 와! All right. Welcome back. Okay. Welcome back. Good to see everybody today. We're going to be going a little bit into more detail about the function of protein. So we looked at the different shapes of proteins, but we didn't really talk about function yet. The one thing I did mention is that proteins are dynamic. So they're flexing around. And today you'll see just a beautiful example of how proteins slice and dice and do all kinds of amazing motions to carry out their function. So today we'll both be talking about proteins, we'll come to that in a second, about a protein that doesn't catalyze a chemical reaction. So you couldn't really say it's an enzyme. An enzyme is a protein that carries out a chemical reaction. Its purpose is to bind something and to vary in a physiological way, bind and release that object at the appropriate time. So perhaps against my better judgment, I thought we would come back to this confusing topic that you guys uncovered. So looking at the Leninger textbook on this topic, one is not less confused. And the primary reason is that these definitions are not standardized. They're sort of, you know it when you see it, sort of definitions. So I thought perhaps instead of giving you very precise molecular distances that define each of these types of things, that I'd give you some examples. But these are for the most part arbitrary. And so we talked about structural motifs and super secondary structure. And here are some examples of that. You can see they're small. They contain limited number of strands for example with the sheets. But here we have one, this zinc finger. And it's on the line of purpose because throughout literature you'll see it described as a motif as well as a domain. Okay, why? Because it's a definition, it's arbitrary, it's not standardized how we differentiate this. Here is a real life protein. The domains are in different colors. Do all of them have a flexible linker between them? So for example, here is one domain, this red helical domain. No, it has a flexible linker within the domain. Now these guys are more globular like, right? So here's a domain, helical domain. Here's a G domain. And here is an EH domain. Those are somewhat distant. But what happened here is someone just said that's the domain and that's the domain, right? One important thing, a tradition for the majority of domains, the amino acids in those domains are contiguous in the primary sequence. And so we have, you'll see this throughout your careers as biomedical researchers, this representation of the primary sequence of a protein. Remember, and these are the actual amino acid numbers here. And so remember we start from the N-terminus going to the C-terminus. So for example, this protein has 543 amino acids. And we have these colored boxes. And each of those boxes is one of these domains. Domains can be defined as a compact structure, a unit of folding, a unit of function such as this domain binds to something, or a unit of evolution. In general in nature, you'll see that different proteins take different combinations of those domains using the function of each of those domains in different ways to accomplish a certain type of chemical transformation. So I don't know that this clarifies anything for you. Structural biologists need to define these standards. So for example, if you gave a thousand structures to a thousand structural biologists and you said what is the average number of domains in these proteins? I bet you would get a nice L-shaped curve in terms of the average number. Okay, so let's look at some more examples. We have a little bit more time today. I had mentioned in the last lecture a particular domain called an SH2 domain. Its structure is here. It binds a phosphotyrosine. So an amino acid tyrosine that in the para position where the hydroxy group is, we've substituted in a phosphate. In that particular substrate of this domain binds in this groove. We have another domain that binds phosphotyrosine called a PTB domain. And so these are some examples of domains. Now we can take these domains and combine them in all sorts of interesting ways. So again, remember these depictions are always from the end to the C-terminus left to right. And so we have a variety of different signaling molecules that have different combinations of domains. And those give those signaling molecules the unique properties necessary for them to communicate signals from outside of the cell down in generally down into transcription. So this is just an overview but I thought it would be useful to highlight that this is a common way in which domains are represented in the primary sequence. But it's not necessarily always the case that domains are contiguous in the primary sequence. It's almost, it's usually the case, such as for these domains here, okay? I'm not gonna ask for any more questions. Oh, so Art, there is a question, however. Does motif have to have contiguous sequence of amino acids like them? Again, there is no definition. Here are some examples of motifs and you can see for these particular examples, they are contiguous, so that's how they define them. Unfortunately, it's a world of gray, not black and white. Okay, it's a little bit of review. So today we're gonna be talking about protein function, some of the most amazing proteins and some of the earliest characterized proteins out there. So we're gonna be looking at the oxygen binding myoglobin and hemoglobin and closely related hemoglobin protein. We're gonna be looking at how their flexibility contributes to their function. We'll look at all kinds of modes of regulation, which will be an ongoing theme in the class. And then we'll give another quick example after that of another protein that binds things. So this is myoglobin. Myoglobin is found in muscles. There are large amounts of myoglobin and shampoo. This was the first protein structure ever obtained. So in terms of human beings, this is the first protein ever seen by a human being. And you can imagine, up to this point it was all theoretical, line is pawling with pieces of paper and winding things up and they saw this and look at this beautiful structure. So this one is all alpha helical. They noticed something red. Well, it probably wasn't red in the X-rays, but this was something that was not attached to the protein covalently. So it's non-covalently attached thing and we'll come back to what that is. And so here it's a pretty simple structure. You just have a combination of helices. You could refer to it as a fold. So this is the globin fold. This protein has one amino acid in addition to how the globin fold is defined. That's arbitrary, right? They're all sort of stuck together. So here's the structure. There's different ways to represent the structure with these cartoon representation. If you have arrows, you're going from the end of the sea terminus, a space filling, or where you're actually showing the atoms. And so that sort of doesn't tell you much. Okay, so this is myoglobin. Here is it, sure, or not? So I'm going to just play it manually. Nice. All right. Today the proteins will not be rotating. I know your heart broken. Okay, so here's another picture of myoglobin since it's not rotating, it adds nothing. So here it's the so-called this non-covalent group. It's adding a function. So amino acids alone in myoglobin are insufficient for its function as an oxygen storage protein. And so these are