Biochemical binding thermodynamics - Kd, Ka, and their interpretation

[@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