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PROFESSOR: So today we're going
to do an example of

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00:00:26,940 --> 00:00:34,780
using some of the equilibrium
concepts that we've learned to

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00:00:34,780 --> 00:00:36,370
drug design.

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00:00:36,370 --> 00:00:38,890
And it's going to be an example
that's out in the

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literature.

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00:00:39,410 --> 00:00:44,210
And potentially a very big
deal if you can do

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00:00:44,210 --> 00:00:46,220
drug design this way.

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00:00:46,220 --> 00:00:49,920
And it's an example of how,
remember how I told you that

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00:00:49,920 --> 00:00:52,680
if you have the Gibbs free
energy, you have everything

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00:00:52,680 --> 00:00:56,730
and how clueless I was as a
graduate student, and when I

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00:00:56,730 --> 00:01:00,130
look back I think how silly it
was for me not to realize how

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00:01:00,130 --> 00:01:01,050
important it was.

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00:01:01,050 --> 00:01:04,750
Well, this is an example where
people calculate delta G's or

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00:01:04,750 --> 00:01:08,720
Gibbs free energy changes for
binding of proteins to

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00:01:08,720 --> 00:01:10,450
receptors on cells,
or ligands.

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00:01:10,450 --> 00:01:14,830
And from that, design drugs that
work much better than the

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00:01:14,830 --> 00:01:15,610
real thing.

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00:01:15,610 --> 00:01:19,330
And it's all about calculating
delta G. We're going to see

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00:01:19,330 --> 00:01:23,580
how that is, and how that comes
in with equilibrium.

27
00:01:23,580 --> 00:01:27,070
So the paper that this
is based on was

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00:01:27,070 --> 00:01:28,230
published in 2002.

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00:01:28,230 --> 00:01:33,240
And since then there have
been larger-scale

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00:01:33,240 --> 00:01:34,600
trials, animal trials.

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00:01:34,600 --> 00:01:39,010
And I believe there have been
human trials of this concept,

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00:01:39,010 --> 00:01:42,420
of this drug that they
have designed.

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00:01:42,420 --> 00:01:47,540
You've got the reference
in the notes.

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00:01:47,540 --> 00:01:51,580
And we're going to have to do
a little bit of review of

35
00:01:51,580 --> 00:01:58,730
biology first, to figure
out what's going on.

36
00:01:58,730 --> 00:02:08,340
And this particular process,
this particular drug, is

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00:02:08,340 --> 00:02:11,650
called the, I have
it right here,

38
00:02:11,650 --> 00:02:13,920
granulocyte stimulating factor.

39
00:02:13,920 --> 00:02:15,880
Where was it in here?

40
00:02:15,880 --> 00:02:32,040
To give you the right
name for it.

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00:02:32,040 --> 00:02:35,680
There it is.

42
00:02:35,680 --> 00:02:40,300
It's a protein drug
called GCSF.

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00:02:40,300 --> 00:02:43,270
Granulocyte Colony Stimulating
Factor.

44
00:02:43,270 --> 00:02:48,280
And it's there's wild
tie for natural

45
00:02:48,280 --> 00:02:49,940
version of this protein.

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00:02:49,940 --> 00:02:54,520
That is generated by
normal tissue.

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00:02:54,520 --> 00:03:01,230
And this protein goes to the
blood, to the bone marrow.

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00:03:01,230 --> 00:03:05,320
And it binds the receptors on
cells that are in the blood

49
00:03:05,320 --> 00:03:07,800
and the bone marrow, and
stimulates the growth of white

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00:03:07,800 --> 00:03:13,650
blood cells, and stem cells, and
also acts to tell the bone

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00:03:13,650 --> 00:03:19,630
marrow to pump out these stem
cells into the blood.

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00:03:19,630 --> 00:03:26,260
And the problem is that if you
have a chemotherapy patient,

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00:03:26,260 --> 00:03:31,210
their bone marrow cells are
largely destroyed through the

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00:03:31,210 --> 00:03:32,370
chemotherapy.

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00:03:32,370 --> 00:03:34,800
And so they have a problem
with the white blood cell

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00:03:34,800 --> 00:03:38,060
counts, and with stem cell
counts and all that stuff.

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00:03:38,060 --> 00:03:40,630
So one of the ways that you
can try to reverse this

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00:03:40,630 --> 00:03:45,460
problem is by stimulating,
artificially stimulating the

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00:03:45,460 --> 00:03:51,610
growth or the proliferation of
these white blood cells.

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00:03:51,610 --> 00:03:56,030
And one of the ways you could
do that is by giving the

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00:03:56,030 --> 00:04:00,180
patient a lot of this protein,
granulocyte colony stimulating

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00:04:00,180 --> 00:04:03,760
factor, to stimulate the output
of white blood cells

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00:04:03,760 --> 00:04:04,850
from the bone marrow.

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Whatever is left of
the bone marrow.

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00:04:07,490 --> 00:04:11,790
To rebuild it up.

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And so that's done with wild
type, with protein.

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You can make the wild
type protein.

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But if you had something that
was basically the same thing

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but somehow mutated, where you
made a few changes to the

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00:04:28,080 --> 00:04:32,780
amino acid sequence, so that it
worked a little bit better,

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00:04:32,780 --> 00:04:37,750
then you might have a lot of
people, a lot of patients.

