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what I want to think about in this video is cell size and in particular how small cells can get and also what tends to be the limiting factors for how large a cell can get and I have some pictures of cells here this this picture right over here this picture of Pseudomonas bacteria each of these pills 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 one millionth of a meter or you can think of it as one thousandth of a millimeter whatever helps you conceptualize this better and then the length here this is about five micrometers this is approximately five 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 these have a diameter of about seven micrometers you see a similar scale for these white blood cells or 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 some of the largest cells you'd find especially if we're talking about spherical especially for talking about spherical cells and this cell here this is going to have a diameter on the order of 100 100 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 you can almost compare them but the first question we asked 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 has DNA it has to be able to replicate itself it has all this metabolic machinery so there I just did some reading and thus the smallest cells observed and they think this might be the smallest cells period although I'm sure you know there might be future ones that are discovered that are even smaller are actually on the order of about a few hundred nanometers remember a thousand nanometers would be the width of this pill so a few hundred nanometers like maybe like something like that would be maybe 300 nanometers these were the smallest cells discovered so far and they're bacterial cells they were discovered at the University of California Berkeley and we think that this is pretty close pretty close to to the lower bound because you gotta remember we have to store all of this genetic information and all the cellular machinery so you know that stuff's complex and you can only get so small but what about the upper bound of cells well one of the things that it 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 volume why does that what is 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 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 and as well or for a certain volume of the cell and as well see as a cell grows they don't 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 to at some point it just can't handle it it can't take in nutrients and get rid of of waste fast enough and to make that little bit more tangible let's think about it mathematically so the volume the volume of a sphere let's say this is a sphere here so let me make it look a little bit more three-dimensional if it has radius R its volume is going to be 4/3 PI R cubed now its surface area is going to be its surface area is going to be 4 PI R squared now let's calculate volume ratio 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 to surface area is equal to it's equal to 4/3 PI R cubed over over 4 PI R squared now luckily this simplifies quite nicely 4 divided by 4 is 1 pi divided by pi is 1 R to the 3rd divided by R squared is just going to be R so this all simplifies very nicely to R over 3 and if we wanted to care about units it would be cubic units of volume or be cubic units / square units when we rode whichever unit we're looking at so this is going to be our over three so let's use this to think about what happens as a cell gets much as a cell gets much larger so for simplicity let's look let's focus on this white blood cell here and just to make the math easy let's assume that it has a radius let's assume it has a radius of 3 3 micrometers I'm going to 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 3 3 we could just say 3 micrometers divided by 3 but I'll put 3 we could say 3 micrometers divided by 3 which of course is just going to be 1 micrometer but having a unit of 1 micrometer for volume to surface area doesn't really make a lot of sense an equivalent unit would say 1 cubic micrometer one cubic micrometer per square micrometer per square micrometer because we're doing volume to surface area and obviously if you let the unit's cancel you do the dimensional analysis you'd be just left with this micrometer but this helps us conceptualize it 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 square micrometer for this for this guy over here it's going to be around that size it's going to handle the processing on average for one cubic micrometer of volume all right 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 a thousand so or increase the radius by a factor of a thousand so and I'm obviously not drawing this to scale but let's say we find some new organism or we theorize some organism that has a that's cellular radius instead of it being 3 micrometers so this was 3 micrometers it's three thousand three thousand millionths of a meter and just to be clear this isn't ginormous by our scales this would be three millimeters this would be three millimeters it would be visible by the human eye the kind of threshold of what the human eye can see is about a tenth of a millimeter which is a hundred micrometers this is approximately or this is 1/10 of a millimeter so on the right conditions you could just barely see a human egg cell but this right over here this is this would be still small by our scales but let's just think about what happens to the volume to surface area volume to surface area 3,000 micrometers divided by 3 3,000 micrometers divided by 3 we'd be left with this is 1,000 micrometers or even better we could write this as 1000 cubic micrometers per square micrometer 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 a thousand a thousand cubic micrometers of volume so it has to handle it has to handle much more much more volume and that's going to break down it's not going to be able to exchange the gases 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 it actually ends up well I'll just talk about I'll just talk about cells in general it's actually tends to be an interesting thing as a lot of things grow volume to surface area or mass or mat well 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 as also as a cell gets larger the machinery has to just traverse more distances you have to transport things over longer distances which also can become cumbersome but the volume to surface areas are really interesting one to think about why we don't tend to see very very very large especially spherical cells and the reason why I emphasize spherical cells is because you do see cells that are longer than even this scale like like 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 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 aren't 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

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