Scalar field line integral independent of path direction

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.970
In the last video, we saw that
if we had some curve in the x-y

00:00:03.970 --> 00:00:07.360
plane, and we just parameterize
it in a very general sense like

00:00:07.360 --> 00:00:11.240
this, we could generate another
parameterization that

00:00:11.240 --> 00:00:13.140
essentially is the same
curve, but goes in the

00:00:13.140 --> 00:00:13.920
opposite direction.

00:00:13.920 --> 00:00:18.350
It starts here and it goes
here, as t goes from a to b,

00:00:18.350 --> 00:00:21.390
as opposed to the first
parameterization, we started

00:00:21.390 --> 00:00:24.710
with t equals a over here,
and it went up like that.

00:00:24.710 --> 00:00:29.410
And the question I want to
answer in this video is how a

00:00:29.410 --> 00:00:33.600
line integral of a scalar field
over this curve, so this is my

00:00:33.600 --> 00:00:37.360
scalar field, it's a function
of x and y, how a line integral

00:00:37.360 --> 00:00:41.940
over a scalar field over this
curve relates to, that's a line

00:00:41.940 --> 00:00:46.650
integral of that same scalar
field over the reverse curve,

00:00:46.650 --> 00:00:49.130
over the curve going in
the other direction.

00:00:49.130 --> 00:00:52.640
So the question is, does it
even matter whether we move in

00:00:52.640 --> 00:00:55.140
this direction or that
direction when we're taking the

00:00:55.140 --> 00:00:56.980
line integral of
a scalar field?

00:00:56.980 --> 00:00:58.770
And in the next video, we'll
talk about whether it

00:00:58.770 --> 00:01:00.020
matters on a vector field.

00:01:00.020 --> 00:01:02.130
And let's see if we can get
a little intuition to our

00:01:02.130 --> 00:01:05.750
answer before we even
prove our answer.

00:01:05.750 --> 00:01:09.990
So let me draw a
little diagram, here.

00:01:09.990 --> 00:01:11.760
Actually, let me do it a little
bit lower, because I think I'm

00:01:11.760 --> 00:01:14.180
going to need a little
bit more real estate.

00:01:14.180 --> 00:01:20.600
So let me draw the y-axis, that
is the x-axis, let me draw

00:01:20.600 --> 00:01:24.140
the vertical axis, just
like that, that is z.

00:01:24.140 --> 00:01:27.250
Let me draw a scalar
field, here.

00:01:27.250 --> 00:01:29.720
So I'll just draw it as some
surface, I'll draw part of it.

00:01:29.720 --> 00:01:35.910
That is my scalar field, that
is f of xy right there.

00:01:35.910 --> 00:01:38.890
For any point on the x-y plane
we can associate a height that

00:01:38.890 --> 00:01:43.860
defines this surface,
this scalar field.

00:01:43.860 --> 00:01:45.650
And let me put a
curve down there.

00:01:45.650 --> 00:01:50.830
So let's say that this is the
curve c, just like that.

00:01:50.830 --> 00:01:53.152
And the way we define it first,
we start over here and we

00:01:53.152 --> 00:01:54.910
move in that direction.

00:01:54.910 --> 00:01:56.220
That was our curve c.

00:01:56.220 --> 00:01:59.630
And we know from several videos
ago that the way to visualize

00:01:59.630 --> 00:02:01.750
what this line integral means,
is we're essentially trying to

00:02:01.750 --> 00:02:04.850
figure out the area of a
curtain that has this curve as

00:02:04.850 --> 00:02:10.000
its base, and its ceiling is
defined by this surface,

00:02:10.000 --> 00:02:11.860
by the scalar field.

00:02:11.860 --> 00:02:16.160
So we're literally just trying
to find the area of this curvy

00:02:16.160 --> 00:02:18.520
piece of paper, or wall, or
whatever you want to view it.

00:02:18.520 --> 00:02:20.440
That's what this thing is.

00:02:20.440 --> 00:02:23.840
Now, if we take the same
integral but we take it the

00:02:23.840 --> 00:02:27.150
reverse curve, instead of
going in that direction,

00:02:27.150 --> 00:02:28.810
we're now going in the
opposite direction.

00:02:28.810 --> 00:02:30.950
We're not taking a curve,
we're going from the

00:02:30.950 --> 00:02:33.450
top to the bottom.

00:02:33.450 --> 00:02:35.290
But the idea is still the same.

00:02:35.290 --> 00:02:38.010
You know, I don't know which
one is c, which one is minus c.

00:02:38.010 --> 00:02:43.400
I could have defined this path
going from that way as c, and

00:02:43.400 --> 00:02:45.260
then the minus c path would
have started here,

00:02:45.260 --> 00:02:46.520
and gone back up.

00:02:46.520 --> 00:02:49.320
So it seems in either case, no
matter what I'm doing, I'm

00:02:49.320 --> 00:02:52.170
going to try to figure out the
area of this curved

00:02:52.170 --> 00:02:53.220
piece of paper.

00:02:53.220 --> 00:02:56.630
So my intuition tells me that
the either these are going to

00:02:56.630 --> 00:03:01.260
give me the area of this curved
piece of paper, so maybe they

00:03:01.260 --> 00:03:02.880
should be equal to each other.

00:03:02.880 --> 00:03:05.500
I haven't proved anything very
rigorously yet, but it seems

00:03:05.500 --> 00:03:06.960
that they should be equal
to each other, right?

00:03:06.960 --> 00:03:10.420
In this case, let's say
I'm taking a, let me

00:03:10.420 --> 00:03:12.290
just make it very clear.

00:03:12.290 --> 00:03:14.120
I'm taking a ds.

00:03:14.120 --> 00:03:16.720
a little change in distance,
let me do it in a

00:03:16.720 --> 00:03:17.450
different color.

00:03:17.450 --> 00:03:20.440
A little change in distance,
and I'm multiplying it by the

00:03:20.440 --> 00:03:25.450
height, to find kind of a
differential of the area.

00:03:25.450 --> 00:03:27.050
And I'm going to add a
bunch of these together

00:03:27.050 --> 00:03:28.070
to get the whole area.

00:03:28.070 --> 00:03:29.300
Here I'm doing the same thing.

00:03:29.300 --> 00:03:31.980
I'm taking a little ds, and
remember, the ds is always

00:03:31.980 --> 00:03:34.185
going to be positive, the
way we've parameterized it.

00:03:37.490 --> 00:03:39.650
So here, too, we're taking
a ds, and we're going to

00:03:39.650 --> 00:03:41.230
multiply it by the height.

00:03:41.230 --> 00:03:44.500
So once again, we
should take the area.

00:03:44.500 --> 00:03:47.160
And I want to actually
differentiate that relative to,

00:03:47.160 --> 00:03:55.030
when you take a normal integral
from a to b of, say, f of x dx,

00:03:55.030 --> 00:03:58.760
we know that when we switch the
boundaries of the integration,

00:03:58.760 --> 00:04:00.370
that it makes the
integral negative.

00:04:00.370 --> 00:04:03.290
That equals the negative
of the integral from

00:04:03.290 --> 00:04:06.570
b to a of f of x dx.

00:04:06.570 --> 00:04:11.350
And the reason why this is the
case, is if you imagine this is

00:04:11.350 --> 00:04:15.230
a, this is b, that
is my f of x.

00:04:15.230 --> 00:04:17.210
When you do it this way,
your dx's are always

00:04:17.210 --> 00:04:18.280
going to be positive.

00:04:18.280 --> 00:04:20.540
When you go in that direction,
your dx's are always going

00:04:20.540 --> 00:04:22.540
to be positive, right?

00:04:22.540 --> 00:04:25.110
Each increment, the right
boundary is going to be higher

00:04:25.110 --> 00:04:25.840
than the left boundary.

00:04:25.840 --> 00:04:27.520
So your dx's are positive.

00:04:27.520 --> 00:04:30.690
In this situation, your
dx's are negative.

00:04:30.690 --> 00:04:32.450
The heights are always going to
be the same, they're always

00:04:32.450 --> 00:04:35.010
going to be f of x, but here
your change in x is a

00:04:35.010 --> 00:04:37.950
negative change in x,
when you go from b to a.

00:04:37.950 --> 00:04:39.660
And that's why you get
a negative integral.

00:04:39.660 --> 00:04:43.250
In either case here, our path
changes, but our ds's are

00:04:43.250 --> 00:04:44.480
going to be positive.

00:04:44.480 --> 00:04:47.310
And the way I've drawn this
surface, it's above the x-y

00:04:47.310 --> 00:04:50.670
plane, the f of xy is also
going to be positive.

00:04:50.670 --> 00:04:53.180
So that also kind of gives the
same intuition that this should

00:04:53.180 --> 00:04:54.920
be the exact same area.

00:04:54.920 --> 00:04:58.620
But let's prove
it to ourselves.

00:04:58.620 --> 00:05:04.770
So let's start off with our
first parameterization, just

00:05:04.770 --> 00:05:05.740
like we did in the last video.

00:05:05.740 --> 00:05:12.920
We have x is equal to x of t, y
is equal to y of t, and we're

00:05:12.920 --> 00:05:17.840
dealing with this from,
t goes from a to b.

00:05:17.840 --> 00:05:19.615
And we know we're going to need
the derivatives of these, so

00:05:19.615 --> 00:05:22.970
let write that down right now.

00:05:22.970 --> 00:05:32.240
We can write dx dt is equal to
x prime of t, and dy dt, let me

00:05:32.240 --> 00:05:41.550
write that a little bit neater,
dy dt is equal to y prime of t.

00:05:41.550 --> 00:05:45.590
This is nothing groundbreaking
I've done so far.

00:05:45.590 --> 00:05:53.140
But we know the integral
over c of f of xy.

00:05:53.140 --> 00:05:56.250
f is a scalar field,
not a vector field.

00:05:56.250 --> 00:06:02.720
ds is equal to the integral
from t is equal to a, to t is

00:06:02.720 --> 00:06:13.930
equal to b of f of x of t y of
t times the square root of dx

00:06:13.930 --> 00:06:20.500
dt squared, which is the same
thing as x prime of t squared,

00:06:20.500 --> 00:06:24.240
plus dy dt squared, the same
thing as y prime of t squared.

00:06:27.740 --> 00:06:31.170
All that under the
radical, times dt.

00:06:31.170 --> 00:06:34.220
This integral is exactly that,
given this parameterization.

00:06:37.480 --> 00:06:40.060
Now let's do the
minus c version.

00:06:40.060 --> 00:06:42.810
I'll do that in
this orange color.

00:06:46.850 --> 00:06:49.250
Actually, let me do the
minus c version down here.

00:06:49.250 --> 00:06:53.250
The minus the c version, we
have x is equal to, you

00:06:53.250 --> 00:06:55.140
remember this, actually,
just from up here, this

00:06:55.140 --> 00:06:56.085
was from the last video.

00:07:10.800 --> 00:07:13.990
x is equal to x of
a plus b minus t.

00:07:19.280 --> 00:07:25.440
y is equal to y of
a plus b minus t.

00:07:25.440 --> 00:07:34.430
And then t goes from a to b, t
goes from a to b, and this is

00:07:34.430 --> 00:07:37.610
just exactly what we did in
that last video. x is equal to

00:07:37.610 --> 00:07:41.650
x of a plus b minus t, y is
equal to y of a plus b minus t,

00:07:41.650 --> 00:07:44.310
same curve, just going in a
different direction as

00:07:44.310 --> 00:07:46.250
t increases a to b.

00:07:46.250 --> 00:07:48.320
But let's get the derivative.

00:07:48.320 --> 00:07:49.860
I'll do it in the
derivative color, maybe.

00:07:49.860 --> 00:07:52.640
So dx dt.

00:07:52.640 --> 00:07:54.970
For this path, it's going
to be a little different.

00:07:54.970 --> 00:07:56.810
We have to do the
chain rule now.

00:07:56.810 --> 00:07:59.750
Derivative of the inside
with respect to t.

00:07:59.750 --> 00:08:01.690
Well, these are constants.

00:08:01.690 --> 00:08:04.800
Derivative of minus t with
respect to t is minus 1.

00:08:04.800 --> 00:08:08.830
So it's minus 1 times the
derivative of the outside

00:08:08.830 --> 00:08:10.180
with respect to the inside.

00:08:10.180 --> 00:08:16.010
Well, that's just x prime
of a plus b minus t.

00:08:16.010 --> 00:08:19.840
Or, we could rewrite this as,
this is just minus x prime

00:08:19.840 --> 00:08:23.160
of a plus b minus t.

00:08:23.160 --> 00:08:27.230
dy dt, same logic.

00:08:27.230 --> 00:08:29.500
Derivative of the
inside is minus 1 with

00:08:29.500 --> 00:08:30.980
respect to t, right?

00:08:30.980 --> 00:08:33.530
Derivative minus t
is just minus 1.