prosthetic groups. So you could also call it a cofactor. And this cofactor is made up of a porphyrin ring. And when you add an iron, it becomes a heme molecule. And you can see the irons are typically octahedral in configuration. They're desired substituents for an octahedral configuration. So the iron is chelated by these four nitrogen atoms. And then you see some wavy line. And what's this? What's this wavy line thing hanging down from lecture one? Histidine. So histidine is showing up today. And then we have an oxygen atom here. Okay. And so this is the prosthetic group. Stably associated with the protein. And now we can look at it in a different way. You can see that there's a plane defined by the heme or the porphyrin ring around the iron atom. And you can see the fifth bond is to this histidine prosthetic group. And then we have an oxygen. And it's important that the protein provides this fifth bond to the histidine group because that helps to prevent the iron from becoming oxidized. So to function in its role of binding oxygen it needs to be iron two plus, okay? And so let's look at this in some other ways. One thing that can happen with irons is yes, they can bind to oxygen. When they do bind to oxygen it's in this bent configuration in relation to the porphyrin ring here. But other molecules combined to iron such as this carbon monoxide. And you can imagine, well that's probably not good. Probably myoglobin or we'll see hemoglobin need to differentiate the binding of this two atom molecule with this two atom molecule. But what a subtle thing for the protein to have to do to discriminate a two atom molecule that's either linear or bent to the side. So that's where we have a second histidine group provided by the myoglobin protein. So these are just hanging out in space but they're actually attached, they're all attached together through myoglobin. This histidine is referred to as the distal histidine and it's providing this exquisite selectivity to block or slow down the binding of carbon monoxide but to facilitate the binding of oxygen through a hydrogen bond, okay? So if we didn't have this histidine, carbon monoxide would bind very tightly. As it turns out, carbon monoxide binds tighter to just plain heme in solution than oxygen. So what is this subtle little difference doing? Well, free heme binds carbon dioxide 25,000 times more tightly than oxygen. The purpose of this myoglobin molecule is not to start carbon monoxide. That's stuff we need for metabolism, we need oxygen. But when you put this heme group in myoglobin, you put that histidine group in the way for carbon monoxide to bind that decreases the binding affinity of the heme 100-fold for carbon monoxide. It's still preferred. So in the atmosphere of Earth, we had a one-to-one mixture of carbon monoxide and oxygen. The gross majority of myoglobin molecules will be filled with carbon monoxide. But fortunately, the atmosphere is very high in oxygen, low in carbon monoxide. And that's reflected in the blood of organisms. So about 1% of myoglobin is normally coordinated with carbon monoxide. And so you can do some calculations. Come out and come back in. My screen's checked. So this binding ratio, binding affinity ratio of myoglobin were 25,000 to 200. Most of myoglobin would be coordinated with carbon monoxide. So this discrimination, there's still, every one of you currently has some carbon monoxide in your myoglobin and in your hemeoglobin. But luckily, you have a lot more oxygen. So it's just a minor binding partner. So where does this carbon monoxide come from? Any ideas? Yeah? Could be. So there's other non-biological sources as well, right? Partial oxidation. So you would not want to be in a sealed environment with an automobile because they produce carbon monoxide. So yeah, carbon monoxide is in the environment from the partial combustion of fuels. Okay, so today we're going to introduce some of the concepts that are gonna be critical in the fourth lecture. Thinking about the equilibrium between proteins and their substrate. So here we talk about a ligand. A ligand is simply something that binds reversibly to a protein. So in our case in myoglobin, the ligand is an oxygen molecule. And so we can describe this equilibrium by equilibrium constant, an association constant and a dissociation constant. Remember, from probably right when you started at Brown or maybe even in high school, you define this as the concentration of products over reactants. Remember that? And so for the association constant, the product is PL, concentration of that divided by concentration of P, concentration of L. In KD, the opposite direction is just the inverse one over K. So so far, might ring some bells. But now I'm gonna throw something new at you. Theta. And this is defined as the fractional occupancy of a protein for its ligand. And so it's defined as the number of occupied sites, binding sites, ligand binding sites on a protein, divided by the total number of sites. You can calculate that by if you know the concentration of the protein that's bound to a ligand compared to the total amount of protein, okay? What's made? So this is just the definition. So to make it crystal clear, we have the red circle method of showing this. And so we have here four red circles. These are proteins. Only one of the four is bound to a ligand. So theta would be 0.25 for this particular case. If half of the binding sites were bound to a ligand, theta would be 0.5. Okay, what's been so far? Not too bad so far. So all we're gonna do now is combine these two equations. We have an equation for the KA and the equation for the fractional occupancy. And if we substitute PL into here and rearrange things, theta is equal to this equation. The concentration of ligand divided by the concentration of ligand plus a constant plus one over KA. So we've just done simple arithmetic rearrangement of these equations and a substitution. And you might recognize this equation. It's a hyperbolic relationship. So the equation of a hyperbola back from maybe even junior high school is X over X plus a constant, okay? So that has this kind of shape to it. So at very low concentrations of ligand, there's a linear relationship between the fractional occupancy and the concentration of the ligand. In other words, this is sort of linear, right? So if looking at the equation, you can see this as well. If L is very small, L would be much smaller than one over KA. So theta would just equal a linear relationship there. And the same thing up here. If L is much larger, the line approaches one. So L divided by L plus something insignificant is one. Does it make sense so far? So we have a hyperbolic relationship between the fractional occupancy of a protein and its ligand concentration. So let's poke around at this equation. So here's the equation again. What happens if half the binding sites are occupied? Remember I said theta would be 0.5 if half the binding sites are occupied. So if you put 0.5 for theta and do some rearrangements, look at how miraculously it simplifies. And so at a theta of 0.5, the concentration of ligand equals KD. So the dissociation constant has units of concentration. Its value is the concentration of ligand necessary to fill half the binding sites. You're like, why are you doing this? It'll become very useful. But for now, that gives you sort of a physical feeling of what is this KD? How can I calculate KD? Well I