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BOGDAN FEDELES: Hello, and
welcome to 5.07 Biochemistry

00:00:24.080 --> 00:00:26.610
on MIT OpenCourseWare.

00:00:26.610 --> 00:00:28.800
I'm Dr. Bogdan Fedeles.

00:00:28.800 --> 00:00:30.930
Let's metabolize some problems.

00:00:30.930 --> 00:00:33.480
This series of videos
is meant to supplement

00:00:33.480 --> 00:00:35.700
some of the other
materials on the site,

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and to give you a more in-depth
and more interactive take

00:00:39.720 --> 00:00:44.150
on some of the topics
covered in 5.07 Biochemistry.

00:00:44.150 --> 00:00:46.530
Specifically, we're going
to be working together

00:00:46.530 --> 00:00:49.980
through one problem from each
problem set from this course.

00:00:53.620 --> 00:00:57.640
Today we're discussing the very
first homework problem of 5.07,

00:00:57.640 --> 00:01:00.520
which is problem one
of problem set one.

00:01:00.520 --> 00:01:02.530
This problem is
meant to give you

00:01:02.530 --> 00:01:05.349
a better sense of the
scales and dimensions

00:01:05.349 --> 00:01:07.870
of the cellular environment.

00:01:07.870 --> 00:01:10.120
Specifically, we're going
to be asking questions

00:01:10.120 --> 00:01:12.590
like, how big is this cell?

00:01:12.590 --> 00:01:14.260
What is the volume of a cell?

00:01:14.260 --> 00:01:16.960
And how many molecules
of a given protein

00:01:16.960 --> 00:01:18.200
are inside a cell?

00:01:21.690 --> 00:01:24.300
One fundamental idea
introduced in this problem

00:01:24.300 --> 00:01:27.750
is that the cellular
environment is very crowded.

00:01:27.750 --> 00:01:31.130
Things inside the cell
are very tightly packed.

00:01:31.130 --> 00:01:35.720
Now take a look at this
picture in your book.

00:01:35.720 --> 00:01:39.780
As you see here, the
constituents of a cell,

00:01:39.780 --> 00:01:44.370
like proteins, enzymes, the
organelles, metabolites,

00:01:44.370 --> 00:01:48.250
are all in very close
proximity to each other.

00:01:48.250 --> 00:01:51.240
Now, this is also reflected
in the concentration

00:01:51.240 --> 00:01:53.940
that we're given for the
proteins inside the cell.

00:01:53.940 --> 00:01:57.180
The problem tells us
there are 350 milligrams

00:01:57.180 --> 00:01:59.370
per milliliter of protein.

00:01:59.370 --> 00:02:02.770
Or in other words,
350 grams per liter.

00:02:02.770 --> 00:02:06.690
Now this is a very high number
in the context of biochemistry.

00:02:06.690 --> 00:02:09.270
Basically, if you
think one liter

00:02:09.270 --> 00:02:14.080
is 1,000 grams then 350
grams of that is protein.

00:02:14.080 --> 00:02:18.840
So we have 350 grams,
35%, of a cell is protein.

00:02:18.840 --> 00:02:21.900
And only 60% to 65% is water.

00:02:21.900 --> 00:02:24.810
Therefore, as the
problem says, when

00:02:24.810 --> 00:02:28.740
we're doing in-vitro experiments
using dilute solutions

00:02:28.740 --> 00:02:31.050
we rarely recapitulate
what actually

00:02:31.050 --> 00:02:33.280
happens inside the cell.

00:02:33.280 --> 00:02:35.840
Now how big is a mammalian cell?

00:02:35.840 --> 00:02:39.180
As you will see, sizes
of cells in an organism

00:02:39.180 --> 00:02:40.600
vary considerably.

00:02:40.600 --> 00:02:44.970
At one extreme we have very tiny
cells like endothelial cells,

00:02:44.970 --> 00:02:46.540
red blood cells.

00:02:46.540 --> 00:02:47.910
These are very, very small.

00:02:47.910 --> 00:02:51.060
On the other end, we
have reproductive cells,

00:02:51.060 --> 00:02:54.650
like the egg, which is 100
to 200 microns in diameter.

00:02:54.650 --> 00:02:57.750
Or even cells that can stretch
for centimeter, like the muscle

00:02:57.750 --> 00:03:00.640
cells and certain nerve cells.

