Equilibria, rates and binding energy Week 2

Question 1

Equilibria in enzyme-catalysed reactions

Answer 1

Enzyme-catalysed reactions are equilibrium reactions: An enzyme that catalyses S→P will also catalyse P→S (so we properly write S ⇌ P).

For the reaction S ⇌ P we can define an equilibrium constant of Keq (or sometimes just K).

𝐾eq = [P] /[S]

If [P] > [S] then Keq is higher than if [S] > [P].

It is possible to link Keq to ΔG of a reaction using the equation:
ΔG = −RT ln Keq
Take-home message:
A reaction where a lot of substrate is converted into product is more energetically favourable than a reaction where not much substrate is converted into product.

Question 2

Rate-limiting steps

Answer 2

In multi-step reactions the step with the highest activation energy is the rate-limiting step. To speed up the overall reaction the rate of this step must be increased.

Some reactions may have multiple steps with similarly high activation energies – all these steps are rate- limiting.

Question 3

How do enzymes interact with substrates?

Answer 3

Enzymes are very effective catalysts and very specific: they can speed up reactions 10[5] to 10[17-fold] and discriminate between very similar molecules.

Chemical reactions take place between the substrate and some of the enzyme’s functional groups (specific amino acid side-chains, metal ions [cofactors], coenzymes…).

Transient covalent bonds may be formed, or a group may be transiently transferred from substrate to enzyme.

Transient noncovalent interaction like hydrogen bonds, ionic interactions and the hydrophobic effect between substrate and enzyme stabilise the ES complex.

Covalent interactions between substrate and enzyme lower the activation energy, and therefore increase reaction rate.

Forming each interaction releases a small amount of free energy.

Question 4

The enzyme-substrate complex and binding energy

Answer 4

The formation of an enzyme-substrate complex (ES) is mediated by the same forces that stabilise protein structure: hydrogen bonds, ionic interactions, and the hydrophobic effect.

Forming each weak interaction in the ES complex releases some free energy that stabilizes the interaction. The energy of all these weak interactions added up is called the binding energy (ΔGB).

Binding energy is used to lower the activation energy of the reaction.

This also explains enzyme specificity: the “wrong” substrate won’t form the right interactions, so won’t release sufficient binding energy.

Weak interactions are optimised in the reaction transition state that the substrate becomes as it is changing into a product. Often the enzyme also undergoes a conformational change. This is induced fit

Question 5

Other ways enzymes help reactions

Answer 5

Entropy reduction: Enzymes restrict movement of substrates (so decrease disorder/entropy) making it more likely that they will collide and react.

Removal of solvation shell: Dissolved substances are surrounded by water molecules that may block reaction sites. A substrate binding to an enzyme usually loses its associated water molecules.

Distortion of substrates: Binding energy can be used to “twist” substrates into the right orientation.

Alignment of functional groups: The functional groups of the substrate and active site are positioned in a way that aids the reaction.

Question 6

Enzyme-substrate interactions are optimised in the transition state

Answer 6

The “lock and key” hypothesis, where substrates fit exactly to the active site, is not thought to be quite correct.

If an enzyme bound the substrate exactly (and the ES complex was very stable) the progress of the reaction would be difficult. Wouldn’t need to be a product

If an enzyme binds preferentially to the transition state the progress of the reaction is easier.

Question 7

Enzyme kinetics is understanding the rate of a reaction

Answer 7

E + S ⇌ ES ⇌ EP ⇌ E + P

E = enzyme, S = substrate, P = product, ES = enzyme-substrate complex,
EP = enzyme-product complex

[E] will usually be much less than [S]. Each reaction step has a rate constant (k).
K1
E + S ⇌ ES ⇌ EP ⇌ E + P

Question 8

V0 , initial velocity

Answer 8

If we increase substrate concentration [S] we might expect the reaction to run more quickly.

However [S] changes during the reaction as substrate gets used up.

We can measure the rate at the beginning of the reaction. This is called initial velocity, V0.

— V0

Question 9

Vmax and Km

Answer 9

As [S] increases, V0 increases, but by an increasingly smaller amount.

Eventually increasing [S] has practically no further impact on the reaction rate, and the reaction is at maximum velocity, Vmax. The max the product could have under these conditions

At Vmax the enzyme is saturated.

The [S] when the reaction rate is half of Vmax is called the Michaelis constant, Km.

Question 10

Km as an indicator of an enzyme’s substrate affinity

Answer 10

It is often said that an enzyme with a low Km has a high affinity for a substrate because it takes a lower concentration of substrate to reach 1Vmax .

This is the same idea as Kd when talking about protein-ligand binding.

