POTENTIAL OF SINUSOIDAL GRADIENTS FOR DOSE RESPONSE ASSAYS IN DROPLET-BASED MICROFLUIDICS

Mark Kielpinski1, Tina Vasold1, Peter Horbert1, Karin Martin2, Günter Mayer1, Thomas Henkel1

1Institute of Photonic Technology (IPHT), Jena, GERMANY and2Leibniz Institute for Natural Product Research and Infection Biology e.V.

Hans-Knöll-Institute (HKI) Jena, GERMANY

ABSTRACTDroplet-based microfluidics became a powerful tool for quantitative high-throughput analysis of molecular and

biological interactions. Gradient dosing can be applied for the generation of large sample collections with systematic variation in the concentration of the ingredients and effectors. Droplets can be incubated in capillary systems preserving their order. In this serial regime the concentration pattern in each droplet can be recalculated from its number, it's creation time and the gradient dosing program, used for the generation of the doplet collection. Up to now, saw-fish-tooth like concentration gradients are widely used for this purpose. In our work we investigate the potential of periodic sinusoidal gradients for this type of screening applications. Due to their periodicity and continuity it is expected, that these types of gradients improve reliability in the gradient generation process due to the lack of discontinuities in the flow rates. On the other hand the key features of these gradients in terms of continuity and periodicity allow improvements in data analysis and error detection to gain more accurate analytical results. This initial hypothesis is proved in droplet-based experiments for the measurement of the minimum inhibitory concentration of the antibiotic Ciprofloxacin to bacterial strain E. coli RV308.

KEYWORDS: droplet-based-microfluidics, dose-response-assay, sinusoidal-concentration-gradient

INTRODUCTIONThe outstanding potential of droplet-based bio-assays for multiparameter dose-response studies has been widely con-

firmed. Gradient dosing of multiple reagents at a multi component droplet generator allows the efficient generation of droplet populations, spanning a multidimensional parameter space. Interpretation of the readout of an individual droplet requires the knowledge of the exact concentration of ingredients at least at the time of its creation. This information can be derived from the applied dosing gradient scheme. Saw-tooth gradients, composed from linear gradient sections are preferred due to the simplicity of the rules for calculation of the concentrations in the droplets. The disadvantage of this type of gradients is its discontinuity with stepwise changes in the flow rates. Due to elasticity of the microfluidic system changes in flow rate settings cannot be expected to immediately result in changing the flow rates at the droplet generator unit. This causes system-dependent uncertainties in the droplet composition and the derived data. In our work we are evaluating periodic, sinusoidal concentration gradients with binary readout in order to implement precise readout with im-proved resolution and error correction.

THEORYAn ideal droplet generator is expected to generate uniform sized droplets at a given flow rate. Deviations from this

behavior due to changes in the viscosity or interface tension of the fluids are left out of consideration. Time periodic sinusoidal flow rate gradients can be expressed by the following relation with the total the flow rate QT, dependent on the time t, the flow rates QMIN,i and QiMAX,i, the period length taui and the phase shift phii as shown in equation 1 for an arbitrary number of up to n fluids Fi.

QT=∑i=1

n

(12

(Q MAX , i−Q MIN , i) (sin((2π t)

τi+ϕi)+1)+Q MIN , i) (1)

Each of the fluids, used for droplet generation has a fixed composition, expressed by the concentration of its ingredients ci,k. The concentration of each component k in a droplet, generated at the time t can be obtained by integration in the limits between t1 and t2 where the droplet formation starts at t1 - the release time of the preceding droplet and ends at t2 - the droplet release time from the generator unit. Due to the continuity and periodicity of the gradient function this rule can be applied without any restrictions to the time t. The initial composition in each droplet can be calculated. In contrast, the final concentration after incubation may be changed due to partial evaporation of the fluid, fluid diffusion between droplets with different osmolarity, consumption of ingredients during the incubation or release of reaction products into the droplet volume. In our study the droplet generator is operated at a constant flow rate. Therefore, an additional culture medium is added with QA to guarantee, that Q = QA+ QT = const.. All droplets have the same volume VD and respectively are created at a constant frequency fD = VD/Q. The period length tau is constant for all components. Readout of the target assay is based on the decision between bacterial growth and growth inhibition. We expect a binary response function with the period length tau, symmetrically with respect to the gradient itself. By analyzing a droplet population, that spans multiple gradient periods the parameter tau as the number of droplets for a single period can be derived from the measured data. This information is sufficient to reconstruct the concentration profile in the measured droplet collection.

978-0-9798064-6-9/µTAS 2013/$20©13CBMS-0001 623 17th International Conference on MiniaturizedSystems for Chemistry and Life Sciences27-31 October 2013, Freiburg, Germany

Figure 1: Experimental setup and microchannel subsystem of the laboratory disk, utilized for the experiments. Left part: Video microscopy setup with integrated laboratory disk, flat panel light source and video microscope (Navitar 12x Zoom lens equipped with a AVT Dolphin 142 camera), mounted on an optical rail. Right part: Microchannel system sketch. Continuous phase fluids are mixed immediately before the the T-shaped droplet generator unit. Droplet distance was minimized by removal of continuous phase fluid at the downstream distance control unit in order to realize dense droplet packaging in the droplet incubation store. For readout the droplet collection is transported through the channel at the readout position after spacing of the droplet distances at the second distance control. immediately before the readout position.

