Worked example: equivalent systems of equations

WEBVTT
Kind: captions
Language: en

00:00:00.285 --> 00:00:02.352
- [Voiceover] "Vivek and Camila's
teacher gave them a system

00:00:02.352 --> 00:00:04.185
"of linear equations to solve.

00:00:04.185 --> 00:00:06.118
"They each took a few steps that lead

00:00:06.118 --> 00:00:08.284
"to the systems shown in the table below."

00:00:08.284 --> 00:00:10.052
So we have the teacher's original system,

00:00:10.052 --> 00:00:12.450
what Vivek got after
doing some operations,

00:00:12.450 --> 00:00:14.552
what Camila got after
doing some operations.

00:00:14.552 --> 00:00:17.484
Which of them obtained a
system that is equivalent

00:00:17.484 --> 00:00:19.018
to the teacher's system?

00:00:19.018 --> 00:00:20.651
So the first question
we should ask ourselves

00:00:20.651 --> 00:00:24.151
is what does it mean to even
have an equivalent system?

00:00:24.151 --> 00:00:26.152
For the sake of this
question, or for our purposes,

00:00:26.152 --> 00:00:29.918
an equivalent system is a system
that has the same solution.

00:00:29.918 --> 00:00:32.418
So if there's some X-Y pair that satisfies

00:00:32.418 --> 00:00:34.585
the teacher's system that is the solution

00:00:34.585 --> 00:00:36.218
to the teacher's system.

00:00:36.218 --> 00:00:38.418
Well Vivek's system, we're
gonna call it equivalent

00:00:38.418 --> 00:00:41.011
if it has the same solution.

00:00:41.011 --> 00:00:45.118
Similarly, if Camila's
system has the same solution,

00:00:45.118 --> 00:00:48.851
then we're gonna call it
equivalent to the teacher's system.

00:00:48.851 --> 00:00:50.751
So let's make some comparisons here.

00:00:50.751 --> 00:00:52.451
So first let's look at Vivek.

00:00:52.451 --> 00:00:55.051
So his first equation
is actually unchanged

00:00:55.051 --> 00:00:56.917
from the teacher's equation,

00:00:56.917 --> 00:00:58.618
is unchanged from the teacher's equation,

00:00:58.618 --> 00:01:02.551
so any solution that meets
both of these equations

00:01:02.551 --> 00:01:05.018
is for sure gonna meet this top equation

00:01:05.018 --> 00:01:07.251
because it's literally the
same as the top equation

00:01:07.251 --> 00:01:08.984
of the teacher, so that works out.

00:01:08.984 --> 00:01:10.521
Also look at the second one.

00:01:12.931 --> 00:01:15.551
The second one is definitely a
different equation over here.

00:01:15.551 --> 00:01:17.551
We can check that it's
not just being multiplied

00:01:17.551 --> 00:01:19.977
by some number on both sides.

00:01:19.977 --> 00:01:22.618
To go from one to zero
if you were multiplying,

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you would have to multiply one times zero

00:01:25.251 --> 00:01:27.351
and then in order to
maintain the equality,

00:01:27.351 --> 00:01:28.918
you would have to do that on both sides.

00:01:28.918 --> 00:01:31.218
But zero times this left-hand
side would have been zero,

00:01:31.218 --> 00:01:33.085
you would have gotten zero equals zero,

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so he didn't just scale
both sides by some number,

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looks like he did another operation.

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He probably looks like
he's adding or subtracting

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something to both sides, so let's see how

00:01:43.252 --> 00:01:45.351
he could have gotten this right over here.

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So he took -4x

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plus 5y is equal to one.

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And it looks like from
that he was able to get

00:01:53.717 --> 00:01:57.118
- 3x plus 7y

00:01:57.118 --> 00:01:59.288
is equal to zero.

00:01:59.288 --> 00:02:02.251
So let's see what he had to do to do that.

00:02:02.251 --> 00:02:04.818
Let's see, he would have had to,

00:02:04.818 --> 00:02:07.217
to go from -4x to -3x,

00:02:07.217 --> 00:02:09.717
he would have had to add an X,

00:02:09.717 --> 00:02:11.384
so I could just write
an X right over there.

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To go from 5y to 7y,

00:02:12.851 --> 00:02:14.917
he would have had to add 2y.

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So on the left-hand side,
he would have to add

00:02:16.717 --> 00:02:18.284
X plus 2y.

00:02:18.284 --> 00:02:20.818
Notice we have an X plus
2y right over there.

00:02:20.818 --> 00:02:23.251
And on the right-hand side,
he would have had to add

00:02:23.251 --> 00:02:25.551
or subtract a one, or add a negative one.

00:02:25.551 --> 00:02:28.251
Notice we see a negative
one right over there.

00:02:28.251 --> 00:02:32.084
So what he essentially did is
he added the left-hand sides

00:02:32.084 --> 00:02:35.451
of these two equations to
get this new left-hand side

00:02:35.451 --> 00:02:38.184
right over here, and he
added the right-hand sides

00:02:38.184 --> 00:02:39.818
to get this new right-hand side.

00:02:39.818 --> 00:02:42.534
And that is a legitimate operation.

00:02:42.534 --> 00:02:44.384
This new equation that you got,

00:02:44.384 --> 00:02:48.452
this new linear equation,
it's going to represent

00:02:48.452 --> 00:02:51.285
a different line than
this one right over here,

00:02:51.285 --> 00:02:55.018
but the resulting system is
going to have the same solution.

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Why do we feel confident
that the resulting system

00:02:56.984 --> 00:02:59.019
is going to have the same solution?

00:02:59.019 --> 00:03:04.019
Well for an X-Y pair that
satisfies both of these equations,

00:03:04.218 --> 00:03:06.351
that's what a solution would be,

00:03:06.351 --> 00:03:09.452
for that X-Y pair, X plus 2y

00:03:09.452 --> 00:03:11.585
is equal to negative one.

00:03:11.585 --> 00:03:13.051
So for that solution,

00:03:13.051 --> 00:03:15.385
we're adding the same thing to both sides.

00:03:15.385 --> 00:03:17.784
We're saying: "Look,
I'm gonna add X plus 2y

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"to the left-hand side.

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"Well if I don't wanna
change the solution,

00:03:23.584 --> 00:03:26.284
"I have to add the same thing
to the right-hand side."

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Well they're telling us for
the solution to this equation,

00:03:29.251 --> 00:03:31.584
X plus 2y is equal to negative one,

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so negative one is the
same thing as X plus 2y

00:03:34.318 --> 00:03:36.917
for that solution, so
we're not gonna change

00:03:36.917 --> 00:03:38.584
the resulting solution of the system,

00:03:38.584 --> 00:03:41.251
so it's a completely legitimate
operation what Vivek did

00:03:41.251 --> 00:03:42.517
is adding the left-hand sides

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and adding the right-hand sides

00:03:43.751 --> 00:03:45.651
to get this new second equation.

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That's not going to change
the solution of the system.

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In fact, that's a technique we often use

00:03:49.518 --> 00:03:52.185
to eventually find the
solution of a system.

00:03:52.185 --> 00:03:54.785
So now let's look at Camila, or Camila.

00:03:54.785 --> 00:03:58.318
So her first equation is
actually the exact same equation

00:03:58.318 --> 00:04:02.617
as the teacher's second equation.

00:04:02.617 --> 00:04:05.318
Now let's see, her second equation,

00:04:05.318 --> 00:04:08.351
how does it relate possibly
to the first equation?

00:04:08.351 --> 00:04:10.317
So just looking at it offhand,

00:04:10.317 --> 00:04:11.819
it looks like it might just be,

00:04:11.819 --> 00:04:14.750
it looks like she just multiplied
both sides times a number.

00:04:14.750 --> 00:04:17.485
And it looks like that
number, she clearly multiplied

00:04:17.485 --> 00:04:20.917
the right-hand side times negative eight.

00:04:20.917 --> 00:04:23.151
So times negative eight.

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Negative one times negative
eight is positive eight.

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And it looks like she also multiplied

00:04:29.051 --> 00:04:30.618
the left-hand side by negative eight.

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Negative eight times X is -8X.

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Negative eight times 2y is -16y.

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So she just multiplied both
sides by the same value

00:04:39.718 --> 00:04:41.284
which actually doesn't
change the equation.

00:04:41.284 --> 00:04:43.105
This actually is going to be--

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It changes it the way it looks,

00:04:44.834 --> 00:04:47.951
but it actually represents the same line.

00:04:47.951 --> 00:04:51.232
So this is definitely
still an equivalent system.

00:04:51.232 --> 00:04:52.851
These are still the same constraints.

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You're going to have the same solution.

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Whenever you're dealing with systems,

00:04:56.118 --> 00:04:58.818
you're not going to change
the solution of the system

00:04:58.818 --> 00:05:02.885
as long as you either multiply
both sides of an equation by

00:05:02.885 --> 00:05:05.651
a scaler, or you are adding
and subtracting the equations.

00:05:05.651 --> 00:05:07.184
When I say add or subtract the equations,

00:05:07.184 --> 00:05:09.085
you're adding the left-hand
side to the left-hand side,

00:05:09.085 --> 00:05:10.752
adding the right-hand side
to the right-hand side

00:05:10.752 --> 00:05:14.285
like we had here, or subtracting
the one from the other

00:05:14.285 --> 00:05:16.651
on the left-hand side and
if we subtract the bottom

00:05:16.651 --> 00:05:17.718
from the top on the left-hand

00:05:17.718 --> 00:05:19.751
and we subtract the bottom
from the top on the right-hand,

00:05:19.751 --> 00:05:21.785
it's not going to change our solution.

00:05:21.785 --> 00:05:25.417
So both of them obtained a
system that is equivalent,

00:05:25.417 --> 00:05:27.385
meaning that it has the same solution

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as the teacher's system.


Systems of equations with graphing: exact & approximate solutions

WEBVTT
Kind: captions
Language: en

00:00:00.184 --> 00:00:03.672
- The following two equations
form a linear system.

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This is one equation; it has X and Y

00:00:05.818 --> 00:00:07.418
so it's gonna define a line.

00:00:07.418 --> 00:00:09.584
And then I have another
equation that involves X and Y,

00:00:09.584 --> 00:00:11.251
so it's gonna define another line.

00:00:11.251 --> 00:00:13.151
It says: "Graph the system of equations

00:00:13.151 --> 00:00:14.551
"and find its solution."

00:00:14.551 --> 00:00:16.284
So we're gonna try to find it visually.

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So let's graph this first one.

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To graph this line, I have
the little graphing tool here.

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Notice if I can figure out two points,

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I can move those points around

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and it's going to define our line for us.

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I'm gonna pick two X values and figure out

00:00:29.385 --> 00:00:33.251
the corresponding Y values
and then graph the line.

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So let's see how I could do this.

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So let's see; an easy one is what happens

00:00:37.084 --> 00:00:38.951
when X is equal to zero?

00:00:38.951 --> 00:00:41.451
Well if X is equal to zero,
everything I just shaded

00:00:41.451 --> 00:00:45.618
goes away and we're left
with -3y is equal to nine.

00:00:45.618 --> 00:00:50.184
So -3y equals nine. Y
would be negative three.

00:00:50.184 --> 00:00:54.584
So when X is equal to zero,
Y would be negative three.

00:00:54.584 --> 00:00:55.552
So let me graph that.

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When X is equal to zero,

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X is zero, Y is negative three.

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Now another easy point
actually instead of trying

00:01:03.652 --> 00:01:06.851
another X value, let's think
about when Y is equal to zero

00:01:06.851 --> 00:01:08.984
'cause these equations
are in a standard form

00:01:08.984 --> 00:01:10.218
so it's easy to just test.

00:01:10.218 --> 00:01:12.418
Well what are the X and Y intercepts?

00:01:12.418 --> 00:01:16.882
So when Y is equal to zero,

00:01:16.882 --> 00:01:20.375
this term goes away,
and you have negative X

00:01:20.375 --> 00:01:25.375
is equal to nine, or X would
be equal to negative nine.

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So when Y is zero, X is negative nine.

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So when Y is zero,

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X is negative nine,

00:01:34.568 --> 00:01:37.718
or when X is negative nine, Y is zero.

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So I've just plotted this first equation.

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So now let's do the second
one. We'll do the same thing.

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What happens when X is equal to zero?

00:01:47.551 --> 00:01:49.851
When X is equal to zero,

00:01:49.851 --> 00:01:53.818
so this is going to be
our Y intercept now.

00:01:53.818 --> 00:01:57.584
When X is equal to zero, -6y
is equal to negative six.

00:01:57.584 --> 00:02:00.118
Well Y would have to be equal to one.

00:02:00.118 --> 00:02:04.718
So when X is zero, Y is equal to one.

00:02:04.718 --> 00:02:07.985
So when X is zero,

00:02:07.985 --> 00:02:10.052
Y is equal to one.

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Get one more point here.

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When Y is zero, when this term is zero,

00:02:14.618 --> 00:02:17.018
Y being zero would make
this entire term zero,

00:02:17.018 --> 00:02:19.584
then 6x is equal to negative six

00:02:19.584 --> 00:02:22.018
or X is equal to negative one.

