Ic50

What is an enzyme?

A protein

What do enzymes do?

They catalyse the conversion of substrates (S) to products (P).

Are enzymes chemically unchanged or changed at the end of a reaction?

Unchanged

Do enzymes change the equilibrium position of the reaction?

No

Enzyme catalytic cycles

What are the 2 models of catalysis?

Lock and key

Induced Fit

Thermodynamic catalysis by enzymes

Most enzymes work by lowering activation energy of the reaction

What is the chemical catalysis of enzyme reactions?

The process by which enzymes speed up (catalyse) chemical reactions in the body by using chemical interactions at their active site.

How do enzymes increase the likelihood of substrate molecules reacting?

By holding substrates and reacting groups close together in the active site.

Why is orientation of reacting groups important in enzyme reactions?

Correct orientation ensures bonds react efficiently, lowering activation energy.

How do enzymes mimic the transition state?

By stretching or bending reacting bonds, making them easier to break.

Why are enzyme active sites often hydrophobic?

To exclude water, stabilize charged groups, and create a favorable reaction environment.

What is the effect of excluding bulk solvent from enzyme active sites?

Charged groups are not masked, enhancing electrostatic interactions.

How can water molecules participate in enzyme-catalyzed reactions?

Ordered water molecules can act as reactants or help stabilize intermediates.

How do enzymes perform acid/base catalysis?

Active site groups donate or accept protons to facilitate bond breaking/forming.

What is nucleophilic catalysis in enzyme reactions?

Formation of a temporary covalent bond (e.g., acyl-enzyme intermediate) with the substrate.

Why are enzymes usually stereospecific?

Their chiral active sites can only accommodate substrates of a certain orientation.

How do cofactors and cosubstrates help enzyme activity?

Metal ions or nucleotide-derived molecules assist in catalysis and are often derived from vitamins/minerals.

How do enzymes stabilize the transition state?

Active sites are complementary to the transition state, distorting bonds to lower activation energy.

Chemical model of Enzyme Catalysis:

Exam Tip

• Small molecules should have the correct bond angles, i.e. a sp3 carbon is tetrahedral (109) and a sp2 carbon is trigonal planar (120)

• Non reacting parts of the molecule can be designated as ‘R’

• Only necessary to draw enzyme residue side chains when covalent interme

Acyl substitution reactions

1. Activation of active site nucleophile by deprotonation

2. Acyl substitution using active site nucleophile

3. Acyl substitution by water to regenerate enzyme

In acyl substitution reactions, what do poor leaving groups require?

Protonation

Do acyl substitution reactions occur for aldehydes and ketones?

No because H atoms, alkyl groups, and aryl groups cannot leave

Step 1) Chymotrypsin

Activation of nucleophile

Step 2) Chymotrypsin. - Formation of an acyl-enzyme intermediate

• Deprotonated nucleophile adds to carbonyl group.

• Tetrahedral intermediate is transiently formed.

• Leaving group is protonated (-NH₂ produced).

Step 3) Chymotrypsin - Hydrolysis of acyl-enzyme intermediate

Mechanism is similar, with formation of tetrahedral intermediate. This time, water is the nucleophile and the enzyme-O- is the leaving group.

Name all the common ways enzymes catalyse reactions:

• Entropic effects.

• Bond stretching and bending. 

• Acid / base catalysis.

• Nucleophilic catalysis.

• Removal of bulk solvent and use of ordered waters.

• Use of cofactors and cosubstrates. 

Name the factors that affect enzyme activity:

• pH – due to changing ionisation state of side-chains. Grossly inappropriate pH unfolds proteins;

• Denaturing reagents (detergents, urea, guanidinium hydrochloride);

• Temperature – higher temperatures increase rate until thermal denaturation (unfolding) of the protein occurs

• Activity is proportional to amount of enzyme

• Substrate concentration

• The presence of inhibitors

How do enzymes work?

• Enzymes are catalysts, therefore enzyme concentration is usually far greater than substrate concentration

• The reaction goes through an enzyme/substrate complex

What do simple models assume?

• Only one molecule of one substrate binds to the enzyme (One substrate reactions are rare – isomerizations and rearrangements);

• Enzyme and substrate form a [ES] complex (rate-limiting step);

• Enzyme converts substrate to product and product release occurs (fast);

• Products bind weakly to enzymes.

