Open course ware

PROFESSOR: Welcome to another help session on recombinant DNA. Today, we're going to be discussing about transformation and protein expression. As you can imagine, there are often many times we will need a large amount of protein. But it can be difficult to get it from the original source. For example, you need insulin to treat diabetes, but it's not exactly practical to get a lot of insulin from humans. In order to get a lot of the desired protein, often other organisms will be used to express this protein. But it's a multi-step process. For example, let's say we want to express our human insulin in bacteria. Well, the human gene has both introns and exons, as you remember from lecture. Exons are what are actually cut together in order to produce the final mature mRNA, which is later used to express the protein. Bacteria, on the other hand, don't have introns. They just have exons. So they are only capable of reading a gene that just has the exons and...

Let's consider another example of continuous mass transfer. Suppose we have a truck, and that truck has some type of plow. And it's plowing snow. And there's some type of external force acting on this truck, friction, pushing the truck forward, so let's just assume we have some type of force, F, on the truck. And this is our snow. And what's happening in this problem is that the truck connects-- picks up the snow. And then, which is at rest initially, gets the snow up to the speed of the truck. And then the snow falls off the plow. So how do we model this problem? Well, let's look at our situation at time t. And what we're going to do is, we're going to consider a certain mass of snow, delta ms, that's at rest. And our truck, it's a fixed mass truck, is moving with a velocity vt at time t, the truck. So now, what happens at time t plus delta t? Well, the truck has picked up the mass of the snow. And the truck has now changed its spe...

PROFESSOR: Another strange observation about mirrors that I've never really understood-- the mirror plane is reflecting me left to right, so it looks as though a mirror has a grain to it. It knows what line to reflect me back and forth. But if I kept the mirror in fixed orientation and I lay down, the thing should reflect me side to side, but it doesn't. It still reflects me from top to bottom. So how can that be? Why does a mirror plane, if I hold it in one orientation, appear to have a direction across which I'm reflected but it doesn't follow me if I move? Know what I mean? You have any explanation of that? Hmm? AUDIENCE: Rotate your eyes, too. PROFESSOR: Rotate my eyes. I can roll them around. I can't rotate in any other fashion. That's strange. I mean, you look at yourself every morning-- several times, perhaps, and you're reflected always left to right. And if you turn the mirror, it doesn't reflect you top to bottom. Or conversely, y...

HAZEL SIVE: Another truism of biochemistry is that many of the molecules within cells are very large. And they're called macromolecules, to indicate this. So macromolecules. So these are often -- Biological molecules are often macromolecules. And these macromolecules are often polymers-- not always-- where a polymer is some kind of repeat of a monomer "n" times. And in formation of macromolecules, there are two kinds of reactions that you need to know. They are called condensation and hydrolysis reactions. And they go something like this. Condensation reactions form bonds. Hydrolysis reactions break bonds. And condensation reactions go something like this. If we call the monomer M, there would be a monomer with a hydroxyl group that interacts with another monomer that has a hydroxyl group. And the outcome of that would be a bond between the two monomers, with the release of water. And the flip of that, during a hydrolysis reaction, is exactly the opposite, w...

So, we have another kind of very interesting piece of the course right now. We're going to continue to talk about genetics, except now we're going to talk about the genetics of diploid organisms, which apart from bacteria, most of the organisms including us are diploid. They have more than one copy of each chromosome, and so we'll go through a segment on this, and also talk about mitosis and meiosis, the central processes of cell division and the segregation of genetic material that underlie life as we know it. And then, were going to charge into a session of recombinant DNA, and some of these technologies, PCR and various things that you see in the newspapers all the time. And then, I'll finish up with the session on the immune system, which a few of you thought was surprising that bacteria recombine. I'll tell you in that system it will feel like science fiction relative to what I've told you up to now. It's an absolutely amazing system. So, ...

Let's now go through another example, which will be a little more challenging. We're going to revisit an old problem. We have a coin that has an unknown bias, Theta. And we have a prior distribution on this Theta. We fix some positive integer, n, we flip a coin n times, that has this unknown bias. And we record the number of heads. On the basis of the number of heads that have been observed, we wish to estimate the bias, Theta, of the coin. To make things more concrete, we're going to assume a prior distribution on Theta that is uniform on the unit interval. Now, this is a problem we have considered before. We have calculated the expected value of Theta given X. And we did find that the expected value takes this particular form. Now, notice that this is a linear function of X. And if it turns out the least mean squares estimator is a linear function of X, then we're guaranteed, since this is the best, that this is also the best within the class of linear e...

PROFESSOR: OK. Let's do another application. I leave one thing. So this is going to be-- but it's called Landau levels. And they're pretty interesting. So it's the problem of solving for the motion of an electron in a magnetic field. So it's called Landau levels for the physicist Lev Landau from Russia that discovered or did this calculation first. So you have a mass m charge q, and the magnetic field b in the z direction. We will solve it. And I think you will find it pretty interesting. Well, you will be left with a little of an uneasy feeling, I think, at the end of the lecture, because the problem of gauging variance is so dramatic that the physics will look a little strange and a bit unrecognizable. So let me remind you that in classical physics, if you have a magnetic field, b, you can have electrons that perform circular orbits, and the main property of those orbits is that they all run at the same frequency called cyclotron frequency, qb over m...