00:02:22.018 --> 00:02:24.218
So when Y is zero, X is negative one

00:02:24.218 --> 00:02:27.118
or when X is negative one, Y is zero.

00:02:27.118 --> 00:02:30.798
When X is negative one,

00:02:30.798 --> 00:02:33.258
Y is zero.

00:02:33.258 --> 00:02:36.028
And so just like that,
I've plotted the two lines.

00:02:36.028 --> 00:02:39.818
And the solution to the
system are the X and Y values

00:02:39.818 --> 00:02:43.819
that satisfy both equations;
and if they satisfy

00:02:43.819 --> 00:02:46.285
both equations, that means
they sit on both lines.

00:02:46.285 --> 00:02:48.585
And so in order to be on both lines,

00:02:48.585 --> 00:02:50.319
they're going to be at
the point of intersection.

00:02:50.319 --> 00:02:52.218
And I see this point of
intersection right over here,

00:02:52.218 --> 00:02:54.984
it looks pretty clear that
this is the point X is equal

00:02:54.984 --> 00:02:59.485
to negative three and Y
is equal to negative two.

00:02:59.485 --> 00:03:02.252
So it's the point negative
three comma negative two.

00:03:02.252 --> 00:03:03.884
So let me write that down.

00:03:03.884 --> 00:03:08.484
Negative three comma negative two.

00:03:08.484 --> 00:03:11.685
And then I could check
my answer; got it right.

00:03:11.685 --> 00:03:13.584
Let's do another. Let's
do another one of these.

00:03:13.584 --> 00:03:16.151
Maybe of a different type.

00:03:16.151 --> 00:03:18.485
So over here it says: "A
system of two linear equations

00:03:18.485 --> 00:03:19.788
"is graphed below.

00:03:19.788 --> 00:03:23.150
"Approximate the solution of the system."

00:03:23.150 --> 00:03:26.285
Alright so here I just have
to just look at this carefully

00:03:26.285 --> 00:03:28.551
and think about where this point is.

00:03:28.551 --> 00:03:30.251
So let's think about first its X value.

00:03:30.251 --> 00:03:32.035
So its X value,

00:03:32.035 --> 00:03:34.585
it's about right there
in terms of its X value.

00:03:34.585 --> 00:03:38.599
It looks like, so this is negative one.

00:03:38.599 --> 00:03:40.752
This is negative two, so negative 1.5

00:03:40.752 --> 00:03:42.652
is gonna be right over here.

00:03:42.652 --> 00:03:46.585
It's a little bit to the
left of negative 1.5,

00:03:46.585 --> 00:03:50.898
so it's even more negative,
I would say negative 1.6.

00:03:50.898 --> 00:03:53.218
And I'm approximating it, negative 1.6.

00:03:53.218 --> 00:03:54.884
Hopefully it has a little leeway

00:03:54.884 --> 00:03:56.918
in how it checks the answer.

00:03:56.918 --> 00:03:58.384
What about the Y value?

00:03:58.384 --> 00:04:00.751
So if I look at the Y value here,

00:04:00.751 --> 00:04:04.650
it looks like it's a little
less than one and a half.

00:04:04.650 --> 00:04:06.751
One and a half would be
halfway between one and two.

00:04:06.751 --> 00:04:08.484
It looks like it's a little
less than halfway between

00:04:08.484 --> 00:04:12.218
one and two, so I'd give it 1.4,

00:04:12.218 --> 00:04:14.451
positive 1.4.

00:04:14.451 --> 00:04:18.521
And let's check the answer,
see how we're doing.

00:04:18.521 --> 00:04:20.184
Yep, we got it right.

00:04:20.184 --> 00:04:23.784
Let's actually just do
one more for good measure.

00:04:23.784 --> 00:04:25.217
So this is another system.

00:04:25.217 --> 00:04:27.652
They've just written the equations in more

00:04:27.652 --> 00:04:29.717
of our slope intercept form.

00:04:29.717 --> 00:04:32.650
So let's see, Y is equal to
negative seven, X plus three.

00:04:32.650 --> 00:04:35.018
When X is equal to zero,
we have our Y intercept.

00:04:35.018 --> 00:04:36.818
Y is equal to three.

00:04:36.818 --> 00:04:40.851
So when X is equal to
zero, Y is equal to three.

00:04:40.851 --> 00:04:43.385
And then we see that our
slope is negative seven.

00:04:43.385 --> 00:04:47.818
When you increase X by one,
you decrease Y by seven.

00:04:47.818 --> 00:04:51.611
So when you increase X
by one, you decrease Y

00:04:51.611 --> 00:04:56.017
by one, two, three, four,

00:04:56.017 --> 00:04:58.884
five, six, and seven.

00:04:58.884 --> 00:05:00.618
When X goes from zero to one,

00:05:00.618 --> 00:05:02.785
Y went from three to negative four,

00:05:02.785 --> 00:05:05.818
it went down by seven,
so that's that first one.

00:05:05.818 --> 00:05:07.685
Now the second one: our Y intercept.

00:05:07.685 --> 00:05:09.985
When X is equal to zero,
Y is negative three,

00:05:09.985 --> 00:05:11.551
so let me graph that.

00:05:11.551 --> 00:05:15.185
When X is zero, Y is
equal to negative three.

00:05:15.185 --> 00:05:18.518
And then its slope is negative one.

00:05:18.518 --> 00:05:22.717
When X increases by
one, Y decreases by one.

00:05:22.717 --> 00:05:25.418
So the slope here is negative one.

00:05:25.418 --> 00:05:29.318
So when X increases by
one, Y decreases by one.

00:05:29.318 --> 00:05:31.851
And there you have it. You have
your point of intersection.

00:05:31.851 --> 00:05:35.385
You have the X-Y pair that
satisfies both equations.

00:05:35.385 --> 00:05:37.117
That is the point of intersection.

00:05:37.117 --> 00:05:38.685
It's gonna sit on both lines

00:05:38.685 --> 00:05:40.318
which is why it's the
point of intersection.

00:05:40.318 --> 00:05:42.485
And that's the point X equals one,

00:05:42.485 --> 00:05:45.051
Y is equal to negative four.

00:05:45.051 --> 00:05:48.118
So you have X equals one

00:05:48.118 --> 00:05:51.484
and Y is equal to negative four.

00:05:51.484 --> 00:05:55.135
And I can check my answer
and we got it right.


Sequences word problems

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:02.250
- [Voiceover] Mohamed
decides to track the number

00:00:02.250 --> 00:00:05.019
of leaves on the tree in
his backyard each year.

00:00:05.176 --> 00:00:08.372
The first year, there were 500 leaves.

00:00:08.853 --> 00:00:10.580
Each year thereafter, the number of leaves

00:00:10.580 --> 00:00:14.101
was 40% more than the year before.

00:00:14.481 --> 00:00:17.325
Let n be a positive integer,
and let f of n denote

00:00:17.325 --> 00:00:19.215
the number of leaves on
the tree in Mohamed's

00:00:19.215 --> 00:00:22.634
back yard in the nth year
since he started tracking it.

00:00:23.339 --> 00:00:26.840
The expression f of n defines a sequence.

00:00:26.894 --> 00:00:29.339
What kind of sequence is f of n?

00:00:29.719 --> 00:00:31.059
So, some of you might be able to

00:00:31.059 --> 00:00:31.933
think about this in your head.

00:00:31.933 --> 00:00:34.473
Each successive year we're growing by 40%,

00:00:34.473 --> 00:00:36.978
that's the same thing
as multiplying by 1.4.

00:00:37.276 --> 00:00:39.450
Each successive term we're multiplying

00:00:39.450 --> 00:00:41.844
or dividing by the same number.

00:00:41.844 --> 00:00:43.126
Well, that's going to be geometric.

00:00:43.567 --> 00:00:45.219
Let's make that a little
bit more tangible,

00:00:45.416 --> 00:00:46.641
just in case.

00:00:46.675 --> 00:00:48.998
So, let's make a little table here.

00:00:49.865 --> 00:00:51.558
So, table.

00:00:51.714 --> 00:00:54.890
So, this is n and this is f of n.

00:00:55.351 --> 00:00:57.084
So when n is equal to one,

00:00:57.139 --> 00:00:59.989
the first year, n equals
one, there were 500 leaves.

00:01:00.308 --> 00:01:01.838
F of n is 500.

00:01:02.340 --> 00:01:03.681
Now, when n is equal to two we're going

00:01:03.681 --> 00:01:05.875
to grow by 40%, which is the same thing

00:01:05.875 --> 00:01:08.035
as multiplying by 1.4.

00:01:08.760 --> 00:01:12.327
So 500 times 1.4, let's
do 40% of 500 is 200,

00:01:12.327 --> 00:01:14.298
so we're going to grow by 200, so we're

00:01:14.298 --> 00:01:16.011
going to go to 700.

00:01:16.431 --> 00:01:19.194
Then in year three, we're
going to grow by 40%

00:01:19.194 --> 00:01:23.981
of 700, which is 280, so
it's going to grow to 980.

00:01:23.981 --> 00:01:28.376
Notice it's definitely not
an arithmetic sequence.

00:01:28.573 --> 00:01:30.300
An arithmetic sequence, we would be adding

00:01:30.300 --> 00:01:32.425
or subtracting the same amount every time,

00:01:32.425 --> 00:01:33.198
but we're not.

00:01:33.198 --> 00:01:35.371
Here, from 500 to 700, we grew by 200,

00:01:35.371 --> 00:01:37.856
and then from 700 to 980, we grew by 280.

00:01:38.135 --> 00:01:40.085
Instead, we're multiplying or dividing by

00:01:40.085 --> 00:01:41.467
the same amount each time.

00:01:41.467 --> 00:01:43.748
In this case, we're multiplying by 1.4,

00:01:44.067 --> 00:01:45.861
by 1.4 each time.

00:01:45.916 --> 00:01:47.751
So we are clearly geometric.

00:01:47.968 --> 00:01:49.756
Depending on your answer
to the question above,

00:01:49.756 --> 00:01:51.869
the recursive definition
of the sequence can have

00:01:51.869 --> 00:01:53.535
one of the following two forms.

00:01:53.535 --> 00:01:55.221
Well this is the arithmetic form, which

00:01:55.221 --> 00:01:57.009
we know isn't the case,
so it's going to be

00:01:57.009 --> 00:01:58.437
in the geometric form.

00:01:59.264 --> 00:02:01.215
And then they ask us, what are the values

00:02:01.215 --> 00:02:03.551
of the parameters A
and B for the sequence?

00:02:03.551 --> 00:02:06.842
So we have our base case
here, f of n is going to be

00:02:06.842 --> 00:02:09.246
equal to A when n is equal to one.

00:02:09.484 --> 00:02:11.190
Well, we know that when n equals one,

00:02:11.190 --> 00:02:14.400
we had 500 leaves on the
tree so A, this A over here,

00:02:14.400 --> 00:02:18.912
is 500, so A is 500,

00:02:19.637 --> 00:02:21.226
and then if we're not in the base case

00:02:21.226 --> 00:02:22.485
for any other year,

00:02:22.485 --> 00:02:24.720
we are going to have,
let's see, it's going to be

00:02:24.720 --> 00:02:27.814
the previous year, the
previous year times what?

00:02:28.418 --> 00:02:31.039
It's going to be the
previous year grown by 40%,

00:02:31.039 --> 00:02:34.860
to grow by 40%, you're
going to multiply by 1.4

00:02:34.935 --> 00:02:37.989
so B is going to be 1.4.

00:02:38.023 --> 00:02:39.445
You take the previous
year and you multiply

00:02:39.445 --> 00:02:41.565
by 1.4 for any other year,

00:02:41.640 --> 00:02:43.291
any year other than n equals one.

00:02:43.712 --> 00:02:46.989
So, B is equal to 1.4, and we're done.

00:02:47.389 --> 00:02:48.425
Let's do another example.

00:02:48.425 --> 00:02:49.915
This is strangely fun.

00:02:50.538 --> 00:02:55.089
All right, so this says:
Seo-Yun hosted a party.

00:02:55.089 --> 00:02:58.597
She had 50 party favors
to give away, and she

00:02:58.597 --> 00:03:01.502
gave away three party
favors to each of her guests

00:03:01.502 --> 00:03:03.112
as they arrived at the party.

00:03:03.473 --> 00:03:07.150
Let n be a positive integer,
and let g of n denote

00:03:07.150 --> 00:03:10.706
the number of party
favors Seo-Yun had before

00:03:10.706 --> 00:03:12.906
the nth guest arrived.

00:03:14.078 --> 00:03:16.090
All right, actually, before I
even look at these questions,

00:03:16.090 --> 00:03:17.431
let me make a table here
because they're saying

00:03:17.431 --> 00:03:18.818
before the nth guest.

00:03:18.833 --> 00:03:21.561
I want to make sure I'm
understanding this properly.

00:03:22.551 --> 00:03:25.476
So this is n,

00:03:26.202 --> 00:03:28.122
and then this is going to be g of n,

00:03:28.122 --> 00:03:29.213
right over here.