00:03:00.640 --> 00:03:03.360
In this problem, we're going to
be dealing with the red blood

00:03:03.360 --> 00:03:06.880
cells, one of the most
abundant cells in the body.

00:03:06.880 --> 00:03:11.410
As you can see in this
very colorful picture,

00:03:11.410 --> 00:03:16.260
a red blood cell can be
approximated by a cylinder 6

00:03:16.260 --> 00:03:19.230
to 8 microns in diameter.

00:03:19.230 --> 00:03:22.200
So knowing that, we can actually
calculate some dimensions

00:03:22.200 --> 00:03:25.320
of the red blood cells,
such as the total volume

00:03:25.320 --> 00:03:26.730
and their surface area.

00:03:29.500 --> 00:03:35.770
Now here is a cylinder by which
we approximate a red blood

00:03:35.770 --> 00:03:37.090
cell.

00:03:37.090 --> 00:03:43.890
And let's say the cylinder
has the height, h,

00:03:43.890 --> 00:03:46.480
and the radius, r.

00:03:46.480 --> 00:03:51.790
From our problem we know h
is about 2 microns and r,

00:03:51.790 --> 00:03:55.660
well we know the diameter
is 6 to 8 microns.

00:03:55.660 --> 00:04:01.180
So r is going to be, let's go
with the middle, 3.5 microns.

00:04:01.180 --> 00:04:05.570
Now as you remember
from geometry,

00:04:05.570 --> 00:04:07.990
then the volume
of the cylinder is

00:04:07.990 --> 00:04:14.050
going to be pi r
squared h, which

00:04:14.050 --> 00:04:17.829
when we substitute
our units, we're going

00:04:17.829 --> 00:04:23.550
to get about 77 cubic microns.

00:04:26.430 --> 00:04:26.930
All right.

00:04:26.930 --> 00:04:30.680
We'll come back to discussing
the units in a little bit.

00:04:30.680 --> 00:04:32.750
Now the surface
area is just going

00:04:32.750 --> 00:04:39.050
to be the area surrounding the
cylinder plus the two circles--

00:04:39.050 --> 00:04:40.590
the top and the bottom.

00:04:40.590 --> 00:04:47.210
So the two circles are 2 pi r
squared plus the surrounding

00:04:47.210 --> 00:04:51.410
area is going to be 2 pi r h.

00:04:51.410 --> 00:05:00.590
And that comes out to be
about 120.95 square microns.

00:05:00.590 --> 00:05:05.519
Now how much is really
one cubic micron?

00:05:05.519 --> 00:05:07.310
Let's try to relate it
to a unit that we're

00:05:07.310 --> 00:05:10.610
more familiar such as liter.

00:05:10.610 --> 00:05:17.990
Well, one milliliter is
actually one cubic centimeter.

00:05:17.990 --> 00:05:24.920
One microliter is
one cubic millimeter.

00:05:24.920 --> 00:05:29.930
Now, one cubic micrometer,
it's like a billion times

00:05:29.930 --> 00:05:31.780
smaller than 1 microliter.

00:05:31.780 --> 00:05:33.830
One microliter is already
a million times smaller

00:05:33.830 --> 00:05:39.590
than a liter, so this is really
10 to the minus 15 liters

00:05:39.590 --> 00:05:42.800
is 1 cubic micrometer.

00:05:42.800 --> 00:05:46.770
Which is 10 to the minus
15 is the femto units.

00:05:46.770 --> 00:05:49.530
It's like one femtoliter.

00:05:49.530 --> 00:05:54.820
Now 77 femtoliters is an
incredibly small volume.

00:05:54.820 --> 00:05:59.150
But as we'll see next
when we look at bacteria,

00:05:59.150 --> 00:06:01.280
bacteria are even smaller.

00:06:01.280 --> 00:06:04.950
Now, let's take a look
at a Staph aureus cell.

00:06:04.950 --> 00:06:09.220
Now Staphylococcus aureus
is a very common bacteria

00:06:09.220 --> 00:06:14.117
that we often find on our skin
or in our respiratory tract.

00:06:14.117 --> 00:06:15.700
Now this is the same
bacteria that you

00:06:15.700 --> 00:06:18.670
might have heard in
that acronym MRSA,

00:06:18.670 --> 00:06:22.150
or Methicillin-Resistant
Staph Aureus.

