[Slide 1 L1.1] Welcome, I'm Professor Rickus.
Professor of Biological Engineering and
Biomedical Engineering at Purdue University.
So welcome to the course, cell and molecular design principals.
In this lecture, our kick off lecture,
we're going to start by talking about cells by the numbers.
So, we're going to get a little grounded in
the quantities of cells in different aspects.
[Slide 2] So specifically, we're going to talk about the motivation.
Why do we need to start here?
Why do we need to ground ourselves in the numbers?
We're going to talk about cell size, volume, mass and composition.
What really the meaning of concentration is inside a cell and
what are some typical concentrations?
What are the time scales that cells function at?
Look at the raw material and energy costs to make a single cell and
think about what are some typical pressure, and
force magnitudes that we might see in cells and cellular systems.
[Slide 3] So first, why are we starting here?
Why start with the numbers?
What we really need-- if we're engineer cells, we really need to build some intuition
about our cellular world at the micro, nano and cellular scale.
So we need to erase some misconceptions that can propagate and influence our
thinking, if we're not really grounding ourselves in what the real numbers are.
Real orders of magnitude and sometimes it's the only way.
Cells very often have nonlinear behavior and nonlinear systems
can be very difficult to predict or even understand without a mathematical model,
and design is an inherently quantitative process.
So, we really need to start here and ground ourselves in the numbers.
And finally, if we're going to design something,
we need to understand what the physical limitations of the cells
are if we want to use them to achieve our goals.
[Slide 4] So, just to bring this point home a little bit more.
Engineers wouldn't design a manufacturing process without doing some calculations
of the raw material and energy cost upfront.
Similarly, engineers wouldn't design a pumping system without doing some
calculations about flow rate and pressure head.
So, why would we as engineers?
Why would we engineer a cell without running some numbers in
advance rather than just trial and error and seeing what we get?
That doesn't make sense.
[Slide 5] So, let's start with size and volume.
Now, cells can vary quite a bit in their size and volume.
And here, we've got some typical examples ranging from E. Coli,
sort of our standard bacterial model commonly used in the lab as well
as our common yeast model and a typical human cell.
In this case, a human fibroblast.
So an E. coli,
this is a great number to sort of remember in the back of your brain.
In culture, one E. coli cell is about a femtoliter volume.
Now yeast get bigger still, about three orders of magnitude.
A typical yeast cell in culture is about a picoliter in volume and human cells can
vary quite a bit in their size and volume, but looking at our human fibroblast,
most human cells are again much larger than bacteria and other microorganisms.
And here, a typical human fibroblast is about an order of
magnitude larger than our yeast about ten picoliters.
[Slide 6] So E. coli as being such a common model in the lab is one of the most studied,
and quantified, and engineered cells.
So, we often use it as a frame of reference of thinking about cells by
the numbers.
E. coli are about one to two microns in size.
And as I pointed out in the last slide,
remember much smaller than a typical human cell.
[Slide 7] So, thinking on the mass of E. coli now.
One cell of E. coli is about half a picogram and
about 50% of that dry mass is composed of protein.
Now, these are some kind of back in enveloped numbers that are really
good to know.
If you, for example, wanted to engineer E coli to be a type of molecular factory,
to produce a lot particular protein you want, for example.
You would need to ask yourself, what's reasonable?
How much percent mass of a cell could I generate?
How much energy is that going to consume?
So you might ask yourself, what's the minimum number of cells you would
need to produce X grams of some protein in Y amount of time?
Or how many glucose molecules would you need to make a hundred more cells?
So, that would be important in both the mass and energy balance of
your system to define really what's realistic for your case.
[Slide 8] So now looking not only on dry weight, but also on number of molecules point of view.
So we said, an E. coli is about half a picogram and
a little-- about 50% of that dry mass is protein.
That translates to a couple million, about 2 times 10 to the 6 individual molecules.
So here we're talking about actual individual molecules of proteins not
different types of proteins, but how many molecules of protein are in that cell.
So, the next most abundant molecule type on a dry weight basis is RNA.
So, there is quite a bit of RNA molecules in the cell.
And here, we're talking about, depending upon the kind of RNA.
Usually when we think of RNA,
most people's brains most people's brain immediately go to mRNA.
But mRNA in terms of number, the least common type of RNA that's in the cell.
So, a typical number would be about 1,400 molecules of mRNA
at any given time in the cell where we have about 200,000
molecules of transfer RNA in the cell at any given time.
So, then we also have our other major biomolecule categories.
We have lipids.
We have phospholipids.
We have lipid polysaccharides in the outer membrane of the cell.
DNA.
So there is a fair number of dry weight of DNA in the cell, but
only two molecules really.
We've got glycogen for sugar storage and then we've got a lot of small molecules,
and those small molecules mostly metabolites, and
ions in the cell make up about 4% of the dry mass of cells.
[Slide 9] So, it's also important to remember that cells are not static entities.
They are changing with time.
So if they're replicating, the dry mass and
the number of molecules in the cell is changing over time.
So, if you look at the cell mass over time relative to the cell cycle.