00:03:29.532 --> 00:03:31.610
So, when n is equal to one,

00:03:32.234 --> 00:03:34.407
when n is equal to one,
g of n is going to be,

00:03:34.407 --> 00:03:37.012
or g of one is going to be
the number of party favors

00:03:37.012 --> 00:03:40.005
Seo-Yun had before the first guest.

00:03:40.730 --> 00:03:43.824
Well, before the first guest,
she had 50 party favors.

00:03:44.428 --> 00:03:45.775
She had 50 party favors.

00:03:46.317 --> 00:03:48.740
Now, the second guest comes.

00:03:48.755 --> 00:03:50.584
Now the number of party
favors she had before

00:03:50.584 --> 00:03:54.444
the second guest, well,
she had to give three

00:03:54.444 --> 00:03:56.313
to the first guest, so she's now

00:03:56.313 --> 00:03:58.676
going to have 47 party favors.

00:03:59.320 --> 00:04:00.824
Now, when n is equal to three,

00:04:00.824 --> 00:04:02.429
how many party favors did she have

00:04:02.429 --> 00:04:04.568
before the third guest?

00:04:04.928 --> 00:04:06.390
Well, she would've had
to give party favors

00:04:06.390 --> 00:04:08.835
to the first and second
guest, who each got three.

00:04:09.194 --> 00:04:13.486
So, she would have 44, and
I think you see the pattern.

00:04:13.928 --> 00:04:17.022
For every time n, when n
equals one, g of n is 50,

00:04:17.199 --> 00:04:19.596
and every time we increase n by one,

00:04:19.596 --> 00:04:23.497
every time we increment
n, we are increasing

00:04:23.497 --> 00:04:28.237
g of n by plus three, by
minus three, I should say

00:04:28.475 --> 00:04:30.838
because she's giving away
party favors, minus three.

00:04:31.665 --> 00:04:32.646
Minus three.

00:04:33.006 --> 00:04:35.058
So because the difference
between successive terms

00:04:35.058 --> 00:04:37.460
is the same, we know this
is an arithmetic sequence.

00:04:38.349 --> 00:04:40.034
This is an arithmetic
sequence and then they say

00:04:40.034 --> 00:04:42.499
write an explicit
formula for the sequence.

00:04:43.055 --> 00:04:44.680
So let's think about this.

00:04:44.680 --> 00:04:48.242
Let's see, g of n is
going to be equal to...

00:04:48.256 --> 00:04:49.949
Let's see, we're going to start at 50

00:04:50.207 --> 00:04:53.590
then we're going to subtract
three, and let's think,

00:04:53.590 --> 00:04:56.787
do we subtract three times n or is it...?

00:04:57.492 --> 00:04:59.503
Let's see, for the first guest,

00:04:59.503 --> 00:05:01.318
we subtract three zero times.

00:05:01.921 --> 00:05:04.406
For the second guest,
we subtract three once.

00:05:04.928 --> 00:05:07.941
For the third guest, we
subtract three twice.

00:05:08.463 --> 00:05:11.125
So, for the nth guest, we're
going to subtract three

00:05:11.125 --> 00:05:13.081
n minus one time.

00:05:13.380 --> 00:05:15.966
Notice, for the nth guest,
we subtracted three twice.

00:05:16.203 --> 00:05:19.237
The second guest, subtracted three once.

00:05:19.495 --> 00:05:21.573
First guest, subtracted three zero times,

00:05:21.669 --> 00:05:22.590
so this works out.

00:05:22.888 --> 00:05:25.576
For the first guest, we would
subtract three zero times,

00:05:25.732 --> 00:05:27.405
and so g of one would be 50.

00:05:27.663 --> 00:05:29.782
We can see that this is
consistent for all of these.

00:05:30.101 --> 00:05:34.372
So I could write 50 minus
three times n minus one,

00:05:34.408 --> 00:05:35.871
and I really recommend
making the table here

00:05:35.871 --> 00:05:37.740
just so you make sure
you get the n minus one

00:05:37.740 --> 00:05:40.915
or the n right and it all gels.


Competitive inhibition

WEBVTT
Kind: captions
Language: en

00:00:00.318 --> 00:00:02.151
- We've already seen that an enzyme helps

00:00:02.151 --> 00:00:05.285
catalyze a reaction, so let's
say this right over here,

00:00:05.285 --> 00:00:10.285
this is our enzyme, and
we have our substrate,

00:00:10.485 --> 00:00:13.885
and it goes and it binds
to the active site,

00:00:13.885 --> 00:00:15.718
to the active site of the enzyme,

00:00:15.718 --> 00:00:18.685
so let's say it binds right over there

00:00:18.685 --> 00:00:21.251
on the enzyme we call it the active site

00:00:21.251 --> 00:00:23.918
where the substrate binds
and then the enzyme catalyzes

00:00:23.918 --> 00:00:26.085
a reaction; maybe it
breaks up this substrate

00:00:26.085 --> 00:00:27.995
into two smaller molecules.

00:00:27.995 --> 00:00:32.605
And so after the reaction,

00:00:32.605 --> 00:00:34.925
the enzyme, whoops.

00:00:34.925 --> 00:00:39.718
After the reaction, the
enzyme is unchanged,

00:00:39.718 --> 00:00:42.818
but a reaction has been catalyzed.

00:00:44.628 --> 00:00:48.052
We now have the substrate being broken up,

00:00:48.052 --> 00:00:50.617
in this case at least,
into two smaller molecules.

00:00:50.617 --> 00:00:52.718
Maybe I'll draw them. That's one of them.

00:00:52.718 --> 00:00:55.085
And this is the other one right over here.

00:00:55.085 --> 00:00:58.251
So they just came from the active site.

00:00:58.251 --> 00:01:01.085
Once the reaction is
catalyzed, they don't have

00:01:01.085 --> 00:01:03.851
the affinity to the active site
anymore and they break off.

00:01:03.851 --> 00:01:06.747
So this enzyme has just
catalyzed this reaction.

00:01:06.747 --> 00:01:08.068
What I wanna talk about in this video

00:01:08.068 --> 00:01:11.051
is how this might be
inhibited, and specifically

00:01:11.051 --> 00:01:13.350
how it might be inhibited competitively.

00:01:13.350 --> 00:01:16.685
So we're gonna talk about
competitive inhibition.

00:01:16.685 --> 00:01:18.785
So competitive--

00:01:18.785 --> 00:01:19.918
Let me write it over here.

00:01:19.918 --> 00:01:24.284
Competitive

00:01:24.284 --> 00:01:26.084
inhibition.

00:01:26.084 --> 00:01:28.284
Inhibition.

00:01:28.284 --> 00:01:31.285
So the classic case of
competitive inhibition:

00:01:31.285 --> 00:01:35.618
if there's some molecule that competes

00:01:35.618 --> 00:01:38.584
for the substrate at the active site,

00:01:38.584 --> 00:01:39.884
as we'll see this isn't the only form

00:01:39.884 --> 00:01:42.151
of competitive inhibition,
but this is the one

00:01:42.151 --> 00:01:44.651
that you will most
typically see in a textbook.

00:01:44.651 --> 00:01:48.352
So that's our enzyme again.

00:01:49.452 --> 00:01:51.251
So that's our enzyme.

00:01:51.251 --> 00:01:53.684
And we've already seen that
this is right over here

00:01:53.684 --> 00:01:56.718
where I'm circling,
that is the active site.

00:01:56.718 --> 00:02:01.718
Active site.

00:02:01.851 --> 00:02:05.318
And if the molecule,
the intended substrate

00:02:05.318 --> 00:02:07.418
I guess you could say, gets
to it and we're gonna have

00:02:07.418 --> 00:02:09.284
this first scenario up here.

00:02:09.284 --> 00:02:11.351
But in classic competitive inhibition,

00:02:11.351 --> 00:02:13.818
or at least the version I'm
just gonna show you right now,

00:02:13.818 --> 00:02:17.060
you could have another molecule

00:02:17.060 --> 00:02:19.351
that let's say it looks
something like this

00:02:19.351 --> 00:02:21.784
that can compete for the active site

00:02:21.784 --> 00:02:26.118
and if it gets to the active site first,

00:02:26.118 --> 00:02:27.685
so if it gets there first,

00:02:27.685 --> 00:02:30.218
let me show what's going to happen,

00:02:30.218 --> 00:02:33.185
so then we have our enzyme,

00:02:33.185 --> 00:02:38.151
we have the other molecule,
not the intended substrate

00:02:38.151 --> 00:02:40.250
binds to the active site first.

00:02:40.250 --> 00:02:42.651
Well now the intended substrate,

00:02:42.651 --> 00:02:45.850
the one for which the enzyme
catalyzed the reaction,

00:02:45.850 --> 00:02:49.918
isn't able to bind and the
reaction isn't going to happen.

00:02:49.918 --> 00:02:51.785
And you can see very clearly
that they are competing

00:02:51.785 --> 00:02:53.417
for the enzyme, and in this case,

00:02:53.417 --> 00:02:55.652
they're competing for the active site.

00:02:55.652 --> 00:02:58.517
Now this isn't the only form
of competitive inhibition.

00:02:58.517 --> 00:03:00.485
Another form of competitive inhibition

00:03:00.485 --> 00:03:03.485
is allosteric competitive inhibition.

00:03:03.485 --> 00:03:04.984
Let me write this down.

00:03:04.984 --> 00:03:08.052
So you have allosteric.

00:03:08.052 --> 00:03:10.495
Allosteric

00:03:10.495 --> 00:03:14.635
competitive

00:03:14.635 --> 00:03:17.705
inhibition.

00:03:17.705 --> 00:03:19.018
Now I'm having trouble writing.

00:03:19.018 --> 00:03:21.118
Inhibition.

00:03:21.118 --> 00:03:25.284
And an allosteric site is a
site other than the active site.

00:03:25.284 --> 00:03:28.518
But in allosteric competitive inhibition

00:03:28.518 --> 00:03:30.184
or competitive allosteric inhibition,

00:03:30.184 --> 00:03:32.951
however you wanna say
it, you have a scenario

00:03:32.951 --> 00:03:37.117
where the competitor doesn't
bind to the active site

00:03:37.117 --> 00:03:39.151
but binds to a site that
is not the active site,

00:03:39.151 --> 00:03:41.051
an allosteric site you could say.

00:03:41.051 --> 00:03:44.718
So in that one, the competitor,
maybe might bind here,

00:03:44.718 --> 00:03:46.584
so that's clearly not the active site.

00:03:46.584 --> 00:03:49.018
So maybe the competitor
looks something like that.

00:03:49.018 --> 00:03:51.817
It didn't bind to the active site,

00:03:51.817 --> 00:03:56.817
but by binding there, the
active site can no longer bind

00:03:57.217 --> 00:04:01.650
to the intended substrate,
so you have the same effect.

00:04:01.650 --> 00:04:04.052
You have the same effect right over here

00:04:04.052 --> 00:04:07.317
where this thing isn't going to bind.

00:04:07.317 --> 00:04:09.417
But if this thing binds first...

00:04:09.417 --> 00:04:11.618
So let me draw that scenario.

00:04:11.618 --> 00:04:15.317
So if the intended substrate binds first,

00:04:15.317 --> 00:04:17.652
then the competitor can't bind.

00:04:17.652 --> 00:04:20.518
So in this scenario, if
the substrate is able

00:04:20.518 --> 00:04:22.485
to get to the active site,

00:04:22.485 --> 00:04:24.385
well then the competitor can't bind,

00:04:24.385 --> 00:04:25.584
so once again, they're competing.

00:04:25.584 --> 00:04:27.752
So I'll draw the competitor up here.

00:04:27.752 --> 00:04:29.552
So then the competitor,

00:04:29.552 --> 00:04:31.851
whoever gets to it first gets the enzyme.

00:04:31.851 --> 00:04:33.784
So in this situation, the
competitor's not going to bind.

00:04:33.784 --> 00:04:35.485
So that's true of whether
you're talking about

00:04:35.485 --> 00:04:37.317
competitive inhibition
where they're competing

00:04:37.317 --> 00:04:39.851
for the active site, if the
competitor gets there first,

00:04:39.851 --> 00:04:42.831
the intended substrate
isn't gonna get there,

00:04:42.831 --> 00:04:45.864
the reaction isn't going to be catalyzed.

00:04:45.864 --> 00:04:48.751
Or if the intended substrate gets first,

00:04:48.751 --> 00:04:51.151
then the competitor's not
going to be able to get there.

00:04:51.151 --> 00:04:52.551
In fact it could have been this situation

00:04:52.551 --> 00:04:56.285
where because the
substrate got there first,

00:04:56.285 --> 00:05:01.285
the competitor isn't
going to be able to bind

00:05:01.618 --> 00:05:03.052
to the active site.

00:05:03.052 --> 00:05:05.451
When we're talking about
allosteric competitive inhibition,

00:05:05.451 --> 00:05:07.118
we're still competing for the enzyme.

00:05:07.118 --> 00:05:08.885
Only one's gonna get it.

