Fig. 4: Experimental data and model fit.

The working electrodes have a diameter of 0.4 mm; therefore, currents of 1 nA correspond to a current density of 2 nA mm⁻². a Experimental layout with the numbering of hanging-drop compartments and what populates them—either a large spheroid (blue sphere), a small spheroid (red sphere), or no spheroid. A schematic of cross-electrode diffusion (D_XE) and cross-drop diffusion (D_XD) shows the possibility of glucose and H₂O₂ transport through the system and how our bare-hydrogel-coated electrodes can quantify this transport. An arrow describing the direction of flow prior to the start of the measurements allows us to define upstream (drops 1, 3, 5, and 7) and downstream (2, 4, 6, and 8) drops. Hashed bare-hydrogel-coated electrodes are shown in drop 8 to highlight the downstream bare-hydrogel-coated electrode (DS) in gray, which will be plotted as a gray dashed line (8-DS) in subfigure c. b Comparison between the bare-hydrogel-coated electrode signal (black line) and the GOx-functionalized signal (red line) in Drop 1, a control drop with no spheroid. Since the bare-hydrogel-coated electrode measures the H₂O₂ concentration around it but does not generate H₂O₂, this figure shows that we can directly measure cross-electrode diffusion D_XE from the GOx-functionalized electrode. c Current signal on all bare-hydrogel-coated electrodes through all drops, demonstrating a similar response across spheroid-populated drops and a distinctly different response in the empty drops. The current measured at bare-hydrogel-coated electrodes is characteristic of bulk H₂O₂ concentration in the hanging-drop compartment. As shown in Fig. S4c, a current of 0.2–0.5 nA results from a bulk H₂O₂ concentration between 2 and 7 µM. In the case of drop 8, where two bare-hydrogel-coated electrodes are present, the electrode closest to the GOx-functionalized electrode (dashed gray line 8-DS) shows a higher current than the furthest electrode (dashed black line). This shows the D_XE effect. d Experimental current data (continuous black line) and fitted sum of exponential currents (orange dotted lines) for the GOx-functionalized electrodes. The sum of exponentials provides an excellent fit for the current data. Spheroid sizes and fitted proportional coefficients and exponential coefficients, used to plot the current fits, are enumerated in Table 1. The glucose concentration dynamics giving rise to such a current fit are shown (blue dotted line).