just keep increasing ligand concentration, test some analytical measurement of the number of proteins bind to the ligand. I have hyperbola, it has some kind of upper level, half of that you track down on the curve and you can find the KD directly from a binding curve because it would be the concentration of ligand necessary to fill half those binding sites. So we can calculate KD. But now in this lecture, our ligand is a gaseous molecule, right? So it's an oxygen molecule. And so you don't usually think of moles of oxygen, right? You think of a partial pressure of oxygen. And so we can define a P50, a partial pressure of oxygen that is necessary to fill half those binding sites, okay? And that's just a definition. So this P50 is the pressure, is KD. So in this case, KD does not have units of concentration, it has units of pressure. You see so far? And it's rambling on, if you wanna interrupt, that's fine. Okay. Okay, so let's think about what does this mean? So the P50, the partial pressure of oxygen necessary to fill half the myoglobin oxygen binding sites is 0.26 kilopascals. So what does that mean in terms of magnitude? The environment of us, we're at sea level, Brown University is right by the sea. The atmospheric pressure here is about 101 kilopascals. I think more of atmosphere is one atmosphere, but you can also say pressure is kilopascals. But oxygen only comprises 21% of the atmosphere. The majority is nitrogen, of course. And so if you calculate 21% of this number, you come to a partial pressure of oxygen of 21 kilopascals, right? But the concentration of oxygen necessary to fill half the myoglobin binding sites is only 0.26 atmospheres, which is 1% of the amount of oxygen that's available to us. So what does that tell you about the, in general terms, the binding affinity of myoglobin for oxygen? Is it low, medium, high? High, right, from the perspective of the environment that we're in. So all of our myoglobin molecules are full with oxygen, right, unless we're running around and we're using that oxygen very rapidly. So it tells you something. So the function of myoglobin is to store... Yeah, all the movies don't work today. The function of myoglobin is to store oxygen. So a battery needs to have a large capacity, it has a large affinity for electrons, right? In this case it has a large, this oxygen battery has a large affinity for oxygen. Okay, so the role, the shape of this binding curve is made in the function of the protein to store oxygen in myoglobin, okay? So myoglobin is a storage molecule for oxygen, but we don't need to just store oxygen, we also need to transport it. I'm breathing in oxygen into my lungs, and that oxygen doesn't just get exhaled again, it needs to get transported in my body to my tissues. So we need another type of protein to transport that oxygen to my tissues. Myoglobin might not be very good. It would be great if it were in my lungs, which it's not to my muscles, but if it were in my lungs, it'd be great at picking up oxygen, but it wouldn't be good on the delivery side of things. It wouldn't wanna let go of that oxygen unless there was an intense demand for that oxygen, right, unless the pressure of oxygen was extremely low in my tissues, so I'm running around, they might release it from my muscles. So hemoglobin fits this role of transport. Hemoglobin is a hetero-tetrameric protein, so it has four polypeptides in its structure. Would this be tertiary or a quaternary structure? Quaternary structure. Each subunit would be a tertiary structure, but all together, this would be the quaternary structure. What is the alpha two, beta two means? That means that there's two subunits that are very similar. So the alpha subunits, there's two of those. They're primary sequences identical, and then we have two beta subunits whose primary sequence differs from the alpha subunit, but they're also identical to each other. But even though their primary sequences are different, the fold is the same. They have the so-called myoglobin fold, right? But there are some differences between them, and those differences are important, as you'll see in a moment, in the interfaces between the subunits that are tied to the function of hemoglobin. So hemoglobin is found in your erythrocytes. They're just chock full of hemoglobin. They're even red, right? So you can see that each of these subunits has a heme prosthetic group, and each of those potentially combined to oxygen. So whereas a single myoglobin protein could bind just one oxygen, hemoglobin combined up to four oxygens. And you can see it has a donut shape. There's a hole in the middle. So today we're gonna put something in that hole, and that's gonna help to regulate this protein. Okay? So far okay? There's left, maybe. All right, so here's that myoglobin fold. So do you see how the tertiary structure of a myoglobin is similar to one of the subunits of hemoglobin? It's all alpha helical. Remember these swirls, these are alpha helices. They orient those helices pretty similarly to the heme prosthetic group. Although they're primary sequences of myoglobin and this beta subunit hemoglobin are very different. They're structurally similar. They have the same fold, okay? But only 27 of the amino acids are the same, as it turns out, so that's pretty cool. So the action, a lot of the understanding of hemoglobin is gonna come at the interface, the noncovalent interfaces between the subunits here, between the alpha and the beta subunits. And there's going to be manipulation of the amino acid and the polypeptide at those interfaces to regulate this protein, to help it to be an even better oxygen transport molecule. And so this slide is often very confusing to people. So I'm gonna tell you what these letters mean in a little bit right now, it's just gonna confuse you. So we have two different states of this protein. What does that mean? That means that there are two crystal structures out there that people were able to determine. One with oxygen bound, the other with oxygen not bound. We do not have a crystal structure in between these states, but we're able to see that when oxygen is bound, it's in this configuration, hemoglobin's in the R state, and when oxygen is not bound, it's in the T state. Look at the dramatic shift in all of these alpha helices. So when you transition from the oxygen not bound to the oxygen bound form, the whole thing is flexing. Hard to find an amino acid that's not moved here. Some, as you'll see of these amino acids, are pointing down in the donut hole, like you could see it here. See this histidine, HC3, so this is a histidine, the C terminus of one of the hemoglobin polypeptides. It rotates way the heck up here. So it's in one state and then it comes up. That's perhaps the most dramatic motion that we can notice between these two states. So we have, again, we have the heme groups, and oxygen is gonna bind at those heme groups. And so here's where the word T and R are defined. T stands for tense and R stands for relax. And so it's tense, because do you see the contortion of this porphyrin ring? It's like, instead of being planar, it's a little bit flexed back. And the iron atom is pulled back, sort of like you would do with a fling shot, right? So this is tense, and when you're thinking about the orientation of this iron atom, you would guess iron's probably gonna wanna sort of sit in the middle of that plane. But in the tense state, it's pulled