Submitted to Microfluidics and Nanofluidics
Supplementary Material
for
Comparison of continuous flow and static chamber μPCR devices through a computational study: The potential of flexible polymeric substrates
Vasileios E. PAPADOPOULOS, George KOKKORIS*, Ioanna N. KEFALA, and Angeliki TSEREPI*
*Corresponding authors: Tel.: ++30 2106503238; Fax: ++30 210 6511723; Email: ,
Institute of Nanoscience & Nanotechnology, NCSR “Demokritos”, Greece
Temperature controller
The manual tuning of the Proportional-Integral-Derivative temperature controller, used for evaluation of a Static Chamber (SC) micro-Polymerase Chain Reaction (μPCR) performance, involved a series of separate time dependent simulations, performed in a trial-and-error manner. Simulation included only solution of heat transfer in both solid and fluid and Joule heating models, with the presence of the temperature control feedback.
For t=0 the SC μPCR device is set at ambient temperature (273 K) and no current is applied to the microheaters. The objective is to find the optimal values of KP, KI, and KD in order to quickly (fast) and accurately reach the temperature setpoint of 345 K without any oscillations. At first KI and KD were set to zero and KP was increased until the system output started to oscillate; KP was set to half of that value, but the setpoint was not reached. In order to correct this offset, KI is increased until the setpoint is reached. Finally, for a quick reach of the setpoint, KD is increased until the duration of the control process reaches its minimum. The time in which the system reaches the setpoint is called settling time. These simulations are applied for heat coefficients of 5 and 10 W/(m2K) leading to a combination of KP, KI, and KD optimal values. These values and the corresponding maximum overshoot percentages (see Fig. S1) with their settling times are shown in Table S1. The threshold for concluding that the temperature setpoints are reached is considered to be ±1oK.
Fig. S1 PID temperature controller performance for a transition from 328 K to at 345 K. Settling time and overshoot percentage is shown.
Table S1 PID temperature controller parameters and performance for various combinations between substrate types, substrate thickness and heat coefficient.
Controller specifications / PCB / Glass50μm / 50μm / 500μm / 1000μm / 1000μm
Kp / 0.1000 / 0.1000 / 0.0700 / 0.0500 / 0.1600
Ki / 0.0320 / 0.0400 / 0.0070 / 0.0020 / 0.0250
Kd / 0.0045 / 0.0040 / 0.0040 / 0.0040 / 0.0000
72 K to 95 K settling time / 4.2 s / 3.8 s / 16.6 s / 53.0 s / 6.5 s
Controller inactivity / 16.2 s / 10.9 s / 39.6 s / 67.1 s / 59.6 s
95 K to 55 K settling time / 6.9 s / 6.0 s / 29.9 s / 0.0 s * / 0.0 s *
55 K to 72 K settling time / 4.2 s / 3.8 s / 16.1 s / 50.4 s / 6.5 s
72 K to 95 K overshoot / 1.6% / 1.6% / 2.7% / 0.0% ** / 1.8%
95 K to 55 K overshoot / 0.6% / 0.8% / 0.0% ** / 0.0% ** / 0.0% **
55 K to 72 K overshoot / 3.8% / 3.4% / 3.5% / 0.0% ** / 5.8%
*During transition from denaturation to annealing phase, controller is switched off. In cases of thicker substrates the temperature drop (K/s) is very low. Therefore there is sufficient time for the PCR mixture to remain in annealing temperature without the operation of the controller, and controller starts again its operation for reaching the extension temperature.
**No overshoot was observed: PCR mixture remained within acceptable bounds of temperature (temperature setpoint ±1 K), but without overshooting beyond the setpoint.
Summary of the results
Table S2. Comparison of CF and SC devices in terms of DNA amplification, energy consumption, and duration for different PCR protocols and heat transfer coefficients. The durations in parentheses include the pumping time.
Device type / CF / SCPCR protocol / 3s:4.2s:6.2s / 1.8s:2.5s:3.7s / 3s:4.2s:6.2s / 1.8s:2.5s:3.7s
Heat coefficient / 5 W/m2K / 10 W/m2K / 5 W/m2K / 5 W/m2K / 10 W/m2K / 5 W/m2K
DNA amplification / 645 / 630 / 300 / 657 / 630 / 436
Energy consumption (J) / 253 / 363 / 150 / 69 / 85 / 61
10 cycle duration (s) / 353 / 353 / 212 / 463 (590) / 391(519) / 409 (536)