Cell size

- What I want to think about in this video is cell size, and in particular how small cells can get, and then also what tends to be the limiting factors for how large a cell can get. And I have some pictures of cells here. This picture right over here, this picture of pseudomonas bacteria, each of these pill-shaped things, this is a bacterial cell. And just to get a sense of scale, the width of this pill is around one micrometer. So, this is approximately one micrometer, which is the same thing as 1 millionth of a meter. Or you could think of it as 1 thousandth of a milimeter, whatever helps you conceptualize this better. And then the length here, this is about 5 micrometers. This is approximately 5 micrometers. Now over here I have some pictures of cells that you would find in the human body, these are red blood cells. These have a diameter of about 7 micrometers. You see a similar scale for these white blood cells. There are some other things in here. Over here we see a human sperm cell about to penetrate a human egg cell, and human egg cells are some of the largest cells you'd find, especially if we're talking about spherical cells. And this cell here, this is going to have a diameter on the order of 100 micrometers. So the first question we would, and it's kind of neat that all of these pictures are almost on the same scale, so you can almost compare them, but the first question we'd ask is how small can a cell get? Well, if you think about it a cell is a living thing, it's actually quite complex. It has to have information, it has DNA, it has to be able to replicate itself, it has all of this metabolic machinery. So, I just did some reading and the smallest cells observed, and I think this might be the smallest cells period although there might be future ones discovered that are even smaller, are actually on the order of about a few 100 nanometers. Remember, 1,000 nanometers would be the width of this pill so a few 100 nanometers like maybe something like that would be maybe 300 nanometers, these are the smallest cells discovered so far. And they are bacterial cells, they were discovered at the University of California Berkeley. And we think that this is pretty close to the lower bound because you've got to remember we have to store all of this genetic information and all this cellular machinery. So, that stuff's complex and you can only get so small. But what about the upper bound cells? Well, one of the things that tends to be the limiting factor and there's other things as well, but it's the ability for, it's the ratio of volume to surface area. And why does the ratio of volume to surface area matter? Well, because the surface is what interfaces the cell with its surroundings. It has to take in nutrients and take out the waste, so each unit of surface area it has to process the inputs and the outputs for a certain volume of cells, for a certain volume of the cell. And as we'll see as a cell grows the volume and surface area don't grow together, the volume increases faster than the surface area does. So, as you grow, each unit of surface area has to handle the processing with the environment for more and more volume. At some point it can't handle it, it can't take in nutrients and get rid of waste fast enough. And to make that a little bit more tangible, let's think about it mathematically. So, the volume of a sphere, let's say this is a sphere here so let me make it look a little more 3-dimensional, if it has radius "r", its volume is going to be (4/3)πr³. Now, it's surface area is going to be 4πr². Now let's calculate the ratio of volume to surface area because that's what we really care about. The ratio of volume to surface area is, I want to do surface area in yellow, is equal to (4/3)πr³ over 4πr². Now, luckily this simplifies quite nicely. 4 divided by 4 is 1, π divided by π is 1, r³ divided by r² is just going to be "r", so this all simplified nicely to r/3. And if we wanted to care about units, it would be cubic units of volume or it would be cubic units divided by square units, whichever unit we're looking at. So this is going to be r/3. So, let's use this to think about what happens as a cell gets much larger. So for simplicity, let's focus on this white blood cell here and just to make the math easy let's assume that it has a radius of 3 micrometers. I'm gonna do this in a color you can see, 3 micrometers. So in that case, for this cell, its volume to surface area is going to be, we could just say 3 micrometers divided by 3 but I'll put 3 micrometers divided by 3, which of course is just going to be 1 micrometer. But having a unit of 1 micrometer for volume of surface area doesn't really make a lot of sense. An equivalent unit would say 1 cubic micrometer per square micrometer, because we're doing volume to surface area and obviously if you let the units cancel and you do the dimensional analysis you'd be just left with this micrometer. But this helps us conceptualize a little bit more because it says that each square micrometer needs to handle one cubic micrometer of cellular volume. So each square micrometer, so the square micrometer for this guy over here is gonna be around that size, it's going to handle the processing on average for 1 cubic micrometer of volume. Alright, that seems about reasonable and that's a reasonable size for a cell. But what if we were to increase things by a factor of 1,000 or increase the radius by a factor of 1,000? So I'm obviously not drawing this to scale, but let's say we find some new organism or we theorize some organism thats cellular radius, instead of being 3 micrometers, so this was 3 micrometers, it's 3,000 millionths of a meter. And just to be clear this isn't ginormous, by our scales this would be 3 millimeters. It would be visible by the human eye, the threshold of the human eye can see is about a tenth of a millimeter, which is 100 micrometers. This is approximately 1/10 of a millimeter. So on the right conditions you can just barely see a human egg cell, but this right over here, this would be still small by our scales, but let's just think about what happens to the volume to surface area. 3,000 micrometers divided by 3, we'd be left with 1,000 micrometers, or even better we could write this as 1,000 cubic micrometers per square micrometer. So now, each square micrometer, in this case it had to handle a cubic micrometer of volume. But now it has to handle 1,000 cubic micrometers of volume. So it has to handle much more volume. And that's gonna break down, it's not gonna be able to exchange the gasses, exchange the nutrients, exchange the waste fast enough for this cell to function. So this is a very important ratio, volume to surface area for cells, and actually ends up, well I'll just talk about cells in general. It actually tends to be an interesting thing as a lot of things grow, volume to surface area or mass or there's a lot of other ratios that are interesting, but this is one of them. Now, the other factor that will play in is also as a cell gets larger, the machinery has to just traverse more distances, you have to transport things over larger distances which also can become cumbersome. But the volume to surface area is a really interesting one to think about, while we don't tend to see very large spherical cells. And the reason why I emphasize spherical cells is because you do see cells that are longer than even this scale, like nerve cells. And they get by with that, they have other adaptations. But one of them is to just be really skinny and long, so this is one way that they can maximize their surface area. So, like that, this is a nerve cell. Other ways that you'll see cells that maximize their surface area is that they have a lot of things that kind of stick out to maximize. So, cells are clearly not all spherical. So, they could have other things that maximize their surface area like that. So there's a bunch of adaptations, but in general, modeling them as a sphere isn't a crazy thing to do and this is why we don't tend to see cells much larger than a human egg cell.