00:08:33.530 --> 00:08:35.560
Times the derivative
of the outside with

00:08:35.560 --> 00:08:36.540
respect to the inside.

00:08:36.540 --> 00:08:43.060
So y prime of a plus b minus
t, same thing as minus y

00:08:43.060 --> 00:08:49.130
prime a plus b minus t.

00:08:49.130 --> 00:08:55.730
So given all of that, what is
this integral going to be equal

00:08:55.730 --> 00:09:03.330
to, the integral of minus c of
the scalar field f of xy ds?

00:09:03.330 --> 00:09:04.910
What is this going
to be equal to?

00:09:04.910 --> 00:09:07.580
Well, it's going to be the
integral from, you could almost

00:09:07.580 --> 00:09:09.880
pattern match it. t is equal
to a to t is equal

00:09:09.880 --> 00:09:13.010
to be of f of x.

00:09:13.010 --> 00:09:17.605
But now x is no longer
x of t. x now equals x

00:09:17.605 --> 00:09:19.050
of a plus b minus t.

00:09:21.940 --> 00:09:23.950
It's a little bit hairy,
but I don't think anything

00:09:23.950 --> 00:09:25.710
here is groundbreaking.

00:09:25.710 --> 00:09:27.190
Hopefully it's not
too confusing.

00:09:27.190 --> 00:09:29.770
And once again, y is no
longer y of t. y is y

00:09:29.770 --> 00:09:31.260
of a plus b minus t.

00:09:36.090 --> 00:09:39.320
And then times a square root,
I'll just switch colors,

00:09:39.320 --> 00:09:43.290
times the square root
of dx dt squared.

00:09:43.290 --> 00:09:44.830
What is dx dt squared?

00:09:44.830 --> 00:09:49.700
dx dt squared is just
this thing squared, or

00:09:49.700 --> 00:09:51.040
this thing squared.

00:09:51.040 --> 00:09:53.800
This thing, if I have minus
anything squared, that's the

00:09:53.800 --> 00:09:55.530
same thing as anything
squared, right?

00:09:55.530 --> 00:10:03.280
This is equal to minus x prime
of a plus b minus t squared,

00:10:03.280 --> 00:10:07.690
which is the same thing is
just x prime of a plus b

00:10:07.690 --> 00:10:09.140
minus t squared, right?

00:10:09.140 --> 00:10:11.640
You lose that minus information
when you square it.

00:10:11.640 --> 00:10:17.340
So that's going to be equal to
x prime of a plus b minus t

00:10:17.340 --> 00:10:21.960
squared, the whole result
function squared,

00:10:21.960 --> 00:10:24.130
plus dy dt squared.

00:10:24.130 --> 00:10:26.870
By the same logic, that's going
to be, you lose the negative

00:10:26.870 --> 00:10:28.030
when you square it.

00:10:28.030 --> 00:10:33.472
y prime of a plus b
minus t squared.

00:10:33.472 --> 00:10:35.360
Let me extend the radical.

00:10:35.360 --> 00:10:38.550
And then all of that dt.

00:10:38.550 --> 00:10:48.980
So that's the line integral
over the curve c, this is

00:10:48.980 --> 00:10:51.040
the line integral over
the curve minus c.

00:10:51.040 --> 00:10:52.600
They don't look equal just yet.

00:10:52.600 --> 00:10:55.070
This looks a lot more
convoluted than that one does.

00:10:55.070 --> 00:10:57.140
So let's see if we can
simplify it little bit.

00:10:57.140 --> 00:10:59.380
And we can simplify it,
perhaps, by making

00:10:59.380 --> 00:11:01.040
a substitution.

00:11:01.040 --> 00:11:05.390
Let's let, let me get a nice
substitution color, let's let

00:11:05.390 --> 00:11:10.560
u equal to a plus b minus t.

00:11:10.560 --> 00:11:12.360
So first we're going to have to
figure out the boundaries of

00:11:12.360 --> 00:11:13.760
our integral, well actually,
let's just figure

00:11:13.760 --> 00:11:14.520
out, what's du?

00:11:14.520 --> 00:11:19.910
so du dt, the derivative of u
with respect to t is just going

00:11:19.910 --> 00:11:24.200
to be equal to minus 1, or we
could say that du, if we

00:11:24.200 --> 00:11:27.330
multiply both sides by the
differential dt, is

00:11:27.330 --> 00:11:29.690
equal to minus dt.

00:11:29.690 --> 00:11:32.460
And let's figure out our
boundaries of integration.

00:11:32.460 --> 00:11:37.280
When t is equal to a,
what is u equal to?

00:11:37.280 --> 00:11:42.860
u is equal to a plus b minus
a, which is equal to b.

00:11:42.860 --> 00:11:49.110
And then when t is equal to b,
u is equal to a plus b minus

00:11:49.110 --> 00:11:52.190
b, which is equal to a.

00:11:52.190 --> 00:11:55.360
So if we do the substitution on
this crazy, hairy-looking

00:11:55.360 --> 00:11:58.270
interval, let's simplify a
little bit, and it changes

00:11:58.270 --> 00:12:02.190
our-- so this integral is going
to be the same thing as the

00:12:02.190 --> 00:12:06.940
integral from u, when
t is a, u is b.

00:12:06.940 --> 00:12:10.500
When t is b, u is a.

00:12:10.500 --> 00:12:16.000
And f of, x of, this thing
right here is just u.

00:12:16.000 --> 00:12:17.360
x of u.

00:12:17.360 --> 00:12:19.000
So it simplified it a good bit.

00:12:19.000 --> 00:12:22.730
And y of, this thing
right here, is just u.

00:12:22.730 --> 00:12:24.830
y of u.

00:12:24.830 --> 00:12:30.020
Times the square root-- let
me do it in the same color.

00:12:30.020 --> 00:12:40.160
Times the square root of x
prime of u squared plus

00:12:40.160 --> 00:12:42.010
y prime of u squared.

00:12:45.200 --> 00:12:49.210
Instead of a dt, we have to
write a, or could write, if we

00:12:49.210 --> 00:12:52.490
multiply both sides of this by
minus, we have dt is

00:12:52.490 --> 00:12:54.900
equal to minus du.

00:12:54.900 --> 00:12:58.100
So instead of a dt, we have
to put a minus du here.

00:12:58.100 --> 00:13:03.330
So this is times minus du, or,
just so we don't think this is

00:13:03.330 --> 00:13:07.140
a subtraction, let's just put
that negative sign out here in

00:13:07.140 --> 00:13:09.300
the front, just like that.

00:13:09.300 --> 00:13:13.110
So we're going from b to a of
this thing, right, like that.

00:13:13.110 --> 00:13:17.370
And just to make the boundaries
of integration make a little

00:13:17.370 --> 00:13:19.430
bit more sense, because we know
that a is less than

00:13:19.430 --> 00:13:21.000
b, let's swap them.

00:13:21.000 --> 00:13:24.110
And I said at the beginning
of this video, for just a

00:13:24.110 --> 00:13:28.010
standard, regular, run of the
mill integral, if you swap, if

00:13:28.010 --> 00:13:34.216
you have something going from b
to a of f of x dx, or du, maybe

00:13:34.216 --> 00:13:35.610
I should write it this way.

00:13:35.610 --> 00:13:38.440
f of u du.

00:13:38.440 --> 00:13:41.290
This is equal to the minus
of the integral from

00:13:41.290 --> 00:13:46.410
a to b of f of u du.

00:13:46.410 --> 00:13:49.220
And we did that by the logic
that I had graphed up here.

00:13:49.220 --> 00:13:53.030
That here, when you switch the
order, your du's will become

00:13:53.030 --> 00:13:55.830
the negatives of each other,
when you actually visualize it,

00:13:55.830 --> 00:13:57.880
when you're actually finding
the area under the curve.

00:13:57.880 --> 00:13:58.670
So let's do that.

00:13:58.670 --> 00:14:00.995
Let's swap the boundaries
of integration right here.

00:14:00.995 --> 00:14:03.310
And if we do that, that
will negate this negative,

00:14:03.310 --> 00:14:04.180
or make it a positive.

00:14:04.180 --> 00:14:07.920
So this is going to be equal
to the integral from a to b.

00:14:07.920 --> 00:14:09.800
I'm dropping the negative
sign, because I swapped

00:14:09.800 --> 00:14:10.410
these two things.

00:14:10.410 --> 00:14:11.800
So I'm going to take the
negative of a negative,

00:14:11.800 --> 00:14:12.980
which is a positive.

00:14:12.980 --> 00:14:28.070
Of f of x of u y of u times the
square root of x prime of u

00:14:28.070 --> 00:14:37.770
squared plus y prime
of u squared du.

00:14:37.770 --> 00:14:40.230
Now remember, everything we
just did was a substitution.

00:14:40.230 --> 00:14:44.130
This was all equal to, just to
remember what we're doing, this

00:14:44.130 --> 00:14:47.550
was the integral of the minus
curve of our scalar

00:14:47.550 --> 00:14:50.430
field, f of xy ds.

00:14:50.430 --> 00:14:54.020
Now how does this compare to
when we take the regular curve?

00:14:54.020 --> 00:14:55.180
How does this compare to that?

00:14:55.180 --> 00:14:57.150
Let me copy and
paste it to see.

00:14:57.150 --> 00:14:59.560
You know, I'm using
the wrong tool.

00:14:59.560 --> 00:15:03.490
Let me copy and paste it
to see how they compare.

00:15:03.490 --> 00:15:08.820
Copy, then let me pick to
down here, edit, paste.

00:15:08.820 --> 00:15:11.620
So how do these two
things compare?

00:15:11.620 --> 00:15:13.340
Let's take a close look.

00:15:13.340 --> 00:15:16.550
Well, they actually look
pretty similar, right?

00:15:16.550 --> 00:15:21.470
Over here, for the minus curve,
we have a bunch of u's.

00:15:21.470 --> 00:15:23.630
Over here, for the positive
curve, we have a bunch

00:15:23.630 --> 00:15:25.130
of t's, but they're in
the exact same places.

00:15:25.130 --> 00:15:28.610
These integrals are the
exact same integrals.

00:15:28.610 --> 00:15:30.510
If you make a u-substitution
here, if you just make the

00:15:30.510 --> 00:15:34.300
substitution u is equal to t,
this thing is going to be

00:15:34.300 --> 00:15:37.610
integral from a to b of,
it's going to be the

00:15:37.610 --> 00:15:38.490
exact same thing.

00:15:38.490 --> 00:15:48.530
Of f of x of u, y of u times
the square root of of x

00:15:48.530 --> 00:15:55.750
prime of u squared plus
y prime of u squared du.

00:15:55.750 --> 00:15:57.930
These two things are identical.

00:15:57.930 --> 00:16:00.120
So we did all the substitution,
everything, but we got

00:16:00.120 --> 00:16:02.250
the exact same integrals.

00:16:02.250 --> 00:16:05.660
So hopefully that satisfies you
that it doesn't matter what

00:16:05.660 --> 00:16:08.630
direction we go on the curve,
as long as the shape of

00:16:08.630 --> 00:16:09.500
the curve is the same.

00:16:09.500 --> 00:16:12.580
Doesn't matter if we go forward
or backward on the curve, we're

00:16:12.580 --> 00:16:13.950
going to get the same answer.

00:16:13.950 --> 00:16:16.510
And I think that meets our
intuition, because in either

00:16:16.510 --> 00:16:21.650
case, we're finding the
area of this curtain.


Parametrization of a reverse path

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:03.920
What I want to do in the next
few videos is try to see what

00:00:03.920 --> 00:00:06.780
happens to a line integral,
either a line integral over a

00:00:06.780 --> 00:00:09.870
scalar field or a vector field,
but what happens that line

00:00:09.870 --> 00:00:12.370
integral when we change the
direction of our path?

00:00:12.370 --> 00:00:14.560
So let's say, when I say change
direction, let's say that

00:00:14.560 --> 00:00:18.820
I have some curve C that
looks something like this.

00:00:18.820 --> 00:00:21.760
We draw the x- and y- axis.

00:00:21.760 --> 00:00:26.180
So that's my y-axis, that is
my x-axis, and let's say my

00:00:26.180 --> 00:00:30.560
parameterization starts there,
and then as t increases, ends

00:00:30.560 --> 00:00:32.120
up over there just like that.

00:00:32.120 --> 00:00:35.230
So it's moving in
that direction.

00:00:35.230 --> 00:00:38.130
And when I say I reverse
the path, we could

00:00:38.130 --> 00:00:39.350
define another curve.

00:00:39.350 --> 00:00:44.430
Let's call it minus C, that
looks something like this.

00:00:44.430 --> 00:00:48.150
That is my y-axis,
that is my x-axis.

00:00:48.150 --> 00:00:51.690
And it looks exactly the same,
but it starts up here, and then

00:00:51.690 --> 00:00:55.260
as t increases, it goes down
to the starting point

00:00:55.260 --> 00:00:56.370
of the other curve.