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00:04:37,750 --> 00:04:40,490
And that's what the basis
of this paper is, that's

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00:04:40,490 --> 00:04:40,970
referenced here.

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00:04:40,970 --> 00:04:46,050
Is how to go about mutating this
protein here to make it a

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00:04:46,050 --> 00:04:47,700
drug that would be
more effective

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00:04:47,700 --> 00:04:49,640
then the natural protein.

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So that you can give
it to patients.

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00:04:54,020 --> 00:04:57,160
So now let me go back and tell
you a little bit about this

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00:04:57,160 --> 00:04:59,270
equilibrium that we're
talking about.

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00:04:59,270 --> 00:05:00,790
So we've been talking
about equilibria of

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molecules coming together.

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And then creating
new molecules,

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00:05:05,820 --> 00:05:07,480
products and reactants.

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00:05:07,480 --> 00:05:10,790
Well, when you're talking about
ligands and receptors on

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cells, the same sort
of ideas come in.

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00:05:12,883 --> 00:05:14,720
The same equilibrium
concepts come in.

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00:05:14,720 --> 00:05:23,550
So if you have a cell membrane,
the cell membrane

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00:05:23,550 --> 00:05:25,820
could have a receptor in it.

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00:05:25,820 --> 00:05:28,760
Which is a protein that extends
through the membrane

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00:05:28,760 --> 00:05:32,270
that's got some sort of
pocket outside here.

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The membrane keeps on going.

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00:05:33,710 --> 00:05:37,820
And you've got the blood on the
outside here, or some of

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the tissue of the cells,
and you've got the

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00:05:39,430 --> 00:05:44,270
inside of the cell here.

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00:05:44,270 --> 00:05:46,910
And this receptor is waiting
for some ligand.

96
00:05:46,910 --> 00:05:53,290
A ligand being another protein
that's floating around.

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00:05:53,290 --> 00:05:58,430
That's specific for binding
to this receptor here.

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And there's the ligand here.

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00:06:00,800 --> 00:06:04,310
There's the receptor here.

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00:06:04,310 --> 00:06:06,770
And every now and then one of
these ligands will find a

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00:06:06,770 --> 00:06:10,130
receptor and bind to it.

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So we write, then, in
equilibrium, ligand plus

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receptor goes to complex.

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This is happening all
the time on cells.

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There are millions of different
kinds of receptors,

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00:06:25,310 --> 00:06:28,170
millions, billions of
kinds of ligands.

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00:06:28,170 --> 00:06:30,710
Wild types, fake ones,
et cetera et cetera.

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00:06:30,710 --> 00:06:35,370
When you've got a binding event,
the cell knows that's

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00:06:35,370 --> 00:06:36,400
something has bound, usually.

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00:06:36,400 --> 00:06:39,410
And that usually triggers a
cascade of other things.

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00:06:39,410 --> 00:06:41,030
It signals a cell to
do a lot of things.

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00:06:41,030 --> 00:06:47,220
So, for instance, in the case
of the GCSF, you've got the

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receptor on the cell.

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And you've got this granulocyte
colony signaling

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00:06:52,630 --> 00:06:54,010
factor, that would be
the ligand here.

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It binds to the receptor
on the cell.

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That triggers the bone marrow
cells to produce more

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00:06:59,440 --> 00:07:02,780
proteins, which signals more
things to happen, and

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00:07:02,780 --> 00:07:06,280
eventually down the way, after
a bunch of signaling

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processes, out come a
burst of stem cells

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or white blood cells.

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It's a complicated process,
and every step of the way

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00:07:14,040 --> 00:07:15,590
needs to be done correctly.

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And for this process at least,
this protein here, this ligand

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00:07:19,860 --> 00:07:22,170
protein, triggers the cascade.

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00:07:22,170 --> 00:07:24,720
And so this binding and
unbinding of this protein then

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00:07:24,720 --> 00:07:27,660
triggers the whole sequence
of reactions.

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So this equilibrium becomes
super-important then.

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00:07:33,230 --> 00:07:33,810
OK.

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00:07:33,810 --> 00:07:37,480
What else should we review
about, I should have used a

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different board than
this, but.

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This is going to
get covered up.

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What else can we review about
biology that would be

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00:07:44,230 --> 00:07:44,630
interesting?

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So, other things that we will
need to remember, need to

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know, is that these receptors
on the surface of the cells

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aren't static.

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The cells recycle
their receptors.

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00:08:00,610 --> 00:08:03,300
Things can happen.

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00:08:03,300 --> 00:08:04,480
Things get degraded.

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00:08:04,480 --> 00:08:08,870
And so the cell is constantly
taking these receptors,

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00:08:08,870 --> 00:08:11,800
bringing them back inside the
cell, merging them with

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00:08:11,800 --> 00:08:16,180
lysosomes, where the pH is five,
or 5.5 compared to the

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00:08:16,180 --> 00:08:19,190
outside of the blood,
which is 7.4.

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00:08:19,190 --> 00:08:22,020
It breaks down the proteins into
their amino acids, the

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00:08:22,020 --> 00:08:24,980
cell can use the amino acids
again to make more proteins.

