Kd, Ka, affinity? What’s this terminology? Are you avid about measuring binding affinity? Curious about the difference between affinity and avidity? If so, today’s post is for you! If no, I hope I can convince you to become curious too! “Affinity” and “avidity” are just a couple of the sometimes-confusing terms biochemists use to discuss biomolecular binding. Ligand, dissociation constants, valency – just a few more you may see. And I don’t want this to scare you away, because this whole “binding thing” is really important. So I want to help you (and me) understand.

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.

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”).

Don’t worry about this kinetics stuff now (although I’ve been worrying about it a lot in the lab so have been reading up more and will probably post more on it later – interested?).

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: https://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.

I’m working to try to get at some rates for something, but most of what I’ve done to date has been equilibrium binding assays (assay is basically just an experiment where you’re measuring the amount of something (like the amount of binding strength)). 

Methods and binding partners vary (for example yesterday 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).

There is a nuance between what we mean by a true Kd and what we measure and the importance of thinking in terms of FREE concentration. IF we are in the appropriate concentration range (where we have a vast excess of one partner) then we don’t need to worry about the concentration of the other. And if we measure in that range the 1/2 bound will be the Kd. But if we are not in the appropriate range, the concentration will come into play in messing up what we measure because we are reducing the free concentration – so we would need to use math stuff to take this into account – we couldn’t simply look to 1/2 of measured binding. The eLife paper I reference goes into this stuff. I find it helpful to think of things from the perspective of a molecule. The Kd tells you the concentration of the other molecule that needs to be around (and free) for that molecule to have a 50/50 chance of being bound at equilibrium. If other molecules are hogging the binding partner, it’s like there’s less of the binding partner. The molecule doesn’t “see it”. Therefore the measured 1/2 max will be skewed from the true Kd which depends on free concentration, which is only the “same” as the concentration you put in (at least within error) when the concentration is in vast excess if the binding partner. If you’re way over the Kd, you’re in the “titration range” where added partner will just be sopped up so you’re really just measuring how much of the thing you have a lot of there is. (Your 1/2 max binding will just happen when you add that much partner, which will be way higher than the Kd). If you’re in between, in the “intermediate range,” you need to take ligand depletion into account, but you can do so mathematically.

Much more on this in this great free article: Inga Jarmoskaite, Ishraq AlSadhan, Pavanapuresan P Vaidyanathan, Daniel Herschlag (2020) How to measure and evaluate binding affinities eLife 9:e57264 https://doi.org/10.7554/eLife.57264

Inga Jarmoskaite, Ishraq AlSadhan, Pavanapuresan P Vaidyanathan, Daniel Herschlag (2020) How to measure and evaluate binding affinities eLife 9:e57264 https://doi.org/10.7554/eLife.57264 

Plot out fraction B bound vs concentration and you can figure out the affinity.

Well, to be a bit more precise, you figure out the “apparent affinity” or the “effective affinity” or the “functional affinity.” In other words, it’s telling you what the measurable affinity is. If you only have 2 binding partners and they each only have 1 binding site for the other (so 1 A can bind 1 B and only 1 B and vice versa), and if all of the A & B molecules are functional, then this apparent affinity is the same as the “true” or “intrinsic” affinity of a single A:B interaction. So no worries. But, what if 1 A can bind multiple Bs and/or 1 B can bind multiple As? Well that complicates things a bit…

Imagine your A molecule has multiple binding sites for B (we call such molecules “multivalent”). For the sake of the example, we’ll say A has 4 identical binding sites for B. In this first example, we’ll say that B only has 1 binding site for A (i.e. B is monovalent), so 1 A can bind 4 B’s. But does it?

You might think that, since each of those A sites are identical, they’ll act just like 4 “normal” binding sites, so you’re only impacting the effective concentration part of the binding equation (that is, you might think that you just need to adjust the equation to think you have 4X as much A as you actually do). But those sites are not actually independent, and the binding of one of them can impact the binding of the others.