00:00:56.370 --> 00:00:59.320
So it's the exact same shape
of a curve, but it goes in

00:00:59.320 --> 00:01:00.530
the opposite direction.

00:01:00.530 --> 00:01:03.310
So what I'm going to do in this
video is just understand how we

00:01:03.310 --> 00:01:06.490
can construct a
parameterization like this, and

00:01:06.490 --> 00:01:08.010
hopefully understand
it pretty well.

00:01:08.010 --> 00:01:11.320
And then next two videos after
this, we'll try to see what

00:01:11.320 --> 00:01:14.320
this actually does to the line
integral, one for a scalar

00:01:14.320 --> 00:01:17.850
field, and then one
for a vector field.

00:01:17.850 --> 00:01:20.430
So let's just say, this
parameterization right here,

00:01:20.430 --> 00:01:22.630
let's just define it in the
basic way that we've

00:01:22.630 --> 00:01:23.500
always defined them.

00:01:23.500 --> 00:01:29.540
Let's say that this is x is
equal to x of t, y is equal to

00:01:29.540 --> 00:01:34.280
y of t, and let's say this is
from t is equal, or t,

00:01:34.280 --> 00:01:36.670
let me write this way.

00:01:36.670 --> 00:01:39.695
t starts at a, so t is
greater than or equal to

00:01:39.695 --> 00:01:42.290
a, and it goes up to b.

00:01:42.290 --> 00:01:47.070
So in this example, this was
when t is equal to a, and the

00:01:47.070 --> 00:01:55.000
point right here is the
coordinate x of a, y of a.

00:01:55.000 --> 00:01:58.590
And then when t is equal to b
up here, this is really just a

00:01:58.590 --> 00:02:00.870
review of what we've seen
before, really just a review of

00:02:00.870 --> 00:02:05.270
parameterization, when t is
equal to b up here, this is

00:02:05.270 --> 00:02:11.160
the point x of b, y of b.

00:02:11.160 --> 00:02:12.980
Nothing new there.

00:02:12.980 --> 00:02:16.570
Now given these functions, how
can we construct another

00:02:16.570 --> 00:02:19.140
parameterization here that has
the same shape, but

00:02:19.140 --> 00:02:20.460
that starts here?

00:02:20.460 --> 00:02:22.660
So I want this to be,
t is equal to a.

00:02:22.660 --> 00:02:24.600
Let me switch colors.

00:02:24.600 --> 00:02:28.570
Let me switch to,
maybe, magenta.

00:02:28.570 --> 00:02:33.460
So I want this to be t is equal
to a, and as t increases, I

00:02:33.460 --> 00:02:36.020
want this to be t equals b.

00:02:36.020 --> 00:02:39.270
So I want to move in the
opposite direction.

00:02:39.270 --> 00:02:42.950
So when t is equal to a,
I want my coordinate to

00:02:42.950 --> 00:02:49.470
still be x of b, y of b.

00:02:49.470 --> 00:02:53.350
When t is equal to a, I want a
b in each of these functions,

00:02:53.350 --> 00:02:56.150
and when t is equal to b, I
want the coordinate to

00:02:56.150 --> 00:03:01.400
be x of a, y of a.

00:03:01.400 --> 00:03:01.630
Right?

00:03:01.630 --> 00:03:02.770
Notice, they're opposites now.

00:03:02.770 --> 00:03:05.180
Here t is equal to a, x
of a, y of a, here t is

00:03:05.180 --> 00:03:06.700
equal to b, our endpoint.

00:03:06.700 --> 00:03:10.460
Now I'm at this coordinate,
x of a, y of a.

00:03:10.460 --> 00:03:12.520
So how do I construct that?

00:03:12.520 --> 00:03:16.450
Well, if you think about it,
when t is equal to a, we want

00:03:16.450 --> 00:03:18.740
both of these functions
to evaluate it at b.

00:03:18.740 --> 00:03:22.210
So what if we define our x, in
this case, for our minus C

00:03:22.210 --> 00:03:27.900
curve, what if we say x is
equal to x of, and when I say x

00:03:27.900 --> 00:03:29.700
of I'm talking about the
same exact function.

00:03:29.700 --> 00:03:33.240
Actually, maybe I should write
it in that same exact color.

00:03:33.240 --> 00:03:37.180
x of-- but instead of putting t
in there, instead of putting a

00:03:37.180 --> 00:03:40.340
straight-up t in there, what if
I put an a plus b

00:03:40.340 --> 00:03:43.030
minus t in there?

00:03:43.030 --> 00:03:43.520
What happens?

00:03:43.520 --> 00:03:45.010
Well, let me do it
for the y as well.

00:03:45.010 --> 00:03:54.310
So then our y, y, is equal
to y of a plus b minus t.

00:03:54.310 --> 00:03:56.920
a plus b minus is t.

00:03:56.920 --> 00:03:59.600
I'm using slightly different
shades of yellow, might be

00:03:59.600 --> 00:04:01.180
a little disconcerting.

00:04:01.180 --> 00:04:04.030
Anyway, what happens
when we define this?

00:04:04.030 --> 00:04:10.000
When t is equal to a, when t is
equal to a, let's say that this

00:04:10.000 --> 00:04:14.000
parameterization is also
for t starts at a and

00:04:14.000 --> 00:04:15.470
then goes up to b.

00:04:15.470 --> 00:04:18.040
So let's just experiment and
confirm that this

00:04:18.040 --> 00:04:20.560
parameterization really is the
same thing as this thing,

00:04:20.560 --> 00:04:22.070
but it goes in an
opposite direction.

00:04:22.070 --> 00:04:24.950
Or at least, confirm in
our minds intuitively.

00:04:24.950 --> 00:04:32.240
So when t is equal to a, when t
is equal to a, x will be equal

00:04:32.240 --> 00:04:39.350
to x of a plus b
minus a, right?

00:04:39.350 --> 00:04:44.040
This is when t is equal to
a, so minus t, or minus a,

00:04:44.040 --> 00:04:45.370
which is equal to what?

00:04:45.370 --> 00:04:50.960
Well, a minus a, cancel out,
that's equal to x of b.

00:04:50.960 --> 00:04:55.280
Similarly, when t is equal
to a, y will be equal to

00:04:55.280 --> 00:04:59.840
y of a plus b minus a.

00:04:59.840 --> 00:05:03.990
The a's cancel out, so
it's equal to y of b.

00:05:03.990 --> 00:05:04.860
So that worked.

00:05:04.860 --> 00:05:09.480
When t is equal to a, my
parameterization evaluates to

00:05:09.480 --> 00:05:12.160
the coordinate x of b, y of b.

00:05:12.160 --> 00:05:15.480
When t is equal to
a, x of b, y of b.

00:05:15.480 --> 00:05:19.210
Then we can do the exact same
thing when t is equal to b.

00:05:19.210 --> 00:05:21.450
I'll do it over here, because
I don't want to lose this.

00:05:21.450 --> 00:05:23.690
Let me just draw a line here.

00:05:23.690 --> 00:05:26.160
I'm still dealing with this
parameterization over here.

00:05:26.160 --> 00:05:28.300
Actually, let me scroll over
to the right, just so that

00:05:28.300 --> 00:05:29.380
I don't get confused.

00:05:29.380 --> 00:05:33.630
When t is equal to b, when t
is equal to b, what does x

00:05:33.630 --> 00:05:39.310
equal? x is equal to x of
a plus b minus b, right?

00:05:39.310 --> 00:05:42.580
a plus b minus b when
t is equal to b.

00:05:42.580 --> 00:05:46.420
So that's equal to x of a.

00:05:46.420 --> 00:05:52.000
and then when she's able to be
why is equal to lie of a plus b

00:05:52.000 --> 00:05:57.080
minus b, and of course, that's
going to be equal to y of a.

00:05:57.080 --> 00:06:00.410
So the endpoints work, and if
you think about it intuitively,

00:06:00.410 --> 00:06:05.010
as t increases, so when t is at
a, this thing is going

00:06:05.010 --> 00:06:06.270
to be x of b, y of b.

00:06:06.270 --> 00:06:07.990
We saw that down here.

00:06:07.990 --> 00:06:14.760
Now as t increases, this
value is going to decrease.

00:06:14.760 --> 00:06:19.340
We started x of b, y of b, and
as t increases, this value is

00:06:19.340 --> 00:06:22.640
going to decrease to a, right?

00:06:22.640 --> 00:06:24.940
It starts from b,
and it goes to a.

00:06:24.940 --> 00:06:28.370
This one obviously starts
at a, and it goes to b.

00:06:28.370 --> 00:06:30.490
So hopefully, that should give
you the intuition why this is

00:06:30.490 --> 00:06:32.610
the exact same curve as that.

00:06:32.610 --> 00:06:36.270
It just goes in a completely
opposite direction.

00:06:36.270 --> 00:06:39.570
Now, with that out of the way,
if you accept what I've told

00:06:39.570 --> 00:06:41.540
you, that these are really
the same parameterizations,

00:06:41.540 --> 00:06:42.770
just opposite directions.

00:06:42.770 --> 00:06:44.050
I shouldn't say same
parameterizations.

00:06:44.050 --> 00:06:47.500
Same curve going in an opposite
direction, or same path going

00:06:47.500 --> 00:06:48.700
in the opposite direction.

00:06:48.700 --> 00:06:51.530
In the next video, I'm going to
see what happens when we

00:06:51.530 --> 00:07:00.550
evaluate this line integral, f
of x ds, versus this

00:07:00.550 --> 00:07:02.760
line integral.

00:07:02.760 --> 00:07:07.020
So this is a scalar field, a
line integral of a scalar

00:07:07.020 --> 00:07:10.750
field, using this curve or this
path, but what happens if we

00:07:10.750 --> 00:07:18.050
take a line integral over the
same scalar field, but we do

00:07:18.050 --> 00:07:20.150
it over this reverse path?

00:07:20.150 --> 00:07:21.690
That's what we're going
to do in the next video.

00:07:21.690 --> 00:07:25.510
And the video after that, we'll
do it for vector fields.


Percent word problem example 1

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:02.070
Let's say I go to the fruit
store today and they

00:00:02.070 --> 00:00:03.720
have a sale on guavas.

00:00:03.720 --> 00:00:07.730
Everything is 30% off.

00:00:07.730 --> 00:00:08.550
This is for guavas.

00:00:11.690 --> 00:00:13.370
And it's only today.

00:00:13.370 --> 00:00:17.750
Only today.

00:00:17.750 --> 00:00:21.550
So I say, you know what, let
me go buy a bunch of guavas.

00:00:21.550 --> 00:00:23.850
So I go and I buy 6 guavas.

00:00:23.850 --> 00:00:27.380
So I buy six guavas.

00:00:27.380 --> 00:00:30.360
And it ends up, when I go to
the register, and we're

00:00:30.360 --> 00:00:33.480
assuming no tax, it's a grocery
and I live in a state where

00:00:33.480 --> 00:00:34.900
they don't tax groceries.

00:00:34.900 --> 00:00:38.680
So for the 6 guavas, they
charge me, I get the 30% off.

00:00:38.680 --> 00:00:42.510
They charge me $12.60.

00:00:42.510 --> 00:00:44.660
$12.60.

00:00:44.660 --> 00:00:48.270
So this is the 30% off
sale price on 6 guavas.

00:00:48.270 --> 00:00:51.293
I go home, and then my wife
tells me, you know, Sal, can

00:00:51.293 --> 00:00:54.050
you go get 2 more
guavas tomorrow?

00:00:54.050 --> 00:00:54.710
I say, sure.

00:00:54.710 --> 00:00:57.770
So the next day I go and I
want to buy 2 more guavas.

00:00:57.770 --> 00:01:00.030
So, 2 guavas.

00:01:00.030 --> 00:01:01.760
But now the sale is off.

00:01:01.760 --> 00:01:03.060
There's no more 30%.

00:01:03.060 --> 00:01:05.580
That was only that first
day that I bought the 6.

00:01:05.580 --> 00:01:09.640
So how much are those two
guavas going to cost me?

00:01:09.640 --> 00:01:14.660
How much are those two guavas
going to cost at full price?

00:01:14.660 --> 00:01:19.800
At full price?

00:01:19.800 --> 00:01:22.530
So, a good place to start
is, to think about how much

00:01:22.530 --> 00:01:25.230
would those 6 guavas have
cost us at full price?

00:01:25.230 --> 00:01:26.610
This is the sale
price, right here?

00:01:26.610 --> 00:01:29.190
This is the sale price.

00:01:29.190 --> 00:01:32.500
How much would those have
cost me at full price?

00:01:32.500 --> 00:01:36.350
So let's do a little
bit of algebra here.

00:01:36.350 --> 00:01:39.580
Pick a suitable color
for the algebra.

00:01:39.580 --> 00:01:40.790
Maybe this grey color.

00:01:40.790 --> 00:01:47.165
So, let's say that x is equal
to the cost of 6 guarvas.

