- Email: [email protected]
Quartz crystal microbalance biosensor design
Sensors and Actuators B 123 (2007) 21–26
Quartz crystal microbalance biosensor design II. Simulation of sample transport Mats J¨onsson a,∗ , Henrik Anderson a,b , Ulf Lindberg a , Teodor Aastrup b a
˚ The Angstr¨ om Laboratory, Solid State Electronics, Uppsala University, P.O. Box 534, SE-751 21 Uppsala, Sweden b Attana AB, Bj¨ ornn¨asv¨agen 21, SE-113 47 Stockholm, Sweden
Received 31 March 2006; received in revised form 19 July 2006; accepted 24 July 2006 Available online 12 September 2006
Abstract The influence of flow cell geometry on sample dispersion in a quartz crystal microbalance (QCM) biosensor system was investigated. A circular and a rectangular flow cell and corresponding sensor electrodes were studied experimentally and modelled using a coupled Navier–Stokes and convection–diffusion model. Finite element simulations showed that dispersion phenomena in a flow cell can be significantly reduced with the rectangular flow cell compared to a circular system. Experimental results from measurement of the time-dependent viscosity change of a model sample indicate that the sample delivery system has a predominant effect on the dispersion of the whole sensor system. Consequently, improvement of the sensor flow cell should be accompanied with improvement of the sample delivery system. With reference to kinetic studies of biological interactions, the current dispersion should have little effect on the results for studies of interaction pairs with relatively slow to normal binding rates such as antibody–antigen interactions. Incentive for further development of the flow cell and sample delivery system exists primarily for applications with high reaction rates such as for certain receptor ligand interactions. © 2006 Elsevier B.V. All rights reserved. Keywords: QCM; Simulation; FEM; Navier–Stokes; Convection and diffusion; Microfluidic
1. Introduction Biosensors based on quartz crystal microbalance (QCM) technology are successfully applied to study molecular interactions [1]. QCM resonators are used for sensing both gases and liquids. Eventhough liquid contact with the resonator damps the resonator oscillation significantly and thereby reduces the sensitivity, the sensors remain adequately responsive [2]. QCM and surface plasmon resonance (SPR) are often compared in their applications as versatile high sensitive biosensors [3]. The high sensitivity of a QCM is due to the mega gravity field created by the quartz resonator, the higher the field, the higher the detection resolution. The amount of material adhered and thus accelerated along with the vibrating crystal is detected resulting in an acceleration-dependent mass and viscosity sensitivity [4].
∗
Corresponding author. Tel.: +46 18 471 7257; fax: +46 18 555095. E-mail address: [email protected] (M. J¨onsson).
0925-4005/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2006.07.028
The crystals chosen for biosensing applications have large circular electrodes since the operation of the crystal in liquid sets high demands on the crystal performance. The flow cells in which the crystal operates are designed with respect to the electrode geometry since the walls of the flow cell should not interfere with the oscillations of the crystal. In more demanding applications, e.g. when measuring the kinetics of biochemical interaction, the dispersion of the sample caused by large flow cells can limit the sensor performance. A different approach would be to have a flow cell with better hydrodynamic properties and then design the crystal electrode with respect to the flow cell. The aim of this report is to study the flow behaviour of circular and rectangular sensor geometries with respect to sample dispersion in a QCM biosensor system. The effect of the geometry change is studied using flow simulations and is compared to experimental data performed on an Attana 80 QCM biosensor. The influence on and aspects of sensor sensitivity on the final sensor response and its applications is discussed. The performance of the rectangular and circular sensor systems as biosensors is evaluated in a preceding report [5].
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M. J¨onsson et al. / Sensors and Actuators B 123 (2007) 21–26
2. Background In a surface based biosensor, the transport of the sample plug to the sensor surface is facilitated by a combination of hydrodynamic and diffusive flow of sample. The flow profile under laminar flow conditions can be described as parabolic, i.e. the flow cross-sectional velocity profile has a parabolic shape with the highest velocity in the centre and zero velocity (no-slip condition) at the channel walls. The hydrodynamic flow moves sample from the injection valve to just above the sensor surface. The diffusive flow during this first process has a limited effect on the delivery of the sample to the sensor chamber, although diffusion combined with the laminar parabolic flow in small fluid channels will cause dispersion of a sample plug. Secondly, due to the parabolic flow profile, the hydrodynamic flow has little influence in the vicinity of the channel walls and in the vicinity of a sensor surface situated in the fluid channel. With respect to mass transport to the sensor surface in a flow channel, this behaviour is described by the presence of a stagnant layer at a distance b from the sensor surface under which the hydrodynamic flow is of minor importance. Consequently, there are two principal factors of importance for the sample delivery in a biosensor; sample dispersion and diffusive mass transport down to the sensor surface. The focus of this study lies with the effects of flow cell geometry on sample dispersion.