00:05:08.885 --> 00:05:10.551
If one gets to the enzyme first,

00:05:10.551 --> 00:05:12.351
then the other one's not
going to be able to get there.

00:05:12.351 --> 00:05:15.484
They are competing for the
enzyme, but the competitor,

00:05:15.484 --> 00:05:18.451
the non-substrate, is just
acting at an allosteric site.

00:05:18.451 --> 00:05:20.350
By binding to an allosteric site,

00:05:20.350 --> 00:05:23.084
it changes the conformation of the enzyme

00:05:23.084 --> 00:05:26.952
so that the active site no
longer binds to the substrate.

00:05:26.952 --> 00:05:28.651
And I wanna really emphasize this point

00:05:28.651 --> 00:05:30.152
because when I first learned this, I said:

00:05:30.152 --> 00:05:31.351
"Oh!"

00:05:31.351 --> 00:05:33.185
And it's often sometimes
confusing, even some things

00:05:33.185 --> 00:05:36.067
you'll read on the
Internet, that they'll say

00:05:36.067 --> 00:05:39.051
that this allosteric type of
inhibition, they'll call this

00:05:39.051 --> 00:05:40.818
non-competitive 'cause
you're not competing

00:05:40.818 --> 00:05:44.718
for the active site, but that
is actually not the case.

00:05:44.718 --> 00:05:46.818
In non-competitive
inhibition, and I'm gonna do

00:05:46.818 --> 00:05:50.051
the whole next video on
non-competitive inhibition,

00:05:50.051 --> 00:05:54.785
in non-competitive inhibition,
the inhibitor right over here

00:05:54.785 --> 00:05:58.351
can bind regardless of
whether the substrate

00:05:58.351 --> 00:06:01.785
has bound or not, but when
the inhibitor does bind,

00:06:01.785 --> 00:06:04.051
it prevents the reaction
from moving forward,

00:06:04.051 --> 00:06:06.684
it changes the conformation of the protein

00:06:06.684 --> 00:06:09.118
so it no longer catalyzes the reaction.

00:06:09.118 --> 00:06:11.684
So non-competitive, they both can bind,

00:06:11.684 --> 00:06:12.985
but if the inhibitor is there,

00:06:12.985 --> 00:06:15.084
the reaction isn't going to proceed.

00:06:15.084 --> 00:06:16.850
In competitive inhibition,
whether we're talking about

00:06:16.850 --> 00:06:20.252
allosteric or non-allosteric
competitive inhibition,

00:06:20.252 --> 00:06:24.084
only one of the substrate or the inhibitor

00:06:24.084 --> 00:06:25.918
is going to be able to bind.

00:06:25.918 --> 00:06:29.200
They are competing for the enzyme.


Noncompetitive inhibition

WEBVTT
Kind: captions
Language: en

00:00:00.358 --> 00:00:02.512
- [Voiceover] In the video
on competitive inhibition,

00:00:02.512 --> 00:00:06.189
we saw that competitive inhibition
is all about a substrate

00:00:06.189 --> 00:00:09.135
or a potential substrate,
an inhibitor competing

00:00:09.135 --> 00:00:10.259
for the enzyme.

00:00:10.415 --> 00:00:12.880
And whoever gets there
first, gets the enzyme.

00:00:12.887 --> 00:00:15.080
If the inhibitor gets there first,

00:00:15.080 --> 00:00:17.397
then the substrate isn't able to bind,

00:00:17.397 --> 00:00:19.814
and of course no reaction is catalyzed.

00:00:19.814 --> 00:00:22.110
If the substrate is
able to get there first,

00:00:22.110 --> 00:00:24.142
then the inhibitor isn't able to bind,

00:00:24.142 --> 00:00:27.108
and the reaction does get catalyzed.

00:00:27.108 --> 00:00:28.612
Now the inhibitor and the substrate,

00:00:28.612 --> 00:00:31.761
they both might compete
for the active site,

00:00:31.761 --> 00:00:33.508
if we're talking about
competitive inhibition.

00:00:33.508 --> 00:00:36.454
But you also have allosteric
competitive inhibition.

00:00:36.454 --> 00:00:38.587
Where they're still trying
to compete for the enzyme,

00:00:38.587 --> 00:00:40.761
whoever gets there first, gets the enzyme.

00:00:40.761 --> 00:00:43.240
But the inhibitor doesn't necessarily bind

00:00:43.240 --> 00:00:46.714
at the active site, they
bind at an allosteric site.

00:00:46.714 --> 00:00:48.136
But it's the same idea.

00:00:48.136 --> 00:00:50.026
If the inhibitor gets
to the allosteric site

00:00:50.026 --> 00:00:52.992
before the substrate
gets to the active site,

00:00:52.992 --> 00:00:55.247
then the confirmation
of the protein changes,

00:00:55.247 --> 00:00:57.909
so that the active site, you
know it changes a little bit,

00:00:57.909 --> 00:01:02.013
something like let me
draw in that same color,

00:01:02.013 --> 00:01:03.902
the confirmation of the
protein changes a little bit.

00:01:03.902 --> 00:01:08.760
And then the actual intended
substrate isn't able to bind.

00:01:08.760 --> 00:01:10.791
If the intended substrate binds,

00:01:10.791 --> 00:01:12.803
then that changes the
confirmation a little bit

00:01:12.803 --> 00:01:15.302
at the allosteric site,
and then the inhibitor

00:01:15.302 --> 00:01:16.765
isn't able to bind.

00:01:16.765 --> 00:01:18.573
So if that's competitive
inhibition, where there's like

00:01:18.573 --> 00:01:20.787
who gets to the enzyme first,

00:01:20.787 --> 00:01:23.652
what is non-competitive
inhibition all about?

00:01:23.652 --> 00:01:25.365
Well let's draw that.

00:01:25.928 --> 00:01:28.148
So, non-competitive inhibition.

00:01:29.300 --> 00:01:34.300
So, non-competitive inhibition.

00:01:37.529 --> 00:01:39.134
And the big picture here is that

00:01:39.134 --> 00:01:41.531
they can both bind.

00:01:41.531 --> 00:01:44.213
Whether one binds to the
enzyme doesn't affect

00:01:44.213 --> 00:01:45.838
whether the other binds.

00:01:45.838 --> 00:01:47.450
So let's talk about it a little bit.

00:01:47.890 --> 00:01:50.497
So, this is my enzyme.

00:01:51.344 --> 00:01:54.453
That's my enzyme, right over there.

00:01:54.453 --> 00:01:57.622
And what we have happening, of course,

00:01:57.622 --> 00:02:01.868
is if the substrate's able
to get to the active site,

00:02:01.868 --> 00:02:04.794
then of course the reaction
is going to be catalyzed.

00:02:04.794 --> 00:02:07.354
And we saw that up here.

00:02:07.354 --> 00:02:09.853
Substrate binds to the active site,

00:02:09.853 --> 00:02:11.560
and then the reaction is catalyzed,

00:02:11.560 --> 00:02:13.429
in this case the substrate got broken up

00:02:13.429 --> 00:02:16.334
into two other molecules.

00:02:16.334 --> 00:02:18.345
But in non-competitive inhibition,

00:02:18.345 --> 00:02:20.499
what happens is a substrate can bind,

00:02:20.499 --> 00:02:23.831
and so can an inhibitor.

00:02:23.831 --> 00:02:26.980
And the inhibitor can bind
at an allosteric site,

00:02:26.980 --> 00:02:30.272
so this is our inhibitor right over here.

00:02:30.272 --> 00:02:32.994
The inhibitor can bind
at an allosteric site,

00:02:32.994 --> 00:02:34.335
and when they're both bound,

00:02:34.335 --> 00:02:36.773
notice they're not
competing for the enzyme,

00:02:36.773 --> 00:02:38.276
they both can be on the enzyme.

00:02:38.276 --> 00:02:41.324
This character can bind
to the enzyme whether

00:02:41.324 --> 00:02:43.092
or not the substrate is there.

00:02:43.092 --> 00:02:44.900
But if this guy binds to the enzyme,

00:02:44.900 --> 00:02:46.871
the substrate can still
bind to the enzyme,

00:02:46.871 --> 00:02:49.634
but now the reaction
isn't going to proceed.

00:02:49.634 --> 00:02:52.884
So now the reaction is
going to look like this:

00:02:52.884 --> 00:02:57.253
so now there's not going to be a reaction.

00:02:57.253 --> 00:03:01.478
If this happens, the only
option is that they both unbind.

00:03:01.478 --> 00:03:04.018
So now this character is just going

00:03:04.018 --> 00:03:05.420
to leave the active site.

00:03:05.420 --> 00:03:09.687
No reaction has been catalyzed.

00:03:09.687 --> 00:03:12.734
So, it just prevented
anything from happening.

00:03:12.734 --> 00:03:16.188
And maybe this guy leaves as well.

00:03:16.188 --> 00:03:18.484
And the way I showed this
non-competitive inhibition,

00:03:18.484 --> 00:03:20.455
I showed it happening
at an allosteric site,

00:03:20.455 --> 00:03:23.766
the inhibitor attaching
at an allosteric site,

00:03:23.766 --> 00:03:25.717
but it actually doesn't even
have to be the same case

00:03:25.717 --> 00:03:27.464
as long as it does not prevent,

00:03:27.464 --> 00:03:31.649
it can actually bind close
to or even at the active site

00:03:31.649 --> 00:03:33.579
as long as it does not
prevent the substrate

00:03:33.579 --> 00:03:35.245
from binding to the active site.

00:03:35.245 --> 00:03:38.055
So you can even have
a situation like this:

00:03:43.933 --> 00:03:45.091
this is the one that's typically given

00:03:45.091 --> 00:03:47.001
for non-competitive
inhibition where you have

00:03:47.001 --> 00:03:48.972
the inhibitor binding
at an allosteric site,

00:03:48.972 --> 00:03:51.674
but the idea here is that both of them

00:03:51.674 --> 00:03:53.949
can bind to the enzyme.

00:03:53.949 --> 00:03:55.392
If one of them binds first,

00:03:55.392 --> 00:03:56.773
then the other one can still bind.

00:03:56.773 --> 00:03:59.496
If the substrate binds first,

00:03:59.496 --> 00:04:01.975
then the inhibitor can still bind.

00:04:01.975 --> 00:04:03.376
If the inhibitor binds first,

00:04:03.376 --> 00:04:05.063
then the substrate can still bind.

00:04:05.063 --> 00:04:10.063
But, the reaction is not
going to be catalyzed.

00:04:11.422 --> 00:04:14.734
But you can even have a situation

00:04:14.734 --> 00:04:17.598
where the inhibitor and the substrate

00:04:17.598 --> 00:04:21.093
can both bind in or
around the active site.

00:04:21.093 --> 00:04:25.603
So that's the inhibitor, and
then this is our substrate,

00:04:25.603 --> 00:04:27.411
this is the substrate.

00:04:27.411 --> 00:04:30.500
But once again, this reaction
is not going to occur.

00:04:30.500 --> 00:04:33.060
We have non-competitive inhibition.

00:04:33.060 --> 00:04:34.868
They're not competing for the thing,

00:04:34.868 --> 00:04:37.184
they can both bind to
it, whether they can bind

00:04:37.184 --> 00:04:39.012
isn't dependent on whether
the other one is bound,

00:04:39.012 --> 00:04:42.324
but if the inhibitor is there
then it's not going to allow

00:04:42.324 --> 00:04:46.286
the reaction to actually be catalyzed.

00:04:46.286 --> 00:04:48.013
As opposed to competitive inhibition,

00:04:48.013 --> 00:04:49.496
whoever gets to the enzyme first,

00:04:49.496 --> 00:04:51.446
gets the enzyme.

00:04:51.446 --> 00:04:52.795
Hopefully that clarifies things.


Oxidative phosphorylation and the electron transport chain

WEBVTT
Kind: captions
Language: en

00:00:00.167 --> 00:00:02.048
- When we looked at glycolysis

00:00:02.048 --> 00:00:04.509
and the conversion of Pyruvate

00:00:04.509 --> 00:00:09.392
to Acetyl-CoA and then the
Krebs or the Citric acid Cycle,

00:00:09.392 --> 00:00:12.639
we were sometimes directly producing ATPs

00:00:12.639 --> 00:00:17.213
but we were also doing a lot
of reduction of NAD to NADH,

00:00:17.213 --> 00:00:19.725
and we later said that NADH,

00:00:19.725 --> 00:00:22.089
that that can later be oxidized, too,

00:00:22.089 --> 00:00:23.915
and that energy from that oxidation,

00:00:23.915 --> 00:00:26.178
that energy that's
released from the electrons

00:00:26.178 --> 00:00:29.383
can be used to actually create ATP,

00:00:29.383 --> 00:00:31.305
and NADH is the main character here,

00:00:31.305 --> 00:00:33.239
but there are other
coenzymes that are involved,

00:00:33.239 --> 00:00:36.741
like coenzyme Q, and you
see that right over here.

