Biochemical binding thermodynamics - Kd, Ka, and their interpretation

Kd (the equilibrium dissociation constant) is a measure of binding affinity & it’s the concentration of one binding partner at which half of the other binding partner is bound. But WHY? Where does that come from? Why should we care? Well, the relationship allows us to use binding assays (experiments), altering the concentration of one partner & measuring the fraction of the other partner bound in order to determine the Kd. Here’s how… 
 
blog form (also has static graphics): bit.ly/bindingaffinityavidity
The whole premise of biochemistry is that molecules interact to do things. For example(s), the protein enzyme (reaction mediator) DNA Polymerase links together nucleotides (DNA letters) to copy DNA; a protein called tubulin assembles itself into structural supports and molecular conveyor belts in your cells; and proteins called antibodies bind to foreign molecules (like viral proteins) and call for help, etc. Pretty awesome, right? But in order for any of this to happen, the molecules have to first bind one another. Which means they have to
1) come into contact with one another and
2) like each other (first enough to bind and then enough to stay bound)
We sometimes call binding partners “ligands” (and sometimes we call one partner a “receptor” and another a “ligand”) - they can be anything from proteins to nucleic acids (DNA or RNA) to “small molecules” (things like pharmaceutical drugs, etc.). The higher the concentration of the partner (the more copies of it there are in some space), the more likely they are to come into contact with one another. And the more they like each other, the more likely they are to stick (and stay stuck) if they do contact one another. Therefore, the amount of sticking (and how much stuck you’ll find if you look) depends on concentration and binding strength.
Another way to think of binding partners is as really really tiny people on dates. The concentration is like how likely they are to run into potential partners (are you in Antarctica? or at a speed dating session?). And affinity is like how likely they are to get married and not get divorced.
Even if the concentration changes, that doesn’t change how much the partners “like each other” (Prince charming is just as charming if you meet him at the bar or on an ice floe). In biochemical terms, the binding strength is constant (at least for a given set of conditions (same temperature, salt concentration, etc.) because it’s a property of the binding partners themselves. And we call this “binding strength” AFFINITY.
We can measure binding affinity by altering the concentrations, measuring the binding, and fitting it to an equation that takes into account the contribution of concentration and “hides it” so you can see the constant part - the affinity! If that didn’t make sense, bear with me and I’ll get into more detail, but the end result is we get a value called the dissociation constant, abbreviated Kd. This value tells us what concentration of one binding partner (we can call it B if you want) would lead to half of its binding partner (we’ll call A) being bound at equilibrium (i.e. once the rates of binding and unbinding have stabilized and the mixture has found its happy ratio of bound & unbound).
The higher the affinity (the more sticky they are for one another) the less ligand is required to reach that value- higher affinity is like thinking the partner’s prince charming - you’ll take him whenever you find him - so lower Kd. But if you think there’s still someone better out there you might “hold off” unless there’s so many of that okay-ish match that you “give in” - so higher Kd.
This is a really important, though potentially confusing, concept to remember:
higher affinity - lower Kd
lower affinity - higher Kd
If you’re wondering why we don’t use the association constant, Ka, which is the inverse of Kd (so Kd = 1/Ka) it’s because that’s not in concentration units - look at the figures if you’re interested, but for now let’s get back to the marriages (and divorces) (and re-marriages)(and re-divorces…)
What’s really happening is that each time 2 molecules collide, they have a certain probability of sticking together. And then, depending on how much they like each other, they can stay stuck for various lengths of time. The more they like each other, the higher the affinity, so they’ll stay stuck. But, if you have a lower affinity, they’ll keep coming apart, so you’ll need more standing by to take their place. So a higher affinity corresponds to a lower Kd.
And what does Kd come from? As an equilibrium constant (more on what this means in a second), Kd is a sort of “endpoint” measurement.
finished in comments

[@thebumblingbiochemist]

