A Fully Unsupervised Compartment-on-Demand Platform for Precise Nanoliter Assays of Time-Dependent Steady-State Enzyme Kinetics and Inhibition

The ability to miniaturize biochemical assays in water-in-oil emulsion droplets allows a massive scale-down of reaction volumes, so that high-throughput experimentation can be performed more economically and more efficiently. Generating such droplets in compartment-on-demand (COD) platforms is the basis for rapid, automated screening of chemical and biological libraries with minimal volume consumption. Herein, we describe the implementation of such a COD platform to perform high precision nanoliter assays. The coupling of a COD platform to a droplet absorbance detection set-up results in a fully automated analytical system. Michaelis–Menten parameters of 4-nitrophenyl glucopyranoside hydrolysis by sweet almond β-glucosidase can be generated based on 24 time-courses taken at different substrate concentrations with a total volume consumption of only 1.4 μL. Importantly, kinetic parameters can be derived in a fully unsupervised manner within 20 min: droplet production (5 min), initial reading of the droplet sequence (5 min), and droplet fusion to initiate the reaction and read-out over time (10 min). Similarly, the inhibition of the enzymatic reaction by conduritol B epoxide and 1-deoxynojirimycin was measured, and Ki values were determined. In both cases, the kinetic parameters obtained in droplets were identical within error to values obtained in titer plates, despite a >104-fold volume reduction, from micro- to nanoliters.


II. Droplet size is a function of suction flow rate and retention time in the aqueous phase and can be adjusted at will
The relationship between theoretical volume input and observed volume was tested by creating droplets of increasing sizes only changing the spatial ratio of the electromagnet from 10% to 100%. The frequency of droplet formation was 0.2, 1, 1 and 1.5 Hz for flow rates of 1, 3, 5 and 7 µL/min respectively. The relationship between theoretical volumes and observed volumes is linear with slopes very close to 1.
Deviations from linearity averaged 10% relative standard deviations. This may be due to the influence of pulsation caused by the syringe pump, which results in oscillating droplet sizes around the theoretical value. To compensate for the small deviations in droplet volumes, the lengths (and thus volumes) of droplets were systematically measured before running assays.

A. Visualization
To visualize droplet catch-up and fusion, a movie was recorded at 30 fps of a small 10 nL droplet (2 mM phenol red in water) followed by a larger droplet (100 nL). The flow rate for droplet generation was 10 nL/s. The droplet pair was stopped and acceleration of the flow rate from zero to 25 µL/min was applied.
In Figure S5, the acceleration was applied from left to right. The movie was subsequently processed using ImageJ. The intensity along a section of the tubing was recorded for all frames. The resulting plot is shown in Figure S5. The plot highlights that the clear gap between the small and larger droplets gets smaller as a function of time and eventually disappears.

B. Quantification of the success rate of droplet fusion
Droplets of various sizes were measured to travel at the same speed when separated by large oil gaps.
However, when placed in close proximity, oil depletion between the two droplets started occurring with maximum effect taking place when a large droplet followed a smaller one or when the second droplet had a higher viscosity.
Fusion of 50 pairs of aqueous droplets containing phenol (1 mM) red was attempted and the merging success was measured as a function of suction rate. The number of successfully fused pairs was measured after a 15 cm distance. The acceleration applied was constant from 0 to 25 µL/min. It was found that merging was most successful when droplets were formed at low flow rates, with the merging success rate declining as droplets were formed more quickly. The success rate reaches as high as 90% with only droplets of roughly equal volume not catching up after the acceleration distance. Most of these droplets were found not to catch up even on distances over 80 cm.
S6 Figure S6. Merging rate as a function of flow rate. The merging rate increases with decreasing inter-droplet distances.

IV. Mixing of droplet contents after hydrodynamic merging of two droplets in round tubing
Content mixing after droplet fusion was studied by merging a small water droplet containing phenol red (1 mM) with a much larger aqueous buffer. Convection of the phenol red can be seen by tracking of the fusion event with a camera at 30 frames per second. Snapshots of the merging process are displayed in Figure S7. Complex mixing patterns form until a uniform distribution is reached after 3 to 5 seconds. As the timescale for this adjustment is much smaller than the timescale of the kinetics (typically recorded over 10 minutes, with time points every 20 sec), the mixing time can be neglected when analysing the reaction kinetics.

