PULSE WIDTH MODULATION OF LIQUID FLOWS:
TOWARDS DYNAMIC CONTROL OF CELL MICROENVIRONMENTS
M. Unger1, S.S. Lee2,3, M. Peter2,3 and H. Koeppl1,3*
1
BISON Group, Automatic Control Laboratory, D-ITET, ETH Zurich, SWITZERLAND,
2
Institute of Biochemistry, D-BIOL, ETH Zurich, SWITZERLAND,
3
Competence Center for Systems Physiology and Metabolic Diseases, SWITZERLAND
ABSTRACT
Advanced methods for live cell analysis help to understand fundamental processes within a cell. We propose a method to
generate specific input stimuli that are essentially needed to get insights to dynamic cellular behavior. By Pulse-WidthModulation (PWM) of liquid flows, we offer a fast and reliable way to generate temporal profiles of media concentration that
can be combined with other microfluidic devices. Its functionality is demonstrated in experiments of salt concentration ramping, which is of high interest and biological relevance for maintaining activation of the Mitogen Activated Protein Kinase
(MAPK) Hog1 in the High Osmolarity Glycerol (HOG) pathway.
KEYWORDS: Pulse Width Modulation, Concentration Ramping, Signaling Pathway
INTRODUCTION
Pulse-Width-Modulation (PWM) is a well-established concept in electrical engineering [1]. We make use of this concept
and transform it to a method for generating temporal profiles of media concentration within cell microenvironments. This
shows to be of vital importance, as recent works [2, 3, 4] have reported the need of advanced input stimuli for the understanding of intracellular dynamics of the HOG pathway in the yeast, Saccharomyces Cerevisiae.
THEORY
A desired output value of electric voltage or current can be realized by averaging over a time series of fast switches between the ON and OFF states of a power supply. The switching ratio between these two states, and thus the width of the individual pulses, defines the realized output value. We now take the concept of PWM from electrical engineering and apply it to
the modulation of liquid flows on a microfluidic scale. This allows a precise dilution of a desired medium concentration [5].
We extend the application of PWM to generate dynamic profiles of media concentration over time. Examples of concentration ramping will be given at a later stage.
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Figure 1: (a) Schematic illustration of the Pulse-Width-Modulation (PWM) setup, as used for perturbing cell microenvironments. The switching between two different input flows is done by a computer controlled solenoid valve. This is connected
to the cell chamber by PTFE tubing, serving as a diffusion channel to filter out individual PWM packages and create the desired media concentration. (b) (left) Specific concentrations C of media are generated in the cell chamber by adapting the
PWM duty cycle D (Eq. 1), determining the On/Off switching ratio between the two input concentrations CA and CB. (right)
Experimental validation of static dilution by fluorescence microscopy. The intensity of fluorescent FITC dye represents the
specific concentration of the medium in the cell chamber. The numbers within the image give the ratio of TA/TB.
978-0-9798064-4-5/µTAS 2011/$20©11CBMS-0001
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15th International Conference on
Miniaturized Systems for Chemistry and Life Sciences
October 2-6, 2011, Seattle, Washington, USA
Consider an output stream, made up of switching between two input streams of different concentrations CA and CB of a
fluid with equal and constant flow rates. As the input streams are selected mutually exclusive, the output flow rate remains
constant and equal to the input flows. Thus we can define liquid packages of equal volume transported sequentially in time T.
The average amount of concentration C after diffusion (low-pass filtering) within each depends on the fraction of the total
package volume consisting of media with concentration CA and CB. The ratio of the time the input stream with concentration
CA is active to the total package time T = TA + TB,
D=
TA
T
(1)
is referred to as duty cycle D. By determining D, and thus defining the ratio of CA and CB within a package, a desired output
concentration C can be diluted:
C=
D · T · CA + (1 − D) · T · CB
T
(2)
We can now extend this concept of media dilution further to dynamic dilution. By computing a new value for the duty cycle
D for each liquid package of time T, we can control the output concentration profile over time:
C[t] = D[t] · CA + (1 − D[t]) · CB
(3)
If, for example, the duty cycle is steadily increased up to D = 1, the concentration ramps to the maximum output concentration CA.
Normalized Medium Concentration [a.U.]