back, and in the relaxed state, it's pushed forward. But confusingly, the binding affinity is in the inverse way of thinking of things. So the binding affinity for oxygen is higher when it's in the relaxed state. So although I've told you that these are tense and relaxed, you feel free to forget that, because it's just going to confuse you. But you do need to remember that in this configuration, in the R state, the binding affinity of the iron atom is higher for oxygen, okay? Just because of the way things are contorted. Does that make sense? Do you see the flex and the puckering in that ring? Now, it's not much of a flex. It's about 0.4 angstroms. Like, so it's just a little boop, right? And you can see, you can see it here a little bit. So we see a little bit of a movement, 0.6 angstroms. This iron atom is boop. But what is the iron atom attached to? Yes, question. I think we should go through the lecture and then I think it'll become obvious. There's a lot of forces that's playing here. There's a lot of, yeah. If I tried to review the lecture, it might not be the best way, but I think if I don't answer your question, please ask it again. Okay, so we have a heme atom or an iron atom and an oxygen bind. The oxygen pulls that iron atom a grand total of 0.6 angstroms. But what's attached to the oxygen or the iron atom? A histidine, right? That's that thing on the back that's preventing it from being oxidized. Well, if you tug on the iron atom, you're tugging on the histidine. What's the histidine attached to? The histidine is attached to the alpha helix. If you tug on the histidine, you're gonna shift the alpha helix. What's the alpha helix attached to? The other alpha helix is, so if you pull on one alpha helix, the rest of them shift. And even between the subunits, you'll have a change in the types of the chemical nature of the surfaces between the subunits as you distort one of the proteins. So sort of head or foot bone, leg bone, knee bone sort of song could be talking about this situation. Okay, so we've made a tiny little tug and all of a sudden helices are moving all over. Some of these amino acids are whipping way or very dramatically magnifying this motion. So does hemoglobin have both the distal and proximal prosthetic groups bound to oxygen? Like why? Only one side of the iron atom binds to oxygen. So when we say distal and proximal, we're describing the histidine residues. So we can go back to that slide real quick. It's a good question. Define somewhere. Anybody see it? Here. So when we say proximal histidine, that's the one that oxygen is not buying on its side. The proximal histidine blocks oxygen from binding to iron. Oxygen does not bind to the histidine. It binds to the iron. The histidine, the proximal histidine blocks oxygen from binding on that side of the iron atom. Remember, there's six coordination points on iron. And this distal histidine enhances the selectivity of both myoglobin and hemoglobin for binding oxygen. It's a good question. Okay. All right, so here's another, yeah. So in this movie, you would see this circle coming out just slightly. And you would see the histidine tracking back and forth with this. And that's shifting. And you would also see this particular amino acid. The alpha helix just shifts a little bit, but this amino acid that's in the donut hole is whipping around between this T and this R state. And also, you would see, I'll put these movies on the webpage afterwards so you can see it for yourself. You would see when comparing the transition between the T and R state, you would pretty much see all of these alpha helices moving in relation to each other. So there's dramatic motions from a little .5 angstrom tug on an iron atom. But then a question comes up, well, what influences the binding affinity of an iron atom in a heme group when oxygen binds in one of these subunits? What happens to the binding affinity to oxygen in the other subunits? Well, so what are we doing? If we bind one oxygen in one subunit that pulls on that alpha helix and all of the fact that an oxygen is bound is being communicated to the other subunits through large motions of the protein. So the subunit is self-changes shape and the changes shape of that one subunit is transmitted to the other subunit at the interface between them. And so you pull on one iron atom and the other subunits are changing their configuration. The iron atom without oxygen bound is pulled out of the plane and as soon as you bind oxygen in one of those four subunits, it gets pulled out or gets pushed to the center of the plane and the other ones also feel that effect. So now iron atoms are moved in the unoccupied, the sites that don't have oxygen, they're moved to the center of the plane and when they're in the center of that plane, they can have a stronger binding affinity to oxygen. So it helps the second, third and fourth binding of oxygen to have that first oxygen bound because there's a conformational change making the rest of the subunits in a more optimal configuration to bind to iron. So these are the interfaces here which these conformational changes are transmitted. And so as we already said, if that oxygen is in the middle of the plane, it has a higher binding affinity to oxygen if the iron atom is in the middle of that plane. So in the R state, that's the state that's relaxed in relation to the porcelain ring where the iron's in the middle. And so if we put one of these subunits in the R state by having it bind oxygen, the others will tend to move towards the same relaxed state. And then when oxygen comes along, they'll have a higher binding affinity to oxygen. So this is a fundamental concept that we'll see throughout the semester of allosteric regulation. The binding of a molecule to the protein at a site other than the active site causes a change of a shape in a protein. And here it's a little confusing because we do have oxygen binding at what you could say as an active site, that the binding, the ligand binding site, but it's also affecting the other sites that aren't binding ligands. This is a positive allosteric regulator. So allosteric means something that changes the shape of a protein. It's a shape-shifting influence. So let's look at the binding curve of hemoglobin. This figure is confusing. I updated this slide a little bit. So if you don't have these words written on there, if you printed it out early, you should add them. So the actual binding curve of hemoglobin for oxygen is in this S shape. But if all of the hemoglobin subunits were locked somehow in the R state, this is what the binding curve would look like. If, hypothetically, all the subunits were locked in the T state, this is what the binding curve would look like. The function of hemoglobin is not just a bind to oxygen, it's to bind it and then release it. And so it binds it somewhere. It binds it in the lungs. So where the partial pressure of oxygen is pretty high. And then it releases it in the tissues. So if we're all locked in this R high affinity state, then you would bind it in the lungs, it would get to the tissues and it would just say, uh-uh-uh, I'm not gonna give it to you, it's mine. It's selfish, selfish little protein. But from the T state, it would get to the lungs like, hey man, there's oxygen and I'm not just hanging out, I'm not gonna party with that oxygen. So it was only just still maybe, you know, I don't know, what is that? 0.5% of