defined as a pressure at the boundary of the inlet. The outflow is set as normal out of the geometry (zero pressure gradient). The simulation of convection and diffusion is based on the formulations for a species of time-dependent concentration of mass, c and diffusion coefficient, D: δts
∂c + ∇ · (−D∇c) = −u · ∇c ∂t
(3)
δts is a time scaling coefficient, c the mass concentration of sample, and t is time. The velocity field u is the coupling variable between the two models. 2.2. Radial sensor sensitivity variation The QCM sensor is used to experimentally measure the sample plug dispersion. The frequency shift is detected as the sample plug passes the sensor surface. The sensor sensitivity varies over the electrode geometry and is proportional to the oscillation amplitude. The sensor signal amplitude has been found to be Gaussian distributed over the sensor surface according to reports by Ward and Delawski [11] and Rodahl and co-workers [12]. The effects of the sensor detection signal intensity decreasing at the periphery of the electrode results in a weighted detector signal. 3. Materials and methods
2.1. Sample flow analysis
3.1. QCM system
Flow injection analysis is a research area of its own and the study of sample plug dispersion has been presented in textbooks by, e.g. Ruzicka and Hansen [6]. The desired ideal square wave sample plug profile is dispersed in the transport line by the valve mechanisms, tubing and associated connections, and in the sensor chamber. Mathematical descriptions of sample plug profiles as an exponentially modified Gaussian function have been discussed by Kolev [7], Berthod [8] and van Akker et al. [9,10]. In our case the sample plug is elongated and an exponentially modified square wave is chosen to model the plug shape provided by the sample delivery system. This plug profile is not verified experimentally but is considered sufficiently valid to be used as input data when the actual sample plug shape is unknown. A Navier–Stokes model combined with a convection and diffusion model is used to present the behaviour of the flow and the sample concentration distribution in the system. The Navier–Stokes equation describes the flow situation in the channel:
Two Attana 80 QCM biosensor (Attana AB) were used for the experiments. The QCM system consists of a peristaltic pump, an eight-way injection valve and the sensor unit with flow cell and oscillation electronics, see Fig. 1. A frequency counter collects frequency data which is transferred to a computer where the data can be monitored and logged. The QCM system operates in a continuous flow mode where the running buffer is continuously flown through the flow cell over the sensor surface. A sample is injected by first filling the injection valve with the sample and then switching the valve. The sample is then switched into the flow line and is transported to the sensor surface by the continuous flow. The response from an injection to the resonance frequency is monitored in real-time by the computer and a mass adsorption to the surface will result in a negative frequency shift. Desorption from the surface will result in an increase in frequency. One of the systems was used in its standard configuration with a circular crystal and circular flow cell and the other system was modified with a rectangular crystal and a correspondingly rectangular flow cell. The electrode geometries for the sensing electrode were 4.5 mm in diameter for the circular electrode and 1 mm × 4 mm for the rectangular electrode as described in the preceding paper [5]. The flow cells were 0.2 mm in height and had slightly larger dimensions than the corresponding crystals in order to reduce the damping of the crystal from the flow cell. The approximate volumes of the circular and rectangular cells were 5 and 1.5 l, respectively. The running buffer for the QCM experiments was phosphate buffered saline (PBS). Test sample to investigate the sample plug
ρ
∂u − η∇ 2 u + ρ(u · ∇)u + ∇p = F ∂t
∇ ·u=0
(1) (2)
The first equation is the momentum balance, and the second is the equation of continuity for incompressible fluids. The following variables and parameters appear in the equations, ρ is the density, u the velocity field, η the dynamic viscosity, p the pressure and F is a volume force field such as gravity. A no-slip boundary condition is set for the chamber walls and the inflow of fluid is
M. J¨onsson et al. / Sensors and Actuators B 123 (2007) 21–26
23
Fig. 1. Schematic of the Attana 80 biosensor system.
appearance for the two systems was PBS with 2% dimethyl sulfoxide (DMSO). A 50 l sample plug was injected at a flowrate of 100 l/min and the frequency shift response was registered and converted into a normalised concentration.
sample plug is defined as the time-dependent concentration at the boundary of the inlet hole. The time-dependent concentration over the sensor area is calculated as the integrated concentration over the active sensor electrode area.
3.2. Flow simulations
4. Results
The flow behaviour for the different crystal geometries has been studied in 2D-simulations using a coupled model of Navier–Stokes (NS) flow and convection–diffusion (CD) using Femlab (COMSOL Multiphysics) software. The NS-model is solved using a non-linear stationary solver and the CD-model by a time-dependent solver. The sample solution is defined by a diffusion coefficient D of 1.00E−9 m2 /s, a normalised sample concentration C0 , a flow of 100 l/min, density 1000 kg/m3 , and viscosity η 1.0E−3 Ns/m2 . The active area of the sensor crystal is 4.5 mm in diameter and 4 mm × 1 mm, respectively, for circular and rectangular geometries. The 100 l/min volume flow corresponds to a linear maximum velocity in the centre of the structure of 3.9 and 12.0 mm/s for the circular and rectangular geometries, respectively. Simulations were carried out both for a non-dispersed, essentially square, sample injection and for a dispersed plug that modelled the sample plug from the sample delivery system. The injected sample concentration profile from the sample delivery system was expressed as an exponential function according to
4.1. Simulations
c(t) = C0 (1 − e−t/k )
The geometry of the sensor system causes variations of the linear velocity across the sensor. From the NS-simulations the velocity profiles in the sensor chamber are extracted as seen in Fig. 2. The inner boundary structures illustrate the sensor electrode areas. The profile is uniformly parabolic along the geometry in the rectangular case, Fig. 2b, whereas in the circular case, Fig. 2a, the speed of the fluid decreases towards the widest
(4)
for the rising part of the curve and according to c(t) = C0 e−t/k
(5)
for the falling part, where C0 is the origin concentration and k is a time constant. The NS-model is first solved using the stationary non-linear solver. The resulting flow velocity profile is then used as the start value to solve the convection and diffusion model in a timedependent analysis (time step 0.2 s). The profile of the injected
Fig. 2. Linear velocity field profiles in the sensor chambers for: circular (a) and rectangular (b) geometries. The positions of vmax and vmin are indicated.
