How many sticks a stick breaker could break if a stick breaker could break sticks depends on if those sticks are breakable! And it turns out sticks are fake-able. My least favorite thing about science is competition – I feel it often inhibits scientific progress – but sometimes in biochemistry you want competition – competitive inhibitors to inhibit unwanted enzymatic progress! (Looking at you proteases). I love enzymes (biochemical reaction speeder-uppers) – but there’s a time and a place for them – and protein purification is not the time nor the place for promiscuous protein-chewers (proteases) to act. So we add protease inhibitors when harvesting the cells containing the protein we want to purify before we break them open. Enzyme inhibitors (different ones) are also useful when cancer-causing mutations cause enzymes to go rogue, like the case of Gleevec being used to target an overactive fusion kinase in a form of leukemia. And they can be useful to target viral enzymes, such as Paxlovid inhibiting SARS-CoV2’s main protease (MPro), preventing the virus from cutting up its long poly protein precursor to make functional individual proteins. These are just a few of the many types and uses for enzyme inhibitors. 

note: originally posted 3/4/20. Refreshed, expanded, & added video 3/22/22

Enzymes are biochemical catalysts – they’re usually proteins, somethings protein/RNA complexes, sometimes just RNA – and they speed up biochemical reactions (everything from DNA copying to protein cutting to cross-membrane molecule moving) without being used up in the process (so once they’re through speeding up 1 reaction they can speed up another, then another, then another).  Much more on them here:

The “general scheme” for a “simple” biochemical reaction is that you have some starting molecules (reagent(s)) that are comfy-ish and you turn them into altered molecules (product(s)) that are more comfy. But along the way you have to go through a really uncomfortable state (transition state) – if you imagine snapping a stick, the transition state is that really tense moment right before the stick breaks. 

“Uncomfiness” is technically called Gibbs free energy (G) – the higher the G, the more uncomfy, and molecules will react & interact in ways that get them to a lower G (so the change in G, ΔG for the reaction will be negative for favorable reactions). But you usually have to put in a little bit of energy & get the molecules less comfy before you can get there. This hump in the reaction road is the activation barrier – you have to put in activation energy to reach the transition state. 

Enzymes offer “alternative routes” to the product with transition states that are less uncomfy – so lower activation energy is required. If you think back to the stick snapping, a stick-snapper enzyme could help hold the stick, lure it into that uncomfortable bent position by providing favorable interactions that are only available in the bent shape, and helping stabilize the really uncomfy times.   

They often work kinda like a matchmaker bringing a couple to city hall – if the couple likes each other it’s easier for them to get married (not only have they found one another in the huge universe of people, but they’re at city hall!), but if they don’t like each other they won’t get married – and if they do get married, they’re also in a place where it’s easy to get divorced. So if a reaction “wants to happen” an enzyme can make it happen faster – but they can’t “force” a reaction to happen – they can’t make reactions that don’t want to happen happen – you can learn a lot more about how they work in the last couple o days – but today I want to tell you about when they *don’t* work. 

The reactions enzymes catalyze can involve multiple molecules, single molecules, multiple steps, etc. so it can get complicated, but basically, the general enzyme-catalyzed reaction scheme is: substrate binds enzymes -> enzyme helps substrate transform into product -> enzyme releases product -> enzyme is free to do it again with another substrate copy 

We can write this as  

E + S ⇌ E + P 

Along the way, you go through a couple transition states – you initially have E bound to S (ES) then S changes to P but it’s still bound to E (so EP) before it gets released (E + P) 

So overall, you can write 

E + S ⇌ ES ⇌ EP ⇌ E + P 

When we looked at thermodynamics, we looked at  ΔG to see how favorable reactions are – this is NOT changed by enzymes (your reactants and products are the same (and thus have the same G) regardless of the path you took to get there.

Then we looked at kinetics – which looks at how fast reactions occur. Going back to our stick-snapper analogy, where the enzymes are stick-snappers and the substrates are sticks, there are a few key values you could measure.

v = reaction velocity; the amount of product formed over time (e.g. sticks snapped per second). This is only the “top possible speed” if the snappers don’t run out of sticks (i.e.. when S>>>>>E). When a group of enzymes is working at top speed, you get the maximum velocity, Vmax. 