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00:08:24,980 --> 00:08:26,560
Make better, make
new receptors.

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00:08:26,560 --> 00:08:29,000
And that's how the cell recycles
the receptors.

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So basically, you end up with
the cell taking the receptor.

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Making a small sort of cavity
around the receptor.

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So there's the cell
sitting here.

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There's the inside
of the cell.

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There's the receptor being
engulfed by the cell, now.

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And it could have the ligand
in on it, also.

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00:08:52,420 --> 00:08:55,850
There's the ligand sitting
right here.

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00:08:55,850 --> 00:09:00,330
It's called an endocytotic
event, or it's endocytosis of

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00:09:00,330 --> 00:09:01,140
the receptor.

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Into the cell.

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00:09:02,670 --> 00:09:07,300
And then once you're inside
the cell, let's put the

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00:09:07,300 --> 00:09:10,570
nucleus in the middle here,
you've got things called

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00:09:10,570 --> 00:09:14,210
lysosomes that are
sitting nearby.

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There's a lysosome here.

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00:09:16,730 --> 00:09:19,460
Lysosome.

164
00:09:19,460 --> 00:09:23,700
And there's your little
vesicle that

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00:09:23,700 --> 00:09:24,790
contains your receptor.

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Merges towards the lysosome,
these two get together.

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00:09:30,900 --> 00:09:44,140
Then you have your ligand, I'm
running out of colors here.

168
00:09:44,140 --> 00:09:48,350
So there's the receptor and the
ligand together in here.

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00:09:48,350 --> 00:09:52,770
And then the pH here becomes
5.5, things break apart.

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00:09:52,770 --> 00:09:55,970
And you've got to find another
receptor, another ligand, to

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00:09:55,970 --> 00:09:59,610
continue the process.

172
00:09:59,610 --> 00:10:03,180
Everybody knows this biology,
or you know it well enough.

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00:10:03,180 --> 00:10:06,520
OK, good.

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00:10:06,520 --> 00:10:14,430
So let's go do this example.

175
00:10:14,430 --> 00:10:17,130
So this is the process
of binding.

176
00:10:17,130 --> 00:10:19,940
We can have a delta G associated
with this, delta G

177
00:10:19,940 --> 00:10:26,830
a, delta G0 is minus
RT log K sub a.

178
00:10:26,830 --> 00:10:31,430
This is the association
equilibrium.

179
00:10:31,430 --> 00:10:36,030
And you can have the reverse
process, where the complex

180
00:10:36,030 --> 00:10:39,890
gets broken up into receptor
plus a ligand.

181
00:10:39,890 --> 00:10:42,680
And then you have a delta
G for this process here.

182
00:10:42,680 --> 00:10:47,800
So this is delta Ga,
let's call it.

183
00:10:47,800 --> 00:10:55,590
This would be delta GD, which is
the negative minus RT log K

184
00:10:55,590 --> 00:11:00,240
sub D. This is the dissociation
process.

185
00:11:00,240 --> 00:11:06,240
And the dissociation process,
K sub D, is equal to R, the

186
00:11:06,240 --> 00:11:09,100
concentration of the receptors
times the concentration of the

187
00:11:09,100 --> 00:11:13,320
ligand, divided by the
concentration of the complex.

188
00:11:13,320 --> 00:11:19,140
And the lower K sub D is, the
smaller this number is, small

189
00:11:19,140 --> 00:11:23,150
means that you're mostly on this
side here, mostly in the

190
00:11:23,150 --> 00:11:27,250
complex, the tighter
the binding.

191
00:11:27,250 --> 00:11:41,350
So small KD means
tight binding.

192
00:11:41,350 --> 00:11:44,150
So if I want, in principle,
then, if I want to design a

193
00:11:44,150 --> 00:11:51,360
drug that's going to signal this
event here, I want K sub

194
00:11:51,360 --> 00:11:53,510
D for this ligand that
I'm going to

195
00:11:53,510 --> 00:11:56,960
design to be very small.

196
00:11:56,960 --> 00:11:58,160
To be small.

197
00:11:58,160 --> 00:12:01,840
Small enough so that it binds
strongly and does its job, so

198
00:12:01,840 --> 00:12:06,130
I don't need too much of it.

199
00:12:06,130 --> 00:12:11,450
Now, you need to do experiments
to figure out

200
00:12:11,450 --> 00:12:12,540
what's going on.

201
00:12:12,540 --> 00:12:13,890
So how do you do these
experiments?

202
00:12:13,890 --> 00:12:15,900
You need to be able to measure,
then these K sub D's,

203
00:12:15,900 --> 00:12:20,630
experimentally, to see whether
or not what you've designed on

204
00:12:20,630 --> 00:12:23,960
the computer, when you calculate
delta G's on the

205
00:12:23,960 --> 00:12:27,260
computer you've got to know
whether or not it's working.

206
00:12:27,260 --> 00:12:32,750
And this is still an
experimental science.

207
00:12:32,750 --> 00:12:33,860
How does it work?

208
00:12:33,860 --> 00:12:38,020
So, usually you do the
experiment with the ligand

209
00:12:38,020 --> 00:12:43,520
concentration very high.

