Microscopic springs: Investigating viscoelastic and elastic tendencies of the cell membrane.

Abstract

Cell membranes are normally thought of as viscoelastic materials because they exhibit both viscous and elastic properties when deforming, however, some researchers describe membranes as elastic only. Our project seeks to quantify the membrane deformations during a splitting event, and mathematically predict membrane tensions if it were an elastic or viscoelastic material. Knowing the mechanical description that is most appropriate can help future research interested in describing cell mechanics when cells split, change shape, or move. First, we quantified cell shape from experimental fluorescently dyed membranes using ImageJ. We assume that knowing the physical location of the cell membrane over time can be used to quantify how the cell membrane changes due to forces acting on/in the membrane. We built MATLAB functions to import coordinates from ImageJ, center them, segment them based on arctan values into specific angle quadrants, and calculate the force the membrane experiences based on its location relative to its angular quadrant when considered an elastic spring or viscoelastic material. Centering the coordinates allows the functions to apply to multiple different cell experiments, while quadrants allowed the accounting of localized growth and shrinkage of the membrane. To model the elastic properties, we used a Hooke's Law spring equation and a viscoelastic equation with elastic and damper components. Our results suggest that the cell membrane can be treated as a viscoelastic material under small time scales (< 3 minutes) and as an elastic spring for larger time scale deformations. These results can be validated experimentally through laser ablation. By ablating a hole in the cell membrane, we can quantify the recoil of the membrane to determine how much tension was present before the ablation and compare the scale of the experimental tension with our model predicted tension.