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Table 1 Linear velocity in the sensor chamber Position
Circular geometry
Rectangular geometry
vmax (mm/s) vmin (mm/s) vcenter (mm/s)
9.1 0.4 3.9
14 6.0 12
part of the chamber and then increases as the geometry contracts towards the outlet. The maximum, minimum and central velocity within the electrode area are presented in Table 1. The maximum velocity, vmax , appears across the boundary close to the inlet and outlet and the minimum velocity, vmin , is found at the centre of the sideboundaries as pointed out in Fig. 2a and b. As a consequence of the velocity variations over the sensor surface, the rectangular and circular systems will display different response behaviour to an injected sample plug. Fig. 3 displays the integrated normalised concentration over the respective sensor surfaces as a result of a non-dispersed injection plug. The dispersion in the rectangular sensor system is negligible whereas the dispersion in the circular system causes a significant time delay before the maximum concentration is reached. However, since the sample injected in a real sensor system such as the Attana 80 described above, will have a dispersed sample plug before even entering the sensor flow cell, these results may not accurately describe the actual sensor response. The sample plug from the sample delivery system was modelled according to Eqs. (4) and (5) and was used as input for the subsequent simulations. The integrated normalised concentration over the active area of the crystals is shown in Fig. 4 for simulations with a dispersed injection plug. The delay time, t0.95 , that is required for the integrated concentration over the sensor surface to reach 95% of the maximum concentration was defined to serve as a measure above which dispersion effects would have only negligible effects on biosensor kinetics determination. The total delay time, including the contribution from dispersion in the transport system, was 7.6 and 6.2 s for the circular and rectangular geometry, respectively. Experimental results
Fig. 4. Simulated sensor concentration profile from a dispersed sample plug for circular and rectangular flow cell geometries. The sample volume is 50 l. The delay time, t0.95 , for circular and rectangular geometry, respectively, is indicated.
for DMSO sample injections indicate similar dispersions for the two sensors as seen in Fig. 5. The delay time for the sensor flow cell provided a non-dispersed sample plug was 3.5 s for the circular system and below 0.5 s for the rectangular system (more accurate determination was not allowed given the chosen time resolution of the simulation of 0.5 s). The flow velocity variations over the sensor surface also cause the sample concentration distribution to vary over the sensor as illustrated in Fig. 6 for the circular flow geometry and in Fig. 7 for the rectangular geometry. The figures illustrate the inflow and outflow of the sample plug through the sensor chamber. The time it takes for the first part of the sample plug to fill the active sensing area is about 5 s for the circular geometry and about 1 s for the rectangular geometry at a flowrate of 100 l/min. Analogously, the circular chamber is emptied at a slower rate and a split tail of residual sample remains in the chamber 25 s after the end of sample injection. The sequence in Fig. 4 indicates that the residual samples left in both the circular and the rectangular cases stay outside of the sensor area. 5. Discussion The velocity and concentration profile results from the simulations indicate that the rectangular geometry has a significantly
Fig. 3. Simulated sensor concentration profile from a non-dispersed and essentially square sample plug for circular and rectangular flow cell geometries. The sample volume is 50 l.
Fig. 5. Experimental results from measurements on DMSO sample plugs for rectangular and circular sensor geometries presented as normalised concentrations.
M. J¨onsson et al. / Sensors and Actuators B 123 (2007) 21–26
Fig. 6. Time-dependent surface sample concentration distributions for the circular crystal geometry. Injection volume is 50 l (0–30 s).
improved flow behaviour. The sample plug is more uniformly transported through the rectangular chamber. The experimental data, however, show similar sensor responses for the two geometries. In order to understand why the simulation results do not reflect the experimental data, a detailed understanding of the entire setup is needed. The fluidics of the system as described above consists of a pump, an injection valve and the sensor. The sample is introduced into the valve as at least twice the desired sample plug volume into the injection loop. The injection valve is then switched and the sample volume is almost instantly placed into the flow line that leads to the sensor. Independent of the QCM systems evaluated here, the flow of the sample from the injection valve to the sensor will cause dispersion. Experimental work involving different tubing diameters between the valve and the sensor has shown that the dispersion in the examined systems is highly dependent on this part of the sample delivery system. As a consequence, the results of the simulation data may be over shadowed by the dispersion in the transport of the sample from the valve to the sensor. Since QCM sensors have a sensitivity maximum in the centre of the crystal this may also have an effect on the measurement results. Depending on the profile of this sensitivity distribution, the tail of the sample plug apparent in Fig. 3 may only to a limited extent affect the sensor. Using simulation as a tool to predict and understand physical phenomena places demands on the model design. A 2D-model has the advantage of simplicity over a 3D-model, although a
25
Fig. 7. Time-dependent surface sample concentration distributions for the rectangular crystal geometry. The injection volume is 50 l (0–30 s).