210
00:12:43,520 --> 00:12:44,630
Very large.

211
00:12:44,630 --> 00:12:48,150
So that the concentration of
the ligand at any time is

212
00:12:48,150 --> 00:12:50,320
basically the same thing as
the concentration of the

213
00:12:50,320 --> 00:12:51,440
ligand you put in.

214
00:12:51,440 --> 00:12:55,470
So you overwhelm the system
with ligands.

215
00:12:55,470 --> 00:12:59,450
So that L is much bigger than
C or R, and so it doesn't

216
00:12:59,450 --> 00:13:02,090
matter which way the
equilibrium is.

217
00:13:02,090 --> 00:13:04,370
L stays roughly the same.

218
00:13:04,370 --> 00:13:06,800
So you know, throughout
the experiment, what

219
00:13:06,800 --> 00:13:08,400
concentration is.

220
00:13:08,400 --> 00:13:16,740
Then you get a bunch of cells.

221
00:13:16,740 --> 00:13:19,450
In a well or something, or a 96
well plate with a bunch of

222
00:13:19,450 --> 00:13:21,030
different kinds of ligands.

223
00:13:21,030 --> 00:13:26,820
And you can take your ligand,
you can label it

224
00:13:26,820 --> 00:13:28,200
radioactively.

225
00:13:28,200 --> 00:13:33,380
So you can take your ligand
as some long protein.

226
00:13:33,380 --> 00:13:39,100
And you can take an iodine 125,
let's say, radioactive

227
00:13:39,100 --> 00:13:41,480
label on your ligand,
on your protein.

228
00:13:41,480 --> 00:13:43,360
So you can keep track of it.

229
00:13:43,360 --> 00:13:45,460
The nice thing about radioactive
labels, and which

230
00:13:45,460 --> 00:13:49,560
is why people use them in
biology or bio-medicine.

231
00:13:49,560 --> 00:13:52,620
We use them to look at, for
instance, bio-distribution of

232
00:13:52,620 --> 00:13:54,200
things in animals.

233
00:13:54,200 --> 00:13:56,800
We want to know where things
are, and whether they all left

234
00:13:56,800 --> 00:13:59,190
the animal, or.

235
00:13:59,190 --> 00:14:01,950
Because you can use a Geiger
counter and you

236
00:14:01,950 --> 00:14:06,440
can count the events.

237
00:14:06,440 --> 00:14:07,810
The radioactive events.

238
00:14:07,810 --> 00:14:13,620
And that gives you extremely
quantitative analysis of where

239
00:14:13,620 --> 00:14:14,690
things are.

240
00:14:14,690 --> 00:14:18,510
So you take those radioactive
ligand.

241
00:14:18,510 --> 00:14:20,940
And, L0, very large
concentration.

242
00:14:20,940 --> 00:14:23,850
You expose this concentration
to the cells.

243
00:14:23,850 --> 00:14:26,220
The cells have some receptors
on the surface.

244
00:14:26,220 --> 00:14:28,940
There's a bunch of receptors
on the surface of the cell.

245
00:14:28,940 --> 00:14:32,020
And some fraction of the
receptors will have the ligand

246
00:14:32,020 --> 00:14:36,980
bound to them.

247
00:14:36,980 --> 00:14:37,840
So you incubate.

248
00:14:37,840 --> 00:14:39,930
You let it wait a while.

249
00:14:39,930 --> 00:14:45,180
Then you wash.

250
00:14:45,180 --> 00:14:47,600
So you get rid of all
the excess ligand

251
00:14:47,600 --> 00:14:49,200
that's on top there.

252
00:14:49,200 --> 00:14:55,860
And then you take your petri
dish, or your 96 well plate.

253
00:14:55,860 --> 00:14:59,610
And you read the radioactivity
that's coming from the cells.

254
00:14:59,610 --> 00:15:01,930
And that signal, that
radioactive signals, tells you

255
00:15:01,930 --> 00:15:06,910
exactly how many ligand you
have on these cells.

256
00:15:06,910 --> 00:15:10,930
You knew what the cell
concentration was initially.

257
00:15:10,930 --> 00:15:14,090
So that tells you what the
concentration of ligands, of

258
00:15:14,090 --> 00:15:16,200
complexes, was.

259
00:15:16,200 --> 00:15:22,760
So this experiment then gets
you, experimentally, gets you

260
00:15:22,760 --> 00:15:27,470
the concentration of
C, the complex.

261
00:15:27,470 --> 00:15:29,530
So now this is something
you know.

262
00:15:29,530 --> 00:15:31,610
You also know what L0
was, because that's

263
00:15:31,610 --> 00:15:33,410
what you put in.

264
00:15:33,410 --> 00:15:35,930
And that's enough for you
to find out what KD is.

265
00:15:35,930 --> 00:15:38,430
And if you know what KD
is, then you know

266
00:15:38,430 --> 00:15:42,080
what delta G0 is.

267
00:15:42,080 --> 00:15:49,880
And so generally, then, let's
go ahead and do that.

268
00:15:49,880 --> 00:15:54,810
So we know what L is.

269
00:15:54,810 --> 00:16:01,750
We know what L0, C is, let me
just do it on this board here.