00:00:36.741 --> 00:00:37.985
And what I want to talk
about in this video

00:00:37.985 --> 00:00:42.606
is the process by which we
actually are able to produce ATP

00:00:42.606 --> 00:00:46.477
from the oxidation of these coenzymes,

00:00:46.477 --> 00:00:49.138
and that process is what we call

00:00:49.138 --> 00:00:51.959
Oxidative Phosphorylation.

00:00:51.959 --> 00:00:55.893
Oxidative, Oxidative Phosphorylation.

00:00:55.893 --> 00:00:57.735
Now the main player, when we're talking

00:00:57.735 --> 00:01:01.086
about cellular respiration
and Oxidative Phosphorylation,

00:01:01.086 --> 00:01:03.508
is NADH.

00:01:03.508 --> 00:01:08.151
NADH, in the process of being oxidized

00:01:08.151 --> 00:01:09.941
to NAD,

00:01:09.941 --> 00:01:13.242
so it gets oxidized to N...

00:01:13.242 --> 00:01:17.636
it gets oxidized to NAD,
which has a positive charge,

00:01:17.636 --> 00:01:21.079
I often call it NAD+, but let's
think about what this says.

00:01:21.079 --> 00:01:24.656
If we just look at this
reaction from the point of view

00:01:24.656 --> 00:01:27.287
of NADH being oxidized, remember,

00:01:27.287 --> 00:01:31.587
oxidation is losing electrons,

00:01:31.587 --> 00:01:34.503
so NAD+, and then you're gonna have

00:01:34.503 --> 00:01:36.936
plus a hydrogen proton

00:01:36.936 --> 00:01:40.559
plus, you're going to have two electrons,

00:01:40.559 --> 00:01:42.996
plus two electrons.

00:01:42.996 --> 00:01:45.059
So this is what's happening when NADH

00:01:45.059 --> 00:01:48.234
is being oxidized into NAD,

00:01:48.234 --> 00:01:50.131
so this is Oxidation right over here.

00:01:50.131 --> 00:01:51.568
Let me do this in another color.

00:01:51.568 --> 00:01:56.180
So this is Oxidation, and
this process of Oxidation,

00:01:56.180 --> 00:02:00.466
if these electrons get the
appropriate acceptor molecule,

00:02:00.466 --> 00:02:02.810
it can release a lot of energy,

00:02:02.810 --> 00:02:05.102
and the eventual acceptor
of those electrons,

00:02:05.102 --> 00:02:09.003
and I can show the corresponding
reduction reaction,

00:02:09.003 --> 00:02:12.501
is we have two electrons,

00:02:12.501 --> 00:02:17.366
two electrons plus two hydrogen protons,

00:02:17.366 --> 00:02:19.553
or really, just two
protons, a hydrogen nucleus

00:02:19.553 --> 00:02:21.535
is just a proton, it
doesn't have a neutron

00:02:21.535 --> 00:02:23.883
for the main isotope of hydrogen.

00:02:23.883 --> 00:02:25.852
So two protons

00:02:25.852 --> 00:02:30.689
plus half of an oxygen molecule yielding,

00:02:31.038 --> 00:02:32.967
you put all of these
two, all of these three,

00:02:32.967 --> 00:02:35.060
all of these things
together, I should say,

00:02:35.060 --> 00:02:37.916
and you are going to get a water molecule.

00:02:37.916 --> 00:02:40.400
So you can think of it as the oxygen

00:02:40.400 --> 00:02:43.120
being the final acceptor of the electrons,

00:02:43.120 --> 00:02:45.424
and oxygen likes to be doing oxid--

00:02:45.424 --> 00:02:46.693
likes to oxidize things,

00:02:46.693 --> 00:02:49.008
that's where the whole
word Oxidation comes from.

00:02:49.008 --> 00:02:50.908
So here, (mumbles)

00:02:50.908 --> 00:02:52.789
oxygen likes to be reduced.

00:02:52.789 --> 00:02:55.147
It likes to hog electrons,

00:02:55.147 --> 00:02:58.738
so this is oxygen is being reduced.

00:02:58.738 --> 00:03:02.985
Oxygen, Oxygen reduced.

00:03:03.336 --> 00:03:06.404
So if you just directly
transferred these electrons

00:03:06.404 --> 00:03:09.357
from our NADH to the Oxygen,

00:03:09.357 --> 00:03:10.916
it would release a lot of energy

00:03:10.916 --> 00:03:12.142
but it would release so much energy

00:03:12.142 --> 00:03:13.505
that you wouldn't be able
to capture most of it.

00:03:13.505 --> 00:03:16.766
You wouldn't be able to use
it to actually do useful work,

00:03:16.766 --> 00:03:19.971
and so the process of
Oxidative Phosphorylation

00:03:19.971 --> 00:03:23.801
is all about doing this
at a series of steps

00:03:23.801 --> 00:03:26.367
and we do it by
transferring these electrons

00:03:26.367 --> 00:03:29.721
from one electron acceptor
to another electron acceptor,

00:03:29.721 --> 00:03:32.904
and every time we do that,
we release some energy,

00:03:32.904 --> 00:03:35.800
and then that energy can be,
in a more controlled way,

00:03:35.800 --> 00:03:38.729
be used to actually do
work, and in this case,

00:03:38.729 --> 00:03:42.065
that work is pumping hydrogen protons

00:03:42.065 --> 00:03:45.002
across a membrane, and then
that gradient that forms

00:03:45.002 --> 00:03:46.983
can actually be used to generate ATP,

00:03:46.983 --> 00:03:48.659
so let's talk through
it a little bit more.

00:03:48.659 --> 00:03:50.221
So we're gonna go, these electrons,

00:03:50.221 --> 00:03:51.247
they're gonna be transferred,

00:03:51.247 --> 00:03:52.544
and I won't go into all of the details,

00:03:52.544 --> 00:03:55.319
this is to just give you a
high-level overview of it.

00:03:55.319 --> 00:03:57.815
They're going to be transferred
to different acceptors

00:03:57.815 --> 00:03:59.735
which then transfer it
to another acceptor,

00:03:59.735 --> 00:04:02.456
so it might go to a Coenzyme,

00:04:02.456 --> 00:04:05.798
Coenzyme Q, and a Cytochrome,

00:04:06.609 --> 00:04:09.999
Cytochrome C, and it keeps
going to different things,

00:04:09.999 --> 00:04:12.974
eventually getting to this
state right over here,

00:04:12.974 --> 00:04:15.381
where those electrons can be accepted

00:04:15.381 --> 00:04:18.590
by the oxygen

00:04:18.590 --> 00:04:21.149
to actually form the
water, and the process,

00:04:21.149 --> 00:04:24.496
every step of the way,
energy is being released.

00:04:24.496 --> 00:04:27.677
Energy is being released,

00:04:27.677 --> 00:04:30.451
and this energy, as we
will see in a second,

00:04:30.451 --> 00:04:34.089
is being used to pump hydrogen protons

00:04:34.089 --> 00:04:37.441
across a membrane, and we're
gonna use that gradient

00:04:37.441 --> 00:04:40.174
to actually drive the production of ATP.

00:04:40.174 --> 00:04:42.194
So let's think about
that a little bit more.

00:04:42.194 --> 00:04:44.275
So let's zoom in on,

00:04:44.275 --> 00:04:45.798
on a mitochondria.

00:04:45.798 --> 00:04:47.621
So this is mitochondria.

00:04:47.621 --> 00:04:49.733
Let's say that's our mitochondria,

00:04:49.733 --> 00:04:52.334
and let me draw the inner membrane

00:04:52.334 --> 00:04:55.770
and then, these folds
in the inner membrane,

00:04:55.770 --> 00:04:57.574
the singular for them is crista.

00:04:57.574 --> 00:05:00.074
If we're talking about plurals, cristae.

00:05:00.074 --> 00:05:03.364
So we have these folds in the inner,

00:05:03.364 --> 00:05:05.760
in the inner membrane right over here.

00:05:05.760 --> 00:05:07.815
So just to be clear, what's going on,

00:05:07.815 --> 00:05:10.211
this is the outer membrane,

00:05:10.211 --> 00:05:11.632
outer membrane.

00:05:11.632 --> 00:05:15.483
That is the inner
membrane, inner membrane.

00:05:15.483 --> 00:05:18.483
The space between the outer
and the inner membrane,

00:05:18.483 --> 00:05:19.840
the space right over here,

00:05:19.840 --> 00:05:23.049
that is the intermembrane space.

00:05:23.049 --> 00:05:25.947
Intermembrane,

00:05:27.032 --> 00:05:29.728
membrane space.

00:05:29.728 --> 00:05:34.414
And then the space inside
the inner membrane,

00:05:34.414 --> 00:05:37.047
let me make that sure you
can read that space properly,

00:05:37.047 --> 00:05:41.414
this space over here, this is the Matrix.

00:05:41.414 --> 00:05:45.063
This is the Matrix, and
that is the location

00:05:45.063 --> 00:05:48.062
of our Citric acid Cycle
or our Krebs Cycle,

00:05:48.062 --> 00:05:50.962
and I can symbolize that
with this little cycle,

00:05:50.962 --> 00:05:52.952
we have a cycle going on here.

00:05:52.952 --> 00:05:56.195
And so that's where the bulk
of the NADH is being produced.

00:05:56.195 --> 00:05:58.738
Now we also talked about
some other coenzymes.

00:05:58.738 --> 00:06:01.677
In some books or classes,
you might hear about FAD

00:06:01.677 --> 00:06:06.055
being reduced to FADH2,
which can then be oxidized

00:06:06.055 --> 00:06:08.505
as part of Oxidative Phosphorylation.

00:06:08.505 --> 00:06:11.407
Other times, well actually,
that's going to be attached

00:06:11.407 --> 00:06:14.737
to an enzyme, and then that FADH2

00:06:14.737 --> 00:06:19.352
is used to reduce
Coenzyme Q to produce QH2,

00:06:19.352 --> 00:06:22.014
and then that participates
in Oxidative Phosphorylation,

00:06:22.014 --> 00:06:24.709
so you could think about
either one of these.

00:06:24.709 --> 00:06:26.531
I'll focus on QH2.

00:06:26.531 --> 00:06:27.972
Well, why should we focus on NADH

00:06:27.972 --> 00:06:30.077
because it's all a similar process?

00:06:30.077 --> 00:06:33.431
FADH2 or QH2 enters a little bit later

00:06:33.431 --> 00:06:34.493
down this process,

00:06:34.493 --> 00:06:37.848
so they don't produce as much energy

00:06:37.848 --> 00:06:41.285
but they still can be
used to help produce ATP,

00:06:41.285 --> 00:06:44.621
but anyway, our Citric acid Cycle,

00:06:44.621 --> 00:06:47.713
which we have shown in previous videos,

00:06:47.713 --> 00:06:49.892
that occurring in the matrix,

00:06:49.892 --> 00:06:52.183
and now let me do a little zoom in here,

00:06:52.183 --> 00:06:53.739
let me do a zoom in.

00:06:53.739 --> 00:06:56.662
So if I were to zoom in, let's say,

00:06:56.662 --> 00:06:59.185
let me do this in a color that we can see,

00:06:59.185 --> 00:07:03.306
so if I were to zoom in right over there,

00:07:03.306 --> 00:07:06.765
let's show this fold
in the inner membrane,

00:07:06.765 --> 00:07:08.639
and it's very, and let's make it clear

00:07:08.639 --> 00:07:10.833
that this is, like all of these membranes,

00:07:10.833 --> 00:07:13.711
these are all phospholipid bilayers,

00:07:13.711 --> 00:07:17.414
so, let me draw,

00:07:17.414 --> 00:07:20.293
let me do the same
color that I did in the,

00:07:20.293 --> 00:07:22.011
the actual diagram.

00:07:22.011 --> 00:07:24.799
So, we have...

00:07:26.912 --> 00:07:30.258
all these, we have a
bilayer of phospholipids

00:07:30.258 --> 00:07:33.879
and I'm clearly not drawing
any of this stuff to scale,

00:07:34.445 --> 00:07:39.215
so, almost done.

00:07:39.215 --> 00:07:42.233
All right, just to make it clear.

00:07:44.757 --> 00:07:46.262
And you have these enzymes

00:07:46.262 --> 00:07:49.443
that go across the phospholipid bilayer,

00:07:49.443 --> 00:07:51.444
and these enzymes are,

00:07:51.444 --> 00:07:54.187
and these protein complexes
are actually what facilitate

00:07:54.187 --> 00:07:56.125
Oxidative Phosphorylation

00:07:56.125 --> 00:07:59.475
and this chain of enzymes,

00:07:59.475 --> 00:08:02.637
this chain of proteins, is
what we call the electron,

00:08:02.637 --> 00:08:05.938
or what we call the
electron transport chain.

00:08:05.938 --> 00:08:08.074
So we draw that.

00:08:08.074 --> 00:08:11.376
So maybe this is one protein,

00:08:11.376 --> 00:08:14.811
and I'm just drawing them
as kind of these abstract...

