welcome back biochemistry class to another episode of chemistry with reef today we are going to be continuing our discussion of hemoglobin and myoglobin and their abilities to bind oxygen right and the chemical properties about why that happens and why it's so important uh and how of course and so we are starting out uh this this uh video by talking about the binding curves of the two uh proteins right that we were interested in so this is the binding curve um of oxygen to myelin this is the real thing and we'll notice um a couple uh interesting things to note one we still have that fraction of binding which is still up to one is the maximum value uh and we'll note though that the oxygen is here instead of concentration units of molarity or something like that this is a gas oxygen's a gas so it's in kilopascals right and that's because oxygen is a gas and so we do it in terms of partial pressure so the partial pressure of oxygen is how we're going to measure the concentration of the ligand and so the theta then right our fraction of bound or a fraction of occupied uh binding sites is equal to the partial pressure of oxygen divided by the partial pressure of oxygen plus what's called the p50 when you're dealing with a gas we call this the kd is related to a key ap 50. it's just basically a way it's the same thing the p50 refers to the pressure at which 50 of the binding sites are occupied all right i know it's really weird but the pv is basically the p50 is the kd here right because we're dealing with the gas we call it a p50 it's the same uh it's the same mathematical thing right it is fundamentally the same exact idea now we can see that myoglobin right is a hyperbolic curve it's hyperbolic right so we're not surprised by that this is a non-allosteric protein right so it's got a hyperbolic uh hyperbolic uh binding curve for its ligand now let's get way more complicated let's talk about hemoglobin hemoglobin we said before is an allosteric protein meaning that the binding of one oxygen affects the binding of another right and this results allosteric proteins typically have significant binding binding curves we're not surprised by that it's an allosteric protein okay so alexteric proteins love to have sigmoidal binding curves now hemoglobin is the most studied of the proteins right in fact hemoglobin is actually the most studied protein uh known in biochemistry period right um so what we're going to note about it right is that hemoglobin is known to have two forms we saw those on the previous slide as the blue and the red form and we talked about the oxygen oxyhemoglobin versus immunoglobulin so the hemoglobin has basically two two states a low affinity state and a high affinity state okay and so for the low affinity state this is referred to as the t state t meaning tense is where it comes from it's the dense this is the dominant form of deoxyhemoglobin okay deoxyhemoglobin uh is the dominant form of the tense state right meaning that it's the tense state tends to happen when you don't have a lot of oxygen bound okay well if you when you have the high affinity state hyphenated state of hemoglobin right is referred to oh no is referred to as the r state it's called the r state actually i shouldn't put the quotes there i apologize it is our state that that's what it's called right the r comes from the term relaxed right and this is the oxy dominant form is oxyhemoglobin right and what we what we know about hemoglobin what we've learned right in our studies of biochemistry not so much pos but uh biochemists and science as a whole is that there's a transition from a low to high affinity states and that creates this sigmoidal curve it's essentially the signal curve comes from essentially an average of the two states here the two binding curves and what this is going to show us is that if hemoglobin didn't have this transition we wouldn't be very good at gaining oxygen in the lungs we want to bond bind oxygen while it's in the lungs and then when the hemoglobin moves to the tissues we want to release the heat the oxygen so we want the infinity of the hemoglobin to decrease moving into the lungs and so how we do this is we get a transition from the low affinity state to the high affinity state right and so we see that when our partial pressure is that of the tissues right we see that we're not binding we're going to we're not binding a whole lot of the oxygen but when we're in the lungs our affinity right is really high and that's because in the lungs the lung is going to have lots of oxygen which is going to promote the our state by binding to the hemoglobin hemoglobin changes forms right when it's in the lungs gathers all that oxygen then when the hemoglobin moves to the tissues it'll transition to the low affinity state right and so it will release the sun right and so now it releases oxygen while it's in the tissues right and so there's a transition from that high low to high infinity state and back and forth as the hemoglobin moves and so this is the overall binding curve and you see the differences in the fraction of binding sites occupied between the in the tissues and in the lungs right because in the lungs we want to bind the o2 in the tissues we want to release it right and so thankfully hemoglobin is allosteric