the hemoglobin molecules. And then they say, okay, I'm going to the tissue now. And only half of the active sites are full, what good is that? They get to the tissue and say, yeah, man, I'll give you, maybe I'll give you some. So I'll give you, you know, then you drop off and then you're still remaining 0.2%. But look at the difference here. The actual binding curve of the hemoglobin that has this shape shift goes between these two curves. So in the lungs, it has extraordinarily high affinity for oxygen, but then it gets to the lungs and that affinity is greatly reduced, right? So that helps it to, in its function, it's not just storing oxygen, it's delivering oxygen to the tissues. Does this figure make sense? I'm going excessively slow today because I have a limited number of slides, so. This is not the normal state of things in biochemistry. Any questions? Okay. Yes, online question. Just one clarification about the R and T states. The R confirmation triggered by oxygen binding to hem, which? The R configuration becomes more favored in the unoccupied subunits when one subunit binds to an oxygen. So when the first, you know, normally, we'll get to sort of ways to think about the ways in which the subunit shifts state in a moment. There's different models for this, concerted or sequential. But for the first binding event, there would be a larger proportion of the subunits would be in the relaxed state. But as soon as you bind one oxygen molecule in one of the subunits, that would pull that iron out and the other irons in the other subunits would also shift slightly more into the plane of the ring so they can make tighter affinity bonds. And that's cooperative. So that's the binding of the first oxygen helps in the binding of subsequent actions and that's why the shape of this curve is sigmoidal. Yes, that's a good question. So you mean on the release? Yes, you would imagine so. Especially, well, it depends. The thing is the problem here is we don't have data. We have an X-ray crystal picture of the R state and an X-ray crystal the picture of the T state. So when say all four are occupied, one's released, how much are the rest are gonna shift? Are they gonna shift independently or all together? Now definitely, when you get to the last one, you would think that it would help but we don't have data. That's a wonderful question. We don't have data because it's flexing and it's not crystallizing, that's one of the reasons. You know that question? And so one more. How does the first oxygen bind? It binds chemically, I don't know what else. Yeah, so it, well, I guess it's in the lungs and the oxygen becomes dissolved in solution. It gets into the red blood cell and it binds to the hemoglobin, one of those iron atoms in the heme group. So diffusion, I guess, is important. That's a good question. Okay, that's why we have discussion. Okay, any other questions? Yes, all right. So we have the shape shifting. We're gonna see examples of positive allosterism where you're helping by the regulator binding in subsequent binding events. We have negative allosteric regulation. We're looking at all types of regulation. Today we'll see different examples beyond just oxygen binding. So but now we had this nasty stuff that we did for myoglobin. We can do a similar mathematical treatment of describing the equilibrium between hemoglobin and its ligand oxygen. So here we could have more than one ligand. So we have to take that into consideration. So we can define a association constant, products divided by reactants. Here we have to raise to the ends of power because we have the possibility of more than one ligand. We can define theta. Theta is defined similarly, right? So remember theta is the percent of active sites that have bound to a ligand. And now we're gonna do something that makes no sense whatsoever. I'm gonna take theta and I'm gonna divide by one minus theta. You're like, oh yeah, that helps, that's good. So we took this nice, tidy little equation and we divided by one minus theta. But then we started to rearrange and I'm not gonna go through it because I'll get you all confused. But if you go through it on your own, you'll see that this nice, tidy equation got even more tidy when I did this manipulation. But this has no real physical meaning. What is fractional occupancy divided by one minus fractional occupancy? All it does is it makes the equation look nice and neat. So, okay, this is a hill equation. And so, but this is in perfect. We want it to be really simple. This is not linear. So back a while ago, they didn't have computers. They had slide rolls. So it was often helpful to make things the slope of the line. Was it me? Oh, it's okay, okay. Can't come to the phone. All right, so all you do is you take the log of both sides. Remember, that's one of the things you're allowed to do. And if you take the log of this side, you get rid of the power. So it becomes a linear relationship between this odd combination of fractional occupancies and ligand concentration with slope of N. So I can determine what N is because I can measure fractional occupancy at a variety of ligand concentrations. You're like, right, yes, you can do that. But what does it tell you? You can think of N as the measure of cooperativity of the binding of a protein for its ligand. So as you increase the concentration of ligand, here it's a gas, so it's expressed as a partial pressure, as you increase the partial pressure of oxygen, you get to a certain point where one of those four subunits has bound an oxygen atom. And when you get to that point, the binding of subsequent oxygen atoms to the remaining three subunits is assisted. It's cooperative. So until you bind that first oxygen atom, it's not cooperative. All of the iron atoms are in this tense state. They have a lower affinity for binding oxygen, but as soon as you bind one, it becomes cloppy. And so the slope goes up. So perfect cooperativity would be a slope before, but what does that mean? I don't know. It's just sort of a metric of how much you're assisting. The degree of the allosteric regulation. Okay, and so for hemoglobin, it's pretty cooperative. If you look at, you can do this type of analysis for lots of different proteins that are regulated allosterically, and you can calculate these hill coefficients for different proteins. And as it turns out, this is very cooperative. So for myoglobin, it's not cooperative. This just is not allosteric regulation. It just binds oxygen and then the story's over. So the slope is one, irregardless of the concentration of the ligand. But here, we're measuring the degree of cooperativity. And so this is just a useful thing that one could do in the lab to measure how allosteric, how much allosteric regulation is changing, the ability of a protein to do its job. Okay, theta divided by one minus theta, right? That's cool. Okay. You have a question? Actually, I should probably just dwell. Yes. Yes. Yeah, exactly. So what this curve, this is not a theoretical of the actual curve, suggests that when the first one binds, it's pretty much already at its maximal level of cooperativity. So this is really useful to compare different proteins, like how much allosteric regulation impacts it, but the actual like three versus two, the physical meaning of that is hard to understand. Because you would imagine that, we have not just one hemoglobin molecule in our experiment, we have lots of