00:08:15.735 --> 00:08:17.755
You could refer to the
electron transport chain as

00:08:17.755 --> 00:08:19.695
these proteins or you could
view it as this process of

00:08:19.695 --> 00:08:21.513
these electrons going from
one acceptor to another,

00:08:21.513 --> 00:08:24.137
eventually making its way
all the way to the oxygen.

00:08:24.137 --> 00:08:26.215
So that might be one protein,

00:08:26.215 --> 00:08:29.984
this is another protein right over here.

00:08:29.984 --> 00:08:30.932
I'll just do a couple,

00:08:30.932 --> 00:08:33.489
and this is really about
a high-level overview,

00:08:33.489 --> 00:08:35.193
and what's happening

00:08:36.974 --> 00:08:39.818
is as the, and this is
just gonna be a very

00:08:39.818 --> 00:08:42.135
high-level simplification of it,

00:08:42.135 --> 00:08:45.305
as you have your, let's say initially,

00:08:45.305 --> 00:08:47.929
your NADH comes in,

00:08:47.929 --> 00:08:50.935
so your NADH comes in,

00:08:50.935 --> 00:08:53.521
and it donates the
protons and the electrons

00:08:53.521 --> 00:08:56.319
and then it become NAD+,

00:08:56.319 --> 00:08:58.896
so it just became oxidized,

00:08:58.896 --> 00:09:00.907
those electrons will go to an acceptor

00:09:00.907 --> 00:09:02.946
which then gets transferred
to another acceptor

00:09:02.946 --> 00:09:05.008
then get transferred to another acceptor,

00:09:05.008 --> 00:09:07.332
and it goes through this
electron transport chain

00:09:07.332 --> 00:09:09.022
and as that energy is released,

00:09:09.022 --> 00:09:13.606
that energy is used to pump
hydrogen protons from the Matrix

00:09:13.896 --> 00:09:15.951
so this side right over here,
the left side right over here,

00:09:15.951 --> 00:09:17.663
this is the Matrix.

00:09:17.663 --> 00:09:20.798
This is where our Citric
acid Cycle occurs,

00:09:20.798 --> 00:09:23.730
so we have protons being pumped out,

00:09:23.730 --> 00:09:27.179
so we have these protons being pumped out

00:09:27.179 --> 00:09:28.850
as we release energy,

00:09:28.850 --> 00:09:31.589
as we go from one electron acceptor

00:09:31.589 --> 00:09:33.819
to another electron acceptor,

00:09:33.819 --> 00:09:36.406
and so electrons are going
from higher energy states

00:09:36.406 --> 00:09:39.180
and they're releasing
energy as they go down

00:09:39.180 --> 00:09:42.892
this kind of a, towards more
and more electronegative things

00:09:42.892 --> 00:09:44.605
and they feel more
comfortable with the water

00:09:44.605 --> 00:09:47.484
than they feel, than
they felt with the NADH,

00:09:47.484 --> 00:09:50.780
and by doing so, by these
electrons going down

00:09:50.780 --> 00:09:52.232
that gradient, I guess you could say,

00:09:52.232 --> 00:09:54.497
or maybe a better way, from going from a,

00:09:54.497 --> 00:09:56.674
a higher energy state
to a lower energy state,

00:09:56.674 --> 00:09:59.194
we are creating this proton gradient,

00:09:59.194 --> 00:10:01.271
so the concentration of protons

00:10:01.271 --> 00:10:03.477
on the right side of this membrane,

00:10:03.477 --> 00:10:05.020
just to be clear where this is.

00:10:05.020 --> 00:10:08.138
This space right over here,
this is right over there,

00:10:08.138 --> 00:10:10.240
that's the intermembrane space

00:10:10.240 --> 00:10:14.593
where the hydrogen proton
concentration is building up.

00:10:14.593 --> 00:10:17.810
Now, this is stored
energy because this is a

00:10:18.213 --> 00:10:20.490
electrochemical gradient,
all this positive charge,

00:10:20.490 --> 00:10:21.680
they want to get away from each other,

00:10:21.680 --> 00:10:25.234
they want to go to this less
positive Matrix right over here

00:10:25.234 --> 00:10:27.005
and also, just you have
a higher concentration

00:10:27.005 --> 00:10:29.362
of hydrogens and just natural diffusion.

00:10:29.362 --> 00:10:31.684
They would want to go down
their concentration gradient

00:10:31.684 --> 00:10:32.621
into the Matrix.

00:10:32.621 --> 00:10:34.699
There's less of the protons here.

00:10:34.699 --> 00:10:37.741
There's less of the protons in the Matrix

00:10:37.741 --> 00:10:40.189
than there are

00:10:40.189 --> 00:10:43.036
in the intermembrane space,

00:10:43.036 --> 00:10:47.181
and so, that's the opportunity
to now take that energy

00:10:47.181 --> 00:10:49.364
and produce ATP with them,

00:10:49.364 --> 00:10:52.189
and the way that this
happens, the way this happens,

00:10:52.189 --> 00:10:54.149
let me extend my membrane a little bit,

00:10:54.149 --> 00:10:56.167
that's a different color,

00:10:56.167 --> 00:10:59.011
so let me extend my membrane a little bit,

00:10:59.011 --> 00:11:02.611
is using a protein

00:11:02.611 --> 00:11:05.224
called ATP synthase.

00:11:05.224 --> 00:11:08.913
ATP synthase is actually a
protein complex, I should say.

00:11:08.913 --> 00:11:11.509
So ATP synthase, really an enzyme,

00:11:11.509 --> 00:11:13.883
and ATP synthase goes across...

00:11:13.883 --> 00:11:16.339
It's actually a fascinating,
fascinating molecule.

00:11:16.339 --> 00:11:18.720
I'll show a better
diagram of it in a second,

00:11:18.720 --> 00:11:21.418
but your ATP synthase
goes across the membrane,

00:11:21.418 --> 00:11:23.969
it actually has a fairly
mechanical structure

00:11:23.969 --> 00:11:25.698
where it has a bit of a housing

00:11:25.698 --> 00:11:29.016
and it has an axle in the housing,

00:11:29.016 --> 00:11:31.867
so it looks, maybe, something like this,

00:11:31.867 --> 00:11:32.903
and it actually has something,

00:11:32.903 --> 00:11:34.988
you can view this as a, as a thing

00:11:34.988 --> 00:11:36.888
that maybe holds it together,

00:11:36.888 --> 00:11:38.220
so it's going across the membrane,

00:11:38.220 --> 00:11:41.017
I'll show a better
diagram of it in a second.

00:11:41.017 --> 00:11:44.313
So then, of course, the
membrane continues on,

00:11:44.313 --> 00:11:47.924
the membrane continues
on, and what happens is

00:11:47.924 --> 00:11:49.794
it allows these hydrogen protons

00:11:49.794 --> 00:11:52.413
to flow down their
electrochemical gradient,

00:11:52.413 --> 00:11:54.706
so these hydrogen protons go down

00:11:54.706 --> 00:11:57.388
and they actually cause the axle to spin,

00:11:57.388 --> 00:11:59.020
and so maybe I'll draw it this way.

00:11:59.020 --> 00:12:03.141
They actually cause the axle to spin

00:12:03.141 --> 00:12:05.157
as they go

00:12:05.157 --> 00:12:07.141
down their electrochemical gradient,

00:12:07.141 --> 00:12:10.537
and as this axle spins,
this axle is not the smooth,

00:12:10.537 --> 00:12:11.997
it's not like it's made
out of metal or something,

00:12:11.997 --> 00:12:14.254
it's made out of amino
acids, so it's got this,

00:12:14.254 --> 00:12:17.246
it's all bumpy and all the rest,

00:12:17.246 --> 00:12:18.918
so it looks something like this,

00:12:18.918 --> 00:12:21.657
and what happens is you have ADPs,

00:12:21.657 --> 00:12:23.452
you have ADPs that get lodged in here,

00:12:23.452 --> 00:12:26.865
so let's say that's an ADP,
and then a phosphate group,

00:12:26.865 --> 00:12:28.422
and they have actually
three different sites

00:12:28.422 --> 00:12:29.943
where this can happen,

00:12:29.943 --> 00:12:32.569
so that's an ADP and a phosphate group,

00:12:32.569 --> 00:12:34.305
and there's another site
that I'm not drawing,

00:12:34.305 --> 00:12:36.099
but as this thing rotates,

00:12:36.099 --> 00:12:38.673
it essentially keeps changing
the confirmation protein

00:12:38.673 --> 00:12:41.244
and jams the phosphate group into the ADP

00:12:41.244 --> 00:12:43.289
which takes energy and
locks them into place

00:12:43.289 --> 00:12:44.444
to form the ATP.

00:12:44.444 --> 00:12:45.804
When they form the ATP,

00:12:45.804 --> 00:12:49.579
they no longer attach to the active site

00:12:49.579 --> 00:12:50.879
and they let go.

00:12:50.879 --> 00:12:52.686
So you have this,

00:12:52.686 --> 00:12:54.172
actually, this mechanical motor,

00:12:54.172 --> 00:12:56.384
you can view this almost like
a turbine, a water turbine.

00:12:56.384 --> 00:12:58.226
The water goes through
it and then that energy

00:12:58.226 --> 00:12:59.610
is used to generate electricity.

00:12:59.610 --> 00:13:01.592
Here, hydrogen protons go down

00:13:01.592 --> 00:13:03.063
their electrochemical gradient,

00:13:03.063 --> 00:13:06.645
that rotary motion is then
used to jam phosphate groups

00:13:06.645 --> 00:13:09.356
onto ADPs to form ATPs,

00:13:09.356 --> 00:13:12.455
and so this is the actual
ATP production going on.

00:13:12.455 --> 00:13:15.760
And to get a better appreciation

00:13:15.760 --> 00:13:16.579
for what's going on,

00:13:16.579 --> 00:13:17.876
this is going on in your body right now,

00:13:17.876 --> 00:13:18.789
this is going on in my body,

00:13:18.789 --> 00:13:19.899
otherwise I wouldn't be able to talk.

00:13:19.899 --> 00:13:22.842
This is how I'm generating my energy.

00:13:22.842 --> 00:13:26.233
This is a more accurate depiction

00:13:26.233 --> 00:13:29.355
of ATP synthase right over here,

00:13:29.355 --> 00:13:31.979
and based on this diagram,

00:13:31.979 --> 00:13:33.260
this is our...

00:13:34.852 --> 00:13:36.763
let me make sure I...

00:13:36.763 --> 00:13:39.006
So this right over here,

00:13:41.962 --> 00:13:45.522
I'm having trouble drawing on this,

00:13:45.522 --> 00:13:47.026
let me see if I can...

00:13:47.580 --> 00:13:51.110
So this part right over here,

00:13:51.110 --> 00:13:53.061
this area right over there,

00:13:53.061 --> 00:13:55.371
that's our intermembrane space.

00:13:55.371 --> 00:13:58.187
This right over here is our,

00:13:58.187 --> 00:14:00.646
this over here is our Matrix.

00:14:01.476 --> 00:14:04.692
This membrane, this is
a phospholipid bilayer,

00:14:04.692 --> 00:14:08.799
so if I wanted, I could draw
the bilayer of phospholipids

00:14:09.378 --> 00:14:10.574
right over here,

00:14:10.574 --> 00:14:11.644
and this is our inner membrane

00:14:11.644 --> 00:14:13.439
or we could say this is a
fold in the inner membrane,

00:14:13.439 --> 00:14:15.842
this could be on our crista,

00:14:15.842 --> 00:14:18.338
and so the hydrogen protons, they build up

00:14:19.508 --> 00:14:21.089
in the intermembrane space

00:14:21.089 --> 00:14:23.348
because of the electron transport chain,

00:14:23.348 --> 00:14:24.929
and then they flow down

00:14:26.284 --> 00:14:28.452
their electrochemical gradient,

00:14:28.452 --> 00:14:29.767
turn this rotor,

00:14:29.767 --> 00:14:32.710
and then they cause the
creation of the ATPs over here,

00:14:32.710 --> 00:14:35.419
so you have ADP

00:14:36.863 --> 00:14:38.311
plus a phosphate group

00:14:38.311 --> 00:14:41.592
and then you produce your ATP.

00:14:41.592 --> 00:14:42.894
So this is fascinating,

00:14:42.894 --> 00:14:44.537
this is going on in
the cells of your body,

00:14:44.537 --> 00:14:45.886
this is going on as we speak.

00:14:45.886 --> 00:14:48.200
It's not some abstract thing
that is somehow separate

00:14:48.200 --> 00:14:49.437
from your reality.

00:14:49.437 --> 00:14:52.438
This is what is making
your reality possible.

00:14:52.438 --> 00:14:54.429
So hopefully, you get a
nice appreciation for this.