and that's why we are alive today oh yeah i go body like i love it every time i breathe i think about hemoglobin right and it changes in its two different forms the t state and the r state our stakes for relaxed right is the high affinity state hemoglobin t state is the tenth state low affinity state deoxyhemoglobin mostly right now let's talk about how this works so how does this happen well we said hemoglobin is an allosteric protein there's another word for that um and the other word for that is called cooperative okay so allosteric and cooperative kind of mean the fundamentally the same thing um the difference is that cooperative proteins can be positively or negatively cooperative right so this is just like allosteric except that when we say allosteric i told you before the allosteric was a broad definition so alastair just means any protein where the binding of one ligand affects that protein's ability to bind the next ligand is an alastair protein i didn't say anything about how it affects it whether it increases the affinity or decreases the infinity cooperativity right is the term for uh allosterics where you can have positive or negative cooperativity right and so we're going to talk about the next two slides how this goes down so these are the hypothetical structural changes for a a cooperative protein no this protein has nothing to do with hemoglobin myoglobin this is simply hypothetical right but what i want to do is i want to walk us through this so this is a picture of an a we have a picture of a two subunit protein here we see one polypeptide chain on each side right and really important to note the key blue regions are regions that are structurally stable green regions are less stable and then the red regions are highly unstable right and so and let's imagine that there are two binding sites here on this side right on each side one on each side and one in each subunit when we bring a ligand representing represented by the red rectangle here when the ligand binds to one site to one side what happens in this particular case is you'll see that the ligand binds and suddenly it creates stability for this one subunit well suddenly that subunit becomes stable it undergoes a conformational change and so what it's going to do is that's going to induce a conformational change in the other subunit by stabilizing this backbone here we're going to stabilize the backbone next to us in the other subunit right so we can do some sort of conformational change in our protein that is made you'll notice this other subunit now less green and less red right so now i've changed slides this is b though this is still the exact same as b right so don't don't don't worry we didn't change this is just showing that we've got one bound by binding that one ligand on the one on the right side of our protein in this case we've suddenly made this this left side subunit more stable meaning that now it is easier to bind a second ligand and that is a is basically how cooperativity works cooperativity works by having the binding of one ligand induce a conformational change that either stabilizes the other binding site to make it more likely to bind or maybe destabilizes it to the left is likely to bind that's why cooperative can be cooperativity can be positive or negative now when you talk cooperativity we would be remiss in biochemistry if we didn't talk about essentially uh more or less the father of cooperativity his name is archibald hill okay in 1910 archibald hill was studying hemoglobin right and he was studying the binding and he was studying the exact co-op this this cooperativity phenomenon the idea that hemoglobin as it binds as it binds oxygens becomes uh basically gains a greater affinity for oxygen and so he came up with the idea that okay hemoglobin is able to bind several oxygens you know we know that np up to four right and so he mathematically came about that with its equation uh with his equation basically saying y is the fraction here but now he put in what he called the hill coefficient n right and so this is called the hill coefficient into the equation right and his whole coefficient uh was based on uh the potential number of active of um occupied sites right the number of binding sites as a cap and what he did is he basically attempted to solve for that n value right now don't worry too much about the math it doesn't make sense to you that's okay we're not going to get into the math bill coefficient we're just going to get to the key takeaway messages and this is the key takeaway message right here okay this is huge huge huge huge huge right right here okay really big and important the healing coefficient of one if you have if you calculated this and you've got a hill coefficient of one there would be no cooperativity and in fact if you put a one in for the ends here you have the exact fraction of dissociated the fraction of association curve the fraction of a binding curve for myoglobin you have the exact uh the exact formula mathematically for that right that the fraction of sites occupied equals the partial pressure of oxygen divided by the p50 plus the partial pressure of oxygen if your value was one now he hill decided he'll determined and figured out that if you mathematically solved and got a value of