00:01:47.165 --> 00:01:53.630
6 guavas, at full price.

00:01:53.630 --> 00:01:56.100
So, essentially, if we
take 30% off of this,

00:01:56.100 --> 00:01:57.950
we should get $12.60.

00:01:57.950 --> 00:01:59.050
So let's do that.

00:01:59.050 --> 00:02:02.235
So if we have the full price
of 6 guavas, we're going

00:02:02.235 --> 00:02:04.190
to take 30% off of that.

00:02:04.190 --> 00:02:07.290
So that's the same
thing as 0.30.

00:02:07.290 --> 00:02:08.680
Or I could just write 0.3.

00:02:08.680 --> 00:02:10.740
I could ignore that
zero if I like.

00:02:10.740 --> 00:02:11.640
Actually, let me
write it like this.

00:02:11.640 --> 00:02:14.470
My wife is always bugging me to
write zeroes before decimals.

00:02:14.470 --> 00:02:20.670
So that's the full price of
6 guavas minus 0.30 times

00:02:20.670 --> 00:02:22.960
the full price of guavas.

00:02:22.960 --> 00:02:26.350
Some I'm just taking 30%
off of the full price,

00:02:26.350 --> 00:02:27.520
off of the full price.

00:02:27.520 --> 00:02:29.900
This is how we figure
out the sale price.

00:02:29.900 --> 00:02:34.480
This is going to be equal to
that $12.60 right there.

00:02:34.480 --> 00:02:37.540
That's going to be
equal to $12.60.

00:02:37.540 --> 00:02:39.900
I just took 30% off
of the full price.

00:02:39.900 --> 00:02:41.200
And now we just do algebra.

00:02:41.200 --> 00:02:43.140
We could imagine there's a
1 in front -- you know, x

00:02:43.140 --> 00:02:45.020
is the same thing as 1x.

00:02:45.020 --> 00:02:50.285
So 1x minus 0.3x is going
to be equal to 0.7x.

00:02:50.285 --> 00:02:54.240
So we get 0.7x, or we could
say 0.70 if you like.

00:02:54.240 --> 00:02:55.170
Same number.

00:02:55.170 --> 00:03:00.070
Point, or 0.7x, is
equal to 12.60.

00:03:00.070 --> 00:03:02.130
And once you get used to these
problems, you might just skip

00:03:02.130 --> 00:03:03.780
straight to this
step right here.

00:03:03.780 --> 00:03:07.670
Where you say, 70% of the
full price is equal to

00:03:07.670 --> 00:03:08.550
my sale price, right?

00:03:08.550 --> 00:03:10.000
I took 30% off.

00:03:10.000 --> 00:03:12.150
This is 70% of the full price.

00:03:12.150 --> 00:03:14.360
You might just skip to this
step once you get used to these

00:03:14.360 --> 00:03:15.270
problems in a little bit.

00:03:15.270 --> 00:03:16.780
And now we just have
to solve for x.

00:03:16.780 --> 00:03:21.040
Divide both sides by 0.7,
so you get x is equal to

00:03:21.040 --> 00:03:26.370
12.60 divided by 0.7.

00:03:26.370 --> 00:03:28.970
We could use a calculator, but
it's always good to get a

00:03:28.970 --> 00:03:31.060
little bit of practice
dividing decimals.

00:03:31.060 --> 00:03:31.860
So let's do that.

00:03:31.860 --> 00:03:38.590
So we get 0.7 goes into 12.60.

00:03:38.590 --> 00:03:41.880
Let's multiply both of these
numbers by 10, which is what we

00:03:41.880 --> 00:03:45.270
do when we move both of their
decimals one to the right.

00:03:45.270 --> 00:03:47.580
So the 0.7 becomes a 7.

00:03:47.580 --> 00:03:49.040
Ignore that right there.

00:03:49.040 --> 00:03:53.980
The 12.60 becomes 126, put
the decimal right there.

00:03:53.980 --> 00:03:55.340
Decimal right there.

00:03:55.340 --> 00:03:57.680
And we're ready to just do
straight up long division.

00:03:57.680 --> 00:04:00.120
So this is now a 7, not a .7.

00:04:00.120 --> 00:04:03.210
So 7 goes into 12 1 time.

00:04:03.210 --> 00:04:05.930
1 times 7 is 7.

00:04:05.930 --> 00:04:08.630
12 minus 7 is 5.

00:04:08.630 --> 00:04:10.870
Bring down the 6.

00:04:10.870 --> 00:04:15.340
7 goes into 56 8 times.

00:04:15.340 --> 00:04:18.380
8 times 7 is 56.

00:04:18.380 --> 00:04:20.410
And then we have no remainder.

00:04:20.410 --> 00:04:22.820
So it's 18, and there's nothing
behind the decimal point.

00:04:22.820 --> 00:04:25.890
So it;s 18, in our case, $18.

00:04:25.890 --> 00:04:30.800
So x is equal to $18.

00:04:30.800 --> 00:04:36.750
Remember what x was? x was
the full price of 6 guavas.

00:04:36.750 --> 00:04:39.920
x was the full price of 6.

00:04:39.920 --> 00:04:42.070
x is the full price
of 6 guavas.

00:04:42.070 --> 00:04:44.670
Now, the question is, how
much will 2 guavas cost

00:04:44.670 --> 00:04:46.220
me at the full price?

00:04:46.220 --> 00:04:52.710
Well, this is full price of 6.

00:04:52.710 --> 00:04:54.340
So you immediately could
figure out what's the

00:04:54.340 --> 00:04:56.530
full price of one guava.

00:04:56.530 --> 00:04:58.640
You divide 18 by 6.

00:04:58.640 --> 00:05:01.770
So 18 divided by 6 is $3.

00:05:01.770 --> 00:05:09.470
That's $3 per guava
at full price.

00:05:09.470 --> 00:05:11.870
And they're asking us,
we want 2 guavas.

00:05:11.870 --> 00:05:14.280
So 2 guavas is going to
be 2 times $3, so this

00:05:14.280 --> 00:05:16.740
is going to be $6.

00:05:16.740 --> 00:05:17.550
$6.

00:05:17.550 --> 00:05:19.050
Another way you could have done
it, you could have just said,

00:05:19.050 --> 00:05:23.000
hey, 6 at full price are
going to cost me $18.

00:05:23.000 --> 00:05:25.640
2 is 1/3 of 6.

00:05:25.640 --> 00:05:28.440
So 1/3 of $18 is $6.

00:05:28.440 --> 00:05:31.130
So, just to give a quick
review what we did.

00:05:31.130 --> 00:05:34.760
We said the sale price
on six guavas, $12.60.

00:05:34.760 --> 00:05:37.360
That's 30% off the full price.

00:05:37.360 --> 00:05:41.290
Or you could say this is
70% of the full price.

00:05:41.290 --> 00:05:45.760
70% of the full price.

00:05:45.760 --> 00:05:49.510
And so you could say, 30% -- so
if you say x is the full price

00:05:49.510 --> 00:05:53.580
of 6 guavas, you could say the
full price of 6 guavas minus

00:05:53.580 --> 00:05:57.790
30% of the full price of 6
guavas is equal to 12.60, and

00:05:57.790 --> 00:06:02.140
that's equivalent to saying,
70% of the full price is 12.60.

00:06:02.140 --> 00:06:04.340
You divided -- then we just
solved this algebraically.

00:06:04.340 --> 00:06:08.150
Divide both sides by 0.7, and
then we got x, the full price

00:06:08.150 --> 00:06:14.820
of 6 guavas, is $18, or that's
$3 per guava or $6 for 2.

00:06:14.820 --> 00:06:17.370
Anyway, hopefully you
found that helpful.


Secondary active transport in the nephron

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:03.130
In the last video on the
nephron, we talked about the

00:00:03.130 --> 00:00:08.690
different parts of the nephron
and what, I guess, molecules

00:00:08.690 --> 00:00:11.750
are reabsorbed by the body
and the different parts.

00:00:11.750 --> 00:00:15.890
If you remember, in the proximal
convoluted tubule, we

00:00:15.890 --> 00:00:20.250
talked about maybe glucose and
amino acids and sodium being

00:00:20.250 --> 00:00:21.230
reabsorbed.

00:00:21.230 --> 00:00:24.500
We talked about the ascending
part of the loop of Henle.

00:00:24.500 --> 00:00:29.110
We talked about salts, so that
sodium, potassium, chlorine

00:00:29.110 --> 00:00:30.460
being reabsorbed.

00:00:30.460 --> 00:00:33.300
In the distal convoluted
tubule, it was

00:00:33.300 --> 00:00:35.220
calcium, other things.

00:00:35.220 --> 00:00:38.860
But at least in my mind, when I
first learned it, I said how

00:00:38.860 --> 00:00:39.580
does that happen?

00:00:39.580 --> 00:00:42.760
How do we actively pump out
these things, especially

00:00:42.760 --> 00:00:45.370
against their own concentration
gradients?

00:00:45.370 --> 00:00:47.170
What I want to do in this video
is get a little bit more

00:00:47.170 --> 00:00:50.770
depth on exactly what's
happening on the borders of

00:00:50.770 --> 00:00:54.000
these tubules to actually
allow these ions to be

00:00:54.000 --> 00:00:59.520
selectively transported out of
the lumen or the inside of

00:00:59.520 --> 00:01:00.760
these tubes or to be

00:01:00.760 --> 00:01:05.410
reabsorbed out of the filtrate.

00:01:05.410 --> 00:01:08.570
The mechanism's actually
reasonably similar in the

00:01:08.570 --> 00:01:10.500
different parts of the nephron,
but let's look at

00:01:10.500 --> 00:01:12.930
each of the parts, because
they're each reabsorbing

00:01:12.930 --> 00:01:14.170
different types of molecules.

00:01:14.170 --> 00:01:15.790
And I won't go through all of
the molecules, but I'll just

00:01:15.790 --> 00:01:16.890
give you a sense of things.

00:01:16.890 --> 00:01:20.320
Let's start with the proximal
tubule right here.

00:01:20.320 --> 00:01:25.520
So let's say if we were to zoom
in right over on that

00:01:25.520 --> 00:01:30.260
part-- so let me draw the
inside of the nephron.

00:01:30.260 --> 00:01:31.780
The inside of the nephron
maybe looks

00:01:31.780 --> 00:01:34.370
something like this.

00:01:34.370 --> 00:01:35.460
So this the inside.

00:01:35.460 --> 00:01:39.400
This is where our filtrate
is right here.

00:01:39.400 --> 00:01:40.680
Actually, let me draw
it a little bit

00:01:40.680 --> 00:01:41.890
different than that.

00:01:41.890 --> 00:01:46.105
So the inside, I'm going to draw
it like this because the

00:01:46.105 --> 00:01:49.840
proximal tubule has these little
things that stick out,

00:01:49.840 --> 00:01:53.340
sometimes referred to
as a brush border.

00:01:53.340 --> 00:01:57.300
So this inside right here,
this is our lumen.

00:02:01.620 --> 00:02:05.090
That is where the filtrate is.

00:02:05.090 --> 00:02:07.400
The glomerular filtrate is
coming in this direction.

00:02:10.820 --> 00:02:14.810
This is, you can imagine, the
inside of the nephron.

00:02:14.810 --> 00:02:18.280
And then the border of
the tubule is made up

00:02:18.280 --> 00:02:19.330
by a bunch of cells.

00:02:19.330 --> 00:02:22.790
So maybe this is one cell right
here, this is another

00:02:22.790 --> 00:02:25.750
cell right here, that's
another cell.

00:02:25.750 --> 00:02:26.866
Obviously, this is
a cross-section.

00:02:26.866 --> 00:02:28.160
It would be actually
more of a cylinder.

00:02:28.160 --> 00:02:29.410
It would go around like that.

00:02:29.410 --> 00:02:30.870
This is to give an idea.

00:02:30.870 --> 00:02:32.410
That's another cell
right there.

00:02:32.410 --> 00:02:37.810
And maybe this is their basal
side right there.

00:02:37.810 --> 00:02:39.920
And when we say basal, we can
imagine that's kind of the

00:02:39.920 --> 00:02:42.110
base of the cell.

00:02:42.110 --> 00:02:44.910
Those are good words to
know, fancy words.

00:02:44.910 --> 00:02:48.960
So the side of the cells that
are facing the lumen, or kind

00:02:48.960 --> 00:02:51.930
of facing the inside of our
tubule, this is called the

00:02:51.930 --> 00:02:53.180
apical side.

00:02:57.040 --> 00:03:00.420
And then this side is normally
referred to the basal lateral

00:03:00.420 --> 00:03:04.620
side, or this membrane, if you
view this as a membrane, this

00:03:04.620 --> 00:03:08.450
would be the basolateral
membrane.

00:03:08.450 --> 00:03:11.800
This is true regardless of what
part of the nephron we're

00:03:11.800 --> 00:03:14.030
in, whether the proximal,
whether the loop of Henle, or

00:03:14.030 --> 00:03:16.020
whether we're in the
distal part.