270
00:16:01,750 --> 00:16:07,530
So we start with rewriting KD as
equal to R times L divided

271
00:16:07,530 --> 00:16:09,160
by the complex concentration.

272
00:16:09,160 --> 00:16:15,680
And now L is basically L0, so we
can use that approximation.

273
00:16:15,680 --> 00:16:17,100
So we have L0 sitting here.

274
00:16:17,100 --> 00:16:18,900
We still have the complex on
the bottom, and that's

275
00:16:18,900 --> 00:16:20,960
something that we've
experimentally discovered.

276
00:16:20,960 --> 00:16:25,860
And the concentration of
receptors, this is the

277
00:16:25,860 --> 00:16:27,550
concentration of receptors
that don't have

278
00:16:27,550 --> 00:16:28,480
anything bound to them.

279
00:16:28,480 --> 00:16:33,030
So it's these guys right here.

280
00:16:33,030 --> 00:16:36,620
That's equal to the
concentration of receptors,

281
00:16:36,620 --> 00:16:40,360
the total number of receptors,
minus those receptors that

282
00:16:40,360 --> 00:16:42,870
have a ligand bound to them.

283
00:16:42,870 --> 00:16:43,720
Complexes.

284
00:16:43,720 --> 00:16:46,570
Something we can

285
00:16:46,570 --> 00:16:49,110
experimentally define, or discover.

286
00:16:49,110 --> 00:16:57,190
So we replace this R here with
RT minus C. And then we're all

287
00:16:57,190 --> 00:16:57,920
at equilibrium.

288
00:16:57,920 --> 00:17:01,990
So we're going to put a little
equilibrium sign under these

289
00:17:01,990 --> 00:17:05,060
C's here. equilibrium.

290
00:17:05,060 --> 00:17:10,390
And then we can rearrange this
equation so that, people like

291
00:17:10,390 --> 00:17:13,100
to have plots that are linear,
in a way that is a linear

292
00:17:13,100 --> 00:17:18,980
plot, where the slope of the
plot is the inverse of the

293
00:17:18,980 --> 00:17:22,320
equilibrium constant.

294
00:17:22,320 --> 00:17:27,480
So you do some massaging
of this equation here.

295
00:17:27,480 --> 00:17:32,430
And you rewrite it in
terms of C over L0.

296
00:17:32,430 --> 00:17:37,600
There's the equilibrium
concentration of the complex.

297
00:17:37,600 --> 00:17:43,250
This is the total receptor
concentration divided by the

298
00:17:43,250 --> 00:17:44,160
equilibrium constant.

299
00:17:44,160 --> 00:17:50,350
And then you have the
equilibrium concentration of

300
00:17:50,350 --> 00:17:57,910
the complex divided by KD.

301
00:17:57,910 --> 00:18:01,920
And so you plot, then,
this ratio.

302
00:18:01,920 --> 00:18:04,420
Which is an experimental
ratio.

303
00:18:04,420 --> 00:18:08,920
You've just measured this
concentration of complexes

304
00:18:08,920 --> 00:18:11,670
using this radioactivity,
radioactive labeling

305
00:18:11,670 --> 00:18:13,210
experiment.

306
00:18:13,210 --> 00:18:16,450
You know what this is, because
that's what you've put in.

307
00:18:16,450 --> 00:18:19,230
This is your x-axis
on your plot.

308
00:18:19,230 --> 00:18:20,680
This is what you've measured.

309
00:18:20,680 --> 00:18:23,020
And this is going
to be the slope.

310
00:18:23,020 --> 00:18:31,000
It's called a Scatchard plot.

311
00:18:31,000 --> 00:18:33,890
After Mr. Scatchard

312
00:18:33,890 --> 00:18:36,630
So you get a straight line.

313
00:18:36,630 --> 00:18:40,560
So we're plotting here
the equilibrium

314
00:18:40,560 --> 00:18:42,410
constant of the complex.

315
00:18:42,410 --> 00:18:45,320
And on this here we're plotting
the ratio of the

316
00:18:45,320 --> 00:18:48,200
complex divided by L0.

317
00:18:48,200 --> 00:18:57,220
And we get this straight line
like this, where the slope is

318
00:18:57,220 --> 00:19:01,590
one over KD.

319
00:19:01,590 --> 00:19:07,290
Minus one over KD.

320
00:19:07,290 --> 00:19:11,820
OK, now there's a couple of
things that you can look at

321
00:19:11,820 --> 00:19:15,350
that are sometimes useful.

322
00:19:15,350 --> 00:19:20,090
In this analysis here.

323
00:19:20,090 --> 00:19:24,710
You can also rewrite this
equation up here in terms of

324
00:19:24,710 --> 00:19:29,950
the ratio of C equilibrium
divided by RT.

325
00:19:29,950 --> 00:19:34,630
So that's basically the ratio
of receptors that have a

326
00:19:34,630 --> 00:19:36,870
ligand attached to them,
divided by the total

327
00:19:36,870 --> 00:19:38,220
concentration of receptors.

328
00:19:38,220 --> 00:19:45,600
So if most of the receptors
are empty, then this is a

329
00:19:45,600 --> 00:19:46,690
small number.