n that's greater than one you have positive cooperativity positive cooperativity like hemoglobin means the binding of one ligand enhances the binding of the next ligand meaning you're going to get more of it increases the affinity he also said that if you have a hill coefficient less than one you have negative cooperativity like ctb synthetase if you wanted one that's an example right where when you're buying one ligand you get less and a lot of times our body can use to do that for a number of reasons by the way there are a number of reasons we might want to do that okay so you can have negative cooperativity if your hill coefficient is less than one and so he came up with this brilliant way of doing this called the hill plot right now what he's done stop your race okay so what he's done is he came up with the hill with his hill equation and the hill plot so what he would do is he would measure the binding right and he would measure the fraction of binding sites occupied right at various partial pressures of oxygen on hemoglobin knowing like the p50 of what he's what he's doing there and so what we would see is if you graph the log of theta divided by one minus theta if you graph this as y and you graph it versus the log of the partial pressure of o2 as x because that's going to change as a variable right then you'll notice that n here kind of looks like well a slope and then that minus log of the p 50 is going to be a constant so what if we called it b well g guy gosh take a look at this we got a y equals mx plus b and this is called a hill plot a whole plot is by definition a graph of the log of theta divided by one minus theta on the y axis versus the log of the partial pressure of oxygen on the x-axis where you can solve for the slope to get the hill coefficient and this is an analysis that you can do to determine if a protein of interest is allosteric or not now or is cooperative and it'll tell you what type of cooperative not just allosteric it'll tell you if it's positively or negatively cooperative so this is what we do we plot the the log log of theta divided by 1 minus theta versus the log of the partial pressure of oxygen and the slope will be the hill coefficient and this is what a plot looks like now no i'm never going to make you draw one of these plots right but we want to be aware of how to interpret them okay and hemoglobin is really really really cool so we grab we have two curves here one in red and one in blue so the blue curve here is the curve for myoglobin right so notice that this is myoglobin right and the red one is hemoglobin myoglobin across this huge range of partial pressures of oxygen the coefficient is one which is exactly what we would suspect my moment is not allosteric until coefficient should be one so it's not cooperative now when we do this for when we do this for a hemoglobin what we get is we get at low concentrations now check this out this is really cool at low concentrations we get an n of one for hemoglobin right well and that's because what we're actually looking at is the hemoglobin and low affinity state well there's so little oxygen there that the odds of the hemoglobin molecule buying multiple oxygens is really low right because there's so little in it however when we hit a magic concentration range right here what we get is we get suddenly a much larger hill coefficient you call we call it three here it's actually technically 2.8 rounds up to three is the hill coefficient for hemoglobin but that's okay and this is the region where there's a transition between the high affinities the highest affinity state the low affinity state so as we raise the concentration of oxygen we're going to change we're going to eventually hit the concentrations where we're going to get a large hill coefficient where we're going to able to bind more oxygen and then the very end this is really cool and very high levels so note over here in this region right you're at high concentrations of o2 and so it goes back to a coefficient of one right which is kind of mind-boggling to hill right but it goes back to growth coefficient one and that's because it's competing for the last active site and so the whole coefficient one is showing hemoglobin with three of its sites occupied only the last one is trying to bind at the very end because you've got so much oxygen and so that's why toe coefficient goes to one and so what we learned is that you take right so for hill what hill did is we we're going to look for the highest so the highest n is your your real is your real accepted n right is a real hill coefficient and so for hemoglobin that's n equals three right for hemoglobin and that's how hill determined that hemoglobin was positively cooperative and is greater than one so it means that the binding of a ligand aka oxygen increases the affinity of hemoglobin for more oxygens super cool stuff all right so this is a good time for us to take a break because when we come back we are going to talk about the structural differences between these high affinity state the r and t states okay and then we will continue talking about cooperativity and hemoglobin and the types the models of cooperativity we're getting some really interesting stuff all right so i will catch you next time on chemistry with reef