Microfluidic system for generation of sinusoidal glucose waveforms for entrainment of islets of Langerhans

Abstract

A microfluidic system was developed to produce sinusoidal waveforms of glucose to entrain oscillations of intracellular [Ca(2+)] in islets of Langerhans. The work described is an improvement to a previously reported device where two pneumatic pumps delivered pulses of glucose and buffer to a mixing channel. The mixing channel acted as a low pass filter to attenuate these pulses to produce the desired final concentration. Improvements to the current device included increasing the average pumping frequency from 0.83 to 3.33 Hz by modifying the on-chip valves to minimize adhesion between the PDMS and glass within the valve. The cutoff frequency of the device was increased from 0.026 to 0.061 Hz for sinusoidal fluorescein waves by shortening the length of the mixing channel to 3.3 cm. The value of the cutoff frequency was chosen between the average pumping frequency and the low frequency (approximately 0.0056 Hz) glucose waves that were needed to entrain the islets of Langerhans. In this way, the pulses from the pumps were attenuated greatly but the low-frequency glucose waves were not. With the use of this microfluidic system, a total flow rate of 1.5 +/- 0.1 microL min(-1) was generated and used to deliver sinusoidal waves of glucose concentration with a median value of 11 mM and amplitude of 1 mM to a chamber that contained an islet of Langerhans loaded with the Ca(2+)-sensitive fluorophore, indo-1. Entrainment of the islets was demonstrated by pacing the rhythm of intracellular [Ca(2+)] oscillations to oscillatory glucose levels produced by the device. The system should be applicable to a wide range of cell types to aid understanding cellular responses to dynamically changing stimuli.

Figure 1. The low pass effect of the mixing channel to analyte pulses

A. Pulses of fluorescein were delivered to the mixing channel at the times specified by the vertical lines. The pulses were delivered at an average frequency of 3.33 Hz with the final concentration of the pulses dictated by the density of the pulses. B. Using the optimum channel dimensions and pumping parameters found in this report, the attenuation of output waveforms as a function of input frequency was modeled with equation 1 using a cutoff frequency (f_C) of 0.061 Hz. The two shaded regions indicate the frequencies used to entrain islets (shaded region 1) and the pumping frequencies (shaded region 2). C. After passing the high frequency pulses shown in A through the microfluidic device with the filter characteristics shown in B, the output was a 0.009 Hz sine wave with an amplitude of 40 μM.

Figure 2. Microfluidic chip and valve design for high pumping frequency

A. Top view of the layout for the microfluidic device used in this report. Pump A and B delivered analyte and solvent pulses, respectively, into the mixing channel while maintaining a total flow rate of 1.5 ± 0.1 μL/min. A zoomed in view of one of the valves is shown in the inset. Pneumatic channels are shown in grey and fabricated in the bottom glass layer of the 3-layer device. Fluidic channels are shown in black and fabricated in the top glass layer. B. Side view of a valve used for rapid pumping. The contact area of glass-PDMS was minimized in the closed and open states by minimizing the distance between the fluid channels and deepening the valve seat, respectively.

Figure 3. Fluorescein waveforms

From left to right, the input frequencies and amplitudes of sine waves were: (i) 0.009 Hz, from 40 μM to 10 μM, (ii) 0.018 Hz, from 10 μM to 40 μM, (iii) 0.030 Hz, from 40 μM to 10 μM, (iv) 0.045 Hz, from 10 μM to 40 μM, (v) 0.090 Hz, from 40 μM to 10 μM, and (vi) 0.060 Hz, from 10 μM to 40 μM. The amplitudes were compared to the intensities of an online dilution of fluorescein from 10 – 90 μM which are shown as the horizontal dashed lines.

Figure 4. Attenuation of sine waves

Sine waves with amplitudes of 40 μM (black triangle, ▼), 30 μM (red triangle, ), 20 μM (blue circle, ), and 10 μM (green square, ) were applied with periods of 0.009 Hz, 0.018 Hz, 0.030 Hz, 0.045 Hz, 0.060 Hz and the attenuation of the output waveforms were determined as described in the text. The dashed line was found from Equation 1 using f_C = 0.061 Hz.

Figure 5. Oscillatory glucose concentrations applied to islets of Langerhans

A. Glucose (red line) was raised from 3 to 11 mM to induce oscillations in [Ca²⁺]_i (black line) from single islets of Langerhans. The glucose concentration was then made to oscillate about a mean of 11 mM, with amplitude of 1 mM and frequency comparable to the natural oscillations of [Ca²⁺]_i. B. The [Ca²⁺]_i trace from Figure 5A is zoomed in on the first two glucose waves. Shown are the times corresponding to the start of the glucose waves (t_g) and [Ca²⁺]_i oscillations (t_C) where the difference in these times are proportional to the phase offset (Δθ) shown in Figure 5C. C. The Δθ between the onset of each [Ca²⁺]_i oscillation and glucose wave was plotted as a function of the number of glucose waves applied (N_g). The glucose waves were started at N_g = 0 with negative values corresponding to [Ca²⁺]_i oscillations that occurred prior to the onset of the sinusoidal glucose waveform. Included is a representative trace from an islet that was exposed to a constant 11 mM glucose () where Δθ did not stabilize and varied throughout the experiment.

Figure 6. 180-degree glucose phase shifts

A. Two representative traces of the [Ca²⁺]_i changes that occurred when a 180° phase shift was introduced to the sinusoidal glucose waveform. The [Ca²⁺]_i oscillation that was affected by the glucose phase shift was much wider than adjacent [Ca²⁺]_i oscillations. B. For all islets tested, there was no change in Δθ after the 180° glucose phase shift, indicating that the islet quickly reset to the new glucose waves.