Alright, something out of being not so related to math like physics or predicting stock prices :)
My friend told me about this kind of like down-to-the-smallest-thing-on-earth principle in biology: the surface area to volume ratio (SA:V)
Now I was talking with a bio person, and she was not an expert at math like I am (flecc👌), so she didn't really take a deeper dive into this thing. However, sadly, I do :) and here I am, and I will do some weird things because I like stuff like that :)
(Side joke intensifies) 🤨
Literally no one:
🅱️incent:
Q: What do you call a mathematician who can spot the mistake in the proof of 0 = 1 very quickly, at under 3 seconds?
A: He's pretty MATH-SA:VVY (savvy) 😉
Alright. Enough (expect more ridiculous things like this in the near future)
So our SA:V ratio will be called R for short:
So this is the thing; SA:V can explain why cells have a limiting size. This is why we contain gazillions of small cells, while we do not contain just one or two big blobs of cell going across our body to make sure we eat and work well and all. The reason is that a cell performs metabolism inside its membrane; it takes energy in for consumption when we have our breakfast, lunch or dinner or some snaccs, and give waste out, and the only way to do this is through the membrane. The membrane's outer area is basically the surface area of this cell, and the amount of things inside it is the volume.
Now, SA:V tells you the surface area per unit volume i.e the amount of membrane's area per the cell's inner content. If this SA:V is small, it means that there are less surface area to volume, and so the diffusion of metabolism (taking in energy) and releasing waste is more limited, because the amount of things going into the cell through the membrane takes longer time, due to a higher volume, meaning that the cell gets filled up with energy at a longer time, because there are still space for others to get in, yet there is little area, so imagine you have a bunch of people trying to get through a subway's door that's small, versus when you have a bunch with a larger door. The SA:V in the first scenario is smaller, assuming the subway's space is the same. You would have to wait in this situation for others to get in, and people will be slow due to this because we can't fit as much through the door. On the other case, SA:V is bigger, and you might be able to get in quicker, because we got more people passing the door per instant. Hence:
SA:V shows how fast the rate of metabolism (energy going in the cell) and the rate of waste is. Higher SA:V indicates lower rates, while lower SA:V indicates higher rates
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