00:06:22.150 --> 00:06:25.270
Now, this MRSA is a
pathogenic bacteria

00:06:25.270 --> 00:06:28.510
that can cause a lot of
problems in the hospitals

00:06:28.510 --> 00:06:31.210
nowadays, because it
is resistant to most

00:06:31.210 --> 00:06:33.370
of the antibiotics that we have.

00:06:33.370 --> 00:06:37.890
Now, here's a picture
of Staph aureus.

00:06:37.890 --> 00:06:41.140
As you can see, it's
a spherical cell.

00:06:41.140 --> 00:06:44.500
And of course this pretty
purple color is added in.

00:06:44.500 --> 00:06:48.640
This is just a electron
micrograph picture

00:06:48.640 --> 00:06:51.040
of a colony of Staph
aureus bacteria.

00:06:51.040 --> 00:06:54.850
So for it too we can
calculate the volume

00:06:54.850 --> 00:06:58.410
of the cell and
the surface area.

00:06:58.410 --> 00:07:02.980
If we assume Staph aureus
to be a sphere, of radius r,

00:07:02.980 --> 00:07:07.100
we are told r is 0.6 microns.

00:07:07.100 --> 00:07:09.640
Then we can calculate
the volume of the cell.

00:07:09.640 --> 00:07:16.110
The volume is simply going
to be 4 pi r cubed over 3.

00:07:16.110 --> 00:07:18.460
And if we plug-in
the numbers, we're

00:07:18.460 --> 00:07:27.880
going to get 0.11
cubic micrometer.

00:07:27.880 --> 00:07:30.280
Similarly for the
surface area, it's

00:07:30.280 --> 00:07:32.550
a surface area of a sphere.

00:07:32.550 --> 00:07:35.420
It's 4 pi r squared.

00:07:35.420 --> 00:07:42.610
And the units come out
to 1.13 square microns.

00:07:42.610 --> 00:07:46.120
Now 0.11 cubic microns.

00:07:46.120 --> 00:07:52.570
And we said a cubic micron
is one femtoliters, like 10

00:07:52.570 --> 00:07:54.890
to minus 15 liters.

00:07:54.890 --> 00:08:03.640
So 0.11 cubic micrometers is
110 times 10 to minus 18 liters.

00:08:03.640 --> 00:08:06.850
Now the prefix for 10
to minus 18 that's atto.

00:08:06.850 --> 00:08:09.625
So it's 110 attoliters.

00:08:12.584 --> 00:08:16.660
So this is an
incredibly small volume.

00:08:16.660 --> 00:08:18.790
So by calculating the
volume and the surface

00:08:18.790 --> 00:08:21.790
area of these cells,
we've essentially

00:08:21.790 --> 00:08:25.630
answered part 1 and
part 2 of this problem.

00:08:25.630 --> 00:08:28.120
Now next we're going to
explore the relationship

00:08:28.120 --> 00:08:30.690
between the volume and the
surface area of the cell.

00:08:34.450 --> 00:08:36.970
As you know from geometry,
the volume typically

00:08:36.970 --> 00:08:39.850
varies with the
cube of the radius,

00:08:39.850 --> 00:08:42.429
whereas the surface
area varies only

00:08:42.429 --> 00:08:44.800
with the square of the radius.

00:08:44.800 --> 00:08:46.900
Therefore, as the
radius of an object

00:08:46.900 --> 00:08:51.010
increases the ratio of
surface area over volume

00:08:51.010 --> 00:08:54.520
will decrease because the
volume increases quicker.

00:08:57.130 --> 00:09:00.950
Now, this is exactly what
we observe with cells.

00:09:00.950 --> 00:09:08.190
Therefore, for a red blood
cell surface area over volume

00:09:08.190 --> 00:09:20.000
it's going to be 12,095 square
microns over 77 cubic microns.

00:09:20.000 --> 00:09:25.065
That comes out to about
1.6 inverse microns.

00:09:35.250 --> 00:09:39.750
Now for a Staph aureus cell,
surface area over volume

00:09:39.750 --> 00:09:47.300
is going to be 1.13
square microns over 0.11

00:09:47.300 --> 00:09:49.500
cubic microns.

00:09:49.500 --> 00:09:56.720
That's approximately 10.

00:09:56.720 --> 00:09:58.090
Why is this important?