EXPERIMENTAL
A schematic illustration of the PWM setup is shown in Figure 1(a). Hydrostatic pressure (0.25 psi) is evenly applied to
reservoirs of different media (concentration CA and CB) to keep their flow rate equal and constant over time. The switching
between the two input media is performed by a computer controlled 3-way solenoid valve. The valve’s outlet is connected to
the cell imaging chamber (µ-slide VI, ibidi) through PTFE tubing that serves as a diffusion channel to filter out individual
PWM packages and create the desired media concentration. Fluorescence dye (FITC-Dextran or Alexa 680-Dextran
M.W.=3000, Invitrogen) was diluted in medium A to visualize output concentrations. Images of budding yeast cells were acquired on a fully automated inverted epi-fluorescence microscope (Ti-Eclipse, Nikon) in a temperature incubator set to 30°C,
using 60x oil objectives and appropriate excitation and emission filters. For Hog1 relocation experiments, the concentration
of NaCl is steadily increased (0.05 – 0.4M), microscopic images are taken in multiple positions. For image analysis, individual cells were tracked using segmentation of the Hta2-CFP images to identify their nuclei, while the cell area was obtained by
segmentation of the RFP image or defocused transmission image.
1
0.8
0.6
30s Ramping − Measurement
30s Ramping − Target
60s Ramping − Measurement
60s Ramping − Target
120s Ramping − Measurement
120s Ramping − Target
240s Ramping − Measurement
240s Ramping − Target
0.4
0.2
0
0
20
40
60
80
100
120
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Time [s]
160
180
200
220
240
Figure 2: Experimental validation of concentration ramping using fluorescence microscopy. Fluorescent dye was diluted
in input medium A to visualize the output concentration. Thus, the average pixel intensity value of the resulting images represents the medium concentration diluted by PWM. Intensity values are normalized for comparison.
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RESULTS AND DISCUSSION
At first, we assessed static dilution of desired medium concentrations, as described in (Eq. 2) with fluorescence microscopy. On the right part of Figure 1(b), images of static flows of three different output concentrations of fluorescent FITC dye
are presented, which are diluted as schematically illustrated in the left part of Figure 1(b). Due to an increased duty cycle D,
the average intensity in the microscopy images increases respectively. Next, we applied our extended version of PWM (Eq.
3) to generate temporal concentration profiles. Throughout the ramping phase, the duty cycle D is constantly increased, leading to increased durations of the high-concentration media pulses. We performed several runs at various ramping speeds and
confirmed that we can successfully ramp media concentrations using PWM (Fig. 2). Finally, we applied the PWM method to
modulate the Hog1 activation by steadily increasing salt concentration (during a time period of 30 min), and observed the accumulation of Hog1 at nuclei (Fig. 3) [3].
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NaCl [M]
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Hog1 relocation [a.U.]
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5
10
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Time [min]
30
35
40
45
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1.3
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10
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Time [min]
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Figure 3: Hog1 nuclear relocation upon increase of salt concentration (NaCl 0.05-0.4M) over duration of 30 minutes.
(left upper panel) Temporal profile of NaCl concentration (left lower panel) Hog relocation (ratiometric average intensity
(Iavg, nucleus/Iavg cyto ) of Hog1-YFP in single cell) (right panel) Example images at given time points; green: Hog1-YFP, red:
Alexa 680 proportional to NaCl concentration
CONCLUSION
We introduced the concept of PWM with a dynamic duty cycle over time for liquid flows. Thus, presenting a robust and
reliable way of generating temporal concentration profiles like concentration ramping. As no custom designed chips are required, it is a method easy to setup that can be integrated in many existing microfluidic environments.
ACKNOWLEDGEMENTS
This work was supported by an Interdisciplinary Pilot Project (IPP) within the Swiss Initiative in Systems Biology
(SystemsX.ch). The authors would like to thank S. Pelet and H. Sharifian for donating the yeast strain.
REFERENCES
[1]
D.G. Holmes and T.A. Lipo, Pulse Width Modulation for Power Converters: Principles and Practice (IEEE Press
Series on Power Engineering), Wiley-IEEE Press, 2003.
[2]
D. Muzzey, C.A. Gómez-Uribe, J.T. Mettetal, and A. van Oudenaarden, “A systems-level analysis of perfect adaptation in yeast osmoregulation.,” Cell, vol. 138, Jul. 2009, pp. 160-71.
[3]
S. Pelet, F. Rudolf, M. Nadal-Ribelles, E. de Nadal, F. Posas, and M. Peter, “Transient activation of the HOG MAPK
pathway regulates bimodal gene expression.,” Science (New York, N.Y.), vol. 332, May. 2011, pp. 732-5.
[4]
Z. Zi, W. Liebermeister, and E. Klipp, “A quantitative study of the Hog1 MAPK response to fluctuating osmotic
stress in Saccharomyces cerevisiae.,” PloS one, vol. 5, Jan. 2010, p. e9522.
[5]
A. Ainla, I. Gözen, O. Orwar, and A. Jesorka, “A microfluidic diluter based on pulse width flow modulation,” Analytical chemistry, vol. 81, Jul. 2009, pp. 5549-56.
CONTACT
*H. Koeppl; koeppl@ethz.ch
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