So here we've got sort of two cell cycles going in our cell, as it's dividing.
That the mass is generally gradually increasing through that period.
And at time of division is when one cell divides into two, cuts into half.
So, the mass of a single cell is not constant.
The DNA, however is constant for a period of time,
except for during the part of DNA replication.
And then the number of molecules doubles right before replication,
that mass doubles.
And then just before division, they come apart.
And during cell division, now that gets cut in half.
This is one of the reasons, for examples, you may know from your biology classes or
experiments in the lab,
that DNA is often a more reliable way to measure the number of molecules in a cell,
because of this sort of binary level and that it's constant for more
period during the cell division.
[Slide 10] Okay, now looking at these numbers from sort of a different point of view.
And putting number of molecules and volumes together,
thinking about number of molecules per cell, or concentration.
So if we look at the number of molecules in a single E. coli cell, we said that
there is on the order of 10 to the 6 proteins in the cell, 2 million proteins.
About 1 million of those are membrane proteins.
Okay, we also have about 10 to the 7 inorganic ions, about 10 to the 7 lipids.
Here is our other proteins not in the membrane, but in the cytoplasm, right?
We've got mRNA around, ribosomes.
So now when you look at the number of these molecules and
you think about that one femtoliter volume of space,
you quickly realize that the cellular interior is a very crowded space.
And it's organized, right?
We sometimes have an image in our mind of this sort of sac
of fluid with molecules floating around, but that's not really how it is.
You can see that in this cartoon representing these molecule types and
sizes and densities in side the cell.
But it's a very packed and crowded space.
This is very different than the dilute aqueous solutions
of a traditional biochemical study, where we might isolate a protein and
look at it independent of the rest of the cellular components.
So this really sort of changes how we think about concentration.
What's the meaning of concentration in this type of crowded environment?
[Slide 11] So let's look into concentration a little bit more.
Okay, so a rule of thumb here, again, it's good to have these rule of thumbs for
our sort of back-of-the-envelope thinking of engineering.
And one rule of thumb is, about two
nanomolar is about one molecule in one cell of E. coli.
Again, this is working on this one femtoliter volume.
And you can see here how concentration now translates for
an E. coli into the number of molecules in the cell, right?
So less than two nanomolars for a typical molecule,
right, is going to be less than one molecule per cell.
So this makes sense now, that the working range of most biochemistry inside
the cell is in this nanomolar to micromolar range.
So this makes sense now of what concentrations
are reasonable inside the cell.
[Slide 12] So let's switch to time a little bit.
And time, when you really start to put together a time scale of all the different
types of biological events, you quickly realize that biology covers
over 23 orders of magnitude of time.
This is pretty amazing to think about this, right?
So thinking from on our shorter end of the time scale, the time for
an enzyme to convert one molecule is in a range of about
one microsecond to one second, right?
So these are very fast events, depending on the particular enzyme itself.
So there's a range there depending on the catalytic rate, some enzymes are slower,
some enzymes are very fast.
A neuronal action potential inside of a cell happens on the order of milliseconds.
You should know this sort of intuitively, right?
Because if those events didn't happen on such fast time scales,
you wouldn't be able to catch a baseball if I threw it at you.
The reaction time from your eye to your mind to your muscles to react and catch
that, those have to be very fast in order for you to be able to do such a thing.
So those neurons have to act on subsecond time scales in order for
you to be able to do that, okay?
The time to transcribe a gene, it's different for prokaryotes and eukaryotes.
In E. coli, a prokaryote cell, the time
to transcribe a gene can be on the order of about a minute, minutes, right?
So to transcribe a gene in human cells is more on the order of 30 minutes.
It's typically longer.
And we'll talk more about that in a later video.
So, and a typical protein half-life in a cell can also range,
generally from minutes to hours.
mRNA typically has a shorter half-time.
E. coli doubling time is about 20 minutes.
Human lifespan, right, up to 100 years, we keep pushing that up.
There are other organisms such as the sequoia tree that lives to be 3,000 years,
right?
And you look at the maximum evolutionary time scale and
we look on these sorts of events, we're talking about billions of years now.
So when you're looking at biological events, both inside the cell and
the cells and populations of cells over time,
we have quite a range of time scales in which we span.
[Slide 13] So going back into our cells, let's ask the question of,
how long does it take to make a cell?
Again, this varies by cell type.
Again, generally different for prokaryotes and
eukaryotes, with prokaryotes being faster.
And it also depends on the environmental context.
So a typical E. coli in culture in the lab can
have a doubling time as fast as 20 minutes, okay?
Yeast, for example, in the lab,
budding yeast, may be about 100 minutes, as a typical number.
Mammalian cells in culture, again, in the lab,
are generally about a day, day and a half, sometimes two days.
But about 24 to 36 hours is very common for mammalian cell lines in the lab.
E. coli in you, right, in the human GI, for example,
has a much longer doubling time.
So E. coli in the human GI tract may
have a doubling time of about 40 hours, very different.
So context is very important.
And mammalian cells in vivo can have quite a range of their doubling time,
from hours to days and weeks, and even cells to the time to death, right?