them. And not all of them are gonna have the exact same number of ligands. There's gonna be some distribution. The other question, this is called the Hill Equation and the Hill Coefficient. And he just got it by playing around with the numbers. Yes, Art. Yep. So what do you think would move and depend on, or depend at all on the type of ligand? I would imagine so. So if we had an example like for, I bet there would be a different, there could potentially be, well, I would guess for the example of hemoglobin, like if you look at carbon monoxide binding versus oxygen binding, I bet you would get a similar Hill curve. Because I bet the binding of carbon monoxide is enhanced by the binding of the first carbon monoxide molecule. But that would have to be experimentally determined. So the Hill coefficient's a bit of a pain for all bioconstrict. Okay, so we can think of, remember, we only have data in each of these two states. We have X-ray structures where all subunits are in the T state, where all subunits are in the R state. So we don't necessarily know what's happening in between these. One possibility is the so-called concerted model, where there's only two possible states, either all subunits are in T or all subunits are in R, and there's nothing in between. In other words, each subunit cannot act independently. Or the other model that fits the existing data, because we only have data on the ends, is that each subunit can individually oscillate between states, right? And so there could be mixtures of subunits, where one subunit has iron atoms in the center of the ring, and the other subunits have iron atoms, not in the center of ring. This is to raise a hypothetical possibility to you. We don't have experimental data yet to differentiate, which is the case. We didn't catch a naughty subunit doing something different than the others in a crystal structure. So this is one way to think about things. Okay, that's also very often confusing. Circle is one state, square is the other. Let's look at some of the other amazing ways in which hemoglobin is regulated. We've seen one positive asteric regulator, oxygen, affecting the binding to the other subunits. Let's think about what hemoglobin is doing. It's taking your oxygen from the lungs and bringing it to the tissues. And so, do you guys remember, if you take CO2 in solution and you shake it up, and you put a pH probe in there, what would you measure? It's acidic, so it's about pH of three. If you take CO2, like the Coca-Cola you drunk today, if you put a nail in Coke, after three days it'll be dissolved. I don't know if it's an old wife tale. That's acidic. It also has phosphoric acid, it adds a flavor, but the carbonic acid is also acidic, so just seltzer water has a pH around three. And so, one of the byproducts you'll see throughout the semester of metabolism is acid. So when cells are respiring, one of the waste products is acid. The other waste products is fully oxidized form of carbon, carbon dioxide, okay? And so, venous blood is more acidic than arterial blood because venous blood in the tissues is picking up all those metabolic end products, acid and CO2, okay? And so, and obviously there's more CO2 in your tissues than in your lungs. So, hydrogen, as it turns out, binds, makes a covalent bond to a particular amino acid that by, I'm sure, not just random chance, exists right at the interface between subunits and affects the interaction of those subunits. We'll see that in a second. So the binding of either protons or carbon dioxide, which also makes a covalent bond to the protein, either of those binding events decreases the affinity of hemoglobin for oxygen. You're like, isn't that bad? Well, so you can look at the binding curve here. So as you decrease the pH, this curve shifts to the right and that means that you're decreasing the affinity. Why? Because KD is increased. KD is one over KA, KA is the reflection of affinity. I just said that really fast. You might wanna process. So as this curve shifts to the right, right? It takes, because it has the hemoglobin, it has a lower affinity for oxygen, it takes a higher concentration of oxygen to fill half the binding sites. Remember, theta of 0.5, that partial pressure of oxygen is the P50. That P50 is shifting up and that's equal to KD. KD is one over KA, KA is the measurement of affinity. Are you with me? So the pH is affecting the binding affinity of hemoglobin for its substrate or for its ligand. So here we have the two states. Remember this amino acid that we tugged on the alfie helix and this one amino acid was going whoop, it's going from the center of the donut hole here all the way out to here. Well as it turns out, this is where the proton is ending up. So in your tissues, hemoglobin comes to the tissue and the tissue says, let go of cargo now please. And there's lots of acid being produced in the tissue, protons, and so this is a histidine. What's the PKA of histidine? Six. And so it's gonna pick, this particular histidine picks up that proton. What can you say about the charge of a histidine when it becomes protonated? It goes from what to what? Okay, remember the structure I might ask you this. So histidine, unpronated is, is uncharged or positively charged? Uncharged. So when you add the proton to histidine it becomes positively charged. Now if you take an amino acid from an uncharged state to a positively charged state, can you imagine that, oh, now it has a new positive charge and that positive charge could potentially or possibly have a charged charge interaction with a negatively charged amino acid. So look what's hanging up here, lurking, right? And a spartic acid. And you have, you know, normally you have an uncharged histidine, it's like, oh, that's nice. But if you have a positively charged histidine, it's like, yeah, and it locks onto that thing, favoring the T-state, right? Do I have this right? Yep, yep, T-state, it's up here. And so that's gonna decrease the binding affinity of hemoglobin for oxygen. What about this CO2? You're like, that's inert, man. It just gets dissolved and fizzles in my drink. No, it can convert, be converted into a reactive form through the action of an enzyme. You can carbamolate an amino group. And the amino group that gets carbamolated in hemoglobin is at the interminous, the actual interminous itself. So we can take a uncharged or a, I guess you would say positively charged a physiological pH amino group and put a negative charge where a positive charge used to be. And that, as you can imagine, you're changing the charge there. And that could affect the interaction of amino acids at this interface. So between subunits, you see the new carbamolation, that negative charge makes a salt bridge with this basic amino acid lysine. Again, affecting which state is preferred. Okay, you with me so far? So subtle little covalent modifications. Even though it's covalent, it's still an allosteric regulator. It's a small molecule that binds to the protein, changing its shape, affecting its affinity for its ligand. In this case, it's a negative allosteric regulator because the binding of a proton or carbon dioxide at this interface decreases the binding affinity of the unoccupied oxygen binding sites to oxygen. That makes sense? Great. Okay. Any more questions on that? Yes. Yes. Yes, but what happens during respiration? Why is this also beneficial? In terms, think about what's happening here. Do