This value is dependent on the enzyme concentration (the more snappers you have, the more sticks can be snapped). So if you want to know the rate at which a single snapper snaps sticks, you have to divide by the number of snappers – and this gives you the “turnover number,” kcat.  

The better the snapper is at snapping sticks, the faster it can snap sticks, and thus the higher the kcat. But – that’s not all that matters – the snapper has to be able to grab and hold the sticks long enough to snap them! And it’s ability to do this is “hidden” if you have so much substrate that if a stick slips out there’s plenty around to quickly take its place.  

So, usually what you do is you measure the initial reaction velocity (V₀) for the same enzyme concentration with a range of substrate concentrations (you want that initial, steady-state velocity before the enzyme runs out of substrate). And then you plot V₀ (vertically) against substrate concentration (on the horizontal) – and if your enzyme follows what’s called Michaelis-Menten kinetics, you’ll see a parabolic curve (/—).  

The plateau is where the enzyme gets saturated (unlike before where we were worried about not enough substrate, here we have not enough enzyme – each enzyme is working at its capacity (kcat) and you have a lot of enzymes, so the overall velocity you observe is Vmax. 

So you look and see where the plateau is, then trace it back over the the y-axis to see what velocity that corresponds to. If you want the kcat, you then just divide that by the enzyme concentration, [E]. 

But if you want to know about the enzyme-substrate affinity (are they really a good match?) you want to divide Vmax by 2 to get the 1/2 Vmax, then trace this back over to the curve and drop down to see what substrate concentration that corresponds to – this value is your KM. 

Take a second to think about what this value means. It’s the amount of substrate that is required to get the enzymes to half their maximum capacity. You can think of it similarly to a binding dissociation constant, like the Kd we’ve looked at, where molecules were looking for love – the Kd told us what concentration of a ligand (binding partner) would lead to half of its binding partner being bound. The higher the affinity (the more sticky they are for one another) the less ligand would be required to reach that value- higher affinity is like thinking the partner’s Prince Charming – you’ll take him when you find him – 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” 

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 we could 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). More on this here:

With KM the difference is that you now have 2 ways for ES to fall apart – the S can just unbind, like we saw with Kd – OR it can turn into substrate. Therefore, KM = (koff+kcat)/kon. In words this means that if you were to look at a an enzyme, the concentration of substrate required to get an enzyme to work at half of its maximum speed is the chance of S “unbinding” (koff) plus the chance of S getting turned to P (kcat) divided by the chance of S binding (kon). 

KM doesn’t depend on enzyme concentrations or substrate concentrations, because it’s based off of the molecules’ inherent affinities for one another. If you have a lot of substrate, an enzyme is more likely to collide with it, but the chance of any of those collisions being “successful” doesn’t change – like how if you buy a ton of lottery tickets, you have a higher chance of winning, but each ticket has the same chance of winning. (the rate constants don’t change because those are like the probability of winning per ticket – but the actual rates you observe will depend on the # of tickets (so you have to multiply by concentrations to get those) – but when you calculate KM it’s relative to Vmax, so although Vmax will be higher if you have more enzyme, KM won’t change – you’ll have to get to a higher “1/2 vmax, but it’s still 1/2.) 

But sometimes the KM we measure isn’t the “true” KM – it’s just the “apparent KM”… 

Above I showed you a really small sampling of the things enzymes can do, and as you might imagine, one enzyme can’t do it all! And you wouldn’t want them to because that wouldn’t allow for any regulation. Instead, enzymes are highly specific – with each enzyme only catalyzing one (or a few similar) reactions – different enzymes have different substrates. 

They get this specificity because in order for the reaction to be catalyzed, the substrate has to bind to the enzyme the “correct way” – the enzyme is optimized for binding it in a way that makes it easiest for the reaction to occur – and stay bound long enough for the change to occur.  