00:09:58.090 --> 00:10:00.590
It's because the
surface area of a cell

00:10:00.590 --> 00:10:05.300
controls how fast molecules
can go in and out of the cell.

00:10:05.300 --> 00:10:09.170
It essentially controls the flux
of molecules across the cell

00:10:09.170 --> 00:10:10.710
membrane.

00:10:10.710 --> 00:10:15.120
Now, if the surface area of
a volume is a large number,

00:10:15.120 --> 00:10:17.360
it means the molecules
can access that volume

00:10:17.360 --> 00:10:20.640
fairly quickly and efficiently.

00:10:20.640 --> 00:10:23.300
But as you can see,
the bigger the cell,

00:10:23.300 --> 00:10:26.840
the smaller the surface area
of a volume number becomes.

00:10:26.840 --> 00:10:30.840
And therefore, for big cells
molecules will have a hard time

00:10:30.840 --> 00:10:33.440
and will take a long time
to get inside the cell

00:10:33.440 --> 00:10:35.040
or out of the cell.

00:10:35.040 --> 00:10:38.960
That's why nature has designed
ways to transport molecules,

00:10:38.960 --> 00:10:42.640
to make them achieve the right
concentration efficiently.

00:10:42.640 --> 00:10:44.540
Now this is why, in
the case of bigger

00:10:44.540 --> 00:10:48.800
cells, such as the eukaryotic
cells or mammalian cells,

00:10:48.800 --> 00:10:51.860
in our case the red
blood cells, nature

00:10:51.860 --> 00:10:55.520
has evolved transport
mechanisms by which

00:10:55.520 --> 00:10:59.600
it can deliver small molecules
throughout the entire volume

00:10:59.600 --> 00:11:00.890
of the cell.

00:11:00.890 --> 00:11:03.170
One example of such
transfer molecules

00:11:03.170 --> 00:11:05.780
is hemoglobin, which
is used to deliver

00:11:05.780 --> 00:11:09.230
oxygen. This is what we're
going to take a look at next.

00:11:13.130 --> 00:11:15.620
We are given that
hemoglobin constitutes

00:11:15.620 --> 00:11:19.680
95% of the proteins in
the red blood cells.

00:11:19.680 --> 00:11:22.100
So let's calculate the
concentration of hemoglobin

00:11:22.100 --> 00:11:24.110
in a red blood cell.

00:11:24.110 --> 00:11:27.590
Now let's start with the
average protein concentration

00:11:27.590 --> 00:11:30.560
in the cell, which we
mentioned earlier, which was

00:11:30.560 --> 00:11:35.250
350 milligrams per milliliter.

00:11:35.250 --> 00:11:38.900
Now if 95% of this
is hemoglobin,

00:11:38.900 --> 00:11:43.160
then the concentration
of hemoglobin

00:11:43.160 --> 00:11:50.440
is going to be about 322
milligrams per milliliter.

00:11:50.440 --> 00:11:56.440
Now I'm going to abbreviate
hemoglobin as Hb.

00:11:56.440 --> 00:12:03.200
We're told that hemoglobin has
a molecular weight of 67,000

00:12:03.200 --> 00:12:10.930
Daltons, which is another way
of saying 67,000 grams per mole.

00:12:10.930 --> 00:12:13.850
So then the concentration
of hemoglobin

00:12:13.850 --> 00:12:23.770
is going to be 322
milligrams per 67,000.

00:12:23.770 --> 00:12:26.200
Grams per mole is the
same as milligrams

00:12:26.200 --> 00:12:31.650
per millimole and
per milliliter.

00:12:31.650 --> 00:12:37.510
The grams go away
and we get 0.0048.

00:12:37.510 --> 00:12:39.790
It's going to be
millimole per milliliter

00:12:39.790 --> 00:12:41.680
and that's the same
as mole per liter.

00:12:41.680 --> 00:12:44.170
That's the molar concentration.

00:12:44.170 --> 00:12:50.230
Or we can write
it 4.8 millimolar.

00:12:50.230 --> 00:12:53.650
Now this is a pretty
important range

00:12:53.650 --> 00:12:56.130
to keep in mind, because
the most abundant proteins

00:12:56.130 --> 00:13:00.430
such as hemoglobin, are going to
be in the low millimolar range.