We have this situation of A + B ⇌ AB, and we can measure the concentrations of one or more of these, and we can denote “concentration of” with brackets, so the situation’s [A] + [B] ⇌ [AB] and when we measure Kd it’s like taking a molecular census of bound [AB] and unbound partners [A] & [B] after the binding & unbinding has stabilized. So Kd is dependent on the rates of binding and unbinding (which are dependent on inherent properties of the molecules & how well they complement one another, as well as conditional things like temperature). We can define Kd in terms of “rate constants” as Kd = koff/kon. In words this means that if you were to look at 2 binding partners, the concentration of one required to get half of the other bound is the chance of “unbinding” (koff) divided by the chance of binding (kon). When you get into talking about rates, you’ve entered the world of “kinetics” and you’ve gotta start measuring things over time. For example, if you’re interested in how fast something unbinds (dissociates), you can bind a small amount of a labeled ligand, take your “0 point” measurement, then add a lot a lot of unlabeled ligand as a “chase.” This way, once the labeled one unbinds, any that it runs into for the “re-bind” is likely to be unlabeled. So the amount of labeled bound will decrease exponentially over time and you can fit that into a nice equation to get koff. You can also do an association assay, where you add labeled ligand and measure its binding over time, but it’s a bit trickier because, unlike the dissociation rate which only depends on the concentration of the AB complex, association depends on the amount of A AND B (it’s bimolecular or “second order”). It can be cool to know the rates, but binding kinetics experiments can be tricky (as I’ve been finding out painstakingly…). So a lot of times, instead of studying kinetics, you turn to thermodynamics, which deals with measuring things at equilibrium. Instead of tracking them over time, we can take a single “census” after we give the molecules enough time to come to a dynamic equilibrium (rates of marriage & divorce are constant so there’s no net change even if the couples themselves are changing). The more you see that are “married” compared to single when you take the census, the greater the affinity between the two. And remember, in order to be legit, you’ve gotta take this census after you’ve given them enough time to reach equilibrium (a time that depends on the rate constants, with slow-offers taking longer to equilibrate. more on this here: elifesciences.org/articles/57264 ) So, in our molecular marriage game, kinetics looks at the *rates* of marriages and divorces and thermodynamics looks at the “end result” (what proportions are married when you take the census). This result comes from the rates but if you only measure Kd you don’t know what contribution is from kon vs. koff. For instance, a higher affinity (thus lower Kd) could come from having a higher kon (being more likely to marry) and/or having a lower koff (less likely to divorce. And a lower affinity (higher Kd) could come from having a lower kon and/or having a higher koff. Methods and binding partners vary (for example in the past I showed you how I use a slot-blot filter-binding assay to measure protein-RNA binding) but the basic gist of most equilibrium binding assays is you do a serial dilution (e.g. half then half of that then half of that) of A. You start with WAY more of A than the labeled B (even at your lowest concentration point) This way, when B binds A there’s still a ton of A left to bind. So in the whole [A] + [B] ⇌ [AB] scheme, when you take some protein out of commission by moving it to the right side, it’s like removing a drop from a bucket - so you can think of the concentration of free A as constant in each mix - A is Prince Charming, you don’t need to worry about copies of B “competing” for Prince Charmings. Instead, what you want is each A deciding for themselves whether to bind based on how much they like the Prince, not how many Princes there are. This is only true if the concentration of the labeled B is way below the Kd of the interaction. If the B concentration is too high, so much of the protein will get bound that it lowers the amount of free Princes in a meaningful way, so you get what’s called “ligand depletion” - to avoid this you want to stay at least 10x under the Kd. And you want the A concentration series to range from ~100-fold less - ~100-fold more than the B concentration (all these concentrations are molarity-wise because we care about the # of molecules and if we went by weights we’d be deceived by bigger molecules). Plot out fraction B bound vs concentration and you can figure out the affinity. much more on binding affinity: bit.ly/bindingaffinityavidity     more on logarithms: bit.ly/logarithmsandexponents     more on slot blots & EMSA: bit.ly/emsaslotblot            more about all sorts of things: #365DaysOfScience All (with topics listed) 👉 bit.ly/2OllAB0 or search blog: thebumblingbiochemist.com

[@andremonteiro7792]

this is actually so helpful, if i pass my biophysics and biochemestry exams, u played a huge part on it :P

[@thebumblingbiochemist]

So happy I could help! Best of luck with the exams!

[@osman4816]

Can you make videos on Enzyme catalysis and regulation? My test is this friday :D

[@thebumblingbiochemist]

I have those yes - please search my enzymes playlist kzbin.info/aero/PLUWsCDtjESrHl3q-SvC8eYt7aZ-hb_DVg

[@SilviaZarnovicanova]

Why Kd is always determined as 1/2 or 50% saturated? and not for example 100%?

[@thebumblingbiochemist]

Kd is a thermodynamic parameter, and so it ultimately comes down to the thermodynamics underlying the equation, rather than just selection of a convenient value