00:03:16.020 --> 00:03:19.040
What we have here, and on the
other sides of these cells,

00:03:19.040 --> 00:03:21.900
we'll have our peritubular
capillaries.

00:03:21.900 --> 00:03:23.850
That's another fancy word.

00:03:23.850 --> 00:03:26.630
So our peritubular capillaries
will look something like this.

00:03:26.630 --> 00:03:28.230
They're actually
cells as well.

00:03:31.370 --> 00:03:33.020
Actually, instead of drawing the
cells, I'll just draw it

00:03:33.020 --> 00:03:36.350
as kind of the tube of-- I'll
just draw it like this.

00:03:36.350 --> 00:03:37.940
They're porous.

00:03:37.940 --> 00:03:40.740
So this is actually blood
flow right here.

00:03:40.740 --> 00:03:41.915
This is blood right here.

00:03:41.915 --> 00:03:44.290
This is blood right here.

00:03:44.290 --> 00:03:46.870
I'm not going to do too much
detail on the actual cells of

00:03:46.870 --> 00:03:48.930
the capillary walls.

00:03:48.930 --> 00:03:50.790
I really want to give you the
idea of how things are

00:03:50.790 --> 00:03:53.400
transported out of the lumen,
how they're selectively

00:03:53.400 --> 00:03:54.650
reabsorbed.

00:03:56.420 --> 00:04:03.450
So this is the peritubular
capillary.

00:04:03.450 --> 00:04:05.980
And once again, fancy
word, but peri means

00:04:05.980 --> 00:04:07.460
around, like perimeter.

00:04:07.460 --> 00:04:08.940
So it's around the tubes.

00:04:08.940 --> 00:04:10.480
These capillaries go
around the tubes.

00:04:10.480 --> 00:04:12.430
If I were overlay it on this
picture, we have these

00:04:12.430 --> 00:04:15.140
capillaries that are going
all around the tubes.

00:04:15.140 --> 00:04:17.810
So when things get secreted
or reabsorbed out of the

00:04:17.810 --> 00:04:21.089
nephrons, they're going into
those capillaries.

00:04:21.089 --> 00:04:24.630
So this is our proximal
convoluted

00:04:24.630 --> 00:04:25.970
membrane right here.

00:04:25.970 --> 00:04:28.540
Let's think about what happens
with the glucose.

00:04:28.540 --> 00:04:33.750
So what happens is we actually
have sodium-potassium pumps on

00:04:33.750 --> 00:04:37.520
the basolateral side
of these cells.

00:04:37.520 --> 00:04:39.040
So this is sodium-potassium
pumps.

00:04:39.040 --> 00:04:41.370
I'll just draw one right here.

00:04:41.370 --> 00:04:42.730
You might want to watch
the video on

00:04:42.730 --> 00:04:44.600
sodium-potassium pumps.

00:04:44.600 --> 00:04:46.250
I have a whole video on it.

00:04:46.250 --> 00:04:51.890
But the idea here is that
sodium, maybe I'll draw as

00:04:51.890 --> 00:04:55.810
plus particles right there,
they'll attach on the inside

00:04:55.810 --> 00:04:58.240
right here, ATP will
come along.

00:04:58.240 --> 00:05:02.150
When ATP attaches to the right
part of this protein, it'll

00:05:02.150 --> 00:05:05.880
change its shape, its
conformation, and then the

00:05:05.880 --> 00:05:09.310
protein will essentially close
on this side and open on that

00:05:09.310 --> 00:05:14.680
side, and then when it's in that
conformation, the sodium

00:05:14.680 --> 00:05:18.010
doesn't want to bond as much to
the protein and it will go

00:05:18.010 --> 00:05:21.090
outside or it'll cross the
basolateral membrane and

00:05:21.090 --> 00:05:24.140
eventually make its way
into the blood.

00:05:24.140 --> 00:05:27.360
And then on the other side, it's
a sodium-potassium pump.

00:05:27.360 --> 00:05:29.810
When it's in this kind of open
configuration-- I'll draw it

00:05:29.810 --> 00:05:36.780
over here; I have a whole video
on this-- at that point,

00:05:36.780 --> 00:05:39.320
potassium likes to bond to it.

00:05:39.320 --> 00:05:42.080
So potassium likes
to bond to it.

00:05:42.080 --> 00:05:43.710
Maybe it bonds to
it over here.

00:05:43.710 --> 00:05:45.580
This is a gross
oversimplification.

00:05:45.580 --> 00:05:48.000
That causes the protein to
change its conformation.

00:05:48.000 --> 00:05:50.600
It doesn't require ATP at that
point, and it goes back to

00:05:50.600 --> 00:05:53.620
this conformation, and then the
potassium doesn't want to

00:05:53.620 --> 00:05:56.870
bond anymore, and then it gets
released, because the protein

00:05:56.870 --> 00:05:57.860
is now a different shape.

00:05:57.860 --> 00:06:00.860
So the general idea:
Sodium bonds.

00:06:00.860 --> 00:06:02.090
ATP bonds.

00:06:02.090 --> 00:06:05.490
The ATP gets its phosphate
popped off of it.

00:06:05.490 --> 00:06:07.830
That changes the shape of
the protein to this.

00:06:07.830 --> 00:06:10.910
Now the sodium wants to get
released, and now potassium

00:06:10.910 --> 00:06:11.870
wants to join.

00:06:11.870 --> 00:06:14.380
When potassium joins, we get
to our original one.

00:06:14.380 --> 00:06:18.310
The end product of this is
we're having sodium being

00:06:18.310 --> 00:06:21.580
pumped out of the cell and we're
having potassium being

00:06:21.580 --> 00:06:24.100
pumped into the cell, and this
is active transport.

00:06:27.390 --> 00:06:29.200
Why is it active transport?

00:06:29.200 --> 00:06:33.160
Because we're using ATP to
drive sodium against its

00:06:33.160 --> 00:06:36.990
concentration gradient to keep
pumping the sodium out of the

00:06:36.990 --> 00:06:40.030
cell, and then potassium kind of
comes in, you could almost

00:06:40.030 --> 00:06:40.920
imagine, passively.

00:06:40.920 --> 00:06:42.950
It doesn't require ATP.

00:06:42.950 --> 00:06:46.850
And that's why this is often
called a sodium-potassium

00:06:46.850 --> 00:06:51.630
ATPase, which means it's a
protein or an enzyme that

00:06:51.630 --> 00:06:52.520
breaks ATP.

00:06:52.520 --> 00:06:55.080
But it breaks ATP, it uses
that energy to change its

00:06:55.080 --> 00:06:58.320
shape to pump sodium out
and potassium in.

00:06:58.320 --> 00:07:00.520
Well, anyway, this is all a
review of what we learned in

00:07:00.520 --> 00:07:03.560
those videos, but how does that
help us, for example, get

00:07:03.560 --> 00:07:06.020
glucose out of our lumen?

00:07:06.020 --> 00:07:10.370
Well, what we have over here
is we have other proteins.

00:07:10.370 --> 00:07:12.250
I'll just do the example
of glucose.

00:07:12.250 --> 00:07:15.760
Let's say we have
a protein here.

00:07:15.760 --> 00:07:17.280
There's a very general
term for this.

00:07:17.280 --> 00:07:19.620
It's a cotransporter
or a symporter.

00:07:26.530 --> 00:07:31.110
Symporter means it transfers two
types of molecules in the

00:07:31.110 --> 00:07:31.790
same direction.

00:07:31.790 --> 00:07:34.580
Cotransporter means one molecule
wants to go through

00:07:34.580 --> 00:07:36.850
because of its concentration
gradient and the other

00:07:36.850 --> 00:07:39.710
molecule kind of goes
along for the ride.

00:07:39.710 --> 00:07:43.270
So you can imagine, we're
actively pumping out sodium.

00:07:43.270 --> 00:07:46.460
So if we're actively pumping
out sodium over here on the

00:07:46.460 --> 00:07:49.890
basolateral side, then we're
going to have a low sodium

00:07:49.890 --> 00:07:51.140
concentration here.

00:07:54.550 --> 00:07:56.925
The more we pump out, the lower
this is, and eventually

00:07:56.925 --> 00:07:58.490
it's going to be lower
than the sodium

00:07:58.490 --> 00:08:00.130
concentration in the lumen.

00:08:00.130 --> 00:08:03.150
So the sodium concentration
gradient, if there was no

00:08:03.150 --> 00:08:06.950
membrane here, sodium would want
to go across this to kind

00:08:06.950 --> 00:08:09.600
of make up for all of the
lost sodiums over here.

00:08:09.600 --> 00:08:13.190
Sodium would want to cross that
if there was no barrier.

00:08:13.190 --> 00:08:15.990
These cells here take advantage
of sodium wanting to

00:08:15.990 --> 00:08:18.430
move down its concentration
gradient, which is happening

00:08:18.430 --> 00:08:20.990
because of this active transport
over here, but it

00:08:20.990 --> 00:08:23.930
uses that energy of sodium going
down its concentration

00:08:23.930 --> 00:08:30.560
gradient to actually also
transport, in this case, maybe

00:08:30.560 --> 00:08:32.140
some glucose.

00:08:32.140 --> 00:08:35.059
So if you had to visualize it,
you could imagine a protein

00:08:35.059 --> 00:08:37.160
that's on this apical
membrane right here.

00:08:41.900 --> 00:08:43.250
Maybe it looks something
like this.

00:08:43.250 --> 00:08:45.780
This is to get some type
of visualization.

00:08:45.780 --> 00:08:50.090
Maybe you have more sodium on
this side than you have on

00:08:50.090 --> 00:08:53.350
this side, so sodium is more
likely to bond here.

00:08:53.350 --> 00:08:57.130
Maybe glucose will bond here.

00:08:57.130 --> 00:08:59.950
This is just a simplification,
but when they bond, this

00:08:59.950 --> 00:09:05.220
protein is going to change its
shape to look something more

00:09:05.220 --> 00:09:10.200
like this when they bond, and
now the sodium is going to be

00:09:10.200 --> 00:09:12.620
here and the glucose is
going to be here.

00:09:12.620 --> 00:09:15.685
We're essentially on the inside
of the cell now, and in

00:09:15.685 --> 00:09:18.190
this conformation, they don't
want to bond as much to the

00:09:18.190 --> 00:09:20.990
amino acids or whatever else
is in the protein, and then

00:09:20.990 --> 00:09:22.020
they get released.

00:09:22.020 --> 00:09:24.360
And when they get released, then
the protein will change

00:09:24.360 --> 00:09:27.190
its shape back to this right
here and we can do this cycle

00:09:27.190 --> 00:09:27.970
over again.

00:09:27.970 --> 00:09:31.940
But this is all stipulated on
the idea that there's more

00:09:31.940 --> 00:09:35.250
sodium over here to bump into
this point to make this

00:09:35.250 --> 00:09:36.190
reaction happen.

00:09:36.190 --> 00:09:38.260
So sodium's going to go down in
its concentration gradient.

00:09:38.260 --> 00:09:41.670
It's taking glucose
for the ride.

00:09:41.670 --> 00:09:44.020
And so essentially glucose
concentration will go up high

00:09:44.020 --> 00:09:47.500
here, and then if we make this
porous to glucose so glucose

00:09:47.500 --> 00:09:50.310
can go through, then glucose
will eventually, if this gets

00:09:50.310 --> 00:09:52.250
high enough, it'll just go
down its concentration

00:09:52.250 --> 00:09:55.000
gradient eventually
into the blood.

00:09:55.000 --> 00:09:58.520
And this same exact process is
happening, maybe not exactly

00:09:58.520 --> 00:10:01.240
with glucose, but throughout
the entire nephron.

00:10:01.240 --> 00:10:04.390
If we go to the loop of Henle,
if we go to the ascending part

00:10:04.390 --> 00:10:07.180
right here, where we're trying
to get the salts out of the

00:10:07.180 --> 00:10:08.875
picture, same idea.

00:10:12.480 --> 00:10:15.660
So let's say that that right
there is the lumen.

00:10:15.660 --> 00:10:22.510
This is a cell that makes up
the wall of the lumen.

00:10:22.510 --> 00:10:25.500
We're in the loop of Henle
now and you have a

00:10:25.500 --> 00:10:28.330
sodium-potassium
pump out here.

00:10:28.330 --> 00:10:31.230
You have sodium being
pumped out.

00:10:31.230 --> 00:10:34.120
You have potassium gets pumped
in, but actually, potassium

00:10:34.120 --> 00:10:36.900
channels are leaky, so potassium
can often make its

00:10:36.900 --> 00:10:38.560
way back out in either
direction.

00:10:38.560 --> 00:10:39.840
So what's happening to

00:10:39.840 --> 00:10:42.390
potassium isn't that important.