Name the 3 simple models:

Differences in simple models:

Michaelis Menten curve

• v = rate;

• [S] = substrate concentration;

• V_max = rate when all enzyme active sites are occupied (the enzyme is saturated);

• K_m = [S] at which v = ½ V_max

What’s the Michaelis-Menten equation?

Why do enzyme reactions saturate?

Enzyme reactions saturate because there are a limited number of enzyme active sites available to bind substrate molecules.

At low substrate concentrations, increasing the substrate makes the reaction go faster — because more enzyme–substrate complexes can form.
However, as substrate concentration keeps increasing, all enzyme active sites eventually become occupied.

Explaining why enzyme reactions saturate using the Michaelis-Menten equation:

• Rearrange ‘Michaelis-Menten’ equation: (v/Vmax)= ([S]/(K_m +[S] ))

• Assume K_m = 1 mM:

• At 1 mM S, v = 0.5 V_max  At 2 mM S, v = 0.666 V_max  

• At low [S] rate (v) increases with increasing [S] (first order);

• At 20 mM S, v = 0.952 V_max   At 21 mM S, v = 0.954 V_max

• At high [S], rate (v) does not increase with further increases in [S] (zero order). Rate only depends on [ES] and k₃  (i.e., saturation has occurred).

What are the assumptions of the steady state model?

• Enzyme concentration is much smaller than substrate concentration ([E] « [S]) (typically nM vs. mM);

• [S] remains constant; Measured rate of reaction is linear at beginning of curve (‘initial rate’);

• [ES] remains the same throughout course of reaction (‘The steady-state approximation’);

• Product binds weakly to enzyme;

• Rate of conversion of product to substrate is negligible (no backward reaction)-

Michaelis-Menten Plot

• Directly plots v against [S]

• Can be difficult to decide when V_max is reached

• Usually requires a computer programme

Lineweaver-Burk Plot

• Plots 1/v against 1/[S]

• Y-intercept = 1/V_max

• X-intercept = -1/K_m

• Higher precision;

• Lower accuracy;

• Errors are not equal at all points (least squares regression is not appropriate).

Direct Linear Plot

• Plot rate and substrate concentration onto axes;

• Connect points;

• Intersections are estimates of K_m and V_max;

• Gives median value;

• Makes no assumptions about the errors;

• Difficult to deviations from ideal behaviour.

V_max

The fastest rate the enzyme can work at- when all the enzyme active sites are full of substrates (all enzymes are saturated)

If V_max = 0.5 what does that mean?

The maximum rate of the enzyme catalysed reaction is 0.5 units per second. When the enzyme is working as fast as it possibly can (all enzyme active sites are full of substrate), it can make 0.5 units of product per unit time.

K_m 

• It tells you how strongly an enzyme binds to its substrate.

• A low Km means the enzyme binds tightly (it works well even at low substrate levels).

• A high Km means the enzyme binds weakly (it needs more substrate to work efficiently).

What is Km often similar to?

Substrate concentration in cell

K_cat 

• K_cat shows how fast the enzyme can convert substrate to product once the substrate is bound.

• V_max / amount of enzyme in, for example, nmoles.

• This is the first order rate constant for conversion of substrate to product.

• K_cat = K₃

Exam Question: In an enzyme kinetic experiment, the value for 1/V_max was 0.102 min/nmol and -1/K_m was -3.45 mM^-1 from a Lineweaver-Burk (double reciprocal) plot. Each assay contained 0.14 mg of enzyme with a molecular weight (M_W) of 47 146 Da. Showing your workings, calculate values for V_max, K_m, k_cat, k_cat/K_m, assuming one active site per monomer (hint: k_cat = V_max divided by amount of enzyme) [10 marks].

K_i

• Inhibition constant

• Measures how strongly an inhibitor binds to the enzyme

• K_i values related to binding energy (ΔG)

• A low K_i means the inhibitor is very effective (binds strongly - more potent).

• A high K_i means it’s a weaker inhibitor (binds less tightly - less potent).