3D-model could have provided information on mass transport to the sensor surface. The 2D-model used was designed with the purpose of studying the sample propagation in a plane in the centre of the chamber parallel to the sensor electrode surface, and was considered appropriate for the examination of sample dispersion as an effect of flow cell geometry. Sensor system dispersion causes the sample concentration over the sensor surface to rise from 0 to 95% of the maximum concentration within 6.2 and 7.6 s for the two electrode geometries, respectively. During this period any determination of reaction association or dissociation rates will be complex, since the sample concentration over the surface is undefined. Consequently, obtaining reaction rates for biological interaction systems that are so fast that most of the binding event occurs already during this dispersion phase will be difficult. Reviewing biosensor literature shows that certain small molecule-enzyme interactions could lie within this field and would therefore be difficult to determine [13]. Other biological systems such as for instance antibody–antigen interactions are normally significantly slower and the kinetics determination on those systems would be only negligible affected by the dispersion phase of the sample plug [14–16]. 6. Conclusions Finite element simulations on a QCM system with rectangular flow cell and sensor electrode has shown that the dispersion
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phenomena in the flow cell can be significantly reduced compared to a standard circular QCM system. Experimental results, however, indicate that the sample delivery system has a predominant effect on the dispersion of the whole sensor system and that no significant improvement could be achieved by enhancement of the sensor flow cell alone. Consequently, improvement of the sensor flow cell should be accompanied with improvement of the sample delivery system. With reference to kinetic studies of biological interactions, the current dispersion should have little effect on the results for studies of interaction pairs with relatively slow to normal binding rates such as antibody–antigen interactions. Incentive for further development of the flow cell and sample delivery system exists primarily for applications with high reaction rates such as for certain receptor ligand interactions. Acknowledgements The authors gratefully acknowledge the helpful comments of Bertil H¨ok and the experimental assistance of Thomas Weissbach. The authors further acknowledge the financial support from the Swedish Research Council and Attana AB. References [1] A. Katerkamp, Chemical and biochemical sensors, in: Ullman’s Encyclopedia of Industrial Chemistry, Wiley/VCH Verlag GmbH, 2001. [2] M. Rodahl, F. Hook, A. Krozer, P. Brzezinski, B. Kasemo, Quartzcrystal microbalance setup for frequency and Q-factor measurements in gaseous and liquid environments, Rev. Sci. Instrum. 66 (1995) 3924– 3930. [3] C. K¨osslinger, E. Uttenthaler, S. Drost, F. Aberl, H. Wolf, G. Brink, A. Stanglmaier, E. Sackmann, Comparison of the QCM and the SPR method for surface studies and immunological applications, Sens. Actuators B: Chem. 24 (1995) 107–112. [4] V.M. Mecea, From quartz crystal microbalance to fundamental principles of mass measurements, Anal. Lett. 38 (2005) 753–767. [5] H. Anderson, M. J¨onsson. U. Lindberg, T. Aastrup, Quartz crystal microbalance biosensor design: I. Experimental study of sensor response and performance, Sens. Actuators B: Chem. (2006), in press. [6] J. Ruzicka, E.H. Hansen, Flow Injection Analysis, vol. 62, 2nd ed., Wiley, New York, 1988. [7] S.D. Kolev, Mathematical-modeling of flow-injection systems, Anal. Chim. Acta 308 (1995) 36–66.
[8] A. Berthod, Mathematical series for signal modeling using exponentially modified functions, Anal. Chem. 63 (1991) 1879–1884. [9] E.B. van Akker, M. Bos, W.E. van der Linden, Convection and diffusion in a micro-flow injection system, Anal. Chim. Acta 373 (1998) 227–239. [10] E.B. van Akker, M. Bos, W.E. van der Linden, Continuous, pulsed and stopped flow in a μ-flow injection system (numerical vs experimental), Anal. Chim. Acta 378 (1999) 111–117. [11] M.D. Ward, E.J. Delawski, Radial mass sensitivity of the quartz crystal microbalance in liquid-media, Anal. Chem. 63 (1991) 886–890. [12] M. Edvardsson, M. Rodahl, B. Kasemo, F. Hook, A dual-frequency QCMD setup operating at elevated oscillation amplitudes, Anal. Chem. 77 (2005) 4918–4926. [13] D.G. Myszka, Analysis of small-molecule interactions using Biacore S51 technology, Anal. Biochem. 329 (2004) 316–323. [14] A. Einhauer, A. Jungbauer, Affinity of the monoclonal antibody M1 directed against the FLAG peptide, J. Chromatogr. A 921 (2001) 25–30. [15] G.H. Choi, D.H. Lee, W.K. Min, Y.J. Cho, D.H. Kweon, D.H. Son, K. Park, J.H. Seo, Cloning, expression, and characterization of single-chain variable fragment antibody against mycotoxin deoxynivalenol in recombinant Escherichia coli, Protein Expres. Purif. 35 (2004) 84–92. [16] A.W. Drake, D.G. Myszka, S.L. Klakamp, Characterizing high-affinity antigen/antibody complexes by kinetic- and equilibrium-based methods, Anal. Biochem. 328 (2004) 35–43.
Biographies Mats J¨onsson received his MSc degree in material engineering in 2000 and the PhD in engineering science with specialization in microsystems technology ˚ in 2006 at the Angstr¨ om Laboratory, Uppsala University, Sweden. His research interest is in development of microsystems for biotechnology applications, especially in electric manipulation of bio-particles and QCM-technology. Henrik Anderson received his MSc degree in chemical engineering from the Royal Institute of Technology, Sweden, in 2000 and currently holds a position as PhD student at the Department of Solid State Electronics, Uppsala University, Sweden. His research interest is in development of biosensors with regards to transducer and surface chemistry development as well as the development of new applications of QCM biosensors. Mr. Anderson is co-founder of Attana AB. Ulf Lindberg received his MSc degree in engineering science in 1985 and his PhD degree in solid state electronics in 1993 both at Uppsala University, Sweden. After working at Biacore AB with microfluidics he rejoined the Department of Solid State Electronics at Uppsala University in 2000. He is currently head of the Microstructure Technology Group with a special interest in Bio-MEMS. Teodor Aastrup received his MSc degree in materials physics at Uppsala University in 1994 and his PhD at the Royal Institute of Technology, Sweden, in 1999. Dr. Aastrup is co-founder and CEO of Attana AB.
