Okay, here's a good question. Why are cells so small? They're just small enough that I don't really notice them when dandruff falls off my head. We talked about dandruff I'm losing a lot of skin cells off of my face and everywhere like that Why are they so small?
Why can't I just be one? Big, giant cell. One singular cell.
I mean, if bacteria can do it, why can't I just be a big, larger version of these? There's lots of things to think about. So try to answer that question. Pause right now.
Don't just skip. head why are cells so small I'm made up of billions billions and billions of cells and they're all super duper tiny I've never met a man my height who's an actual full-sized singular cell. That would be amazing.
That would be amazing. But unfortunately, I haven't met one. They don't exist. And there's good reasons for why that is. So let's jump ahead and talk about Jimmy.
So here is Jimmy. Jimmy just represents a little kid. That's just a head. I couldn't find a body.
So if we put Jimmy and he represents a head, let's pretend like he's a particle. When he goes inside this classroom right here and he's sitting there doing his classwork and stuff like that, if he needs to get out. to pass on a message or go home or something like that and come back in it's pretty fast he can actually move in and out of the classroom relatively quickly relatively quickly okay here's jimmy again but this time we place him in a stadium so here he goes there he goes okay probably tinier than that for that size he's still a pretty big dude but anyways now jimmy imagine him trying to leave the stadium because he needs to go deliver a message, it's quite a long walk to get out of the stadium. So I'm going to use several silly analogies here to try and help us understand this idea. If Jimmy represents something like a...
a carbon dioxide molecule. And I'm a cell and I've just produced some carbon dioxide and it's a toxin or a poison, I need to get rid of it. It's a lot easier if carbon dioxide is in this situation. It can get out relatively quickly, pretty efficiently.
But if I'm carbon dioxide here, it's gonna take a lot longer to get that carbon dioxide molecule all the way out. Similarly, if I'm trying to get glucose in or energy in or oxygen in, this is a much better situation provided that it's at least big enough that I can have oxygen come in and do all the things it needs to do inside here. Okay, so I'm using this as an analogy to show you that the smaller a cell is, it gets a little bit more complicated than this, but for now, the smaller a cell is, the easier it is for molecules to move in and out pretty quickly, whether it's getting rid of waste or taking up nutrients. And that's something that our cells need to be able to do pretty well. It's going to take Jimmy a lot longer.
to get out. Another thing to think about before we jump into the math of this is compare an elephant and a mouse, or better yet, a sumo wrestler and a me. You can't see me right now, but if you've ever seen me before, I'm not exactly a sumo wrestler.
I'd say I'm the complete opposite. My hands are really cold. Does that give you an idea?
If I say my hands are really cold when everybody else's hands are really warm, you imagine a frail... like skinny pathetic looking dude that's not too far off from where I am but you know you've met people who are like taught like like skinny and small and they're always complaining about being cold I'm cold I'm always so cold my hands are so cold on time so cold and they tend to be really really skinny but you see a sumo wrestler no disrespect to sumo wrestlers but I would bet you that in a game of basketball a sumo wrestler would probably start sweating faster than that tiny little skinny girl who's so cold but the sumo wrestler would probably start sweating that is a clue in terms of getting rid of heat getting rid of heat it's a lot easier for a small skinny girl to get rid of heat because that heat has less distance to travel to get out of the body as opposed to a sumo wrestler where there's a lot of volume there's a lot of volume so it takes a lot longer for that heat to get out okay now we're gonna use a mathematical model I apologize to all sumo wrestlers. I've always wanted to be one.
I just can't do it. I eat. My belly sticks out, but nothing else.
No muscle increase. Let's continue. Okay, we are going to pretend that cells are the shape of cubes, perfect cubes.
You know what a cube looks like? The lengths are all exactly the same. You should know how to calculate the surface area. A cube has six sides, one, two, three, four, top and a bottom, six sides. And the total volume is calculated by, obviously, the side length cubed or the length.
times the width times the height, which should all be the same thing. So we're going to assume, let's see what happens here. And actually, if I were you, I would pause the video, copy down this diagram, and do all the math yourself really quick just to see how the numbers all work out. It's actually pretty interesting.
So if I do this, okay, cube side length 1, the total surface area, each face of the cube, I'm just going to talk through it once, then I'm just going to show you all the numbers. 1 times 1. So I'm going to get a side length of... Should I draw this?
Okay, let's just draw this. Okay, so if you have a cube, let's draw a cube. I'm really good at drawing three-dimensional shapes here.
All right. Okay, if this is a cube, the side length is 1. This is 1. This is 1. 1 times 1 is 1. But there's 6 sides, so 1 times 6. So the total surface area is going to be 6. If it's 2, if it's 2, same thing. If the side length... Oh, I should be drawing it bigger.
Okay, if it's 2... Ugh, it's going to take forever. Ugh.
Ugh. Ugh. Oh my goodness, what have I started?
Ugh. 2 times 2 times 2. 2 times 2 is 4, but there's 6 sides, so 4 times 6 is 24. Anyways, I do this. 3 times 3, 9 times 6, 54. 4 times 4, 16 times 6 sides. It's going to be 96 centimeters squared.
surface area for these cubes as they get bigger. So the point is getting bigger. Small, big, bigger down here.
What's the total volume? It's gonna be one times one times one. In this case, it's just gonna be one centimeter cubed. If the side length is two, it's gonna be two times two is four times two. Then we get eight, 27, and then 64. So what I want you to notice is check out how these numbers are going up, those of you who like looking for patterns.