00:13:00.430 --> 00:13:02.080
Most of the other
proteins are going

00:13:02.080 --> 00:13:06.870
to be in the micromolar
range in a cell.

00:13:06.870 --> 00:13:11.390
Now let's calculate how
many molecules of hemoglobin

00:13:11.390 --> 00:13:12.800
we have in the red blood cell.

00:13:15.500 --> 00:13:21.370
So we calculated before that
the volume of a red blood cell

00:13:21.370 --> 00:13:26.590
is actually 77 femtoliters.

00:13:26.590 --> 00:13:31.460
That's once again 77 times
10 to minus 15 liters.

00:13:34.380 --> 00:13:38.370
Now we know in this volume the
concentration of hemoglobin

00:13:38.370 --> 00:13:40.920
is 4.8 millimolar.

00:13:40.920 --> 00:13:43.410
So we can calculate
the number of moles.

00:13:43.410 --> 00:13:46.020
So the new number
of moles is going

00:13:46.020 --> 00:13:50.860
to be the concentration
times the volume.

00:13:50.860 --> 00:13:58.500
So we have 4.8 millimolar
times 77 times 10 to minus 15

00:13:58.500 --> 00:14:02.840
liters equals--

00:14:02.840 --> 00:14:06.000
now of course, millimolar--

00:14:06.000 --> 00:14:07.890
we have to transform
this back into molar.

00:14:07.890 --> 00:14:09.480
We have mole per liters.

00:14:09.480 --> 00:14:10.970
The liters are
going to cancel out

00:14:10.970 --> 00:14:12.570
so we're going to get moles.

00:14:12.570 --> 00:14:20.740
And it's 369, or so, times
10 to minus 18 moles.

00:14:20.740 --> 00:14:23.820
Remember 10 to minus
18 that's attomoles.

00:14:23.820 --> 00:14:31.920
So 369 attomoles of hemoglobin
we have in a red blood cell.

00:14:31.920 --> 00:14:36.450
Now we know one mole
contains the Avogadro

00:14:36.450 --> 00:14:38.560
numbers of molecules.

00:14:38.560 --> 00:14:41.100
So if you multiply this
with the Avogadro number,

00:14:41.100 --> 00:14:44.420
we should get the actual
number of molecules.

00:14:44.420 --> 00:14:51.770
So number of molecules is just
Avogadro number times number

00:14:51.770 --> 00:15:00.440
of moles, and Avogadro number
is approximately 6.022 times 10

00:15:00.440 --> 00:15:04.430
to the 23rd power,
so a gigantic number,

00:15:04.430 --> 00:15:11.090
times 369 times 10
to minus 18 moles.

00:15:11.090 --> 00:15:16.760
We're going to get about 2.2
times 10 to the 8 molecules.

00:15:21.410 --> 00:15:28.700
Or in other words, this
is 220 million molecules.

00:15:28.700 --> 00:15:34.640
So the problem was telling us
about a Google search in which

00:15:34.640 --> 00:15:38.000
we came up for different numbers
and one of them was 2,000,

00:15:38.000 --> 00:15:43.070
one of them was 200 million,
so obviously the answer we got,

00:15:43.070 --> 00:15:47.600
220 million, is closer to
the 200-300 million molecules

00:15:47.600 --> 00:15:50.862
that our Google search returned.

00:15:50.862 --> 00:15:52.820
That's the answer for
that part of the problem.

00:15:56.610 --> 00:16:00.320
Finally, let's see how the
size of a hemoglobin molecule

00:16:00.320 --> 00:16:02.480
compares to the size of a cell.

00:16:02.480 --> 00:16:11.070
We're told hemoglobin is
roughly spherical in shape,

00:16:11.070 --> 00:16:16.350
with a diameter of
about 55 Angstrom.

00:16:16.350 --> 00:16:19.290
Now as you recall from
Intro to Chemistry,

00:16:19.290 --> 00:16:24.510
one Angstrom is 10 to
the minus 10 meters.

00:16:24.510 --> 00:16:27.540
That's 0.1 nanometer.

00:16:27.540 --> 00:16:33.530
So our radius here is going
to be half the diameter,

00:16:33.530 --> 00:16:43.250
so it's 27.5 Angstrom
is 2.75 nanometers.

00:16:43.250 --> 00:16:46.340
So the volume of a
hemoglobin molecule

00:16:46.340 --> 00:16:51.080
is going to be 4
pi r cubed over 3.