Mode of action for Inhibitors

• Inhibitors can resemble the substrate in structure

• Inhibitors affect either K_m, V_max or both

Competitive inhibition

• K_m increases. X-intercept changes

• K_m(I) = K_m (1 + [I]/K_i)

K_m(I) = apparent Km (with inhibitor)

[I] = inhibitor concentration

K_i = inhibition constant (strength of inhibitor)

• No change in V_max. Y-intercept does not change

• Inhibition decreases with increased substrate concentration

Non-competitive inhibition

• V_max is reduced. Y-intercept changes.

• V_max/K_m (I) = V_max/K_m(1 + [I]/K_i)

V_max​ = The enzyme’s maximum velocity — how fast it can go when fully saturated with substrate.

K_m (I) = apparent Km (with inhibitor)

[I] = inhibitor concentration

K_i = inhibition constant (strength of inhibitor)K_m is not affected. X-intercept does not change.

• Inhibition is not reduced by increasing substrate.

Mixed-competitive inhibition

• K_m is increased (as for competitive inhibition). X-intercept changes.

• V_max is decreased (as for non-competitive inhibition). Y-intercept changes.

• α factor defines the competitive and non-competitive components.

Uncompetitive inhibition

• Inhibitor binds to the ES complex

• Parallel lines in Lineweaver-Burk plot

• Both K_m and V_max reduced by same amount, (1 + [I]/K_i)

• Increasing substrate concentration increases inhibition.

What do dose response curves measure?

They measure the drug potency at a fixed substrate concentration

Example of a dose response curve:

IC₅₀ curves

IC₅₀ curves

• IC₅₀ = concentration of drug required for 50% reduction in activity

• Value depends on assay conditions (especially substrate concentration)

• IC₅₀ not the same as K_i (can be calculated from IC₅₀ for some inhibitors).

What is tight-binding inhibition?

• Tight-binding inhibition means the inhibitor binds so strongly to the enzyme that it’s almost irreversible — the inhibitor and enzyme form a very stable complex.

• Tight-binding inhibition means the inhibitor “grabs” the enzyme so strongly that it barely lets go. It’s like a super strong magnet — not a casual, reversible attachment.

• These inhibitors are very potent and often used as drugs because they effectively “shut down” enzymes even at low concentrations.

When does tight binding inhibition occur?

When the concentrations of active enzyme and inhibitor are similar.

This means that the concentration of free inhibitor does not approximate to total inhibitor

In tight binding inhibition, what will happen to the K_i value if you increase the enzyme concentration?

It will increase

Features of tight-binding inhibition

• The apparent K_i value will increase with increasing enzyme concentration;

• Tight-binding inhibition often has very slow onset, and the enzyme inhibitor complex can have a very long half-life (K_i = k_off/k_on);

• This means that infrequent dosing regimens can be used (easier for patient, reduced side-effects etc.). Therefore, many drug discovery programmes aim to develop a tight-binding inhibitor.

What’s the importance of K_i as the parameter defining potency?

• Independent of enzyme and substrate concentrations

  • Unlike IC₅₀ (the inhibitor concentration that reduces activity by 50%), Ki is a true thermodynamic constant — it depends only on binding strength, not on experimental conditions.

  • This makes it a universal measure for comparing inhibitors across studies.

• Directly reflects binding affinity

  • Ki comes from the equilibrium between enzyme and inhibitor — it quantifies how “sticky” the inhibitor is for the enzyme.

• Useful for drug design

  • In pharmacology, a low Ki means the drug can be effective at low doses, reducing side effects and increasing specificity.

Irreversible Inhibitors

• Examples include penicillins and other β-lactam antibiotics;

• Enzymes inhibited are penicillin-binding proteins (PBPs);

• Inhibitors act as pseudo-substrates but get ‘stuck’ (at acyl-enzyme intermediate);

• Kinetic behaviour is more similar to chemical systems.

Exam Question) In an enzyme kinetic experiment -1/K_m was -5.0 mM^-1 and in the presence of an inhibitor -1/K_m was -1.818 mM^-1 when measured using a Lineweaver-Burk (double reciprocal) plot. The value for 1/V_max did not change. In this experiment 25 μL of a 10 mM stock solution of inhibitor was added to a final assay volume of 1 mL. What sort of inhibitor is it? Show your workings and calculate the K_i value [9 marks]