330
00:19:46,690 --> 00:19:48,860
Then most of the receptors are
taken up, this is a number

331
00:19:48,860 --> 00:19:49,760
close to one.

332
00:19:49,760 --> 00:19:53,140
It can't be anywhere, it can't
be ever bigger than one,

333
00:19:53,140 --> 00:19:55,320
because the biggest number of
complexes you can get is the

334
00:19:55,320 --> 00:19:56,990
total number of receptors.

335
00:19:56,990 --> 00:19:59,410
So if you take this equation
here and you massage it a

336
00:19:59,410 --> 00:20:10,630
little bit, one over one plus KD
over L0, and that, you can

337
00:20:10,630 --> 00:20:14,410
also plot that.

338
00:20:14,410 --> 00:20:19,400
As a function of L0.

339
00:20:19,400 --> 00:20:21,390
How much ligands you put in.

340
00:20:21,390 --> 00:20:25,370
And you find this is something
that saturates at one.

341
00:20:25,370 --> 00:20:27,390
So this ratio here is going
to saturate at one.

342
00:20:27,390 --> 00:20:34,670
This is C equilibrium divided by
total number of receptors.

343
00:20:34,670 --> 00:20:42,200
And so if L0 is small enough, if
L0 is small enough, meaning

344
00:20:42,200 --> 00:21:05,690
that it's smaller than KD, so if
L0 is much smaller then KD,

345
00:21:05,690 --> 00:21:14,390
then you can rearrange this
ratio here so that C

346
00:21:14,390 --> 00:21:24,980
equilibrium divided by RT
is roughly L0 over KD.

347
00:21:24,980 --> 00:21:27,180
So that's linear, with a
slope of one over KD.

348
00:21:27,180 --> 00:21:33,670
So this slope here is one
over KD is the slope.

349
00:21:33,670 --> 00:21:39,280
And as you get L0 to be quite
large, bigger than KD, then

350
00:21:39,280 --> 00:21:40,330
this saturate to one.

351
00:21:40,330 --> 00:21:42,780
And this one over something very
large become zero, and

352
00:21:42,780 --> 00:21:46,510
basically you end up with
something close to one.

353
00:21:46,510 --> 00:21:49,030
So you saturate at one.

354
00:21:49,030 --> 00:21:51,240
So that's another way
of doing this.

355
00:21:51,240 --> 00:21:54,020
But this is really what we
want to concentrate here.

356
00:21:54,020 --> 00:21:56,400
The fact that you can get KD
out of experimentally.

357
00:21:56,400 --> 00:22:00,970
If you have KD, you
have delta G.

358
00:22:00,970 --> 00:22:05,330
So now let's go back and think
about this whole process here.

359
00:22:05,330 --> 00:22:09,750
If we're going to design this
drug here, this protein,

360
00:22:09,750 --> 00:22:11,440
artificially.

361
00:22:11,440 --> 00:22:13,450
So what you want, then, is you
want something that's going to

362
00:22:13,450 --> 00:22:18,170
bind strongly enough to
receptor, to stimulate the

363
00:22:18,170 --> 00:22:24,480
growth of granulocytes, or the
colony of granulocytes.

364
00:22:24,480 --> 00:22:29,770
But when the cell decides to
recycle the receptor, and

365
00:22:29,770 --> 00:22:34,840
destroy it, chew it apart in
the lysosome here, you want

366
00:22:34,840 --> 00:22:38,220
this drug not to be degraded.

367
00:22:38,220 --> 00:22:41,280
Because you have to keep
injecting in the patient.

368
00:22:41,280 --> 00:22:45,210
So you want this drug to release
from the receptor,

369
00:22:45,210 --> 00:22:48,830
before the lysosome has a
chance to chew it up.

370
00:22:48,830 --> 00:22:51,470
So that means that you want the
equilibrium constant at pH

371
00:22:51,470 --> 00:22:58,120
5.5, you want that KD, to be
much larger at 5.5 than you

372
00:22:58,120 --> 00:23:00,060
want it at 7.4.

373
00:23:00,060 --> 00:23:02,790
You want strong binding at
pH 7.4, and you want weak

374
00:23:02,790 --> 00:23:05,020
binding at pH 5.5.

375
00:23:05,020 --> 00:23:07,980
That way the drug
gets recycled.

376
00:23:07,980 --> 00:23:11,290
Can find, go back
to the blood.

377
00:23:11,290 --> 00:23:14,760
Bind to a receptor again,
generate the signaling events,

378
00:23:14,760 --> 00:23:16,310
gets engulfed by the cell.

379
00:23:16,310 --> 00:23:18,220
Releases before it has
a chance to be

380
00:23:18,220 --> 00:23:19,300
chewed up, et cetera.

381
00:23:19,300 --> 00:23:22,990
The wild type will
get chewed up.

382
00:23:22,990 --> 00:23:25,020
The regular kind will get chewed
up, and so that's why

383
00:23:25,020 --> 00:23:27,400
you have to, with the patients
you have to keep giving them

384
00:23:27,400 --> 00:23:28,750
this drug over and over again.

385
00:23:28,750 --> 00:23:34,620
Because it gets chewed
up by the cells.