Quartz crystal microbalance biosensor design II. Simulation of sample transport Mats J¨onsson a,∗ , Henrik Anderson a,b , Ulf Lindberg a , Teodor Aastrup b a
˚ The Angstr¨ om Laboratory, Solid State Electronics, Uppsala University, P.O. Box 534, SE-751 21 Uppsala, Sweden b Attana AB, Bj¨ ornn¨asv¨agen 21, SE-113 47 Stockholm, Sweden
Received 31 March 2006; received in revised form 19 July 2006; accepted 24 July 2006 Available online 12 September 2006
Abstract The influence of flow cell geometry on sample dispersion in a quartz crystal microbalance (QCM) biosensor system was investigated. A circular and a rectangular flow cell and corresponding sensor electrodes were studied experimentally and modelled using a coupled Navier–Stokes and convection–diffusion model. Finite element simulations showed that dispersion phenomena in a flow cell can be significantly reduced with the rectangular flow cell compared to a circular system. Experimental results from measurement of the time-dependent viscosity change of a model sample indicate that the sample delivery system has a predominant effect on the dispersion of the whole sensor system. Consequently, improvement of the sensor flow cell should be accompanied with improvement of the sample delivery system. With reference to kinetic studies of biological interactions, the current dispersion should have little effect on the results for studies of interaction pairs with relatively slow to normal binding rates such as antibody–antigen interactions. Incentive for further development of the flow cell and sample delivery system exists primarily for applications with high reaction rates such as for certain receptor ligand interactions. © 2006 Elsevier B.V. All rights reserved. Keywords: QCM; Simulation; FEM; Navier–Stokes; Convection and diffusion; Microfluidic
1. Introduction Biosensors based on quartz crystal microbalance (QCM) technology are successfully applied to study molecular interactions [1]. QCM resonators are used for sensing both gases and liquids. Eventhough liquid contact with the resonator damps the resonator oscillation significantly and thereby reduces the sensitivity, the sensors remain adequately responsive [2]. QCM and surface plasmon resonance (SPR) are often compared in their applications as versatile high sensitive biosensors [3]. The high sensitivity of a QCM is due to the mega gravity field created by the quartz resonator, the higher the field, the higher the detection resolution. The amount of material adhered and thus accelerated along with the vibrating crystal is detected resulting in an acceleration-dependent mass and viscosity sensitivity [4].
∗
Corresponding author. Tel.: +46 18 471 7257; fax: +46 18 555095. E-mail address: [email protected] (M. J¨onsson).
0925-4005/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2006.07.028
The crystals chosen for biosensing applications have large circular electrodes since the operation of the crystal in liquid sets high demands on the crystal performance. The flow cells in which the crystal operates are designed with respect to the electrode geometry since the walls of the flow cell should not interfere with the oscillations of the crystal. In more demanding applications, e.g. when measuring the kinetics of biochemical interaction, the dispersion of the sample caused by large flow cells can limit the sensor performance. A different approach would be to have a flow cell with better hydrodynamic properties and then design the crystal electrode with respect to the flow cell. The aim of this report is to study the flow behaviour of circular and rectangular sensor geometries with respect to sample dispersion in a QCM biosensor system. The effect of the geometry change is studied using flow simulations and is compared to experimental data performed on an Attana 80 QCM biosensor. The influence on and aspects of sensor sensitivity on the final sensor response and its applications is discussed. The performance of the rectangular and circular sensor systems as biosensors is evaluated in a preceding report [5].
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M. J¨onsson et al. / Sensors and Actuators B 123 (2007) 21–26
2. Background In a surface based biosensor, the transport of the sample plug to the sensor surface is facilitated by a combination of hydrodynamic and diffusive flow of sample. The flow profile under laminar flow conditions can be described as parabolic, i.e. the flow cross-sectional velocity profile has a parabolic shape with the highest velocity in the centre and zero velocity (no-slip condition) at the channel walls. The hydrodynamic flow moves sample from the injection valve to just above the sensor surface. The diffusive flow during this first process has a limited effect on the delivery of the sample to the sensor chamber, although diffusion combined with the laminar parabolic flow in small fluid channels will cause dispersion of a sample plug. Secondly, due to the parabolic flow profile, the hydrodynamic flow has little influence in the vicinity of the channel walls and in the vicinity of a sensor surface situated in the fluid channel. With respect to mass transport to the sensor surface in a flow channel, this behaviour is described by the presence of a stagnant layer at a distance b from the sensor surface under which the hydrodynamic flow is of minor importance. Consequently, there are two principal factors of importance for the sample delivery in a biosensor; sample dispersion and diffusive mass transport down to the sensor surface. The focus of this study lies with the effects of flow cell geometry on sample dispersion.