00:14:54.429 --> 00:14:55.870
I mean, we spent a lot of time

00:14:55.870 --> 00:14:57.495
talking about cellular respiration,

00:14:57.495 --> 00:14:59.090
we spent a lot of time talking about,

00:14:59.090 --> 00:15:01.282
OK, we can produce some ATPs directly

00:15:01.282 --> 00:15:04.770
through glycolysis and
through the Citric acid Cycle,

00:15:04.770 --> 00:15:06.489
but mostly, most of the energy

00:15:06.489 --> 00:15:08.404
is because of the reduction
of these coenzymes

00:15:08.404 --> 00:15:10.930
and especially, NAD to NADH,

00:15:10.930 --> 00:15:13.573
and then in Oxidative Phosphorylation

00:15:13.573 --> 00:15:15.163
and the electron transport chain,

00:15:15.163 --> 00:15:19.304
we use the Oxidation of the NADH

00:15:19.304 --> 00:15:22.874
to pump hydrogen protons from the Matrix

00:15:22.874 --> 00:15:24.429
to the intermembrane space,

00:15:24.429 --> 00:15:26.211
and then let them go back through,

00:15:26.211 --> 00:15:29.203
through the ATP synthase
which jams the phosphate

00:15:29.203 --> 00:15:31.941
into the ADP to produce the ATP,

00:15:31.941 --> 00:15:35.153
which is our biological
currency of energy.


Overview of cellular respiration

WEBVTT
Kind: captions
Language: en

00:00:00.511 --> 00:00:02.211
- [Voiceover] So what I
wanna do in this video

00:00:02.211 --> 00:00:06.131
is give ourselves an overview
of cellular respiration.

00:00:06.131 --> 00:00:08.991
It can be a pretty involved
process, and even the way

00:00:08.991 --> 00:00:10.591
I'm gonna do it, as messy as it looks,

00:00:10.591 --> 00:00:12.511
is going to be cleaner
than actually what goes

00:00:12.511 --> 00:00:15.111
on inside of your cells,
and other organs themselves,

00:00:15.111 --> 00:00:16.892
because I'm going to show clearly from

00:00:16.892 --> 00:00:18.782
going from glucose,
and then see how we can

00:00:18.782 --> 00:00:22.521
produce ATP through glycolysis,
and the Krebs cycle,

00:00:22.521 --> 00:00:24.261
and oxidative phosphorylation,

00:00:24.261 --> 00:00:26.642
but in reality, all sorts
of molecules can jump in

00:00:26.642 --> 00:00:28.463
at different parts of the
chain, and then jump out

00:00:28.463 --> 00:00:31.323
at different parts of the chain,
to go along other pathways.

00:00:31.323 --> 00:00:35.097
But I'll show, kind of
the traditional narrative.

00:00:35.097 --> 00:00:37.957
So we're gonna start
off, for this narrative,

00:00:37.957 --> 00:00:39.356
we're gonna start off with glucose.

00:00:39.356 --> 00:00:42.336
We have a six-carbon-chain
right over here.

00:00:42.336 --> 00:00:45.816
And we have the process of
glycosis, which is occurring

00:00:45.816 --> 00:00:49.736
in the cytosol, the cytosol of our cells.

00:00:49.736 --> 00:00:51.336
So if this is a cell right over here,

00:00:51.336 --> 00:00:53.737
you can imagine, well the glycolysis,

00:00:54.307 --> 00:00:58.119
the glycolysis could be
occurring right over there.

00:00:58.429 --> 00:01:01.972
And that process of glycolysis
is essentially splitting up

00:01:01.972 --> 00:01:04.175
this six-carbon glucose molecule

00:01:04.175 --> 00:01:05.655
into two three-carbon molecules,

00:01:05.655 --> 00:01:07.995
and these three-carbon molecules,

00:01:07.995 --> 00:01:11.365
we go into detail in another
video, we call these pyruvate.

00:01:11.849 --> 00:01:14.119
Pyruvate.

00:01:14.369 --> 00:01:16.549
And in the process of
doing so, and this is,

00:01:16.549 --> 00:01:18.289
I guess you could say,
the point of glycolysis,

00:01:18.289 --> 00:01:21.026
we're able to, on a net
basis, produce two ATP's.

00:01:21.026 --> 00:01:23.366
We actually produce four,
but we have to use two,

00:01:23.366 --> 00:01:25.866
so on a net basis, we produce two ATP's.

00:01:25.866 --> 00:01:27.806
I'm gonna keep a little
table here, to keep track.

00:01:27.806 --> 00:01:32.283
So we produce two ATP's, and we are also,

00:01:32.283 --> 00:01:34.922
we're also, in the process of that,

00:01:34.922 --> 00:01:39.308
we reduce two NAD molecules to NADH.

00:01:39.308 --> 00:01:41.748
Remember, reduction is
gaining of electrons.

00:01:41.748 --> 00:01:43.988
And you see over here,
this is positively charged,

00:01:43.988 --> 00:01:46.728
this is neutrally charged, it
essentially gains a hydride.

00:01:46.728 --> 00:01:48.410
So this is reduction.

00:01:48.956 --> 00:01:49.476
Reduction.

00:01:49.476 --> 00:01:52.203
And if we go all the
way through the pathway,

00:01:52.203 --> 00:01:54.083
all the way to oxidative phosphorylation,

00:01:54.083 --> 00:01:58.343
the electronic transport chain,
these NADH's, the reduced

00:01:58.343 --> 00:02:02.619
form of NAD, they can be, then, oxidized,

00:02:02.619 --> 00:02:05.699
and in doing so, more energy
is provided to produce

00:02:05.699 --> 00:02:07.999
even more ATP's, but we'll get to that.

00:02:07.999 --> 00:02:10.549
So you're also gonna get two NADH's.

00:02:10.866 --> 00:02:13.756
Two NADH's get produced.

00:02:14.266 --> 00:02:16.166
Now at that point, you
could kind of think of it

00:02:16.166 --> 00:02:17.846
as a little bit of a decision point.

00:02:17.846 --> 00:02:19.966
If there's no oxygen around, or if

00:02:19.966 --> 00:02:21.806
you're the type of organism that doesn't

00:02:21.806 --> 00:02:23.326
want to continue, for some reason,

00:02:23.326 --> 00:02:25.226
with cellular respiration,
or doesn't know how,

00:02:25.226 --> 00:02:27.826
this pyruvate can be
used for fermentation.

00:02:27.826 --> 00:02:30.006
We have videos on fermentation,

00:02:30.006 --> 00:02:32.935
lactic acid fermentation,
alcohol fermentation,

00:02:32.935 --> 00:02:35.695
and fermentation is all
about using the pyruvates

00:02:35.695 --> 00:02:40.196
to oxidize your NADH back into NAD,

00:02:40.196 --> 00:02:42.682
so it could be re-used
again, for glycolysis.

00:02:42.682 --> 00:02:45.400
So even though the NADH has energy

00:02:45.400 --> 00:02:47.480
that could eventually
be converted into ATP,

00:02:47.480 --> 00:02:48.984
and even though pyruvates have energy

00:02:48.984 --> 00:02:51.806
that could eventually
be converted into ATP,

00:02:51.806 --> 00:02:54.286
when you do fermentation,
you kinda give up on that,

00:02:54.286 --> 00:02:55.826
and you just view them as waste products,

00:02:55.826 --> 00:02:59.986
and you use the pyruvate to
convert the NADH back into NAD,

00:02:59.986 --> 00:03:03.196
And then, glycolysis can occur again.

00:03:03.196 --> 00:03:05.436
But let's assume we're not gonna go down

00:03:05.436 --> 00:03:07.816
the fermentation pathway, and we're

00:03:07.816 --> 00:03:09.176
gonna continue with traditional

00:03:09.176 --> 00:03:12.217
aerobic cellular
respiration, using oxygen.

00:03:12.787 --> 00:03:14.247
Well, the next thing
that's going to happen,

00:03:14.247 --> 00:03:16.467
is that the carboxyl group, and

00:03:16.467 --> 00:03:17.458
and everything I'm going to show now,

00:03:17.458 --> 00:03:19.047
it's going to happen for
each of these pyruvates.

00:03:19.047 --> 00:03:21.147
So, you can imagine these
things all happening twice.

00:03:21.147 --> 00:03:24.080
So I'm gonna multiply a
bunch of things, times two.

00:03:24.230 --> 00:03:25.548
But what happens in the next step,

00:03:25.548 --> 00:03:29.548
is this carboxyl group, this
carboxyl group is stripped

00:03:29.548 --> 00:03:33.168
off of the pyruvate, and it, essentially,

00:03:33.168 --> 00:03:35.351
is going to be released as carbon dioxide.

00:03:35.351 --> 00:03:38.135
So this is our carbon
dioxide being released here,

00:03:38.135 --> 00:03:40.735
and then the rest of our
pyruvate, which is, essentially,

00:03:40.735 --> 00:03:45.260
an acetyl group, that
latches onto coenzyme A.

00:03:45.610 --> 00:03:47.150
And you'll hear a lot about coenzyme A.

00:03:47.150 --> 00:03:49.810
Sometimes I'll write just CoA, like this.

00:03:49.810 --> 00:03:51.470
Sometimes I'll do CoA, and then

00:03:51.470 --> 00:03:53.825
the sulfur, bonded to the hyrdrogen.

00:03:53.825 --> 00:03:55.485
And the reason why they'll
draw the sulfur part,

00:03:55.485 --> 00:03:57.885
is because the sulfur is what bonds

00:03:57.885 --> 00:04:00.695
with the acetyl group, right over here.

00:04:01.702 --> 00:04:04.600
So, you have the carbon
dioxide being released, and

00:04:04.600 --> 00:04:09.020
then the acetyl group,
bonding with that sulfur,

00:04:09.020 --> 00:04:13.078
and by doing that, you form acetyl-CoA.

00:04:13.130 --> 00:04:14.825
And acetyl-CoA, just so
you know, you only see

00:04:14.825 --> 00:04:15.801
three letters here, but this is

00:04:15.801 --> 00:04:17.431
actually a fairly involved molecule.

00:04:17.741 --> 00:04:19.361
This is actually a picture of acetyl-CoA,

00:04:19.361 --> 00:04:20.961
I know it's really small, but hopefully

00:04:20.961 --> 00:04:23.201
you'll appreciate that it's
a more involved molecule.

00:04:23.201 --> 00:04:25.241
That, the acetyl group
that we're talking about

00:04:25.241 --> 00:04:29.292
is just this part, right over
here, and it's a coenzyme.

00:04:29.292 --> 00:04:32.292
It's really acting to
transfer that acetyl group,

00:04:32.292 --> 00:04:33.692
and we'll see that in a second.

00:04:33.692 --> 00:04:35.552
But it's also fun to
look at these molecules,

00:04:35.552 --> 00:04:37.112
because once again, we see these patterns

00:04:37.112 --> 00:04:40.252
over and over again in
biology or biochemistry.

00:04:40.252 --> 00:04:43.032
Acetyl-CoA, you have an
adenine right over here.

00:04:43.032 --> 00:04:45.329
It's hard to see, but you have a ribose,

00:04:45.329 --> 00:04:47.909
and you also have two phosphate groups.

00:04:47.909 --> 00:04:50.841
So this end of the
acetyl-CoA is essentially,

00:04:50.841 --> 00:04:53.471
is essentially an ADP.

00:04:53.701 --> 00:04:54.797
But it's used as a coenzyme.

00:04:54.797 --> 00:04:56.157
Everything that I'm talking about,

00:04:56.157 --> 00:04:57.657
this is all going to be facilitated

00:04:57.657 --> 00:04:59.837
by enzymes, and the enzymes will have

00:05:00.227 --> 00:05:03.830
cofactors, coenzymes, if
we're talking about organic

00:05:03.830 --> 00:05:06.375
cofactors, that are gonna
help facilitate things along.

00:05:06.375 --> 00:05:08.675
And as we see, the acetyl group joins on

00:05:08.675 --> 00:05:11.722
to the coenzyme A, forming acetyl-CoA,

00:05:12.012 --> 00:05:13.852
but that's just a temporary attachment.

00:05:13.852 --> 00:05:16.432
The acetyl-CoA is,
essentially, gonna transfer

00:05:16.432 --> 00:05:19.252
the acetyl group over to,
and now we're going to

00:05:19.252 --> 00:05:22.633
enter into the citric acid cycle.

00:05:22.633 --> 00:05:24.492
It's gonna transfer these two carbons

00:05:24.492 --> 00:05:28.552
over to oxaloacetic acid,
to form citric acid.

00:05:28.552 --> 00:05:30.472
So it's gonna transfer these two carbons

00:05:30.472 --> 00:05:33.832
to this one, two, three,
four carbon molecule,

00:05:33.832 --> 00:05:38.382
to form a one, two, three,
four, five, six carbon molecule.

00:05:38.692 --> 00:05:39.947
But before we go into the depths

00:05:39.947 --> 00:05:41.907
of the citric acid cycle,
I wanna make sure that

00:05:41.907 --> 00:05:43.827
I don't lose track of my accounting,

00:05:43.827 --> 00:05:46.968
because, even that step right over here,

00:05:46.968 --> 00:05:49.588
where we decarboxylated the pyruvate,

00:05:49.588 --> 00:05:53.088
we went from pyruvate to acetyl-CoA,

00:05:53.088 --> 00:05:56.370
that also reduced some NAD to NADH.

