Finite element analysis of microelectrotension of cell membranes

Abstract

Electric fields can be focused by micropipette-based electrodes to induce stresses on cell membranes leading to tension and poration. To date, however, these membrane stress distributions have not been quantified. In this study, we determine membrane tension, stress, and strain distributions in the vicinity of a microelectrode using finite element analysis of a multiscale electro-mechanical model of pipette, media, membrane, actin cortex, and cytoplasm. Electric field forces are coupled to membranes using the Maxwell stress tensor and membrane electrocompression theory. Results suggest that micropipette electrodes provide a new non-contact method to deliver physiological stresses directly to membranes in a focused and controlled manner, thus providing the quantitative foundation for micreoelectrotension, a new technique for membrane mechanobiology.

Fig. 1

Microelectrode and 2-D axial symmetry simulation model. a The microelectrode and cell. b Meshed G1. c Meshed G2. d Zoomed-in image of meshed G2 indicated as black box in (c). Position illustrates ME tip area. r_in and r_out: inner (0.3 µm) and outer (0.5 µm) radii of ME tip, d_c: cleft size (µm), d_p: distance from pipette axis (µm)

Fig. 2

Simulated surface electric potential. a Simulated results of G1: ME and cell in the media. b Simulated results of G2: simulated voltage on the plane of ME tip of G1 was extruded into top surface of G2 as boundary voltage. c Zoomed-in image under the ME tip indicated as red box in (b): voltage drop occurred predominantly across cell membrane. Color-scale refers to electric potential (V)

Fig. 3

a The quantitative relationship between peak value of TP (i.e. TP at d_p = 0) and cleft size. The normalized peak TPs were calculated by dividing the peak TP values for each input voltage by the corresponding peak TP values for 0.1 µm cleft size. (inset) Peak TPs as a function of cleft size

Fig. 4

The quantitative relationships between a TP and b ET and input voltages for 0.1 µm cleft size. The two vertical dashed lines represent the glass pipette wall. The horizontal dashed lines represent the lysis-inducing threshold TP (~1.1 V) and tension (~5.7 mN/m)

Fig. 5

The quantitative relationships between membrane strain and distance from pipette axis at 0.1 µm cleft size. a ε_z normalized to input voltage squared $(V_i^2)$. b, c ε_r for physiological level of tension (0.65–3 V) and pore- and lysis-inducing level of tension (5–20 V), respectively. The two vertical dashed lines represent the glass pipette wall

Fig. 6

The quantitative relationships between membrane stress and distance from pipette axis at 0.1 µm cleft size. a Normalized σ_z was a function of square of input voltage. b, c σ_r for physiological level of tension (0.65–3 V) and pore-inducing level of tension (5–20 V), respectively. The two vertical dashed lines represent the glass pipette wall