defined as a pressure at the boundary of the inlet. The outflow is set as normal out of the geometry (zero pressure gradient). The simulation of convection and diffusion is based on the formulations for a species of time-dependent concentration of mass, c and diffusion coefficient, D: δts
∂c + ∇ · (−D∇c) = −u · ∇c ∂t
(3)
δts is a time scaling coefficient, c the mass concentration of sample, and t is time. The velocity field u is the coupling variable between the two models. 2.2. Radial sensor sensitivity variation The QCM sensor is used to experimentally measure the sample plug dispersion. The frequency shift is detected as the sample plug passes the sensor surface. The sensor sensitivity varies over the electrode geometry and is proportional to the oscillation amplitude. The sensor signal amplitude has been found to be Gaussian distributed over the sensor surface according to reports by Ward and Delawski [11] and Rodahl and co-workers [12]. The effects of the sensor detection signal intensity decreasing at the periphery of the electrode results in a weighted detector signal. 3. Materials and methods
2.1. Sample flow analysis
3.1. QCM system
Flow injection analysis is a research area of its own and the study of sample plug dispersion has been presented in textbooks by, e.g. Ruzicka and Hansen [6]. The desired ideal square wave sample plug profile is dispersed in the transport line by the valve mechanisms, tubing and associated connections, and in the sensor chamber. Mathematical descriptions of sample plug profiles as an exponentially modified Gaussian function have been discussed by Kolev [7], Berthod [8] and van Akker et al. [9,10]. In our case the sample plug is elongated and an exponentially modified square wave is chosen to model the plug shape provided by the sample delivery system. This plug profile is not verified experimentally but is considered sufficiently valid to be used as input data when the actual sample plug shape is unknown. A Navier–Stokes model combined with a convection and diffusion model is used to present the behaviour of the flow and the sample concentration distribution in the system. The Navier–Stokes equation describes the flow situation in the channel:
Two Attana 80 QCM biosensor (Attana AB) were used for the experiments. The QCM system consists of a peristaltic pump, an eight-way injection valve and the sensor unit with flow cell and oscillation electronics, see Fig. 1. A frequency counter collects frequency data which is transferred to a computer where the data can be monitored and logged. The QCM system operates in a continuous flow mode where the running buffer is continuously flown through the flow cell over the sensor surface. A sample is injected by first filling the injection valve with the sample and then switching the valve. The sample is then switched into the flow line and is transported to the sensor surface by the continuous flow. The response from an injection to the resonance frequency is monitored in real-time by the computer and a mass adsorption to the surface will result in a negative frequency shift. Desorption from the surface will result in an increase in frequency. One of the systems was used in its standard configuration with a circular crystal and circular flow cell and the other system was modified with a rectangular crystal and a correspondingly rectangular flow cell. The electrode geometries for the sensing electrode were 4.5 mm in diameter for the circular electrode and 1 mm × 4 mm for the rectangular electrode as described in the preceding paper [5]. The flow cells were 0.2 mm in height and had slightly larger dimensions than the corresponding crystals in order to reduce the damping of the crystal from the flow cell. The approximate volumes of the circular and rectangular cells were 5 and 1.5 l, respectively. The running buffer for the QCM experiments was phosphate buffered saline (PBS). Test sample to investigate the sample plug
ρ
∂u − η∇ 2 u + ρ(u · ∇)u + ∇p = F ∂t
∇ ·u=0
(1) (2)
The first equation is the momentum balance, and the second is the equation of continuity for incompressible fluids. The following variables and parameters appear in the equations, ρ is the density, u the velocity field, η the dynamic viscosity, p the pressure and F is a volume force field such as gravity. A no-slip boundary condition is set for the chamber walls and the inflow of fluid is
M. J¨onsson et al. / Sensors and Actuators B 123 (2007) 21–26
23
Fig. 1. Schematic of the Attana 80 biosensor system.
appearance for the two systems was PBS with 2% dimethyl sulfoxide (DMSO). A 50 l sample plug was injected at a flowrate of 100 l/min and the frequency shift response was registered and converted into a normalised concentration.
sample plug is defined as the time-dependent concentration at the boundary of the inlet hole. The time-dependent concentration over the sensor area is calculated as the integrated concentration over the active sensor electrode area.
3.2. Flow simulations
4. Results
The flow behaviour for the different crystal geometries has been studied in 2D-simulations using a coupled model of Navier–Stokes (NS) flow and convection–diffusion (CD) using Femlab (COMSOL Multiphysics) software. The NS-model is solved using a non-linear stationary solver and the CD-model by a time-dependent solver. The sample solution is defined by a diffusion coefficient D of 1.00E−9 m2 /s, a normalised sample concentration C0 , a flow of 100 l/min, density 1000 kg/m3 , and viscosity η 1.0E−3 Ns/m2 . The active area of the sensor crystal is 4.5 mm in diameter and 4 mm × 1 mm, respectively, for circular and rectangular geometries. The 100 l/min volume flow corresponds to a linear maximum velocity in the centre of the structure of 3.9 and 12.0 mm/s for the circular and rectangular geometries, respectively. Simulations were carried out both for a non-dispersed, essentially square, sample injection and for a dispersed plug that modelled the sample plug from the sample delivery system. The injected sample concentration profile from the sample delivery system was expressed as an exponential function according to
4.1. Simulations
c(t) = C0 (1 − e−t/k )
The geometry of the sensor system causes variations of the linear velocity across the sensor. From the NS-simulations the velocity profiles in the sensor chamber are extracted as seen in Fig. 2. The inner boundary structures illustrate the sensor electrode areas. The profile is uniformly parabolic along the geometry in the rectangular case, Fig. 2b, whereas in the circular case, Fig. 2a, the speed of the fluid decreases towards the widest
(4)
for the rising part of the curve and according to c(t) = C0 e−t/k
(5)
for the falling part, where C0 is the origin concentration and k is a time constant. The NS-model is first solved using the stationary non-linear solver. The resulting flow velocity profile is then used as the start value to solve the convection and diffusion model in a timedependent analysis (time step 0.2 s). The profile of the injected
Fig. 2. Linear velocity field profiles in the sensor chambers for: circular (a) and rectangular (b) geometries. The positions of vmax and vmin are indicated.