00:05:56.370 --> 00:05:58.910
Now, this is gonna happen
once for each pyruvate,

00:05:58.910 --> 00:05:59.701
but we're gonna-

00:05:59.701 --> 00:06:00.605
all the accounting we're gonna

00:06:00.605 --> 00:06:02.483
say, is for one glucose molecule.

00:06:02.483 --> 00:06:03.883
So for one glucose molecule, it's

00:06:03.883 --> 00:06:05.623
gonna happen for each of the pyruvates.

00:06:05.623 --> 00:06:07.223
So this is going to be times-

00:06:07.223 --> 00:06:09.682
This is going to be times two.

00:06:09.682 --> 00:06:10.844
So we're gonna produce two,

00:06:12.855 --> 00:06:15.215
two NADH's in this step, going

00:06:15.215 --> 00:06:17.425
from pyruvate to acetyl-CoA.

00:06:17.855 --> 00:06:20.055
Now, the bulk of, I guess you could say,

00:06:20.055 --> 00:06:23.397
the catabolism, of the
carbons, or the things that

00:06:23.397 --> 00:06:26.355
are eventually going to produce our ATP's,

00:06:26.355 --> 00:06:27.815
are going to happen in what we call

00:06:27.815 --> 00:06:29.862
the citric acid, or the Krebs cycle.

00:06:29.862 --> 00:06:32.122
It's called the citric
acid cycle because, when we

00:06:32.122 --> 00:06:35.200
transferred the acetyl
group from the coenzyme A

00:06:35.200 --> 00:06:38.621
to the oxaloacetic acid,
we formed citric acid.

00:06:38.621 --> 00:06:40.281
And citric acid, this is the thing

00:06:40.281 --> 00:06:42.921
that you have in lemons, or orange juice.

00:06:42.921 --> 00:06:45.581
It is this molecule right over here.

00:06:45.581 --> 00:06:49.181
And the citric acid cycle, it's
also called the Krebs cycle,

00:06:49.181 --> 00:06:51.722
when you first learn it,
seems very, very complex,

00:06:51.722 --> 00:06:54.262
and some could argue
that it is quite complex.

00:06:54.262 --> 00:06:57.782
But I'm just gonna give you an
overview of what's going on.

00:06:57.782 --> 00:07:00.382
The citric acid, once again, six-carboned,

00:07:00.382 --> 00:07:03.322
it keeps getting broken
down, through multiple steps,

00:07:03.322 --> 00:07:06.302
and I'm really not showing
all of the detail here,

00:07:06.302 --> 00:07:08.742
all the way back to oxaloacetic acid,

00:07:08.742 --> 00:07:12.042
where, then, it can accept
the two carbons again.

00:07:12.042 --> 00:07:14.121
And just to be clear, once the two carbons

00:07:14.121 --> 00:07:16.516
are released by the coenzyme A,

00:07:16.516 --> 00:07:18.835
then that coenzyme A can be used

00:07:18.835 --> 00:07:21.816
again, to decarboxylate some pyruvates.

00:07:21.816 --> 00:07:23.555
So there's a bunch of cycles going on.

00:07:23.555 --> 00:07:26.119
But the important take-away,
is as we go through the citric

00:07:26.119 --> 00:07:29.029
acid cycle, as we go from
one intermediary to the next,

00:07:29.029 --> 00:07:33.083
we keep reducing NAD to NADH,

00:07:33.083 --> 00:07:37.538
in fact, we do this three
times for each cycle

00:07:37.538 --> 00:07:39.318
of the citric acid cycle, but remember,

00:07:39.318 --> 00:07:42.438
we're gonna do this for each acetyl-CoA.

00:07:42.438 --> 00:07:43.798
For each pyruvate.

00:07:43.798 --> 00:07:46.158
So all of this stuff is
going to happen twice.

00:07:46.158 --> 00:07:47.917
So we're going to go through it twice

00:07:47.917 --> 00:07:50.126
for each original glucose molecule.

00:07:50.312 --> 00:07:55.032
So, here we have one, two,
three NADH's being produced,

00:07:55.032 --> 00:07:57.250
but since we're going
to go through it twice,

00:07:57.250 --> 00:07:58.231
and we're gonna be accounting for

00:07:58.231 --> 00:07:59.911
the original glucose
molecule, we could say

00:07:59.911 --> 00:08:01.494
that we have six

00:08:03.384 --> 00:08:06.065
six NADH's,

00:08:06.694 --> 00:08:10.584
or you could say, six
NAD's get reduced to NADH.

00:08:11.174 --> 00:08:12.434
Now, you also, in the process,

00:08:12.434 --> 00:08:14.901
as you're breaking down, going from

00:08:14.901 --> 00:08:17.221
the six-carbon molecule
to four-carbon molecule,

00:08:17.221 --> 00:08:20.420
you're releasing carbon,
as carbon dioxide,

00:08:20.420 --> 00:08:24.100
and you also have, traditionally
GDP being converted

00:08:24.100 --> 00:08:28.599
into GTP, or sometimes
ADP converted into ATP,

00:08:28.599 --> 00:08:32.166
but functionally, it's
equivalent to ATP, either way.

00:08:32.166 --> 00:08:34.466
So, we could also say
that we're gonna directly-

00:08:34.466 --> 00:08:36.329
Remember, we're gonna do
all of this stuff twice.

00:08:36.329 --> 00:08:40.133
So, we could say that two,

00:08:40.133 --> 00:08:41.733
I'll just say two ATP's,
to make it simple.

00:08:41.733 --> 00:08:44.833
We could say GTP, but I'll say two ATP's.

00:08:45.529 --> 00:08:47.672
Because once again, this
happens once in each cycle,

00:08:47.672 --> 00:08:50.410
but we're gonna do two
cycles, for each glucose.

00:08:50.410 --> 00:08:53.849
And then, we have this other
coenzyme right over here,

00:08:53.849 --> 00:08:56.715
FAD, that gets reduced to FADH2,

00:08:56.715 --> 00:08:59.147
but that stays covalently
attached to the enzymes

00:08:59.147 --> 00:09:01.779
that are facilitating it, so eventually,

00:09:02.839 --> 00:09:05.099
that's being used to reduce .

00:09:06.156 --> 00:09:08.802
coenzyme Q to QH2.

00:09:08.802 --> 00:09:10.682
So I'm just gonna write the QH2 here, but

00:09:10.682 --> 00:09:12.482
once again, you're gonna get two of these.

00:09:16.332 --> 00:09:21.102
So two QH2's.

00:09:21.594 --> 00:09:22.854
Now let's think about what the

00:09:22.854 --> 00:09:25.314
net product, over here, is going to be.

00:09:25.314 --> 00:09:28.254
And to think about it, we
should just, we'll just-

00:09:28.254 --> 00:09:30.914
I'll do a little bit of a shorthand.

00:09:30.914 --> 00:09:32.734
We'll go into more
detail in future videos.

00:09:33.509 --> 00:09:36.539
These coenzymes, the NADH,

00:09:36.539 --> 00:09:40.619
the QH2, these are going to be oxidized,

00:09:40.619 --> 00:09:42.979
during oxidative phosphorylation,

00:09:42.979 --> 00:09:44.999
and the electron transport chain,

00:09:44.999 --> 00:09:47.319
to create a proton gradient across

00:09:47.319 --> 00:09:50.638
the inner membrane of mitochondria.

00:09:50.638 --> 00:09:52.098
We're gonna go into much
more detail in the future,

00:09:52.098 --> 00:09:53.516
but that proton gradient is going

00:09:53.516 --> 00:09:56.434
to be used to produce more ATP.

00:09:56.434 --> 00:09:58.901
And one way to think about it, is

00:09:58.901 --> 00:10:03.221
each NADH is going to produce,

00:10:03.221 --> 00:10:06.421
and I've seen accounts, it
depends on the efficiency,

00:10:06.421 --> 00:10:08.623
and where the NADH is actually going

00:10:08.623 --> 00:10:11.081
to be produced, but it's going to produce

00:10:11.081 --> 00:10:15.641
anywhere between two and three ATP's.

00:10:17.666 --> 00:10:21.414
Each of the reduced coenzyme Q's,

00:10:21.414 --> 00:10:23.874
so QH2,

00:10:23.874 --> 00:10:27.311
that's going to each produce
about one and a half ATP's.

00:10:27.311 --> 00:10:28.830
And people are still getting a good handle

00:10:28.830 --> 00:10:30.230
on exactly how this is happening.

00:10:30.230 --> 00:10:31.610
It depends on the efficiency of the cell,

00:10:31.610 --> 00:10:33.914
and what the cell is
actually trying to do.

00:10:34.637 --> 00:10:37.277
So, using these ranges, actually I'll say

00:10:37.277 --> 00:10:41.267
one and a half to two ATP's.

00:10:41.783 --> 00:10:43.743
And these are approximate numbers.

00:10:43.743 --> 00:10:46.366
So let's think about what
our total accounting is.

00:10:46.366 --> 00:10:49.226
So if we just count up
the ATP or the GTP's,

00:10:49.226 --> 00:10:52.906
we're gonna get two there, two there.

00:10:52.906 --> 00:10:55.067
So we're gonna have four direct,

00:10:55.067 --> 00:10:58.997
or very close to direct,
ATP's net, being created.

00:10:59.147 --> 00:11:00.827
And then how many NADH's?

00:11:00.827 --> 00:11:04.117
We have two, four, and then we add six.

00:11:04.117 --> 00:11:05.433
We have ten NADH's.

00:11:05.923 --> 00:11:09.159
Ten NADH's.

00:11:09.721 --> 00:11:13.677
And then, we have two of the coenzyme Q's.

00:11:13.773 --> 00:11:16.323
Two QH2's.

00:11:16.633 --> 00:11:18.453
So that's gonna be four ATP's,

00:11:18.453 --> 00:11:20.037
this is going to be between-

00:11:20.037 --> 00:11:24.257
this is going to be
between 20 and 30 NADH's.

00:11:24.257 --> 00:11:25.937
Sorry, 20 and 30 ATP's.

00:11:25.937 --> 00:11:28.687
20 to 30 ATP's.

00:11:29.837 --> 00:11:32.327
And then, this is going
to be three to four.

00:11:32.879 --> 00:11:34.810
Three to four ATP's.

00:11:35.259 --> 00:11:36.120
So if you add them all together,

00:11:36.120 --> 00:11:37.940
if you add the low ends
of the range, you get,

00:11:37.940 --> 00:11:40.780
let's see, 20 plus three, plus four.

00:11:40.780 --> 00:11:42.982
That's 27 ATP's.

00:11:42.982 --> 00:11:46.282
27 ATP's.

00:11:46.282 --> 00:11:48.305
And the high end of the range, let's see.

00:11:48.305 --> 00:11:51.055
You have four plus 30 plus four.

00:11:51.385 --> 00:11:52.531
You have 38.

00:11:52.531 --> 00:11:55.161
38 ATP's.

00:11:55.271 --> 00:11:57.531
And 38 ATP's is currently
considered to become

00:11:57.531 --> 00:11:59.791
the theoretical maximum,
but when we actually

00:11:59.791 --> 00:12:01.414
observe things in cells, it looks like

00:12:01.414 --> 00:12:05.217
it comes right at around 29 to 30 ATP's.

00:12:05.217 --> 00:12:06.837
And once again, it depends what the cell's

00:12:06.837 --> 00:12:10.097
trying to do, the type of cells,
and the type of efficiency.

00:12:10.097 --> 00:12:13.458
But all of this is happening
through cellular respiration.

00:12:13.458 --> 00:12:14.878
And just to get a better sense

00:12:14.878 --> 00:12:16.958
of where all of this is occurring.

00:12:16.958 --> 00:12:17.746
Where all of this is occuring,

00:12:17.746 --> 00:12:20.006
we said glycolosis is
occurring in the cytosol.

00:12:20.006 --> 00:12:23.726
The citric acid cycle,
this is occurring in

00:12:24.831 --> 00:12:28.311
the matrix of the mytochondria.

00:12:28.311 --> 00:12:30.771
So this space right over here,

00:12:30.771 --> 00:12:32.414
that is the citric acid cycle,

00:12:32.414 --> 00:12:34.994
in that little magenta
space that I've drawn.

00:12:34.994 --> 00:12:36.334
So that's the matrix.

00:12:36.334 --> 00:12:37.614
In the video on mitochondria, we go

00:12:37.614 --> 00:12:39.214
into much more detail on that.

00:12:39.214 --> 00:12:41.834
And then, the actual conversion of

00:12:41.834 --> 00:12:44.674
the coenzymes, of the
electron transport chain,

00:12:44.674 --> 00:12:47.734
that's occurring across
the membrane of the crista.

00:12:47.734 --> 00:12:51.314
And the crista are these
folds, these kind of,

00:12:51.314 --> 00:12:53.554
inner membrane folds, of our mitochondria.

00:12:53.554 --> 00:12:57.354
So, it's occurring across the membranes

00:12:57.354 --> 00:13:01.634
of those, actually the plural is cristae.

00:13:01.634 --> 00:13:05.697
Crista is the singular of the cristae.

00:13:05.697 --> 00:13:08.527
And we'll go into more detail
into that, in other videos.