we want that CO2 to just accumulate and get all puffy in your tissue? So it's hitching a ride on the protein. A lot of the carbon dioxide has been turned into carbonate, bicarbonate, right? So it's an ion, it's in the blood itself. So that's one way that CO2 can be transported out. But erythrocytes are full of tremendous amounts of hemoglobin, so they can also hitch a covalent ride out of your body, right? And then when you get to the lungs, you can release the carbon dioxide and you can remove this proton, too. So only the, I believe it's the beta subunit becomes covalently modified. And there's two of them. Yes. Yeah. So is that gonna help you in the lungs? No. Aha, exactly. It's not just an oxygen storage molecule. It aids not in the pickup of the oxygen, but in the delivery phase. It allows the tissue to communicate to the protein saying, please give me some of what you have, right? Because the tissue is respiring, it's making these byproducts. And those byproducts cause hemoglobin to increasingly release their oxygen, decrease their affinity for oxygen. Does it make sense? Okay. Any mountain climbers in the room? Anybody climbed? Cool. So when you climbed, did you go to different base stations or you just did a one day climb? Yeah, so if you wanna climb Mount Everest, right, you have to go up a little bit and up a little bit. And the reason has to do with oxygen. So you might think, well, hemoglobin probably has some role to play. So not only can your tissues communicate to hemoglobin, they can, hemoglobin protein can respond to the environment. So when you're climbing up a, yes, hi. A different amino acid, the picture here is confusing. Cause the histidine that gets protonated is actually on the C-terminus, but they're actually really close together, the C and the N-terminus. The N-terminus gets carbamylated and the histidine gets protonated. And they're actually, if you look at the primary, so you can see it here, it's confusing, they're far apart. But in the tertiary structure, they're right on top of each other. Okay. You have a question? Yeah, okay. So why do you have to go to these different base stations? Why can't you just go marching all the way up? Well, it's because your body needs time to adjust. Well, what is it doing? Well, as you climb the mountain, there's less oxygen, right? So to get more oxygen, you have to breathe quicker. You have to hyperventilate. If you hyperventilate, what's gonna happen to carbon dioxide levels? It's gonna go down. What happens if it goes down in terms of the acidity of your blood? Think about it. Yes, acidity, Lord, the pH goes, yep, you're right. Yep, sorry. So what does that mean? Well, there's actually a small molecule called 2,3-bisphosphoglycerate. In this semester, we'll learn about glycolysis. One of the metabolites in glycolysis is 1,3-bisphosphoglycerate. This is a byproduct of glycolysis. It's made by an enzyme that is regulated by pH. So as the pH goes down, the enzyme makes less of this 2,3-bisphosphoglycerate. You say, okay, yeah, right. So what does that mean? So if the acidity, as you climb the mountain of your blood, or if pH is going up, right, so you're gonna make more of this 2,3-bisphosphoglycerate. And this, do you see how much charge is on this molecule? This is just a little ball, intense ball of negative charge. This thing very precisely nestles down into this open donut hole in the T state of the enzyme, the low affinity state. And it binds, it makes non-covalent interactions with all these histidines at the center of the donut hole. And it tends to reduce the ability of the hemoglobin molecule to go to the R state. Like, yeah, and what does that mean? Well, let's think about this. So as you climb the mountain, the acidity of your blood goes down, the pH goes up, right? The enzyme gets turned on to a higher degree that makes this bisphosphoglycerate. The higher levels of bisphosphoglycerate interact with their hemoglobin, increasing and decreasing the affinity of hemoglobin for oxygen. So as you climb the mountain, your hemoglobin will have less affinity for oxygen. How could that be good? Doesn't that seem paradoxical? Yeah, you got it. It's a two-picture story. You pick it up in the lungs. So if you have lower affinity in the lungs, that's not necessarily good, but the partial pressure of oxygen in the lungs is pretty high. So having a little bit lower affinity for oxygen in the lungs would be not so bad. But in the tissue, they would be more efficient at delivering it. This figure is very confusing. So let's consider the concentration of bisphosphoglycerate that occurs in your cells, in your erythrocytes, at sea level. So at sea level, you pick up oxygen pretty well, and then you deliver about 38% of the oxygen to your tissues, right? So this is the partial pressure of oxygen in your tissues, and so the delta here is 38%. Now, if you climb the mountain and you have the same amount of bisphosphoglycerate, well, you would pick up less and deliver the same amount. So only 30, so each hemoglobin, trip of the hemoglobin protein from your lungs to your tissue would only deliver 30%. So your tissues are starving for oxygen. But look what happens when we add bisphosphoglycerate. Yes, we pick up less, but we deliver more. And the degree of decrease here is not as big as the degree of decrease here. So overall, you're back to the efficiency of delivery of oxygen to your tissues that you had at sea level. So as you climb up, you have these physiological responses because you need more oxygen. There's less oxygen, you're gonna breathe more, you gotta get it in there. But there's a negative consequence of that, right? You decrease the acidity of your blood, that's particularly bad, right? What does acidity do? So if we have decreased the acidity of the blood, what state will that favor? R, the high affinity state. So if our blood pH is changing, that's gonna make it less efficient to transport the oxygen, right? So this thing is compensating both for the change of acidity, but it's also aiding in addition to that. So we're balancing things out. Your tissues are your tissues. Your tissues are the same no matter whether you're on top of Mount Everest or at sea level, but it takes a while. This bisphosphoglyphus rate is produced metabolically, so it takes days for you to hyperventilate, pants a lot, and then eventually build up the concentration. Smokers have a higher level of bisphosphoglyphus rate. Any medical condition causing you to hyperventilate could potentially cause this alkalosis, this increase in pH in your blood, which would need to be compensated metabolically, okay? Is that cool? I think that's just amazing. Does this make sense? What an amazing thing. There's all this sensing of the environment. Okay, there's also problems that can arise with hemoglobin. You can have hemoglobin proteins that have a mutation. So you guys have heard of sickle cell anemia, right? I had a good friend with this, and it's a horrible disease. And it's caused by a mutation of a glutamic acid in the beta subunit of hemoglobin to a valine. And this glutamic acid, you might imagine, is on the surface of the hemoglobin protein. Where a lot of the charged amino acids tend to hang out. But if you put a valine on the surface of an amino acid and on the surface of a protein, and you have two of these subunits, think about what you've done. Sticky patch, sticky patch. Two sticky