5 BehaviorofProteinsII Kineticsincomplete

The Behavior of Proteins: Enzyme Kinetics II

Outline

• Michaelis-Menten enzyme kinetics

- KM, Vmax, kcat • enzyme inhibition

• on Wednesday, we covered a lot of ground on ENYZYME KINETICS • we discussed:

- thermodynamic favorability - kinetics as a concept - the energy of activation - the transition state - enzyme-substrate binding

• we should now have a general understanding of these concepts

• but, we’re probably missing the intimate relationship between all of these things • every enzymatic reaction involves “all of the above”

• Michaelis-Menten enzyme kinetics is simply a way at looking at enzymatic reactions clearly and informatively

Michaelis-Menten Enzyme Kinetics

• devised in 1913, it is still the most widely used way of understanding _____________________ enzymes

• consider the simplest enzymatic reaction: substrate converted into product S → P

• the entire reaction – including _______________ – could be represented as E + S ES → E + P

• once the ES complex progresses to product, there is NO _____________ reaction – product can not be converted back into substrate by this reaction

• again, to return to a key point – the enzyme is always ____________________!

• the rate of an enzymatic reaction depends on the _________________________ of substrate (not surprisingly…)

• we can measure the velocity (speed, or rate) of a reaction at different substrate

______________________________ and graph those results

• at low levels of substrate, this reaction looks like a _________ order reaction - one thing is affecting the rate

- the concentration of substrate

• at high levels of substrate, this reaction looks like a ___________ order reaction - nothing is affecting the rate

- it just is what it is

- those cars are going across that two-lane bridge as fast as they can

• at high levels of substrate concentration, all of the active sites on all of the enzymes are

• if the Toyota plant can crank out a maximum of 100 cars a day - that’s its maximum productivity

- if you delivered sheet metal, engines, tires, and paint – would this boost the number of cars being made…?

• when the enzymes are saturated, the reaction is going as fast as it possibly can

• no matter how much more substrate you pumped into the reaction, it will not go any faster - Vmax

• Vmax is important because it’s the fastest our reaction can go - and that’s often a good property to know about a reaction

• but Vmax gives us another very important value:

KM (the ____________________ constant)

• KM is the concentration of substrate needed to get the velocity of the reaction to be

_______________ its fastest speed

- said more succinctly: KM is the substrate concentration at ________________ Vmax • why is KM important?

- it tells us something about how well an enzyme binds a substrate

- inversely related: lower→______________

• these assumptions only hold true if the enzymatic reaction is in a STEADY STATE - this is when the concentration of the ES complex remains constant

- BUT, it is only constant because the enzyme is saturated

- in other words, every time one ES complex breaks down to E + P another ES complex takes its place forming from E + S

• the text goes through all the mathematical equations and derivations to demonstrate to you rate constants for enzymatic reactions

- be my guest….

- but what comes out of that math is: • the Michaelis-Menten equation

- this lets you determine the velocity of an enzymatic reaction at ANY substrate concentration – if you know Vmax and KM

• most of the time, Vmax is not so easy to determine from the graph - it’s often hard to tell when a reaction has stopped increasing in velocity • without a clear and obvious Vmax, we cannot predict KM

- why…? what’s KM, again….? • but, God forbid we do any math!

• we can transform the previous graph into one a bit more easily read

by simply taking the _________________________ of all terms - we’re gonna turn the Michealis-Menten equation upside-down

- it’s a _________!!! - Y-axis is 1/v - X-axis is 1/[s] - slope is KM/Vmax - y-intercept is 1/Vmax

- a very easy graph to decipher

• we call this graph a Lineweaver-Burk double reciprocal plot

- to draw a line all you need is a single point (y-intercept) and the slope

- also, you can just as easily use experimental data to generate either graph (one is just the reciprocal of the other)

• the Lineweaver-Burk plot lets you easily determine Vmax and KM • we’re going to a whole lot of trouble for KM and Vmax

- why…?

• again, KM is the substrate concentration when the velocity of an

enzymatic reaction is _________ its maximal rate (_______________ Vmax)

• you could interpret this to mean that KMis the substrate concentration where 50% of the enzymes have bound substrate

- because Vmax represents saturation - all enzymes bound by substrate

• now, if you had one enzyme with a KM of 50mM – that would mean you need 50mM of substrate to fill half that enzyme’s active sites

- if you had another enzyme with a KM of 15mM – you would need 15mM of substrate to fill its active sites

• which enzyme binds to its substrate better, tighter, more efficiently…? • two guys are hanging off a wall…

- one needs 50 feet of rope to hang on - the other needs 15 feet of rope to hang on

- who holds onto the rope better, tighter, more efficiently?