00:10:42.390 --> 00:10:44.730
But so sodium concentration
becomes low here.

00:10:44.730 --> 00:10:51.520
So what we have are symporters
over here, just like we had

00:10:51.520 --> 00:10:54.210
with glucose, but in this case,
sodium wants to enter

00:10:54.210 --> 00:10:57.240
just as the case with glucose,
but here we're trying to

00:10:57.240 --> 00:10:59.950
transport chlorine and
potassium ions.

00:10:59.950 --> 00:11:01.680
So that's what we're
going to join.

00:11:01.680 --> 00:11:03.520
That's what's going to take
advantage of sodium's

00:11:03.520 --> 00:11:04.790
concentration gradient.

00:11:04.790 --> 00:11:08.240
We're going to have potassium
and we're going to have

00:11:08.240 --> 00:11:09.670
chlorine ions.

00:11:09.670 --> 00:11:11.930
And actually, this symporter
right here, it's called the

00:11:11.930 --> 00:11:16.160
sodium-potassium-chlorine
cotransporter, and it's

00:11:16.160 --> 00:11:19.020
actually the second variation
that you actually get in the

00:11:19.020 --> 00:11:20.250
ascending loop of Henle.

00:11:20.250 --> 00:11:22.380
So eventually, you're going to
end up with a lot of chlorine

00:11:22.380 --> 00:11:25.270
here-- actually, potassium from
both directions-- but as

00:11:25.270 --> 00:11:27.410
long as this is porous
to chlorine, if this

00:11:27.410 --> 00:11:29.300
concentration gets high enough,
the chlorine is going

00:11:29.300 --> 00:11:32.590
to make its way out and help
make the medulla that much

00:11:32.590 --> 00:11:35.460
saltier along with the sodium.

00:11:35.460 --> 00:11:38.240
Same thing in the distal
convoluted tubule.

00:11:38.240 --> 00:11:39.440
There, calcium.

00:11:39.440 --> 00:11:40.750
It's a little bit different.

00:11:40.750 --> 00:11:46.320
So if we're in the distal
convoluted tubule, these kind

00:11:46.320 --> 00:11:48.690
of villi, these things that
stick out-- this is only in

00:11:48.690 --> 00:11:53.590
the proximal convoluted tubule,
those brush borders.

00:11:53.590 --> 00:11:56.250
But over there-- and just so
you know, this idea where

00:11:56.250 --> 00:11:58.910
we're using a concentration
gradient that's driven by some

00:11:58.910 --> 00:12:02.120
type of active transport to
transport other things, this

00:12:02.120 --> 00:12:04.220
is called secondary
active transport.

00:12:11.280 --> 00:12:12.190
That's nice to know.

00:12:12.190 --> 00:12:15.870
And then just finishing up at
the distal convoluted tubule.

00:12:15.870 --> 00:12:16.560
So this was the lumen.

00:12:16.560 --> 00:12:20.130
Let's say that this is the lumen
right here, so we have

00:12:20.130 --> 00:12:21.860
cells on either side of that.

00:12:21.860 --> 00:12:23.340
I think you get the
general idea.

00:12:23.340 --> 00:12:25.330
The distal's a little bit
different so let's say this is

00:12:25.330 --> 00:12:28.570
a cell, and let's say that
this is a peritubular

00:12:28.570 --> 00:12:29.400
capillary right here.

00:12:29.400 --> 00:12:31.430
This is our blood.

00:12:31.430 --> 00:12:34.070
What we have here is
once again, we're

00:12:34.070 --> 00:12:38.400
pumping sodium out.

00:12:38.400 --> 00:12:38.920
Sodium-potassium pumps.

00:12:38.920 --> 00:12:41.860
I have a whole video on that,
and that pumps potassium in,

00:12:41.860 --> 00:12:46.880
so you end up with a lot
of sodiums over here.

00:12:46.880 --> 00:12:49.650
The apical membrane that
faces the lumen,

00:12:49.650 --> 00:12:51.880
it's porous to calcium.

00:12:51.880 --> 00:12:53.340
Whatever the concentration
of calcium here,

00:12:53.340 --> 00:12:54.590
it's going to be here.

00:12:54.590 --> 00:12:56.910
So maybe you have calcium.

00:12:56.910 --> 00:13:01.040
These are calcium ions just
like that floating around.

00:13:01.040 --> 00:13:04.020
And right here, what you
have is an antiporter.

00:13:04.020 --> 00:13:06.640
So our concentration in the
blood of sodium is going to be

00:13:06.640 --> 00:13:09.150
higher because we keep
pumping it out.

00:13:09.150 --> 00:13:12.390
And so sodium, if you let it
go down its concentration

00:13:12.390 --> 00:13:14.070
gradient, it would go back in.

00:13:14.070 --> 00:13:18.490
And so maybe right here you have
some sodium going down,

00:13:18.490 --> 00:13:21.830
its concentration gradient going
back in, and then when

00:13:21.830 --> 00:13:24.120
that goes in, that you can
almost imagine it's some type

00:13:24.120 --> 00:13:28.540
of a rotating door, it makes
the calcium go out.

00:13:28.540 --> 00:13:30.760
You can try to visualize it
yourself how a protein would

00:13:30.760 --> 00:13:31.250
actually do that.

00:13:31.250 --> 00:13:32.700
I kind of imagine a
revolving door.

00:13:32.700 --> 00:13:34.400
The sodium makes the
door revolve.

00:13:34.400 --> 00:13:35.960
The calcium is at the other
part of the door and

00:13:35.960 --> 00:13:37.330
it gets spit out.

00:13:37.330 --> 00:13:39.110
So this is called an antiporter
because they're

00:13:39.110 --> 00:13:43.850
going in different directions,
but once again, it's secondary

00:13:43.850 --> 00:13:46.400
active transport, because the
only way that this could work

00:13:46.400 --> 00:13:50.360
is if we have active transport
using ATP of the sodium out of

00:13:50.360 --> 00:13:53.660
the basolateral membrane in
every one of these cases.

00:13:53.660 --> 00:13:55.590
Anyway, hopefully, you
found that useful.

00:13:55.590 --> 00:13:58.370
It's more detailed than you
normally get on how the

00:13:58.370 --> 00:14:02.990
nephron is actually pumping
things out of the lumen into

00:14:02.990 --> 00:14:05.940
the peritubular capillaries, but
for me, it made things a

00:14:05.940 --> 00:14:07.020
lot more concrete.

00:14:07.020 --> 00:14:09.950
It helps me really kind of
internalize what the

00:14:09.950 --> 00:14:12.200
nephron is up to.


The kidney and nephron

WEBVTT
Kind: captions
Language: en

00:00:00.340 --> 00:00:02.190
What I want to do in this video
is talk a little bit

00:00:02.190 --> 00:00:05.500
about the kidney-- and this is
a big picture of a kidney--

00:00:05.500 --> 00:00:08.200
and to talk about how it
operates at its-- I guess you

00:00:08.200 --> 00:00:10.500
could call it its smallest
functional level and that's

00:00:10.500 --> 00:00:11.420
the nephron.

00:00:11.420 --> 00:00:16.700
So we're going to talk about
the kidney and the nephron.

00:00:16.700 --> 00:00:18.780
And I think you might already
know the kidney.

00:00:18.780 --> 00:00:19.680
We have two of them.

00:00:19.680 --> 00:00:23.270
They're the organ that, I guess,
is most famous for

00:00:23.270 --> 00:00:27.860
producing or allowing
us to excrete waste.

00:00:27.860 --> 00:00:32.229
But part of that process, it
also helps us maintain our

00:00:32.229 --> 00:00:36.410
water, the correct level, and
actually the amount of salts

00:00:36.410 --> 00:00:39.010
or electrolytes we have and our
blood pressure, but I'll

00:00:39.010 --> 00:00:40.870
just say maintain water.

00:00:40.870 --> 00:00:42.960
And it also produces hormones
and things, and I'm not going

00:00:42.960 --> 00:00:45.190
to go into a lot of detail
on that right now.

00:00:45.190 --> 00:00:48.580
I really just want to focus on
these first two to kind of

00:00:48.580 --> 00:00:52.210
just understand the overview
function of the kidney.

00:00:52.210 --> 00:00:54.130
And most of us have
two of these.

00:00:54.130 --> 00:00:57.480
They're kind of closer to our
back on either sides of our

00:00:57.480 --> 00:00:59.210
spine behind our liver.

00:00:59.210 --> 00:01:02.470
And this is a zoomed-in
version of it.

00:01:02.470 --> 00:01:04.239
If you're watching this in full
screen, it's not going to

00:01:04.239 --> 00:01:07.150
be as big as this picture is,
but we've sliced it so we can

00:01:07.150 --> 00:01:10.980
see what's going on
inside the kidney.

00:01:10.980 --> 00:01:15.130
Just to understand the different
parts here, just

00:01:15.130 --> 00:01:17.660
because it will actually be
significant when we start

00:01:17.660 --> 00:01:20.520
talking about the functional
units or the nephron within

00:01:20.520 --> 00:01:24.930
the kidney, this area right here
from here to here, this

00:01:24.930 --> 00:01:28.910
is called the renal cortex.

00:01:28.910 --> 00:01:31.550
Whenever we talk about something
with the kidney, if

00:01:31.550 --> 00:01:34.110
you see a renal anything, that's
actually referring to

00:01:34.110 --> 00:01:34.580
the kidney.

00:01:34.580 --> 00:01:36.800
So this right here is
a renal cortex, that

00:01:36.800 --> 00:01:38.230
outer part right there.

00:01:38.230 --> 00:01:44.380
And then this area right here,
this is the renal medulla.

00:01:44.380 --> 00:01:46.480
And medulla comes from middle.

00:01:46.480 --> 00:01:49.050
So you can almost view it as
the middle of the kidney.

00:01:52.400 --> 00:01:55.680
Besides just understanding these
words, we're going to

00:01:55.680 --> 00:01:58.350
see that they actually play a
very important role in this

00:01:58.350 --> 00:02:01.720
actual filtration or this
excretion of waste and this

00:02:01.720 --> 00:02:05.730
ability to not dump too much
water or excrete too much

00:02:05.730 --> 00:02:09.020
water when we're trying to
filter out our blood.

00:02:09.020 --> 00:02:11.720
So I've said before, and you
might have heard it already

00:02:11.720 --> 00:02:14.330
from other lectures or from
other teachers, that the

00:02:14.330 --> 00:02:16.490
functional unit of the kidney
is the nephron.

00:02:22.510 --> 00:02:25.040
And the reason why it's called
a functional unit-- I'll put

00:02:25.040 --> 00:02:28.290
it in quotes-- is because that's
the level at which

00:02:28.290 --> 00:02:30.250
these two things
are happening.

00:02:30.250 --> 00:02:32.980
The two major functions of the
kidney: the waste excretion

00:02:32.980 --> 00:02:36.580
and the maintenance
of the water level

00:02:36.580 --> 00:02:37.730
in our blood system.

00:02:37.730 --> 00:02:41.730
So just to get an idea of how a
nephron fits in within this

00:02:41.730 --> 00:02:45.840
picture of a kidney-- I got this
picture from Wikipedia.

00:02:45.840 --> 00:02:48.420
The artist tried to draw a
couple of nephrons over here.

00:02:48.420 --> 00:02:50.630
So a nephron will look something
like this, and it

00:02:50.630 --> 00:02:53.680
dips down into the medulla, and
then it goes back into the

00:02:53.680 --> 00:02:56.640
cortex, and then it dumps into
collecting ducts, and

00:02:56.640 --> 00:02:59.620
essentially the fluid will end
up in the ureters right here

00:02:59.620 --> 00:03:02.960
and end up in our urinary
bladder that we can later

00:03:02.960 --> 00:03:05.880
excrete when we find
a suitable time.

00:03:05.880 --> 00:03:07.770
But that's about-- I guess
you can imagine

00:03:07.770 --> 00:03:10.780
the length of a nephron.

00:03:10.780 --> 00:03:13.030
This is where it starts and
then it dips down again.

00:03:13.030 --> 00:03:14.840
So multiple nephrons are going
to keep doing that, but

00:03:14.840 --> 00:03:15.840
they're super thin.

00:03:15.840 --> 00:03:18.140
These tubes or these tubules,
maybe I should

00:03:18.140 --> 00:03:20.800
say, are super thin.

00:03:20.800 --> 00:03:26.190
Your average kidney will contain
on the order of one

00:03:26.190 --> 00:03:27.440
million nephrons.

00:03:31.320 --> 00:03:34.470
You can't really say, my
nephrons are microscopic.

00:03:34.470 --> 00:03:39.390
They kind of have a-- at least
their length when they dip

00:03:39.390 --> 00:03:41.880
down, you can say, I can
see that distance.

00:03:41.880 --> 00:03:45.510
You can still jam a lot of them
inside of one kidney.