patches, polymerization, right? So we have a valine, a glutamic acid cannot make any kind of productive interaction with another glutamic acid on a different hemoglobin protein molecule. But two valines can have a hydrophobic interaction. And there's two subunits. So this occurs just on the beta subunit. And so you have sticky patch. So you begin to form a polymer of hemoglobin. And it's so bad that it causes the erythrocytes that are chocked full of hemoglobin to change their shape. And they get all stuck to each other, and it affects the circulation of blood in your body. And so you might wonder, this is awful. Why does it exist? Why does evolution allow this to exist? It's a horrific disease. Well, there's a really neat discovery that they made. They look at the incidents of sickle cell anemia in the world, and then they looked at the incidents of malaria. And they say, ha, it was nearly overlapping. So although having, being homozygous for this mutation infers sickle cell disease, sickle cell trait where you're heterozygous for this mutation, you have a reduced concentration of the mutant protein. And this actually is good. And the reason it's good is because of the way in which a plasmodium protozoa interacts with your cells. It affects cellular pH. And for whatever reason, the shift in pH, having a one copy of the mutant hemoglobin, the shift in pH causes aggregation of the hemoglobin and change of shape of the infected erythrocyte. So it basically has a malaria detectorometer. And so malaria comes in to cell changes shape because it has this valine, and for whatever reason the change in pH causes this aggregation. So it's a positive effect is that people don't get malaria when they have sickle cell trait, when they have sickle cell disease. It's not a good ending. Any questions? So there's all kinds of medical implications. Perhaps there's some pre-medical students here. I'm not being sarcastic. Okay, I love you guys. Okay, so I do. I'm actually gonna teach medical biochemistry next year, so I have to learn this stuff. All right, so I'll learn with you. Maybe some of you will be with me. Okay, so another protein whose function is to bind other things is immunoglobulin. And this is a structure of immunoglobulin. It's a hetero-tetrameric protein that has, it's very similar to alpha-2-beta-2 hemoglobins in the fact that it has two so-called heavy chain polypeptides and two light chain polypeptides. And here's the structure of an antibody. At the ends of these structured regions that's hyper-variable regions that flap around, okay? And so here is another picture of this. And you could see here, these hyper-variable regions. It's all random coil here. And there's a huge amount of genetic variation of the types of amino acid sequences that occur in these variable regions. And so what's gonna happen here is these antibodies are gonna bind to their substrate, the ligand to the antibody, the epitope, and these variable regions are very flexible. And they're gonna actually wrap around the ligands. So this is not a static Y shape, and it's not peace for us all. This is some kind of, look at the motions that occur here. So here's an antibody without binding to its ligand. And they've highlighted some of the charged residues here on the surface. And then this is the structure of the antibody bound to the ligand but hiding the ligand. So here's this here. And look at the movements here. So these things, this protein is wrapped around there and it makes the tightest interaction if it's the right type of substrate. It has complementarity in terms of the non-covalent bonds that it makes. And so we'll look at lots of practical examples of immunoglobulins throughout the semester. Many of you do biomedical research where you exploit the flexibility of this protein to recognize the presence or absence of certain proteins in a solution. And so one of the ways you do this is using something called immunoblot. And the majority have done immunoblots? Yep, yep, okay. But some have not. So immunoblots, if you're from the 60s, you call it immunoblot. These days we call it a western blot. I find the terminology a bit arbitrary. It's not a southwestern blot. I mean, okay. So, but to do this, we separate the proteins based on their size using SKS page gel electrophoresis. We talked about this previously. Then we use the flexibility of these immunoglobulins to bind so we transfer the proteins from a gel onto a nitrocellulose paper which is also somewhat arbitrary but it's sticky of proteins. So then you have proteins on a piece of paper. You put a nice little solution of your antibody on there and they will only bind where the right epitope is located. So these proteins are separated by molecular weight and you'll have a signal here where this antibody is bound selectively to its substrate. We then have, there's many ways to do western blots. One way is to have a so-called secondary antibody binding to the constant region of the heavy chain of the antibody. And this antibody could be covalently conjugated to an enzyme. So you guys might have done ECL. Have you guys done ECL using X-ray developer? Okay, I'm not that old. So these days we use fluorescence blots, something called Lycor. But so this enzymatic reaction converts a invisible substrate to a detectable product. And so you get these bands that show up. And the reason you need that is because it amplifies the signal. If you don't, an enzymatic reaction converts more than one invisible substrate to a visible product. And so we'll learn more about that later but this is just a side. So any questions from today's lecture? So when you think about your blood you have new thoughts about what's happening in your body. So just one more. One more question, guys. Why the valines on the surface of hemoglobin lead to the subunit sticking? I didn't hear the last part. Why the valines on the surface of hemoglobin lead to the subunit sticking? Yeah, so valine can interact with other valines with hydrophobic interactions. Whereas the glutamic acid, the wild-type hemoglobin glutamic acid would actually repel another glutamic acid. It would be a negative charge on a negative charge. So it's a hydrophobic interaction. OK, goodbye. No, excuse me. OK, I have to make an announcement here. So last lecture, there were five people that turned in their clicker votes at the end of class after I announced the answer. And so we're not creating a curve. We're not competing against each other. But that's not allowed. Just to be clear, it might be a little stressful because it doesn't work and you've got to run down. But you have to make it to Alex before we tell you the answer. OK, turn in your votes. Also, maybe while we're polling, maybe we could talk to Alex after polling because some people need to come in and deliver their vote on a piece of paper. Has anybody not voted? Anybody not voted? Like, here comes a paper. Alex, you've got to let people in with their papers. We can't tell the answer until everybody's voted. Hey, Alex, if you close your laptop, it will shut down following you. You've got it awfully, OK. OK, everybody, if you vote, if it receives your vote, you should have seen a green light show. Alex's laptop was pretty far closed. So I want to make sure everybody got their vote in. How many total? 246. All right. This is Go Find a Slide Scavenger Hunt clicker question. So what's the answer? Thank you. You guys are geniuses.