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Current time:0:00Total duration:5:12

AP.BIO:

ENE‑1 (EU)

, ENE‑1.B (LO)

, ENE‑1.B.1 (EK)

- [Instructor] So let's
say that this is a cell. So we know that all sorts
of activity is going on inside of this cell here,
and we will study that in a lot more depth as we go further in our study of biology. But it's important to
realize that this cell and the activity in that cell
is not operating in isolation. That in order to live,
that cell needs resources from the outside world. So resources need to
make their way through that outer membrane of
the cell so it can be used inside that cellular machinery. And as that cell does what it does, it's also going to
generate waste products, and that needs to be released
somehow across that membrane. So you also have waste. And you also have energy that
is going to be transferred either from the inside of
the cell to the outside or from the outside to the inside. A lotta times, we imagine
that all of the activity inside the cell is
generating thermal energy that has to be dissipated somehow, and that is usually the case, not always. And so you have thermal energy
that has to be dissipated. Now you might see something interesting, or maybe you haven't seen it just yet, is that you have all of
this activity operating in the volume of the cell,
but then all of this exchange, all of the resources coming
in, the waste coming out, the thermal energy going
in either direction, it has to be somehow
diffused across this surface, across this two-dimensional surface. So this raises an interesting question. As our volume increases,
what happens to the ratio of our surface to our volume? Because you could imagine,
maybe at some point, the volume gets large
enough that you don't have enough surface area to do
these three things well. And so let's think about this ratio. Let's think about the ratio
of our surface area to volume. And I'm gonna get a little bit mathy here. You don't have to know
the math for the context of a biology course, but you need to know what the conclusion is that
the math is going to give us. So if this is a sphere of radius r, the surface area of this sphere is going to be four pi r squared, and the volume of this sphere is going to be 4/3 pi r cubed. So this pi would cancel with that pi. If we divide the numerator and
the denominator by r squared, we get a one there and
then we just get an r right over here. If we divide both of these
by four, you get a one there, and this is just going to be a 1/3. And so we are going to be left with one over 1/3 r or we could just write this is this is equal to three over r. And so we see at least for
a spherical cell like this, as r increases, as our cell
gets larger and larger, the ratio between our surface
area to volume decreases. So let me write that. As r goes up, then the ratio between our surface area to
volume, surface area to volume, is going to go down. The bigger your denominator,
the lower the value is going to be. And so what that tells us
is is that as the volume of our cell increases,
as our cell gets bigger and bigger and bigger,
we have less surface area per unit of volume. And so it's going to make that
exchange of the resources, the waste, and that energy
harder and harder and harder. And we would get a
similar result if instead of doing a spherical cell, let's
say we did a cuboidal cell. So let's do it like this, a cuboidal cell. You might see this in some plants, something that's roughly cuboidal or rectangular in some way, or rectangular prism I should say. But let's say it's x by x by x. We could do the same exercise. Our ratio of surface area to
volume is going to be what? Well our surface area, you have six faces that are each have an area of x squared, so our surface area's
going to be six x squared. And then our volume is going
to be x times x times x, over x to the third. And so this is going to
be, divide the numerator and denominator by x
squared, you get six over x. So once again, you see
that as x increases, our ratio of surface
area to volume decreases. As our denominator increases, well then that whole expression
is going to decrease. So given this phenomena, it makes it hard for larger and larger cells to exist. Because for all the activity
happening in the volume, they don't have enough surface area to do all of this exchange. Now there are things we
see in biological systems that help cells get further
than what we see here. If you imagine the
two-dimensional cross-section of this cell, one way to increase
the surface area to volume is for the membrane to
look more like this. The more folds you have, the
higher surface area to volume that you are going to have. And you indeed see this
in a lot of biology. Anytime you want a high
surface area to volume, you tend to see things like these folds in the membranes of the cells.

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