And there are cells such as neurons that, once they differentiate into neurons,
are now non-dividing, right?
So they have an infinite doubling time, essentially, they're post-mitotic.
So the points to make here is that the doubling time can vary quite
a bit based on the cell type.
And it's very context dependent, as I mentioned.
And that there are implications for this, for gene expression,
including the makeup of the overall proteome expression, and
the dynamics, which we will get to in a future lecture in more detail.
[Slide 14] So let's think about, from sort of a manufacturing point of view,
making another cell from one cell.
What has to happen, right?
So there are raw material and energy costs that go into making another cell.
So the basic building blocks that we need to make another cell, we need energy,
usually in the form of ATP is our common energy equivalent in cells.
Cells also use ion gradients to store energy as electrochemical potential.
We need precursor metabolites.
And here's sort of a list of the essential precursor metabolites that need to get,
then, into building blocks for our macromolecules, right?
We also need some reducing power, very typically as the molecule NADPH or
NADH, which is an electron-rich molecule.
So this can act as an electron donor in our systems.
So in depending on the cell type, we can bring in energy in different ways,
through organic nutrients, or through sunlight, right.
And so these building blocks, these essential components, get assembled
into the sort of basic building blocks of bio-macro molecules that make up the cell.
So fatty acids, there's about eight different essential fatty acids, sugars,
there's about 25 different ones that are needed, amino acids about 21 and
about eight different nucleotides that we need, in order, as building blocks.
So those building blocks, those monomers polymerize to form
macromolecules our lipids, our proteins, our DNA and RNA.
And those macromolecules self assemble into the structures of the cells.
The organelles, that complete and
form our flagella, all those parts that make up the cell.
[Slide 15] So looking at energy costs in a little more detail.
How much energy does it take to make a cell?
So ATP as we said, is our primary currency in cellular systems.
It's our primary high energy molecule and
if we convert the biosynthetic costs to make a cell, in ATP equivalence,
we can see that making up all the protein of the cell takes up the most energy,
or close to the most energy here, right?
So on the order of about 10 to the 9, same for RNA and our phospholipids, right?
For our DNA and for our lipopolysaccharides and
others, we have about ten to the eight.
So, our estimates here are in the range by type, about 10 to the 7,
10 to the 9, ATP equivalence.
So this from an engineering standpoint,
tells us how much energy input needs to go into a system to make a new cell.
[Slide 16] So let's think about some pressure and forces.
Now a really interesting model system that biophysicists have looked at
over the years is phage infection of bacteria.
So phage are viruses that infect bacteria, here we have an electron micrograph
of a typical phage, with a capsid head.
Now viruses, as you know, infect and
inject their DNA or RNA into the cell that they're infecting.
So the capsid head contains, in this case our DNA, and we've got a tail.
And that tail acts as an injector, a physical injector,
that inserts the genetic material into the host cell.
So there's, this pumping mechanism, there must be forces and energy,
this virus has to do work, in order to pump this DNA into the cell.
So first when the phage assembles, it must pack this DNA
into the formed capsid this head, using a motor protein.
Now, DNA is a charged molecule and
within this space that molecule's very highly packed.
So, it takes energy to put that DNA to even pack it in, right?
And pressure then,
from that packed capsid head can be used to inject DNA into the cell of the host.
So as I said, this has been an interesting model system for biophysicists,
looking at forces, and velocities, and pressures, accumulated in here.
And to give you a range of, sort of, ideas of orders of magnitude.
So the forces of DNA in this injection process into the host,
about tens of piconewtons.
Okay?
And the estimated or measured pressure inside that capsid head with that packed
charged DNA molecule in there, is about one to six megapascals, pretty high.
And the velocity of that DNA going into the cell,
is on the order about through process it varies,
from about 5 to about 150 base pairs of DNA per second going into the cell.
So that gives you sort of a sense of on a single cell and
in this case virus level, what sort of pressures and forces and
velocities you may see in a biological system.
[Slide 17] So I want to point a couple of resources here.
A really excellent textbook that many of the figures in this particular
lecture came from is, Philips Physical Biology of the Cell.
Very excellent textbook.
And there's also a wonderful online resource BioNumbers.
And this is a curated database of all kinds of numbers from biological systems,
that you can search and find that property or value.
Get a number and find the reference for that.
So if, for example, you forget some of your rule of thumbs and
say, what's the volume of an E. coli?
You can go to BioNumbers,
search that, find some places where people have actually measured and reported this.
Same thing for something like,
what's a typical half-life of MRNA in a mammalian cell or an E. coli?
Again, BioNumbers would be a great place to quickly go and
find that curated number along with a reference.
[Slide 17] So, coming up, we will be talking about cells as machines now and
focusing in a little bit less on their structure and more on their function.
What kinds of functions do cells do that are useful to us as engineers?
How they behave as sensors, oscillators, pumps, reactors.
And then we'll also look at bio-inspiration for engineering design
particularly looking at a case study of photoreceptors as a cellular device.
What is the performance of photoreceptors as a photon detector?
And what are the design principles that enable it to achieve those functions?
See you next time.
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