frequency shift due to cells that were directly in contact with the surface of the membrane. Using the initial optical density, eq 1, eq 5, and the slope of the fitted line, the effective settling diameter, D ˆ p, was determined. The effective diameter for an E. coli W3110 was determined to be 2.87 µm for data sets with initial OD600 of 0.2, 0.3, and 0.4. This value is reasonable because it lies between the values of Lh µ and D h µ. Considering a thin plate (the FPW membrane) loaded with a fluid, it can be shown that the ultrasonic plate waves introduce a displacement field in the fluid which decays exponentially away from the membrane as e-h/δ, where h is the perpendicular distance from the membrane.15 The acceleration of the fluid, and thus the reaction force on the membrane, F ) ma, is given by the second time derivative of the displacement field, which must also have an exponential dependence. The resonant frequency of the membrane is found by solving the differential equation for the sum of the forces acting on the membrane. Consequently, the influence of a mass on the resonant frequency of the device is exponentially related to the distance of the mass from the membrane. In the cell-settling experiments, the density of the liquid varies with height above the membrane. A cell close to the membrane will therefore be detected better than one farther from the membrane. In other words, the effective mass of a cell near the membrane is greater than that of a cell far from the membrane. The effective mass of a single cell is given by
m(h) ) V h µ(Fp - F)e-h/δ
(6)
Figure 3. Measured frequency curves for cell-settling experiments with C medium (no cells), OD600 ) 0.2, and OD600 ) 0.4. As the cells settle, mass accumulates near the membrane, resulting in a negative frequency shift.
parallel to the FPW membrane (3.3 × 1011 cells/cm3). The effective mass contributed by the layer of cells at a given height, h, can be expressed as
meffective ) Vs(Fp - F)V h µOD600Rte-h/δ
(7)
where OD600 is the initial optical density of the solution, R converts OD600 to initial cell concentration and has a value of 3.9 × 108 cells/cm3, and t is time. The total mass detected by the sensor is hcell
∆mtotal )
∑m
effective
(8)
h)0
where hcell denotes the height of the packed cell region and can be expressed as
hcell ) VsOD600Rt/nˆ packAmemD hµ
(9)
where Amem is the area of the FPW membrane (8 mm × 3 mm). The height, h, is incremented by the cell diameter (height of a cell layer). Thus, the final expression for the resonant frequency shift, ∆f, is given by hcell
∆f(t) ) Smf
∑V (F s
p
- F)V h µOD600Rte-h/δ
(10)
h)0
The total number of cells at a given height above the membrane depends on how the cells pack into layers as they settle onto the surface of the membrane, as shown in Figure 2. In the absence of a model of how cells pack when they settle under the influence of gravity, we have used the packing density as a fitting parameter. The packing density was determined for data sets with initial OD600 of 0.2, 0.3, and 0.4. The packing densities, ηˆ pack, were determined to be 3.6 × 1010, 3.75 × 1010, and 7.5 × 1010 cells/cm3, respectively. These values are reasonable because they are ∼ an order of magnitude less than the packing density of cells in a close-packed arrangement in which the long axes of the E. coli are oriented (14) Martinez-Salas, E.; Martin, J. A.; Vicente, M. J. Bacteriol. 1981, 147, 97100. (15) Wenzel, S. W. Ph.D. Dissertation, UC Berkeley, 1992; p 46.
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RESULTS AND DISCUSSION Cell-Settling Experiments. The measured frequency curves (∆f vs t) for C medium without cells and for cell suspensions with OD600 of 0.2 and 0.4 are shown in Figure 3. Figure 3 shows that the slopes of the frequency curves are larger for larger optical densities, as predicted by the model. The frequency shift becomes more negative as more cells settle onto the surface of the membrane and mass loads the sensor. Figure 4 shows the measured and modeled frequency curves for a cell suspension with OD600 of 0.4; the modeled curve depends on the fitting parameters, D ˆ p and nˆ pack. There is good agreement between the experimental data and the modeled frequency shift. To obtain good agreement between the actual data and modeled frequency
samples with OD600 of 0.2 and 0.4 were much largers4 and 8 kHz, respectively. CONCLUSIONS We have shown that the FPW can measure on-line changes in the concentration of E. coli W3110 in real time. This technique could potentially be used to detect changes in concentrations of larger cell types, such as yeast and red blood cells. This technique has applications as a device to measure or monitor cell growth rates in a variety of environments, such as fermentors, wastewater treatment facilities, and immobilized cell reactors. Figure 4. Comparison of measured and modeled frequency curves for cell-settling experiment with initial OD600 of 0.4.
shift for data sets with different optical densities, a range of values is required for both fitting parameterssthe effective settling diameter and the packing density. In addition to being able to detect mass changes, the FPW device is also sensitive to changes in temperature. The fluctuations in the resonant frequency correspond with the periodic cycling of the temperature in the incubator. During control experiments that were run without cells, the resonant frequency of the sensor varied by (500 Hz. In contrast, during cell-settling experiments, the observed frequency shifts for
ACKNOWLEDGMENT We thank Kristala L. Jones (Department of Chemical Engineering, University of California at Berkeley) for her assistance with cell culture techniques and John P. Hecht (Department of Chemical Engineering, University of California at Berkeley) for his input on the cell-settling model. All FPW sensors were fabricated at the Berkeley Microfabrication Facility. S.E.C. was supported by a National Institute of Health Training Grant.
Received for review September 2, 1998. Accepted April 29, 1999. AC9809884
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