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Table 1 Linear velocity in the sensor chamber Position
Circular geometry
Rectangular geometry
vmax (mm/s) vmin (mm/s) vcenter (mm/s)
9.1 0.4 3.9
14 6.0 12
part of the chamber and then increases as the geometry contracts towards the outlet. The maximum, minimum and central velocity within the electrode area are presented in Table 1. The maximum velocity, vmax , appears across the boundary close to the inlet and outlet and the minimum velocity, vmin , is found at the centre of the sideboundaries as pointed out in Fig. 2a and b. As a consequence of the velocity variations over the sensor surface, the rectangular and circular systems will display different response behaviour to an injected sample plug. Fig. 3 displays the integrated normalised concentration over the respective sensor surfaces as a result of a non-dispersed injection plug. The dispersion in the rectangular sensor system is negligible whereas the dispersion in the circular system causes a significant time delay before the maximum concentration is reached. However, since the sample injected in a real sensor system such as the Attana 80 described above, will have a dispersed sample plug before even entering the sensor flow cell, these results may not accurately describe the actual sensor response. The sample plug from the sample delivery system was modelled according to Eqs. (4) and (5) and was used as input for the subsequent simulations. The integrated normalised concentration over the active area of the crystals is shown in Fig. 4 for simulations with a dispersed injection plug. The delay time, t0.95 , that is required for the integrated concentration over the sensor surface to reach 95% of the maximum concentration was defined to serve as a measure above which dispersion effects would have only negligible effects on biosensor kinetics determination. The total delay time, including the contribution from dispersion in the transport system, was 7.6 and 6.2 s for the circular and rectangular geometry, respectively. Experimental results
Fig. 4. Simulated sensor concentration profile from a dispersed sample plug for circular and rectangular flow cell geometries. The sample volume is 50 l. The delay time, t0.95 , for circular and rectangular geometry, respectively, is indicated.
for DMSO sample injections indicate similar dispersions for the two sensors as seen in Fig. 5. The delay time for the sensor flow cell provided a non-dispersed sample plug was 3.5 s for the circular system and below 0.5 s for the rectangular system (more accurate determination was not allowed given the chosen time resolution of the simulation of 0.5 s). The flow velocity variations over the sensor surface also cause the sample concentration distribution to vary over the sensor as illustrated in Fig. 6 for the circular flow geometry and in Fig. 7 for the rectangular geometry. The figures illustrate the inflow and outflow of the sample plug through the sensor chamber. The time it takes for the first part of the sample plug to fill the active sensing area is about 5 s for the circular geometry and about 1 s for the rectangular geometry at a flowrate of 100 l/min. Analogously, the circular chamber is emptied at a slower rate and a split tail of residual sample remains in the chamber 25 s after the end of sample injection. The sequence in Fig. 4 indicates that the residual samples left in both the circular and the rectangular cases stay outside of the sensor area. 5. Discussion The velocity and concentration profile results from the simulations indicate that the rectangular geometry has a significantly
Fig. 3. Simulated sensor concentration profile from a non-dispersed and essentially square sample plug for circular and rectangular flow cell geometries. The sample volume is 50 l.
Fig. 5. Experimental results from measurements on DMSO sample plugs for rectangular and circular sensor geometries presented as normalised concentrations.
M. J¨onsson et al. / Sensors and Actuators B 123 (2007) 21–26
Fig. 6. Time-dependent surface sample concentration distributions for the circular crystal geometry. Injection volume is 50 l (0–30 s).
improved flow behaviour. The sample plug is more uniformly transported through the rectangular chamber. The experimental data, however, show similar sensor responses for the two geometries. In order to understand why the simulation results do not reflect the experimental data, a detailed understanding of the entire setup is needed. The fluidics of the system as described above consists of a pump, an injection valve and the sensor. The sample is introduced into the valve as at least twice the desired sample plug volume into the injection loop. The injection valve is then switched and the sample volume is almost instantly placed into the flow line that leads to the sensor. Independent of the QCM systems evaluated here, the flow of the sample from the injection valve to the sensor will cause dispersion. Experimental work involving different tubing diameters between the valve and the sensor has shown that the dispersion in the examined systems is highly dependent on this part of the sample delivery system. As a consequence, the results of the simulation data may be over shadowed by the dispersion in the transport of the sample from the valve to the sensor. Since QCM sensors have a sensitivity maximum in the centre of the crystal this may also have an effect on the measurement results. Depending on the profile of this sensitivity distribution, the tail of the sample plug apparent in Fig. 3 may only to a limited extent affect the sensor. Using simulation as a tool to predict and understand physical phenomena places demands on the model design. A 2D-model has the advantage of simplicity over a 3D-model, although a
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Fig. 7. Time-dependent surface sample concentration distributions for the rectangular crystal geometry. The injection volume is 50 l (0–30 s).
