Kd (equilibrium dissociation constant) - biochemical basis and analysis of of binding affinity

Note: Updated and recut a past video for my 2024 classes. I also added a quick review version: : • Quick overview of Kd (...
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/bindinga...
 
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…)  
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