Schematic of the experimental apparatus. Silver/silver chloride electrodes are inserted into inlet and outlet ports for impedance measurements. In parallel with the electrodes are fluid-filled tubes that route cells into the inlet port, through the loading channel, and finally into the tapered channel. Screen captures of an AML2 cell illustrate its shape changes at two different positions (P1 and P2). Cells are pressurized using a custom pumping system.44
(a) and (b): Circuit models used for fitting the impedance and phase spectra generated by an empty channel (a), and a single cell trapped in the channel (b). A membrane-bound cell has a cytoplasmic resistance, Rcell, and a membrane capacitance, Cm = C1C2/(C1 + C2). To account for space between the cell perimeter and the channel walls, a seal resistance, Rgap, is introduced. Experimental amplitude (d) and phase (e) spectra of one measured cell are fitted with the circuit models in (a) and (b).
SEM images of the tapered channel: (a) top-view and (b) view through the cross-section.
(a) Three-dimensional geometry of the microfluidic chip. (b) A moderately sized box surrounding the cell and channel facilitated meshing between the large PDMS domain and the much smaller channel domain. (c) and (d) For illustrative purposes, a side view of the microfluidic channel reveals lines of current density coloured according to their strength (blue= weak, red = strong). Similarly, the background colour represents electric potential. In this demonstration, the membrane thickness, δ, is 100 nm and zgap = 250 nm. At low frequencies (Fig. 4(c)–4 kHz), current is redirected through the shunt pathways (zgap). At high frequencies (Fig. 4(d)–1 MHz), current is permitted through the cell.
Specific membrane capacitances versus cell-to-channel gap, cell length, cell position and seal resistance. The error bars represent the 95% confidence intervals for the fitted SMC.
Current density versus position along the horizontal and vertical edges of the membrane.
(a)-(d): Specific membrane capacitance (SMC) values for cells in solutions of different osmolalities. Cells in isotonic or marginally hypertonic solutions yield essentially identical SMC values (), while very-hypertonic solutions induced significant increase () in the SMC. (e)-(g): Specific membrane capacitance values of 23 AML2 and 23 NB4 cells in DMEM. Based on the SMC distributions across each cell population, the mean SMC values of AML2 and NB4 cells are found to be significantly different (). Cells initially parked at a position, P1, are later parked at a more constrictive position, P2.
SMC values and variations versus membrane permittivity. For three relative membrane permittivities (10, 20, 30), the theoretical (based on parallel-plate (p.p.) capacitance formula) and curve-fitted SMC values (units are mF/m2) are evaluated as a function of cell-to-channel gap, cell length, cell position and seal resistance. The error ranges correspond to the fitted SMC variations across the gap, length, position, and seal resistance ranges in Fig. 5.
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