The substrate usually binds the enzyme in a specialized pocket called the “active site” (aka catalytic site”) that, with a little readjusting (induced fit) can nicely hug specific substrates because the shape’s right and it offers favorable binding interactions by having attractive side chains (the unique part of protein letters (amino acids) sticking out into it). This helps enzymes select for substrates so they don’t change the wrong things. But they can be fooled – and this can fool you… 

The 3 main types of enzyme inhibition are: competitive, noncompetitive, and uncompetitive (aka anti-competitive) 

Competitive Inhibitors – it’s like mixing in metal sticks with the regular sticks – these fakers the enzyme tricks! Competitive inhibitors typically* bind in the same place as the substrate (so they’re usually shaped similarly) & since they’re binding in the same place and 2 things can’t be in the same place at once, if a snapper grabs a fake stick it can’t grab a real stick until it releases the fake stick – no stick hogging allowed! 

But if you have way more real stick than fake stick the snapper is more likely to grab a real stick, so it will eventually reach the same Vmax – but it’ll take a higher stick concentrations – so a competitive inhibitor will make the Km for an enzyme *appear* to be higher – but the “true” KM isn’t really higher – it’s just that the competitor is kinda “diluting” the substrate

So competitive inhibitors decrease the apparent KM but not Vmax (plateau later (right-shifted) but at same height) 

*we call the inhibitors that bind in the active site where the substrate normally binds orthosteric inhibitors. There are also ones that bind somewhere else and we call these allosteric inhibitors. Typically we’re talking and thinking about orthosteric inhibitors when we discuss competitive inhibitors, but you can also have allosteric competitive inhibitors which bind to somewhere other than the active site, but lower the affinity of the substrate for the active site. These show different trends between substrate concentration and activity – there’s a more complicated “curvilinear” relationship you’ll see rather than a normal linear one.

This is the “opposite” of the effects you see with Noncompetitive Inhibitors – they decrease Vmax, but not KM (plateau lower but at same time). This happens because noncompetitive inhibitors bind somewhere else on the enzyme – so they don’t affect the substrate binding (KM stays the same) – but they prevent the changing of substrate to product so some of your enzyme’s “useless” – you can have your stick (a real one!) but you can’t snap it! Imagine a snapper grabbing a stick but having her arms in casts so she can’t snap it.  

Note: in pure noncompetitive inhibition, the inhibitor doesn’t care whether or not the substrate is there (it binds E & ES with equal affinity). But, there’s also a messier situation called mixed inhibition where the inhibitor can bind either but prefers one (there are differences in affinity for inhibitor binding to E vs ES) and this complicates the calculations (and confuddles the brain…).

The 3rd main type is the uncompetitive inhibitor. This is similar to the noncompetitive in that it doesn’t compete for the active site but, unlike the noncompetitive inhibitor, it will only bind the ES complex – it won’t bind E when E’s alone.  In some cases this is because binding to the substrate causes a conformational change in the enzyme that reveals a binding site on the enzyme. Other times, the uncompetitive inhibitor actually binds to the enzyme & substrate. A really cool example of this can be seen with sequence-specific ribosome inhibitors. More here: 

Uncompetitive inhibition leads to a *decrease* in KM AND Vmax (curve shorter and shifted – and this time it’s shifted to the left! A decrease in Km means that the uncompetitive inhibitor is making it seem like the enzyme likes the substrate more than it really does because binding the inhibitor stabilizes the ES state so it kinda traps it there even though it can’t do much with it. It’s kinda like you have a weird stick-snapping event stalker that watches for snappers to grab sticks, then goes in and distracts them so they don’t snap the sticks 

So, in summary: 

the values to look at:

  • v is the rate at which product is formed over time
    • vmax is a special case of v when you have an excess of substrate so the enzyme doesn’t run out, so product is formed at max velocity 
    • all v’s depend on the enzyme concentration because the more enzymes you have making product, the more product you can make – so v’s look at the performance of the group
  • kcat looks at the performance of each enzyme molecule – not personally going one by one and checking them, or anything, but by assuming they’re all identical and then dividing vmax by the number of enzymes. kcat is aka “turnover number” because it tells you how many substrates an enzyme can turn into product in a given time (often second)
    • the higher the kcat, the better the enzyme is at changing the substrate it binds
  • KM looks at how well that substrate binds and it depends on how good a match the enzyme & substrate are. The better the match, the more likely they are to bind & stay bound – and then once they’re bound they can get converted. So the KM correlates with v. Specifically, KM is the concentration of substrate at which the enzyme is working at 1/2 vmax. It does NOT depend on enzyme or substrate concentration just like each lottery ticket you buy has the same chance of winning. You’ll “win more” if you have more enzyme molecules, but each enzyme has the same chance of binding. 

what inhibitors do to those values: 

  • Competitive inhibitors bind to the active site, preventing the real substrate from binding. You can compete the competitor out by adding more substrate – so you reach the same Vmax as if the competitor weren’t there. but you’ll need to add more substrate than you would have done to get there. So competitive inhibitors increase apparent KM but don’t change Vmax. 
  • Noncompetitive inhibitors & uncompetitive inhibitors both bind elsewhere on the enzyme (not at the active site) so they do NOT prevent substrate binding, but noncompetitive inhibitors can bind the enzyme when it’s substrate-bound OR unbound, whereas uncompetitive inhibitors only bind when it’s bound. Both of them prevent the enzyme from converting the substrate to product, so you have less active enzyme, so it’s effectively decreasing your enzyme concentration. And if you have less enzyme, you get less product, so your vmax decreases.  
    • But with a noncompetitive inhibitor, which can bind both the unbound and bound, it doesn’t affect that equilibrium of E + S vs ES, so Km isn’t changed. But with an uncompetitive inhibitor it “decreases competition” for substrate – it’s like there’s more substrate available for the uninhibited portion – and since KM is looking at substrate concentrations, it looks like you need less substrate – apparent KM decreases.  

Those types of enzyme inhibitors are “reversible” inhibitors – they only bound the enzyme through weak, non-covalent bonds* – I call them weak and, individually they are (because their electrons are just hanging out near each other, not actually shacking up (no electron sharing)) – but a lot of weak interactions can lead to a pretty strong binding. 

But each of those individual interactions is vulnerable, so it can kinda “peel off” if something better comes along. So reversible inhibitors can be “diluted out” so that if the inhibitor falls off, the enzyme is unlikely to easily find another inhibitor to bind to. 

*There’s also a really cool class of inhibitors that’s gaining traction – reversible covalent inhibitors. They form covalent bonds but “vulnerable” ones. Basically there’s a part of the inhibitor that’s like a “normal” inhibitor – often a competitive one that binds in the active site through non-covalent interactions. That lets it get its foot in the door and provides good specificity. But then there’s a chemical “warhead” part that will react covalently to a residue in the binding site – often a lysine or a cysteine, which, because of their nucleophilicity, can attack electrophilic warheads like aldehyde groups. These bonds, although covalent, are reversible. They can break, typically through hydrolysis. But they allow the inhibitor to stay on longer than normal reversible inhibitors. And because they require that interacting protein residue to be in a precise spot, they offer high specificity for the covalent binding step (even if the non-covalent part isn’t totally specific). I think this is a really cool topic I’m currently reading more into and hope to do more on it in future posts. Here’s a cool recent News & Views piece: 

An example of a reversible covalent inhibitor is Paxlovid:

There are also enzyme inhibitors that we call irreversible inhibitors – they can’t fall off – so even if you remove all the excess inhibitor so that if it were to fall out there wouldn’t be more to bind, it wouldn’t matter because it can’t fall off! 

The antibiotic penicillin is an example of a special type of irreversible inhibition that’s aka “suicide inhibition” (aka “suicide inactivation” aka “mechanism-based inhibition”). In these cases, the irreversible complex is formed during the course of the normal catalysis reaction – it gets partway there and then gets stuck. These “suicide inhibitors” are similar to the competitive inhibitors in that they bind the active site and prevent the “real deal” from binding, but unlike competitive inhibitors you can’t outcompete them.  Here’s more on how penicillin works: 

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