In reality it is a bit more complex than this, but it’s good to keep in mind.
The bigger the km the more concentration of the substrate
The lower = higher affinity for the substrate for the enzyme

Question 11

The Michaelis-Menten equation links [S] and reaction rates

Answer 11

Most enzymatic reactions give a similarly-shaped curve when we plot V0 against [S]. These are said to follow Michaelis-Menten kinetics.

We can describe this with the Michaelis-Menten equation:

You should learn this equation!
V0= Vmax s/ Km + [s]

All the terms in the equation are relatively easy to measure experimentally.

V0 initial velocity (μM/min)
Vmax maximum velocity
Km Michaelis constant (Km = [S] when V0 = 1V/2 max)
[S] substrate concentration (mM)

Question 12

Michaelis Menten vs Lineweaver-Burk

Answer 12

Michaelis-Menten plots are useful to visualise the relationship between Km and Vmax, but are not the most convenient way of showing it.

Instead we use a double reciprocal plot, aka Lineweaver-Burk plot.

Lineweaver-burk
X= 1/s
Y 1/vo

1/vmax

Question 13

Lineweaver-Burk (double reciprocal) plots

Answer 13

Instead of plotting V0 against [S], we plot their reciprocals: 1/V0 against 1/[S].

Note units also become reciprocals.

This makes it easier to determine other kinetic parameters:
Intercept with x-axis = − 1/𝐾m

Intercept with y-axis = 1/𝑉max

Slope = 𝐾m/ 𝑉max

Question 14

α-amylase

Answer 14

Secreted in saliva.
Contains Ca2+ and Cl- cofactors.
Catalyses hydrolysis of starch→maltose.

Test for starch: iodine turns blue.
Potatoes have lots of starch, apples have lots of maltose.

Question 15

Enzyme inhibitors

Answer 15

Enzyme inhibitors reduce the rate of reaction or stop catalysis altogether. This could be good or bad.

Aspirin is an enzyme inhibitor the blocks synthesis of prostaglandins: molecules that cause pain.

Cyanide inhibits cytochrome c oxidase: this blocks cellular respiration.

Inhibitors can also be a good way to regulate enzymes: The product of one enzyme in a pathway might inhibit another enzyme in the pathway.

Question 16

Reversible

Answer 16

Competitive
Uncompetitive
Mixed

Irreversible

Question 17

Competitive inhibition

Answer 17

While the inhibitor (I) occupies the active site (forming an EI complex), it prevents the substrate binding the enzyme.

Bound inhibitor doesn’t inactivate the enzyme, when the inhibitor dissociates, the enzyme binds the substrate as normal.

KI is the equilibrium constant for I binding to E.

Question 18

Uncompetitive inhibition

Answer 18

The inhibitor binds at a separate site from the active, but only binds the ES complex (forming ESI).

E has undergone a conformational change upon binding S.

Question 19

Mixed inhibition

Answer 19

Inhibitors bind at a separate site to the active site, but may bind to either E or ES.

Forms either EI or ESI.

Question 20

Irreversible inhibition

Answer 20

Irreversible inhibitors strongly bind to or destroy a functional group on an enzyme that is essential for the enzyme’s activity, inactivating the enzyme.

Suicide inactivators (mechanism-based inactivators) are molecules that are unreactive until they bind the active site of an enzyme and are converted into irreversible inhibitors. This is important in drug design.

Chemists have designed transition state analogues. These are molecules that mimic a substrate’s transition state, and therefore bind the enzyme more tightly than the substrate. Once bound they are “stuck”, stopping the enzyme from binding its substrate.

Reaction of chymotrypsin with diisopropylfluorophosphate (DIFP), which modifies Ser195, irreversibly inhibits the enzyme

Question 21

Regulatory enzymes

Answer 21

Many enzymes work together in metabolic pathways where the product of one reaction becomes the substrate of the next reaction: A ⇌ B ⇌ C ⇌ D…

The product of one reaction may regulate another enzyme in the pathway, either positively (as an effector or modulator) or negatively (as an inhibitor).

Enzymes often have catalytic and regulatory subunits.

An allosteric enzyme undergoes a conformational change when it binds an effector at a site other than the active site.

Question 22

Regulation by reversible covalent modifications

Answer 22

Some enzymes are chemically altered as a regulatory mechanism.
There are many more examples than this.
Phosphorylation
Adenylylation
Acetylation

Question 23

Regulation by proteolytic cleavage

Answer 23

An inactive protein (zymogen) is cleaved to form a functional enzyme.
Many proteolytic enzymes (proteases) of the stomach and pancreas are
regulated in this way.

A cascade of zymogens, with the activated enzyme from one cleaving the next zymogen in the pathway is how blood coagulation proceeds.