386
00:23:34,620 --> 00:23:38,530
So that's the design principle
that these authors had in mind

387
00:23:38,530 --> 00:23:39,950
when they started their study.

388
00:23:39,950 --> 00:23:42,840
And so they knew what the
sequence, what the amino acid

389
00:23:42,840 --> 00:23:46,470
sequence was, for this wild type
drug, and they started

390
00:23:46,470 --> 00:23:48,720
doing point mutations.

391
00:23:48,720 --> 00:23:50,870
Changing one amino acid
here and there.

392
00:23:50,870 --> 00:23:54,990
And cranking out the calculation
to calculate delta

393
00:23:54,990 --> 00:23:59,740
G for binding of this protein
to this receptor.

394
00:23:59,740 --> 00:24:02,990
At pH 7.4 and at pH
5.5, and getting

395
00:24:02,990 --> 00:24:05,120
differences of delta G's.

396
00:24:05,120 --> 00:24:11,770
So let me then review again.

397
00:24:11,770 --> 00:24:19,390
What is the motivation here.

398
00:24:19,390 --> 00:24:27,260
The motivation is to try to
get the ratio, KD, at 5.5

399
00:24:27,260 --> 00:24:33,040
divided by KD at 7.4, pH 7.4.

400
00:24:33,040 --> 00:24:35,750
And you want this to
be bigger than one.

401
00:24:35,750 --> 00:24:39,720
And really as large
as possible.

402
00:24:39,720 --> 00:24:42,660
As possible, of course
within limits.

403
00:24:42,660 --> 00:24:47,150
So we want this to
bind at pH 7.4.

404
00:24:47,150 --> 00:24:57,940
And the point of comparison
is the wild types.

405
00:24:57,940 --> 00:25:07,770
Which at 7.4 has a KD
of 270, roughly.

406
00:25:07,770 --> 00:25:18,690
And at the ratio of pH
5.5 to 7.4 is 1.7.

407
00:25:18,690 --> 00:25:23,150
So it's a little bit weaker
binding at 5.5.

408
00:25:23,150 --> 00:25:27,570
Remember, large KD means
weak binding.

409
00:25:27,570 --> 00:25:30,890
Small KD means tight binding.

410
00:25:30,890 --> 00:25:34,820
So the fact that KD at 5.5 is
bigger than KD at 7.5 means

411
00:25:34,820 --> 00:25:38,540
that it's slightly weaker
binding at 5.5 than 7.4.

412
00:25:38,540 --> 00:25:43,570
So this is sort of the baseline
that the protein

413
00:25:43,570 --> 00:25:46,120
designers had to deal with.

414
00:25:46,120 --> 00:25:53,800
So everything gets compared
to this guy here.

415
00:25:53,800 --> 00:25:58,480
So they don't actually, in
a calculation they don't

416
00:25:58,480 --> 00:26:00,990
actually measure this.

417
00:26:00,990 --> 00:26:03,920
What they do is, they
look at delta G's.

418
00:26:03,920 --> 00:26:09,630
And so they look at differences
of delta G's.

419
00:26:09,630 --> 00:26:16,750
They look at delta G0 for
the binding of the

420
00:26:16,750 --> 00:26:18,590
ligand to the receptor.

421
00:26:18,590 --> 00:26:28,650
At 7.4 minus the delta G0 at
pH 5.5, let's call this the

422
00:26:28,650 --> 00:26:38,070
delta delta G. Since you know
delta G is minus RT log K,

423
00:26:38,070 --> 00:26:45,990
this is equal to minus the delta
of log KD, which is log

424
00:26:45,990 --> 00:26:54,310
KD at 5.5 divided
by KD at 7.4.

425
00:26:54,310 --> 00:26:58,460
So then they calculate delta
delta G0, and it's completely

426
00:26:58,460 --> 00:27:04,060
related to this ratio that you
measured in the experiment.

427
00:27:04,060 --> 00:27:12,570
And so for the wild type, this
delta delta G is just

428
00:27:12,570 --> 00:27:15,620
basically the log of
this number here.

429
00:27:15,620 --> 00:27:23,060
Is 0.53.

430
00:27:23,060 --> 00:27:26,540
So now they go ahead and
do their calculation.

431
00:27:26,540 --> 00:27:31,640
And they find a couple
of mutants.

432
00:27:31,640 --> 00:27:34,620
Where, and they focus
on delta delta G0.

433
00:27:34,620 --> 00:27:37,980
They want something that's
bigger than this.

434
00:27:37,980 --> 00:27:40,950
And then they'll worry about
whether there are more

435
00:27:40,950 --> 00:27:42,540
problems associated with it.

436
00:27:42,540 --> 00:27:47,260
So they found two mutants,
let's call

437
00:27:47,260 --> 00:27:58,660
them D110H and D113H.

438
00:27:58,660 --> 00:28:02,580
I think it's a histidine
mutation, point mutation at

439
00:28:02,580 --> 00:28:10,835
110 and 113, where this ratio
here was 8.3 and 17.

440
00:28:10,835 --> 00:28:14,260
So, huge differences here.

441
00:28:14,260 --> 00:28:19,220
More than a factor of 20, or
factor of 30 difference in the

442
00:28:19,220 --> 00:28:22,280
change in the binding
efficiency, at least according

443
00:28:22,280 --> 00:28:27,540
to these delta delta G, between
pH 5.5 and pH 7.4.