The surface area here is obviously it's increasing, right? The volume here is also increasing, but look at this rate of increase. These numbers, if we actually do the ratio in a second, you're going to find out that the volume, as the cell gets bigger, as this cube gets bigger, the volume is actually increasing a lot faster than the surface area. So the volume is increasing faster than the surface area. If I do a little math, let's do the ratio of the surface area over the volume.
Well, 6 divided by 1 is 6. 24 divided by 8 is 3. 54 by 27 is two. 96 divided by 64 is 1.5 and you'll notice that these numbers start getting smaller and smaller. So mathematically what is happening? As the cube gets larger and larger, this is probably the trickiest part here, as the cube gets larger and larger the surface area is definitely increasing. All the surface area around this cube is definitely increasing.
So is the volume. The space inside is also increasing. But the key point here is they are not increasing at the same rate.
So look at what's happening here. The surface area to volume ratio is getting smaller and smaller and smaller. So as a cell gets bigger, as a cell gets bigger, okay, this one's going to be huge down here. As a cell gets bigger, the surface area to volume ratio is small. A couple key things you want to remember here is that basically this is a good thing.
A big surface area to volume ratio is a good thing for cells. That takes us back to the Jimmy situation. If you have a big surface area to volume ratio, that means... You can get, molecules can get in and out really quickly, or heat can actually move in and out really quickly.
It just makes things a lot more efficient. Okay? Now let's go on to the specific language that you would need to know, and then hopefully try to make it easier.
make sense of all this stuff. So cells are small. There's lots of short ways to say this.
Cells are small because it allows life to be much more efficient. Specifically here, a couple things. The size of a cell is limited by its need to exchange resources with its environment.
So cells have to be transferring molecules back and forth all the time. The whole point of our systems, our respiratory system, circulatory system, is to help us bring in molecules that we need like glucose and oxygen in an efficient manner, to help us get rid of unnecessary heat to help cool our bodies down in an efficient manner, to get rid of molecules like urea. and carbon dioxide in an efficient manner so they don't build up in our blood and we actually end up poisoning ourselves to death.
So that is important, key point about cells. It's about exchanging resources. Okay, volume. When you think about the volume of the cell, so here's a, I guess you think of a cell as more spherical.
The space inside, the space inside, the volume inside here is Related to how fast the cell does a couple things. It produces, how fast it produces heat and waste, because that's all happening inside. So you gotta think about that, what's actually happening inside.
Inside, heat and waste are being produced, and how quickly resources get consumed. Consumed meaning that is happening also inside. So resources, once they're inside here, they're getting broken down. working with mitochondria and various other organelles.
So it's all happening inside. That's related to volume. So when you think volume, you should be thinking heat, waste production, and consumption of resources. But remember, consumption is happening inside. So that's related to...
the volume. So how quickly a cell can produce heat and produce waste or how quickly it can consume resources has to do with how much volume is actually inside there. That's different from the surface area. So the surface area is the outside of this thing.
You should know how to calculate the surface area of a sphere, the volume of a sphere. I'm not going to talk about that here. Oops, I'm covering this up a little bit. Now when you talk about surface area, so the area on the outside.
So if you pick up a basketball, just the part that you can touch around the outside. You can't stick your hand inside the basketball. The part that you can touch on the outside is called the surface area and when you think surface area you should be thinking about how quickly things can actually move in and move out.
Because think about it, if something has to go into the cell it has to pass through this outer barrier and this outer barrier is the is part of the surface area. So the rate with which resources are taken up, taken up means moving in, I need a different color here. Or things are released. So this is talking about heat or waste as well too, but be very careful that you can make this distinction. The heat or waste being released, leaving the cell, is related to the surface area.
The production of the heat or waste. is related to the total amount of volume that's inside. Total amount of volume that's inside. So if you are a small, tiny little cell, then all the heat or waste, you have relatively small volume compared to the surface area.
In other words, actually a better way to say that is you have tons of skin surrounding the outside relative to the volume. So any of the little things that you produce inside here can get out really, really quickly. There's many more doors to pass out. But if you're a giant cell, and you're looking at small molecules here, there are so many other molecules, all this space inside, there's so much in here. So, for each little molecule or particle that's here, there are fewer doors to go out, you can think of it like that.
There's less surface area because the volume here is so much. Going from small size to big size, the volume has increased so dramatically, whereas the surface area has only increased relatively little by the same proportion. Does that make sense?
Okay. So as a cell size increases, its volume increases much faster than its surface area, basically making it less efficient in the exchange of materials and energy. So back to my question. If I were walking on the street and I met a dude who was not made of billions of cells like me, each of my cells doing different jobs, skin cells, I've got heart cells, they're all doing different things, instead I just met a dude my size, but just one giant, cell one blob one nucleus in the center no real brain just a just one blob with the cell membrane and a few things i would expect this person to probably uh be really warm because they have trouble getting rid of heat and just able not able to do things as efficiently as i am like for them to eat they would have to fold their outer cell membrane they'd have to transfer all those glucose molecules all the way i've got a whole bunch of specialized things going on with all my individual cells.
My villi are folded, those cells are folded to increase the surface area. Just not only do I have tiny cells that allow molecules to travel a shorter distance to get where they need to go, but you've got all these other adaptations that we can do by having all these small specialized cells. Multicellular organisms are pretty awesome.
Plants, me. Humans, animals, fungi are multicellular as well too. Okay, that was a lot.
There's a diagram to show you what's going on as well too. Let's see, what's this magic question box that I put here? In other words, as size increases, volume grows much faster than surface area.
If you know these sentences, you're probably okay. You can regurgitate this, you'll be alright. But this is a very, very important concept here about surface area volume ratio. It runs through all of biology, so it's really, really important that you try to grasp this. Come up with your own analogies and explanations and share them online, please, and post any questions that you have.
Alright. Huh? Alright.