• so, the larger the KM – the ______________ that enzyme binds its substrate - but it makes common, intuitive sense

- it needs more substrate around to get to 50% binding because it’s a ________ efficient binder

• Vmax is intimately related to the _______________________ NUMBER - this value is called kcat (but is actually equal to k2)

• kcat is the amount of substrate turned into product per enzyme at Vmax • one last point to emphasize before we switch gears:

- KM, Vmax, kcat are properties or characteristics of an enzyme - each enzyme may have different values for these properties - but an individual enzyme’s KM, Vmax, and kcat never changes

- it’s like an enzyme’s eye color - the enzyme is born with them…

Enzyme Inhibition

• enzymes are wonderful catalysts – they make reactions possible that would not otherwise occur

• but, this is not always a good thing

• sometimes we would like a reaction NOT to occur

- e.g., we don’t want to break down and release stored glucose immediately after a full, glucose-rich meal

• also, enzymes behaving inappropriately (wrong time, wrong place, etc) can be corrected by inhibition

- many drugs are enzyme inhibitors

- see the text for a great write-up on HIV inhibitor therapies

• inhibitors can work to slow down enzyme function in one of two general ways:

- a _______________________ inhibitor binds an enzyme, inhibits its function and then lets go leaving the enzyme in its original state

- enzymes inhibited in this way can return to normal

- _______________ inhibitors also often recycle and can inhibit other identical enzymes

- an ____________________ inhibitor binds to the enzyme irreversibly - usually covalently

- after binding to the inhibitor, the enzyme is useless and can never return to normal

- ___________________ inhibitors are also referred to as _______________ INHIBITORS because they too never recycle

• we will focus on reversible inhibitors

• there are three classes of reversible inhibitors: - competitive, uncompetitive, and noncompetitive - I didn’t name them… don’t blame me…

• COMPETITIVE INHIBITORS are the easiest to understand

- this inhibitor has a very ___________________ structure to the true substrate of the enzyme being inhibited

- the inhibitor ‘competes’ with the true substrate for ___________ to the ___________ site - when the inhibitor wins and binds to the active site, the true substrate can’t bind the enzyme - no substrate binding, no enzyme catalysis

- therefore, inhibition

- what shape might make the best inhibitor? • now, let’s go back to some common sense…

• if the ratio of competitive inhibitor to true substrate is 50:50, there will be a huge inhibitory effect

- enzymes have a “coin-flips” chance of being inhibited

• if that ratio is 75:25, substrate:inhibitor – then any given enzyme has a 25% chance of being inhibited

• what about ratios of 99:1 or greater?

- by increasing the amount of substrate, you can _________________ the effect of the inhibitor - the inhibitor relies on being an effective competitor, but if it doesn’t “have the numbers”, it

can’t compete

- this is the hallmark trait of competitive inhibitors • let’s take that one step further…

• if you’ve got 99,999 molecules of substrate, 1 molecule of competitive inhibitor, and 50 enzymes – will those enzymes be saturated?

- will the rate of the reaction be Vmax?

- Vmax is _____________________ by a competitive inhibitor

• but, KM is defined as the substrate concentration required to get to _______________ of Vmax - in the presence of the inhibitor, we can still reach Vmax – but it takes a whole lot more substrate

to get there

- we have to swamp out the inhibitor

• KM goes __________ with competitive inhibitors – it looks like a _________________ binder

Competitive Inhibition

• Vmax unchanged (we can still reach our maximal velocity)

• KM goes _________ (it takes more substrate to reach Vmax, and therefore more substrate to reach one-half Vmax)

• kcat unchanged (once ES complex forms, it’s a typical enzymatic reaction – inhibitor only affects the rate of formation of the ES complex)

• uncompetitive inhibitors are not thoroughly explained in the text - but we can learn quite a bit from them

• uncompetitive inhibitors bind (and only bind) the ES complex and stop it from progressing to E + P

• this class of inhibitor __________________ substrate to bind ________________ - once ESI forms, that enzyme is out of the game

• therefore, as a result, _________________________ of substrate can ‘out-compete’ this inhibitor, because there’s no competition in the first place

• in the presence of an uncompetitive inhibitor, Vmax is _______________

- the maximum possible rate of the reaction is lower because the inhibitor results in fewer functional enzymes

• KM is also ________________ in the presence of an uncompetitive inhibitor… … what?!

• who can tell me what a low KM means?

• why would an inhibitor binding the ES complex make it appear as though the enzyme were a

_____________________ binder to substrate?

- because the inhibitor is actually __________________ the ES complex - that’s how it inhibits!

- it _______________ the ES complex so much, _________________ state never forms and product is never made

Uncompetitive Inhibition

• Vmax goes _____________ (we can’t reach our uninhibited maximal velocity)

• KM goes ____________ (the inhibitor stabilizes the ES complex – the enzyme looks like a better binder)

• noncompetitive is the most confusing, and so we’ll keep it short and sweet – but

noncompetitive inhibitors are important because they are _______________________ • the inhibitor can bind either the enzyme alone or the ES complex

- it can do this because it binds to its own distinct site, far from the active site – an allosteric site • noncompetitive inhibitors do not affect ________________ __________________ at all

- so which value do you think will not change…?

• but, noncompetitive inhibitors do slow down the rate of the reaction by impeding catalysis - so which value(s) do you think will change…?

- up or down…?

Noncompetitive Inhibition

• Vmax goes ______________ (we can’t reach our uninhibited maximal velocity

• KM is __________________ (the inhibitor does not affect substrate binding)

• kcat goes _______________ (kcat is directly related to Vmax – the reaction is slower) • once again, increasing the amount of substrate has no effect because

the inhibitor is not influencing substrate binding in any way

Summary

• the most widely used way of understanding ___________________________ enzymes

• rate of enzymatic reaction depends on the _________________________ of substrate • at high levels of substrate concentration, all of the active sites on all enzymes are

__________________ - reaction is going as fast as it can - Vmax

• KM is the concentration of substrate needed to get the velocity of the reaction to be

_______________ its fastest speed

- KM is the substrate concentration at ________________ Vmax

- KMis the substrate concentration where 50% of the enzymes have bound substrate

- the larger the KM – the __________________ that enzyme binds its substrate