444
00:28:27,540 --> 00:28:31,610
That means that this protein
here with the point mutation,

445
00:28:31,610 --> 00:28:35,940
with this one point mutation, if
it binds as strongly to the

446
00:28:35,940 --> 00:28:40,100
receptor on the surface, as soon
as the lysosome comes in

447
00:28:40,100 --> 00:28:46,430
and begins to decrease pH inside
the cell, this ligand

448
00:28:46,430 --> 00:28:48,300
is going to come off.

449
00:28:48,300 --> 00:28:49,930
And it's going to be
able to float away.

450
00:28:49,930 --> 00:28:52,550
Hopefully, before it
gets recycled.

451
00:28:52,550 --> 00:28:53,750
Before it gets chewed up.

452
00:28:53,750 --> 00:28:57,320
So they can be used again.

453
00:28:57,320 --> 00:29:03,600
So that's good.

454
00:29:03,600 --> 00:29:07,950
Alright, so experiments
were done.

455
00:29:07,950 --> 00:29:17,520
And on the D110H
and the D113H.

456
00:29:17,520 --> 00:29:19,935
And KD was measured in
the experiments.

457
00:29:19,935 --> 00:29:22,140
And remember, the wild
type is 270.

458
00:29:22,140 --> 00:29:24,750
The KD's were at 370.

459
00:29:24,750 --> 00:29:28,620
And 320, with some error bar.

460
00:29:28,620 --> 00:29:33,590
And the different, the ratios
of KD's were measured.

461
00:29:33,590 --> 00:29:37,160
There were 4.4 and 6.8.

462
00:29:37,160 --> 00:29:39,930
With some error bars.

463
00:29:39,930 --> 00:29:42,880
And they turned out to match
reasonably well, at least as

464
00:29:42,880 --> 00:29:46,030
far as comparison between
experiment and theory.

465
00:29:46,030 --> 00:29:49,020
Still not great for these sorts
of calculations, because

466
00:29:49,020 --> 00:29:50,490
pretty involved.

467
00:29:50,490 --> 00:29:52,150
A lot of approximations
go on in there.

468
00:29:52,150 --> 00:29:56,360
And it gives you
a rough guide.

469
00:29:56,360 --> 00:29:59,160
So this 17 here is probably not
quite right, because it

470
00:29:59,160 --> 00:30:01,300
doesn't quite translate
to 6.8 here.

471
00:30:01,300 --> 00:30:04,040
This difference between 4.4 and
6.8 doesn't quite match

472
00:30:04,040 --> 00:30:06,270
the difference that they saw
here in the calculation.

473
00:30:06,270 --> 00:30:07,940
But it's the right
direction, right?

474
00:30:07,940 --> 00:30:11,090
And that's why you still
need to do experiments.

475
00:30:11,090 --> 00:30:13,170
This number here is a
little bit bigger

476
00:30:13,170 --> 00:30:13,990
than this number here.

477
00:30:13,990 --> 00:30:19,370
Which means that these don't
bind quite as strongly.

478
00:30:19,370 --> 00:30:21,910
Because KD small means
strong binding.

479
00:30:21,910 --> 00:30:24,380
That means the initial binding
of the ligand to the receptor

480
00:30:24,380 --> 00:30:28,340
is not quite as good
as the wild type.

481
00:30:28,340 --> 00:30:29,210
That's often the case.

482
00:30:29,210 --> 00:30:31,340
It's often not so easy to find
something that binds as

483
00:30:31,340 --> 00:30:34,000
strongly as the wild version.

484
00:30:34,000 --> 00:30:36,360
But, it's good enough.

485
00:30:36,360 --> 00:30:39,540
And this ratio is really
what clamps the deal

486
00:30:39,540 --> 00:30:43,550
in this case here.

487
00:30:43,550 --> 00:30:59,080
And so, these mutants, in fact
these two mutants are the ones

488
00:30:59,080 --> 00:31:03,060
that have undergone
the animal trials.

489
00:31:03,060 --> 00:31:06,770
That are in the pipeline.

490
00:31:06,770 --> 00:31:07,880
This is a big deal.

491
00:31:07,880 --> 00:31:12,400
This is a big deal because this
is a huge, huge market.

492
00:31:12,400 --> 00:31:15,720
There's a very large number of
people that are affected with

493
00:31:15,720 --> 00:31:16,480
chemotherapy.

494
00:31:16,480 --> 00:31:21,720
And this is basic thermodynamics
here.

495
00:31:21,720 --> 00:31:24,990
It's basic thermodynamic
calculation of a complicated

496
00:31:24,990 --> 00:31:32,980
molecule with some fairly simple
equilibrium concepts.

497
00:31:32,980 --> 00:31:47,460
OK, any questions on this?

498
00:31:47,460 --> 00:31:53,180
OK, well, we're ended
really early today.

499
00:31:53,180 --> 00:31:57,120
I don't have the phase
transition ready, but Keith

500
00:31:57,120 --> 00:31:59,980
Nelson is going to start a phase
transition next time.

501
00:31:59,980 --> 00:32:00,120