00:16:51.080 --> 00:16:56.040
And with plugging
in 2.75 nanometers.

00:16:56.040 --> 00:17:00.500
So it's going to come up to
be 8.7 times 10 to the minus

00:17:00.500 --> 00:17:03.005
eighth cubic microns.

00:17:06.130 --> 00:17:09.550
Now, you remember the
volume of a red blood cell

00:17:09.550 --> 00:17:16.780
was 77 cubic microns,
so if you look

00:17:16.780 --> 00:17:20.920
at the relationship
between the two,

00:17:20.920 --> 00:17:26.109
how many volumes of a hemoglobin
can we fit in a red blood cell?

00:17:26.109 --> 00:17:32.920
Well, we just divide the
volume of the red blood cell

00:17:32.920 --> 00:17:34.690
to the volume of the hemoglobin.

00:17:34.690 --> 00:17:39.010
77 over 8.7 times 10
to the minus eighth.

00:17:39.010 --> 00:17:43.550
Both are cubic microns.

00:17:43.550 --> 00:17:49.750
And that gives us 8.8 times
10 to the eight molecules.

00:17:52.510 --> 00:17:58.900
So this is 880 million
molecules of hemoglobin

00:17:58.900 --> 00:18:02.950
would fit in the volume
of a red blood cell.

00:18:02.950 --> 00:18:05.770
If only hemoglobin
would be in there.

00:18:05.770 --> 00:18:07.930
Obviously this number
is an overestimation,

00:18:07.930 --> 00:18:12.040
because when you're
packing spherical objects,

00:18:12.040 --> 00:18:14.750
they're not going to pack
very tightly with each other.

00:18:14.750 --> 00:18:18.220
And as we said, the shape is
only approximately spherical,

00:18:18.220 --> 00:18:21.250
but nevertheless it's on
the same order of magnitude

00:18:21.250 --> 00:18:25.360
as the 200- 300 million
molecules of hemoglobin

00:18:25.360 --> 00:18:28.240
that we calculated earlier
based on the concentration.

00:18:28.240 --> 00:18:30.940
So from both the volume
standpoint and concentration

00:18:30.940 --> 00:18:34.600
standpoint we now
have calculated

00:18:34.600 --> 00:18:38.960
how many molecules of hemoglobin
can fit in a red blood cell.

00:18:38.960 --> 00:18:42.070
This result we just got actually
highlights a very important

00:18:42.070 --> 00:18:44.870
take home message,
which is, if we

00:18:44.870 --> 00:18:48.160
look at the molecular
and atomic scale,

00:18:48.160 --> 00:18:50.920
it is as distant from
the cellular scale

00:18:50.920 --> 00:18:52.810
as the cellular
scale is different

00:18:52.810 --> 00:18:55.510
from the macroscopic scale.

00:18:55.510 --> 00:18:58.510
Now if we take one
milliliter of blood,

00:18:58.510 --> 00:19:03.580
we find a few billion red
blood cells inside it.

00:19:03.580 --> 00:19:05.800
Now within each
red blood cell we

00:19:05.800 --> 00:19:09.820
find hundreds of millions of
molecules such as hemoglobin.

00:19:09.820 --> 00:19:11.470
That's it for this problem.

00:19:11.470 --> 00:19:14.770
I hope you now have a
better sense of the sizes

00:19:14.770 --> 00:19:17.770
and scales relevant for
biochemistry and cell biology

00:19:17.770 --> 00:19:19.280
in general.

00:19:19.280 --> 00:19:21.700
Keep in mind our discussion
of the surface area

00:19:21.700 --> 00:19:27.010
to volume ratio and why as
the cell size gets bigger,

00:19:27.010 --> 00:19:29.320
we need transport
mechanisms to make sure

00:19:29.320 --> 00:19:32.560
the nutrients and
metabolites get to where

00:19:32.560 --> 00:19:34.810
they need to go efficiently.

00:19:34.810 --> 00:19:37.930
Also keep in mind some of
the concentration ranges

00:19:37.930 --> 00:19:40.180
that we discussed,
as these will become

00:19:40.180 --> 00:19:43.870
very important in understanding
the biological significance

00:19:43.870 --> 00:19:45.880
of some of the
constants that we're

00:19:45.880 --> 00:19:50.460
going to calculate for
enzymes later in the course.