V. Automated gradient generation
The control program of the robot was modified to allow input of pairs with linearly varying sizes.
Specifically, the volume of the first droplet was increased while the volume of the second decreased, so that the sum of the volumes of the two droplets remained constant. Merging of droplets with size ratios close to 1:1 was unreliable because oil leaked equally from the front and the rear droplet. To tackle this issue, a margin factor M was introduced to preserve a size difference between front and rear droplets. As the Labview program allows control of the frequency at which droplets are generated, the input frequency f 1i for the first droplet at pair i of N pairs was calculated from a fixed start frequency f start and final frequency f end . The equation for the frequency of generation of the front droplet f 1i was calculated as follows: For the rear droplet, the equation was: The program was tested for merging 50 phenol red (2mM)/water droplet pairs covering a range of size ratios such that the proportion of phenol red varied from 96.6% to 50%. The absorbance of these S8 Figure S8. After merging phenol red (2 mM) and buffer in droplets of varying sizes, a linear gradient is created from high to low concentration of phenol red (2 mM down to 1 mM). The red line indicates the oil baseline.
In addition to size difference, it was found that more viscous droplets (for instance with mM amounts of substrate) tended to catch up with smaller and less viscous droplets in a faster manner and even over the 1:1 size ratio.

VI. Back and forth measurements
Droplets were moved back and forth by automatically reversing the flow, in response to detection of two droplets of high concentration (1 mM 4-nitrophenol) that were placed at the start and the end of the droplet sequences. A typical absorbance reading is shown in Figure S9, where a droplet sequence is read four times. The flow direction is indicated by black arrows. We refer to the alternation of their direction corresponds as a 'back-and-forth pattern'. The voltage corresponds to the raw signal detected by the photo-detector and is used to quantify absorbance units.

VII. Background reaction
Control droplets containing only substrate in buffer at different concentrations were generated at the end of every kinetic sequence. The readings from these droplets were found to have a slope which is consistent with a self-hydrolysis process. Figure S10 shows the initial rates obtained for 5 droplets of substrate. Performing the same control without introducing any enzymes in clean tubing and with a fresh oil bath resulted in similar results indicating this product formation is not linked with residual enzyme contamination. These initial rates represented typically 10-20% of the rates found in the catalyzed reaction. Therefore a correction factor proportional to substrate concentration was applied to each enzyme-substrate mix to correct for the observed hydrolysis. This phenomenon possibly occurs at the interface between carrier and aqueous phase.

VIII. Comparison with microtiter plate readings
Steady-state kinetics were performed with β-glucosidase from sweet almonds at 78 nM. The enzyme concentration was calculated so that the reaction would be linear over a timescale of 10 minutes while generating enough signal to produce quantitative plots from microdroplets.
Kinetic absorbance measurements were carried out in a SpectraMax Plus spectrophotometer (Molecular Devices). The Michaelis-Menten data for hydrolysis of 4-nitrophenyl glucopyranoside by β-glucosidase was measured to validate the microdroplet-generated data. In a 96-well plate, 100 µL reactions were carried out consisting of constant enzyme concentration (78 nM) and substrate concentration ranging between 0 and 40 mM. Rates were measured in triplicate at room temperature (21 °C) and initial rates plotted in Figure S11. Inhibition by 1-deoxynojirimycin hydrochloride (DNM) and conduriol B epoxide (CBE) was carried out at fixed enzyme and substrate concentrations (78 nM and 30 mM, respectively). The structures of both inhibiting compounds are shown in Figure S11 and normalized initial rate decreases are plotted versus inhibitor concentration in Figure S12.  The fit for DNM gave an IC 50 =100 ± 30 µM translating into a mean K I value of 30 µM. The literature value for K I is 47 µM.
Normalized rate V/V 0 A B