Life sciences, cells, and material movement / principles and exploration
Cell size and material exchange — principles and investigation
As cells grow larger, it can become difficult for them to exchange needed substances from within through their surfaces. Compare the volume ratio penetrated by the substance by changing the size, diffusion coefficient, and observation time of the agar cube. Observe the geometric relationship that surface area and volume grow at different rates along length.
How does it work?
Smaller cubes have a larger surface area/volume and reach a larger volume ratio with the same depth of diffusion. The penetration rate is 1−((a−2d)/a)³ and is 100% if a≤2d.
d = √(2Dt) · SA/V = 6/a
Try this investigation
- In the cross section of an agar cube drawn at the same scale, green is the penetration area, and purple is the center that has not yet been reached. Assume that it permeates to the same depth on all six sides of the surface.
- Run 1 cm and 2 cm on a side with the same time and diffusion coefficient and record the surface area/volume and penetration rate.
- After comparing by increasing only one side to 3·4 cm, only the diffusion coefficient is doubled from 2 cm.
Interpreting your results
What is the penetration volume ratio when a=2 cm and penetration depth d=0.5 cm?
The remaining central side is 2−2×0.5=1 cm. The uninfiltrated volume ratio is 1³/2³=1/8, so the infiltration ratio is 87.5%.
Assumptions and limitations
It is a model that penetrates an agar cube uniformly from six sides with a constant diffusion coefficient. A sharp boundary and d=√(2Dt) are approximate. The actual concentration distribution, cell membrane transport, metabolism, and spherical cell geometry are omitted. The color area ratio of the cross section and the three-dimensional penetration volume ratio are different.