00:03:45.510 --> 00:03:49.580
With that said, let's actually
figure out how a nephron

00:03:49.580 --> 00:03:52.880
filters the blood and actually
makes sure that not too much

00:03:52.880 --> 00:03:56.530
water or not too much of the
good stuff in our blood ends

00:03:56.530 --> 00:03:58.330
up the urine.

00:03:58.330 --> 00:04:04.070
So let me draw here a nephron.

00:04:04.070 --> 00:04:07.200
So I'm going to start
like this.

00:04:07.200 --> 00:04:08.850
We'll start with
the blood flow.

00:04:08.850 --> 00:04:13.480
So the blood's going to come
in an arteriole -- that's an

00:04:13.480 --> 00:04:15.780
arterial capillary,
you could say.

00:04:15.780 --> 00:04:17.589
So it's going to come
in like that.

00:04:17.589 --> 00:04:21.820
This is actually called
the afferent arteriole.

00:04:21.820 --> 00:04:23.230
You don't have to know
the names, but you

00:04:23.230 --> 00:04:24.480
might see that sometime.

00:04:26.670 --> 00:04:28.170
Blood is coming in.

00:04:28.170 --> 00:04:32.060
Then it goes into this
big windy place.

00:04:32.060 --> 00:04:34.810
It really winds around
like that.

00:04:34.810 --> 00:04:36.060
This is called the glomerulus.

00:04:43.490 --> 00:04:45.870
And then it leaves via the
efferent arteriole.

00:04:57.100 --> 00:04:58.610
Efferent just means away
from the center.

00:04:58.610 --> 00:05:02.750
Afferent towards, efferent
away from the center.

00:05:02.750 --> 00:05:04.340
And I'll talk about it more
in the future, but it's

00:05:04.340 --> 00:05:05.830
interesting that we're
still dealing with an

00:05:05.830 --> 00:05:07.040
artery at this point.

00:05:07.040 --> 00:05:08.770
It's still oxygenated blood.

00:05:08.770 --> 00:05:12.260
Normally, when we leave a
capillary system like the

00:05:12.260 --> 00:05:14.950
glomerulus right there, we're
normally dealing with the

00:05:14.950 --> 00:05:18.650
venous system, but here we're
still an arterial system.

00:05:18.650 --> 00:05:21.280
And it's probably because
arterial systems have higher

00:05:21.280 --> 00:05:22.760
blood pressure, and what we
need to do is we need to

00:05:22.760 --> 00:05:28.730
squeeze fluid and stuff that's
dissolved in the fluid out of

00:05:28.730 --> 00:05:30.970
the blood and in the glomerulus
right here.

00:05:30.970 --> 00:05:35.420
So this glomerulus is very
porous and it's surrounded by

00:05:35.420 --> 00:05:37.460
other cells.

00:05:37.460 --> 00:05:38.710
This is kind of a
cross-section.

00:05:44.470 --> 00:05:49.200
It's surrounded like that by
this structure, and these are

00:05:49.200 --> 00:05:53.350
cells here so you can imagine
these are all cells over here.

00:05:53.350 --> 00:05:56.980
And, of course, the actual
capillaries have cells that

00:05:56.980 --> 00:05:58.960
line them so there
are cells here.

00:05:58.960 --> 00:06:01.140
So when I draw these lines,
these lines are actually made

00:06:01.140 --> 00:06:03.420
up of little cells.

00:06:03.420 --> 00:06:04.540
What happens is the
blood comes in

00:06:04.540 --> 00:06:05.900
at really high pressure.

00:06:05.900 --> 00:06:06.960
This is very porous.

00:06:06.960 --> 00:06:10.410
These cells out here, they're
called podocytes.

00:06:10.410 --> 00:06:11.880
They're a little bit more
selective in what gets

00:06:11.880 --> 00:06:14.630
filtered out, and essentially
about a fifth of the fluid

00:06:14.630 --> 00:06:20.640
that's coming in ends up going
into this space right here

00:06:20.640 --> 00:06:22.550
that's called the
Bowman's space.

00:06:22.550 --> 00:06:23.690
Well, actually, this whole
thing is called

00:06:23.690 --> 00:06:24.940
the Bowman's capsule.

00:06:28.270 --> 00:06:30.650
It's a sphere with an opening in
here that the capillary can

00:06:30.650 --> 00:06:34.050
kind of wind around in, and the
space right here, this is

00:06:34.050 --> 00:06:36.890
the Bowman's space.

00:06:36.890 --> 00:06:41.270
It's the space inside the
Bowman's capsule, and the

00:06:41.270 --> 00:06:42.150
whole thing has cells.

00:06:42.150 --> 00:06:44.200
All these structures are
obviously made-- or maybe not

00:06:44.200 --> 00:06:46.830
so obviously-- they're
made up of cells.

00:06:46.830 --> 00:06:48.730
And so we end up having
filtrate in it.

00:06:48.730 --> 00:06:53.190
Filtrate is just the stuff
that gets squeezed out.

00:06:53.190 --> 00:06:56.380
We can't call it urine just yet
because there's a lot of

00:06:56.380 --> 00:07:01.720
steps that have to occur for
it to earn the name urine.

00:07:01.720 --> 00:07:04.400
So it's only filtrate right now,
and essentially what get

00:07:04.400 --> 00:07:07.220
squeezed out, I said it's about
a fifth of the fluid,

00:07:07.220 --> 00:07:10.450
and things that are easily
dissolved in fluid, so small

00:07:10.450 --> 00:07:16.430
ions, sodium, maybe some small
molecules like glucose, maybe

00:07:16.430 --> 00:07:19.570
some amino acids.

00:07:19.570 --> 00:07:21.086
There are tons of stuff
in here, but this is

00:07:21.086 --> 00:07:22.080
just to give an idea.

00:07:22.080 --> 00:07:25.370
The things that do not get
filtered are things like red

00:07:25.370 --> 00:07:31.340
blood cells or larger molecules,
larger proteins.

00:07:31.340 --> 00:07:32.510
They will not get filtered.

00:07:32.510 --> 00:07:36.700
It's mainly the micromolecules
that'll get filtered, that'll

00:07:36.700 --> 00:07:40.910
be part of this filtrate
that shows up here

00:07:40.910 --> 00:07:42.390
in the Bowman space.

00:07:42.390 --> 00:07:45.110
Now, the rest of what the
nephron does, the Bowman's

00:07:45.110 --> 00:07:46.960
capsule is kind of the beginning
of the nephron, and

00:07:46.960 --> 00:07:51.280
just to get an idea of our big
picture of our kidney, let's

00:07:51.280 --> 00:07:54.760
say we're near an arteriole.

00:07:54.760 --> 00:07:56.980
This is a Bowman's capsule
right here.

00:07:56.980 --> 00:07:59.075
It looks something like that,
and the whole nephron is going

00:07:59.075 --> 00:08:00.580
to be convoluted like this.

00:08:00.580 --> 00:08:03.150
It's going to dip down into
the medulla, and then come

00:08:03.150 --> 00:08:06.220
back, and then it's going to
eventually dump into a

00:08:06.220 --> 00:08:07.980
collecting duct, and I'll
talk more about that.

00:08:07.980 --> 00:08:12.250
So what I've drawn just here,
this is a zoomed-in version of

00:08:12.250 --> 00:08:14.660
that part right there.

00:08:14.660 --> 00:08:16.250
Now what I want to do is zoom
out a little bit because I'm

00:08:16.250 --> 00:08:17.550
going to run out of space.

00:08:17.550 --> 00:08:19.290
So let me zoom out.

00:08:19.290 --> 00:08:23.220
So we had our arteriole go in.

00:08:23.220 --> 00:08:26.520
It gets all bunched in the
glomerulus, and then most of

00:08:26.520 --> 00:08:30.160
the blood leaves, but
one-fifth of it gets

00:08:30.160 --> 00:08:33.390
essentially filtered in to
the Bowman's capsule.

00:08:33.390 --> 00:08:34.780
That's the Bowman's capsule
right there.

00:08:34.780 --> 00:08:36.450
I've just zoomed out
a little bit.

00:08:36.450 --> 00:08:39.530
So we have our filtrate here.

00:08:39.530 --> 00:08:41.080
Maybe I'll make it a
little bit yellow.

00:08:44.440 --> 00:08:46.800
The filtrate that just comes out
at this point, sometimes

00:08:46.800 --> 00:08:49.270
it's called the glomerular
filtrate because it's been

00:08:49.270 --> 00:08:52.170
filtered by the glomerulus, but
it's also been filtered by

00:08:52.170 --> 00:08:55.060
those podocyte cells
on the inside of

00:08:55.060 --> 00:08:56.470
the Bowman's capsule.

00:08:56.470 --> 00:08:59.120
But now it's ready to go
to the proximal tubule.

00:09:03.080 --> 00:09:06.530
Let me draw something
like this.

00:09:06.530 --> 00:09:08.300
And obviously, this is not
exactly what it looks like,

00:09:08.300 --> 00:09:09.580
but it gives you the sense.

00:09:09.580 --> 00:09:17.470
This right here, this is
the proximal tubule.

00:09:17.470 --> 00:09:20.560
And it sounds like a very fancy
word, but proximal just

00:09:20.560 --> 00:09:23.590
means near and tubule, you can
imagine, is just a small tube.

00:09:23.590 --> 00:09:25.740
So it's a small tube that's
near the beginning.

00:09:25.740 --> 00:09:27.880
That's why it's called
a proximal tubule.

00:09:27.880 --> 00:09:29.700
And it has two parts.

00:09:29.700 --> 00:09:31.245
The whole thing is
often called a

00:09:31.245 --> 00:09:32.870
proximal convoluted tubule.

00:09:35.870 --> 00:09:37.390
That's because it's
all convoluted.

00:09:37.390 --> 00:09:38.830
The way I've drawn
it is all curvy.

00:09:38.830 --> 00:09:40.750
And I just drew it curvy
in two dimensions.

00:09:40.750 --> 00:09:43.170
It's actually curvy in
three dimensions.

00:09:43.170 --> 00:09:45.470
But the reality is there's a
curvy part and then there's a

00:09:45.470 --> 00:09:48.220
straight part near the end
of the proximal tubule.

00:09:48.220 --> 00:09:50.570
So we'll call this whole thing
the proximal tubule.

00:09:50.570 --> 00:09:52.060
This is the convoluted part.

00:09:52.060 --> 00:09:53.670
That's the straight
part, but we don't

00:09:53.670 --> 00:09:55.340
have to get too picky.

00:09:55.340 --> 00:09:59.040
But the whole point of this part
of the nephron-- and just

00:09:59.040 --> 00:10:02.810
to remember where we are, we're
now at this point of the

00:10:02.810 --> 00:10:05.890
nephron right there-- the
whole point is to start

00:10:05.890 --> 00:10:09.700
reabsorbing some of the stuff
that is in the filtrate that

00:10:09.700 --> 00:10:10.670
we don't want to lose.

00:10:10.670 --> 00:10:11.880
We don't want to lose glucose.

00:10:11.880 --> 00:10:13.900
That's hard-earned stuff
that we ate that

00:10:13.900 --> 00:10:15.090
was good for energy.

00:10:15.090 --> 00:10:18.790
We don't want to lose
necessarily as much sodium.

00:10:18.790 --> 00:10:24.040
We've seen in multiple videos
that that's a useful ion to

00:10:24.040 --> 00:10:24.480
have around.

00:10:24.480 --> 00:10:26.490
We don't want to lose
amino acids.

00:10:26.490 --> 00:10:30.490
Those are useful for building up
proteins and other things.

00:10:30.490 --> 00:10:32.320
So these are things we don't
want to lose so we start

00:10:32.320 --> 00:10:33.670
absorbing them back.

00:10:33.670 --> 00:10:35.840
I'll do a whole video on exactly
how that happens, but

00:10:35.840 --> 00:10:37.480
it's done actively.

00:10:37.480 --> 00:10:40.575
Since we're using ATP, and just
as a bit of a summary,

00:10:40.575 --> 00:10:43.900
you're using ATP to actually
pump out the sodium and then

00:10:43.900 --> 00:10:45.660
that actually helps bring
in the other things.

00:10:45.660 --> 00:10:48.160
That's just kind of a tidbit
on what's happening.

00:10:48.160 --> 00:10:52.190
So we're reabsorbing, so just
imagine what's happening.

00:10:52.190 --> 00:10:56.370
You have cells lining the
proximal tubule right now.

00:10:56.370 --> 00:10:58.310
And actually, they have little
things that jut out.

00:10:58.310 --> 00:10:59.790
I'll do a whole video on that
because it's actually

00:10:59.790 --> 00:11:00.630
interesting.

00:11:00.630 --> 00:11:01.910
So you have cells out here.

00:11:01.910 --> 00:11:04.660
On the other side of the cells,
you have an arterial

00:11:04.660 --> 00:11:08.110
system, or a capillary system,
I should say, actually.

