Why are Cells Small?

Hi. It's Mr. Andersen and today I'm trying to answer that question that may puzzle you and it's called, why are cells small? Why are all cells microscopic? And so before I get to that I want to kind of start with a problem. So if we take a piece of paper. We'll call this paper one. We'll call this next one paper two. And we were to roll them up into a cylinder. And so paper one I'm going to roll up into a cylinder like this. So we're going to call this one tall and skinny. And then paper two we're going to roll up like this. So we're going to go the other way. And we're going to roll is up like this. So we'll call that a little shorter. And a little more round. And so the question is, which of those is have the greatest volume? So you may want to think about that for a second. This is a problem that I missed the first time I ever saw it. And so we've got two cylinders. I've kind of done it with the same, it's 8.5 by 11 paper. I've rolled this one into that tall and slender. And this one in the short and not so slender. And so the question is, which one of these has the greatest volume. So you might think one does. You might thing two does. Or you might, if you're really bright, might think that they're going to have same exact volume. So there's really only one way to figure that out. We could do geometry, but what I'm going to do is, since I teach biology, is I'm going to fill this one up with bark. A little bit more to top it off. Okay. So we'll say that one, so cylinder one, is filled up with this much bark. So now I'm going to take cylinder two and put that over the top like that. And so if I pull out one, a few things could happen. Number one, if one has a great volume then it's going to overflow two. If two has a greater volume, it's not going to quite fill it up. And if they have the same volume it should kind of top it off. Or it might just fall apart and make a total mess. So let's see, make sure you've locked in your guess. So I'm going to pull this up. So the right answer is that two has a greater volume than one. So that might seem a little weird. I showed this one in class and one kid accurately figured out that surface area isn't the same. Because this one is going to have a greater surface area on the top than this one. But something happened when we went from something real tall and skinny to something fat and not so skinny. And you could imagine if we kept going and going and going there'd be like a perfect object right here that would have the greatest amount of volume for the least amount of surface area. And that would be a sphere. And so there's a few things going on. One big thing is that we're trying to maximize the volume. And so in biology if we ever try to maximize the volume something is going to look a lot like a sphere. And so this is set to something called Allen's Rule. And it applies to all endotherms or all warm-blooded animals. And the idea is this. The farther you live from the equator, the more you're going to look like a sphere. And so if we look at early pictures, this is an early picture of an Eskimo family, on an Inuit family, we're going to find that they're going to have shorter legs, shorter arms, stalkier appearance and the reason why, just like a polar bear, is that they want to maximize their volume because the don't want to loose a lot energy in the form of heat. Likewise, when we go towards the equator the people are going to look more tall and more skinny. And that's because they're going to maximize they're surface area. And so they want to get rid of heat. So these are some Masai Warriors doing this jumping dance. And they're going to be really tall and slender. But it also gets to the idea of why cells are small. And so why are cells small? Well by making them smaller and smaller and smaller and smaller, what we can do is we could maximize their surface area. So this is a bunch of bark. But it used to be one chunk of bark. And with that one chunk of bark, you had a relatively small surface area compared to the volume. But by chopping it up now we have all the surface area and all sides of the bark. And so you know this, if you're trying to start a fire it's important to cut that wood down to small bits. And so we can have reactions around the outside. It's much easier to get chemical reactions. It's much easier to start the fire. But likewise our cells are small for the same exact reason. Our cells are small because we want to maximize the surface are on the outside. And the reason why is that we have to get nutrients into the cell, oxygen. We have to get waste products out, like carbon dioxide. And so if we can make ourselves really really small then we have a large surface area. And also that oxygen then doesn't have to diffuse so far to get into the cell or carbon dioxide diffuse so far to get out. So that's why cells are small. If you're smart, you should be thinking, okay. If cells are small that's good. Why aren't they infinitely small? Why don't we make them as small as they possibly could be? And the reason why is that if we make them too small then we can't fit the machinery of the cell inside it. And so we can't fit the DNA, the proteins and the machinery of the cell. And so the neat thing is that there's about a perfect sweet spot for all eukaryotic cells. And a sweet spot for all prokaryotic cells. And they're all roughly the same size. And it all goes back to maximizing surface area compared to volume. And so that's cells. That's wood. That's cylinders, a little geometry and I hope that's helpful.