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Math Equations in Biology 1) Surface Area to Volume Ratio

 Surface Area to Volume Ratio

This is a very short lesson on a bit of math you'll encounter in biology, but it's fairly important. 

Remember how the mitochondrion has a double membrane? Here's a simplified drawing of the mitochondrion. 



In the Electron Transfer Chain (ETC), ATP energy is created. It is found in the inner membrane of the mitochondrion. 

Compare these two pictures: which one has more ETCs?



The wrinkled mitochondrion has more ETCs, which means it can produce more energy. More energy means the cell will be more successful. Notice that the wrinkled mitochondrion has more membrane than the rounded mitochondrion - if we were to stretch the inner membrane until it was flat and without wrinkles, there would be much more membrane. 

This idea, that more membrane equals more ETCs, can be exhibited by the Surface Area to Volume Ratio. More membrane per volume means a higher surface area to volume ratio (6 units^2 SA: 1 unit^3 V) (so, more wrinkled). A lower surface area to volume ratio (2 units^2 SA: 1 unit^3 V) (little to no wrinkles) would be seen as an equal or almost equal amount of membrane to the volume. 

The surface area to volume ratio must be as big as possible to maximize the amount of surface area, to maximize energy output.

In the following scenarios, which cell is the most efficient? (The numbers are SA: V format)
    1) A: 3:2 or B: 4:9

    2) A: 1:8 or B: 8:1

    3) A: 5:9 or B: 4:8

    4) A: 2:1 or B: 3:2

    5) A: 4:2 or B: 8:4


Answers: 
1) A
2) B
3) A
4) A
5) They're the same.

That's it! 



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Comments

  1. Jeremy CAugust 21, 2024 at 3:08 PM

    Is this going to be on the AP biology test?

    ReplyDelete
    Replies
    1. Aspiring to be a rich doctorAugust 22, 2024 at 8:22 AM

      We don't know the exact questions on the upcoming test, but the content/ knowledge should be the same as previous years; that being said, there may be a question on this exact topic (something like "explain why the mitochondria creates more energy with a wrinkled inner membrane") or something that assumes you know this knowledge to answer another question (like "Cell A's mitochondria has a higher SA:V ratio than Cell B's mitochondria. A medicine was added to cell A that inhibited ETCs in the mitochondria. Which cell would create more energy?"). Either way this is very important knowledge and it's likely there will be a question on the AP test on this topic.

      Delete
  2. DonusiaSeptember 2, 2024 at 6:34 PM

    Is it always in SA:V format, or is it ever V:SA format?

    ReplyDelete
  3. Finnigan GallagherSeptember 5, 2024 at 3:25 PM

    I know you mentioned it somewhere but I cant find it - what other organelle depends on this?

    ReplyDelete
    Replies
    1. Aspiring to be a rich doctorSeptember 5, 2024 at 4:18 PM

      The chloroplast! I believe it's mentioned in the organelles lesson.

      Delete

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