00:11:08.110 --> 00:11:12.080
So let's say you have a
capillary system here that is

00:11:12.080 --> 00:11:16.580
very close to the cells lining
the proximal tubule, and so

00:11:16.580 --> 00:11:19.140
this stuff actually gets
actively pumped, especially

00:11:19.140 --> 00:11:23.000
the sodium, but all of it, using
energy, gets pumped back

00:11:23.000 --> 00:11:24.890
into the blood selectively,
and maybe a

00:11:24.890 --> 00:11:25.870
little bit of our water.

00:11:25.870 --> 00:11:32.480
So we're pumping back some
sodium, some glucose, and

00:11:32.480 --> 00:11:34.710
we'll start pumping a little
bit of the water back in

00:11:34.710 --> 00:11:36.540
because we don't want to
lose all of that water.

00:11:36.540 --> 00:11:38.620
If all of the water that was
originally in the filtrate we

00:11:38.620 --> 00:11:41.560
were just leaving in our urine,
we'd be excreting

00:11:41.560 --> 00:11:44.240
gallons and gallons of water
every day, which we do not

00:11:44.240 --> 00:11:45.310
want to do.

00:11:45.310 --> 00:11:46.500
So that's the whole point.

00:11:46.500 --> 00:11:49.130
We're starting the absorption
process.

00:11:49.130 --> 00:11:51.400
And then we'll enter the loop
of Henle, and actually, this

00:11:51.400 --> 00:11:52.610
is, in my mind, the most

00:11:52.610 --> 00:11:55.370
interesting part of the nephron.

00:11:55.370 --> 00:11:59.930
So we're entering the loop of
Henle, and it dips down, and

00:11:59.930 --> 00:12:03.680
then comes back up.

00:12:03.680 --> 00:12:05.740
And so most of the length
of the nephron

00:12:05.740 --> 00:12:07.900
is the loop of Henle.

00:12:07.900 --> 00:12:10.916
And if I go back to this diagram
right here, if I'm

00:12:10.916 --> 00:12:13.270
talking about the loop of Henle,
I'm talking about this

00:12:13.270 --> 00:12:15.440
whole thing right there.

00:12:15.440 --> 00:12:17.450
And you can see something
interesting here.

00:12:17.450 --> 00:12:21.050
It crosses the border between
the cortex, this light brown

00:12:21.050 --> 00:12:24.820
part, and the renal medulla,
this kind of reddish or orange

00:12:24.820 --> 00:12:27.170
part right there, and it does
that for a very good reason.

00:12:27.170 --> 00:12:28.000
I'm going to draw it here.

00:12:28.000 --> 00:12:32.710
So let's say this is the
dividing line right here.

00:12:32.710 --> 00:12:35.460
This right here was
the cortex.

00:12:35.460 --> 00:12:39.550
This right here is
the medulla.

00:12:39.550 --> 00:12:42.060
So the whole point-- well,
there's two points

00:12:42.060 --> 00:12:43.590
of the loop of Henle.

00:12:48.570 --> 00:12:57.830
One point is to make the renal
medulla salty, and it does

00:12:57.830 --> 00:13:00.502
this by actively pumping
out salts.

00:13:00.502 --> 00:13:03.090
So it actively pumps out salts,
and it does that in the

00:13:03.090 --> 00:13:06.140
ascending part of the
loop of Henle.

00:13:06.140 --> 00:13:12.390
So it actively pumps out salts:
sodium, potassium,

00:13:12.390 --> 00:13:14.440
chloride, or chlorine,
I should say.

00:13:14.440 --> 00:13:17.500
Chlorine ions.

00:13:17.500 --> 00:13:21.990
It actively pumps out these
salts right here to make the

00:13:21.990 --> 00:13:27.670
entire medulla salty, or if we
think about it in terms of

00:13:27.670 --> 00:13:29.990
kind of osmosis, make
it hypertonic.

00:13:29.990 --> 00:13:33.320
You have more solute out here
than you have in the filtrate

00:13:33.320 --> 00:13:36.010
that's going through
the tubules.

00:13:36.010 --> 00:13:37.240
And it uses ATP to do this.

00:13:37.240 --> 00:13:39.910
All of this stuff requires ATP
to actively pump against a

00:13:39.910 --> 00:13:41.570
concentration gradient.

00:13:41.570 --> 00:13:46.110
So this is salty and it's
salty for a reason.

00:13:46.110 --> 00:13:50.820
It's not just to take back these
salts from the filtrate,

00:13:50.820 --> 00:13:53.230
although that's part of the
reason, but by making this

00:13:53.230 --> 00:13:57.620
salty, the ascending part is
only permeable to these salts

00:13:57.620 --> 00:13:59.270
and these ions.

00:13:59.270 --> 00:14:00.830
It's not permeable to water.

00:14:06.110 --> 00:14:09.050
The descending part of the
loop of Henle is only

00:14:09.050 --> 00:14:10.300
permeable to water.

00:14:13.390 --> 00:14:14.380
So what's going to happen?

00:14:14.380 --> 00:14:17.430
If this is all salty because the
ascending part is actively

00:14:17.430 --> 00:14:21.260
pumping out salt, what's going
to happen to water as it goes

00:14:21.260 --> 00:14:23.110
down the descending loop?

00:14:23.110 --> 00:14:24.870
Well, it's hypertonic
out here.

00:14:24.870 --> 00:14:28.830
Water will naturally want to go
and kind of try to make the

00:14:28.830 --> 00:14:30.540
concentrations balance out.

00:14:30.540 --> 00:14:31.510
I've done a whole
video on that.

00:14:31.510 --> 00:14:33.680
It doesn't happen by magic.

00:14:33.680 --> 00:14:36.710
And so the water will-- because
this is hypertonic,

00:14:36.710 --> 00:14:39.620
it's more salty, and this is
only permeable to water, the

00:14:39.620 --> 00:14:42.930
water will leave the membrane on
the descending part of the

00:14:42.930 --> 00:14:44.560
loop of Henle right now.

00:14:44.560 --> 00:14:48.710
And this is a major part
of water reabsorption.

00:14:48.710 --> 00:14:52.870
I've thought a lot about why
don't we use ATP somehow to

00:14:52.870 --> 00:14:54.360
actively pump water?

00:14:54.360 --> 00:14:55.850
And the answer there
is, there's no

00:14:55.850 --> 00:14:56.650
easy way to do that.

00:14:56.650 --> 00:15:01.130
Biological systems are good at
using ATP to pump out ions,

00:15:01.130 --> 00:15:03.360
but it can't actively
pump out water.

00:15:03.360 --> 00:15:06.360
Water's kind of a hard thing
for proteins to operate on.

00:15:06.360 --> 00:15:09.580
So the solution is to make it
salty out here by pumping out

00:15:09.580 --> 00:15:12.540
ions and then water, if you
make this porous only to

00:15:12.540 --> 00:15:14.750
water, water will naturally
flow out.

00:15:14.750 --> 00:15:18.170
So this is a major mechanism of
gaining back a lot of the

00:15:18.170 --> 00:15:20.820
water that gets filtered
out up here.

00:15:20.820 --> 00:15:23.390
And the reason why this is so
long is to give time for this

00:15:23.390 --> 00:15:27.560
water to secrete out, and that's
why it dips nice and

00:15:27.560 --> 00:15:31.490
pretty far down into
this salty portion.

00:15:31.490 --> 00:15:34.710
So then we'll leave the loop of
Henle and then we're almost

00:15:34.710 --> 00:15:36.110
done with the nephron.

00:15:36.110 --> 00:15:38.790
Then we're in another convoluted
tubule, and you

00:15:38.790 --> 00:15:41.710
might even guess the name of
this convoluted tubule.

00:15:41.710 --> 00:15:44.860
If this was the proximal one,
this is the distal one.

00:15:44.860 --> 00:15:47.070
And actually, just to make my
drawing correct, it actually

00:15:47.070 --> 00:15:51.560
passes very close to the
Bowman's capsule, so let me do

00:15:51.560 --> 00:15:52.810
it in a different color.

00:15:57.230 --> 00:16:01.920
The distal convoluted tubule
actually goes pretty close to

00:16:01.920 --> 00:16:03.970
the Bowman's capsule.

00:16:03.970 --> 00:16:06.000
And once again, I've made
it all convoluted in two

00:16:06.000 --> 00:16:07.740
dimensions, but it's actually
convoluted in three.

00:16:07.740 --> 00:16:09.840
And it's not that long, but I
just had to get over here and

00:16:09.840 --> 00:16:11.830
I wanted to get over that
point right there.

00:16:11.830 --> 00:16:12.830
It's called distal.

00:16:12.830 --> 00:16:14.510
Distal is further away.

00:16:14.510 --> 00:16:16.750
It's convoluted and
it's a tubule.

00:16:16.750 --> 00:16:24.450
So this right here is the distal
convoluted tubule, and

00:16:24.450 --> 00:16:27.690
here we have more reabsorption:
calcium, more

00:16:27.690 --> 00:16:28.820
sodium reabsorption.

00:16:28.820 --> 00:16:31.250
We're just reabsorbing more
things that we didn't want to

00:16:31.250 --> 00:16:32.600
lose in the first place.

00:16:32.600 --> 00:16:34.180
There's a lot of things we
could talk about what get

00:16:34.180 --> 00:16:36.330
reabsorbed, but this is
just the overview.

00:16:36.330 --> 00:16:39.870
And we're also reabsorbing a
little bit of more water.

00:16:39.870 --> 00:16:41.420
But then at the end
right here, our

00:16:41.420 --> 00:16:42.800
filtrate has been processed.

00:16:42.800 --> 00:16:44.290
A lot of the water's
been taken out.

00:16:44.290 --> 00:16:45.760
It's a lot more concentrated.

00:16:45.760 --> 00:16:47.700
We've reabsorbed a
lot of the salts,

00:16:47.700 --> 00:16:49.290
electrolytes that we want.

00:16:49.290 --> 00:16:52.100
We've reabsorbed the glucose and
a lot of the amino acids.

00:16:52.100 --> 00:16:53.770
Everything that we want,
we've taken back.

00:16:53.770 --> 00:16:55.630
We've reabsorbed.

00:16:55.630 --> 00:16:59.710
And so this is mainly waste
products and water that we

00:16:59.710 --> 00:17:01.670
don't need anymore and then
this gets dumped into

00:17:01.670 --> 00:17:02.920
collecting ducts.

00:17:05.140 --> 00:17:07.230
And you can kind of view this
as the trash chute of the

00:17:07.230 --> 00:17:12.384
kidney, where multiple
nephrons are going

00:17:12.384 --> 00:17:13.740
to dump into this.

00:17:13.740 --> 00:17:16.960
So that might be the distal
tubule of another nephron

00:17:16.960 --> 00:17:22.010
right here and this is a
collecting duct, which is just

00:17:22.010 --> 00:17:23.569
a tube that's collecting
all the

00:17:23.569 --> 00:17:27.040
byproducts of the nephrons.

00:17:27.040 --> 00:17:28.620
And the interesting thing is
that the collecting duct

00:17:28.620 --> 00:17:31.040
further goes into the
medulla again.

00:17:31.040 --> 00:17:34.210
It goes into the medulla again
to the salty part again.

00:17:34.210 --> 00:17:36.090
So if we're talking about the
collecting duct, maybe the

00:17:36.090 --> 00:17:40.400
collecting duct's coming back
into the medulla, collecting

00:17:40.400 --> 00:17:43.070
all of the filtrate from
the different nephrons.

00:17:43.070 --> 00:17:46.860
And because it goes back through
that super salty spot

00:17:46.860 --> 00:17:50.240
in the medulla, we actually
have four hormones called

00:17:50.240 --> 00:17:54.540
anti-diarrhetic hormone that
can dictate how porous this

00:17:54.540 --> 00:18:00.910
collecting tube is, and if it
makes it very porous, it

00:18:00.910 --> 00:18:04.430
allows more water to leave as we
go to the medulla, because

00:18:04.430 --> 00:18:06.110
this is very salty,
so the water will

00:18:06.110 --> 00:18:07.690
leave if this is porous.

00:18:07.690 --> 00:18:10.740
And when we do that, what that
does is it makes the

00:18:10.740 --> 00:18:13.100
filtrate-- and we can maybe
start calling it urine now--

00:18:13.100 --> 00:18:17.170
even more concentrated so we
lose even less water, and it

00:18:17.170 --> 00:18:19.490
keeps collecting, collecting,
collecting until we end up

00:18:19.490 --> 00:18:23.650
here, and it leaves the kidney
and goes via our ureters to

00:18:23.650 --> 00:18:25.030
the urinary bladder.

00:18:25.030 --> 00:18:27.200
So hopefully, you found
that helpful.

00:18:27.200 --> 00:18:29.650
I think the neatest thing here
is just how we actively

00:18:29.650 --> 00:18:33.150
reabsorb the water and how we--
well, actually, in my

00:18:33.150 --> 00:18:36.770
mind, that is the neatest part
in the loop of Henle.