For example, if B is some cell surface protein, so it’s a protein that’s embedded into the outer cell membrane (plasma membrane) and sticks out into the extracellular space, then once a single A site binds, A is tethered onto the cell. And if there are a bunch of B molecules on that cell surface, A now sees more B molecules than it did before (there’s a higher effective concentration of B). It’s like A went from a coed school to an all guy’s school and as soon as it breaks up with one there are plenty more to try out. (note: I’m using guy/girl here for ease of explanation, but I’m totally cool with anyone loving whomever they want!).

This concept of avidity comes up a lot with regards to antibodies. I’ve talked a lot about antibodies and you can review them here: http://bit.ly/antibodytypesanduses

But basically know they’re little proteins shaped like Ys and at the tips of the Ys are “antigen binding sites” (we call the ligands for antibodies antigens – told you there were a lot of terms!). The arms are identical so the tips are identical, so you have 2 binding sites per Y. The “single Y” you usually see is in the IgG class, but there are other classes such as M which have multiple Ys, so you have even more binding sites. So lots of avidity effect potential. So, for example, once one site of one Y binds to a protein on the surface of a viral particle, you’ve brought those other sites into close proximity with other copies of that viral protein. So they can bind. And this gives you a binding boost, raising the “apparent affinity.” And this is really important because, especially in the beginning, the antibodies your body makes to fight an infection don’t have very high affinity (those individual antibody-antigen interactions are weak) and if you didn’t have the avidity boost they’d probably fall off. So your body starts out with IgM and then, as it makes higher-affinity and more specific antibodies for the viral protein, etc. it can go with single copies.

Higher affinity is often associated with better specificity (pickiness about binding partner) because in order for the partners to really like each other, they have to offer one another a lot of favorable interactions (be a really good molecular fit). And, since all molecules are different, there are few that’ll fit that well.

So, high avidity can compensate for low intrinsic affinity and low specificity.

Biochemical systems often used as a sort of strategy to allow them to use less specific binders. We saw that in the antibody example. And, in another example, the same site on a lectin (carbohydrate-binding protein) can bind multiple different types of carbs. We take advantage of avidity in the lab as well. For example, we can use a 8X His tag in Ni-affinity chromatography. I don’t have time to get into that here, but if that made sense for you, I’m glad. And if you want to learn more about it: http://bit.ly/histagpurification

Another final terminology notes: “substrate” is something that an enzyme binds & transforms into “product.” remember Substrate->Start. It’s the “S” in E + S <-> [ES] <-> P (where E is enzyme, S is substrate, and P is product).

In terms of equilibrium binding measuring methods, it’ll depend largely on what binding partners you’re studying. 

I use this thing called a “slot blot” to do a “filter binding assay” which you can learn a lot more about in yesterday’s post: https://thebumblingbiochemist.com/365-days-of-science/binding-affinity-dot-blot-filter-binding-assay-for-measuring-protein-nucleic-acid-interactions/

A basic overview is you mix protein and labeled RNA (or DNA), let them reach a steady marriage/divorce rate (binding equilibrium), then separate the couples from the singles & compare. You do the separation by using vacuum suction to pull them through a membrane sandwich – on top is a nitrocellulose membrane that the protein *can’t* get through – but free RNA *can*. And, waiting bellow it to capture that free RNA is another membrane that RNA *can* bind But RNA can only make it to the lower membrane if it’s free – remember the protein sticks to the top – so if the RNA’s stuck to the protein and the protein’s stuck to the top membrane, the RNA will get stuck up there too. And then you compare how many singles vs couples there are by comparing how much RNA is trapped where.

Other methods for equilibrium binding assays are things like EMSA (gel shift assays), isothermal titration calorimetry (ITC, surface plasmon resonance [SPR], and fluorescence anisotropy. And this is a really good practical article on planning these sort of experiments: https://www.molbiolcell.org/doi/10.1091/mbc.e10-08-0683

Methods for looking at binding kinetics include things like ITC (isothermal calorimetry) and SPR (surface plasmon resonance) but I’m not going to get into those here.

sorry this post is pretty technical. I hope this helps some people, but I only confused you more, I’m really sorry!

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉 http://bit.ly/2OllAB0

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