3D-model could have provided information on mass transport to the sensor surface. The 2D-model used was designed with the purpose of studying the sample propagation in a plane in the centre of the chamber parallel to the sensor electrode surface, and was considered appropriate for the examination of sample dispersion as an effect of flow cell geometry. Sensor system dispersion causes the sample concentration over the sensor surface to rise from 0 to 95% of the maximum concentration within 6.2 and 7.6 s for the two electrode geometries, respectively. During this period any determination of reaction association or dissociation rates will be complex, since the sample concentration over the surface is undefined. Consequently, obtaining reaction rates for biological interaction systems that are so fast that most of the binding event occurs already during this dispersion phase will be difficult. Reviewing biosensor literature shows that certain small molecule-enzyme interactions could lie within this field and would therefore be difficult to determine [13]. Other biological systems such as for instance antibody–antigen interactions are normally significantly slower and the kinetics determination on those systems would be only negligible affected by the dispersion phase of the sample plug [14–16]. 6. Conclusions Finite element simulations on a QCM system with rectangular flow cell and sensor electrode has shown that the dispersion
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phenomena in the flow cell can be significantly reduced compared to a standard circular QCM system. Experimental results, however, indicate that the sample delivery system has a predominant effect on the dispersion of the whole sensor system and that no significant improvement could be achieved by enhancement of the sensor flow cell alone. Consequently, improvement of the sensor flow cell should be accompanied with improvement of the sample delivery system. With reference to kinetic studies of biological interactions, the current dispersion should have little effect on the results for studies of interaction pairs with relatively slow to normal binding rates such as antibody–antigen interactions. Incentive for further development of the flow cell and sample delivery system exists primarily for applications with high reaction rates such as for certain receptor ligand interactions. Acknowledgements The authors gratefully acknowledge the helpful comments of Bertil H¨ok and the experimental assistance of Thomas Weissbach. The authors further acknowledge the financial support from the Swedish Research Council and Attana AB. References [1] A. Katerkamp, Chemical and biochemical sensors, in: Ullman’s Encyclopedia of Industrial Chemistry, Wiley/VCH Verlag GmbH, 2001. [2] M. Rodahl, F. Hook, A. Krozer, P. Brzezinski, B. Kasemo, Quartzcrystal microbalance setup for frequency and Q-factor measurements in gaseous and liquid environments, Rev. Sci. Instrum. 66 (1995) 3924– 3930. [3] C. K¨osslinger, E. Uttenthaler, S. Drost, F. Aberl, H. Wolf, G. Brink, A. Stanglmaier, E. Sackmann, Comparison of the QCM and the SPR method for surface studies and immunological applications, Sens. Actuators B: Chem. 24 (1995) 107–112. [4] V.M. Mecea, From quartz crystal microbalance to fundamental principles of mass measurements, Anal. Lett. 38 (2005) 753–767. [5] H. Anderson, M. J¨onsson. U. Lindberg, T. Aastrup, Quartz crystal microbalance biosensor design: I. Experimental study of sensor response and performance, Sens. Actuators B: Chem. (2006), in press. [6] J. Ruzicka, E.H. Hansen, Flow Injection Analysis, vol. 62, 2nd ed., Wiley, New York, 1988. [7] S.D. Kolev, Mathematical-modeling of flow-injection systems, Anal. Chim. Acta 308 (1995) 36–66.
[8] A. Berthod, Mathematical series for signal modeling using exponentially modified functions, Anal. Chem. 63 (1991) 1879–1884. [9] E.B. van Akker, M. Bos, W.E. van der Linden, Convection and diffusion in a micro-flow injection system, Anal. Chim. Acta 373 (1998) 227–239. [10] E.B. van Akker, M. Bos, W.E. van der Linden, Continuous, pulsed and stopped flow in a μ-flow injection system (numerical vs experimental), Anal. Chim. Acta 378 (1999) 111–117. [11] M.D. Ward, E.J. Delawski, Radial mass sensitivity of the quartz crystal microbalance in liquid-media, Anal. Chem. 63 (1991) 886–890. [12] M. Edvardsson, M. Rodahl, B. Kasemo, F. Hook, A dual-frequency QCMD setup operating at elevated oscillation amplitudes, Anal. Chem. 77 (2005) 4918–4926. [13] D.G. Myszka, Analysis of small-molecule interactions using Biacore S51 technology, Anal. Biochem. 329 (2004) 316–323. [14] A. Einhauer, A. Jungbauer, Affinity of the monoclonal antibody M1 directed against the FLAG peptide, J. Chromatogr. A 921 (2001) 25–30. [15] G.H. Choi, D.H. Lee, W.K. Min, Y.J. Cho, D.H. Kweon, D.H. Son, K. Park, J.H. Seo, Cloning, expression, and characterization of single-chain variable fragment antibody against mycotoxin deoxynivalenol in recombinant Escherichia coli, Protein Expres. Purif. 35 (2004) 84–92. [16] A.W. Drake, D.G. Myszka, S.L. Klakamp, Characterizing high-affinity antigen/antibody complexes by kinetic- and equilibrium-based methods, Anal. Biochem. 328 (2004) 35–43.
Biographies Mats J¨onsson received his MSc degree in material engineering in 2000 and the PhD in engineering science with specialization in microsystems technology ˚ in 2006 at the Angstr¨ om Laboratory, Uppsala University, Sweden. His research interest is in development of microsystems for biotechnology applications, especially in electric manipulation of bio-particles and QCM-technology. Henrik Anderson received his MSc degree in chemical engineering from the Royal Institute of Technology, Sweden, in 2000 and currently holds a position as PhD student at the Department of Solid State Electronics, Uppsala University, Sweden. His research interest is in development of biosensors with regards to transducer and surface chemistry development as well as the development of new applications of QCM biosensors. Mr. Anderson is co-founder of Attana AB. Ulf Lindberg received his MSc degree in engineering science in 1985 and his PhD degree in solid state electronics in 1993 both at Uppsala University, Sweden. After working at Biacore AB with microfluidics he rejoined the Department of Solid State Electronics at Uppsala University in 2000. He is currently head of the Microstructure Technology Group with a special interest in Bio-MEMS. Teodor Aastrup received his MSc degree in materials physics at Uppsala University in 1994 and his PhD at the Royal Institute of Technology, Sweden, in 1999. Dr. Aastrup is co-founder and CEO of Attana AB.