EXPERIMENTAL A laboratory disc based lab-on-a-chip system for serialized microbial assays including multiple incubation and read-

out cycles was utilized for these experiments. The system comprises droplet generators, droplet distance controls, droplet-dosing and droplet merging units. It is prepared from two polycarbonate half shells by thermo diffusion bonding. Novec-HPFE 7500 with 0.5% PicoSurf-1 was utilized as the continuous phase, Luria-Bertani-broth (LB) as culture medium. Each droplet was created at a four port droplet generator with an average of 10 cells of E.coli RV308 per droplet and the antibiotic ciprofloxacin (MIC of 0.5 mg/l). The concentration of the antibiotic was varied using sunusoidal concentration gradient between 0 µg/ml and 2.28 µg/ml. The period of the gradient was set to 180 s with a QT

of 35 nl/s and a droplet volume of 33 nl. Readout of bacterial growth was performed by transmission mode video mi-croscopy and subsequent image data analysis as discussed below.

RESULTS & DISCUSSION Up to 1600 individual droplets spanning a total of 8 gradient periods can be created within a time of 1500 s and

loaded into the droplet incubation lop of the microfluidic laboratory disk. The disk can be incubated in water and separa -tion fluid saturated atmosphere for more than a week at 37°C without significant evaporations of the droplet volumes. For readout the complete droplet sequence is transported through a detection window of the video microscope. Droplet dis-tance is additionally increased by adding continuous phase fluid at the distance control(see figure 1). Bacterial growth can be detected by transmission-mode video microscopy in combination with in-house video image sequence analysis tools, based on the openCV toolkit.

No bacterial growth Bacterial growth

Figure 2: Recorded video images of droplets with and without bacterial growth of E.coli RV308. Illumination and detection system are optimized to enable automatic detection of channel wall boundaries and droplet interfaces for the separation of the inner droplet area from the image. Due to the half circular channel side walls additional optical arti-

facts due to light refraction are observed which has to be considered in the image analysis procedure.

Droplet micrographs of a droplet without and with bacterial growth are given in figure 2. The obtained growth pattern reflects the gradient periodicity and the concentration of the antibiotic. Bacterial growth patterns strongly correlate with the applied concentration gradient. For derivation of the results, the periodicity of the gradient and the minimum and max-imum concentration of the effector are required only. Improved resolution can be obtained by averaging multiple cycles,

DropletGenerator

DistanceControl

ReadoutPosition

Droplet Incubation Store

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false positive and false negative results can be clearly discriminated. For the reference experiment a one dimensional con-centration gradient of the antibiotic Ciprofloxacin was applied for the analysis of the dose dependent growth inhibition of E.coli RV308 (see figure 3). The gradient spans a concentration range between 0 and 2.28 mg/l. The minimum inhibitory concentration (MIC) is given with 0.5 mg/l. After an incubation time of 18 h bacterial growth could be reliably detected in droplets with antibiotic concentrtration below the MIC. No growth was detectable in droplets with an antibiotic con-centration above the MIC. So, at least for this reference experiment no false positive results were detected. In contrast, a population of false negative results, where no bacterial growth was detected even at antibiotic concentrations below the MIC. Due to the short incubation time it can be expected, that the bacterial growth in the droplets has not reached the de -tection limit for all of the droplets. So it can be expected, that the rate of false negative results will decrease with increas -ing incubation time. For binary high-throughput assays the Z-Factor has been introduced as quality criterion. Values above 0.5 are classified as excellent assays. For our assay a Z-Factor of 0.44 was observed. These results confirm the high potential of sinus-shaped concentration gradients for dose response assays. Future investigation will focus on the ap-plication of this concept even for multidimensional concentration gradients and the readout of dynamic signals.

Figure 3: Experimental Results for the dose response assay. Left: Mean gray values of the droplet collection and classification into droplets with bacterial growth (green dots) and non-growth (red dots). The average gray values of the droplet area refere to the left axis. The blue line indicates the concentration gradient of the antibiotic. The concentration

referes to the right axis. Right part: correlation plot of droplet gray value dependent on the antibiotic concentration.

Droplet Area average gray value statistics

Class N Mean Min Max Stdev

No Growth 1289 167.8 165.2 171.0 1.199

Growth 271 148.7 142.2 161.8 2.320

For the reference experiment a one dimensional concentration gradient of the antibiotic Ciprofloxacin was applied for the analysis of the dose dependent growth inhibition of E.coli RV308 (see figure 3). The gradient spans a concentration range between 0 and 2.28 mg/l. The minimum inhibitory concentration (MIC) is given with 0.5 mg/l. After an incubation time of 18 h bacterial growth could be reliably detected in droplets with antibiotic concentration below the MIC. No growth was detectable in droplets with an antibiotic concentration above the MIC. So, at least for this reference experi -ment no false positive results were detected. In contrast, a population of false negative results, where no bacterial growth was detected even at antibiotic concentrations below the MIC. Due to the short incubation time it can be expected, that the bacterial growth in the droplets has not reached the detection limit for all of the droplets and that the rate of false neg -ative results will decrease with increasing incubation time.

For binary high-throughput assays the Z-Factor has been introduced as quality criterion. Values above 0.5 are classi-fied as excellent assays. For our assay a Z-Factor of 0.44 was observed.

These results confirm the high potential of sinus-shaped concentration gradients for dose response assays. Future in-vestigation will focus on the application of this concept even for multidimensional concentration gradients and the read-out of dynamic signals.

ACKNOWLEDGEMENTSThis work was funded by the German BMBF in the research projects DiNaMiD and BactoCat. Special thanks are ad-

dressed to Dr. Nils Gleichmann for programming the video sequence analysis software tools and performing the image analysis tasks.

CONTACT thomas.henkel@ipht-jena.de

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