Enzymes Function and Kinetics

Enzymes catalyze chemical reactions (thousands). Most would not occur alone at physiological conditions. Enzymes facilitate chemical reactions by increasing their rate. They act as a catalyst, i.e., the enzyme is regenerated: They are specific: they carry out specific reactions on specific substrates.

Thermodynamics vs. Kinetics ΔG: the change in the Gibbs free energy for the reaction ΔG = G(product) G(reactant) A B reactant product If G(reactant) > G(product), ΔG is negative. - ΔG is the driving force for the reaction. The reaction is spontaneous and energy will be released. ΔG is also related to the equilibrium constant (Keq): ΔGo = -RT ln Keq ΔG for the reaction says nothing about how fast the reaction will go.

Kinetics (how fast?) G Enzymes can increase rates by 106-1014-fold.

“Active Site” Region of the protein that: 1) binds substrate 2) catalyzes the chemical reaction Example: Carboxypeptidase A --synthesized in the pancreas --delivered to the small intestine lumen --role in digestion of protein Removes amino acids from the C-terminus of peptides Peptide..........a.a COO-

A Substrate: H3N-Gly-Tyr-COO- + (H2O) Glycine + Tyrosine In water, no bond cleavage takes place.

Carboxypeptidase A Active Site: Binding of Substrate

Enzyme Contains Zinc Ion

Active Site: Catalytic Mechanism

Whole protein involved (induced fit)

Types of Enzyme Reactions Oxidoreductases --electrons, H or O atoms moved from one substrate to another one (e.g, alcohol dehydrogenase; alcohol to aldehyde) Transferases --transfer of a chemical group from one molecule to another (e.g., a kinase that moves a phosphate from ATP to a protein) Hydrolases --use water to make two products from a substrate (e.g., carboxypeptidase A described above) Lyases --cleave –C-C-, –C-N- or C-O bonds, or sometimes make them (synthase) Isomerases --move a group or a double bond within the molecule Ligases --join atoms together using energy, usually from ATP (synthetases)

Coenzymes and Cofactors Many enzymes just use their own amino acids for catalysis. Others require nonpolypeptide coenzymes/cofactors for catalysis. Cosubstrate: modified during reaction and leaves the active site. Prosthetic group: tightly bound, regenerated after reaction. Metal ions Cofactor

Enzyme Kinetics (Rates in mathematical terms)

E + S E∙S P E + S E∙S P k1 k3 k2 k1 kcat k2 kcat is the catalytic rate constant (for the rate-determining step) Add enzyme to substrate; measure substrate and product concentrations over time

Effect of [S] on Initial Velocity S1 to S4: increasing [S] v0 = initial velocity (change in [product] over time; d[P]/dt)

Initial Velocity vs. [S] [Eo ] Km v = kcat [S] + Michaelis-Menten Equation

[Eo ] is total enzyme concentration Km v = kcat [S] + [Eo ] is total enzyme concentration kcat [Eo ] = Vmax (Maximum velocity at a given [Eo] ) Km = k1 k2 + k3 If k3 << k2 , Km is the dissociation constant (affinity) E∙S kcat and Km are constants!! Km v = [S] + Vmax If Km = [S], v = 0.5 Vmax Km is equivalent to the [S] that gives a velocity of one-half Vmax .

[S] >> Km [S] ≈ Km [S] << Km

Vmax = kcat [Eo] Initial Velocities (Product vs. Time) for Different [Eo] at high [S]

How Fast Does an Enzyme Go, Actually? Given by kcat in units of sec-1 kcat = Vmax [Eo ] Also known as the turnover number: the number of substrate molecules converted to product per enzyme molecule per second

Determining Vmax and Km Transform Data to a Lineweaver-Burk Plot:

Determining Vmax and Km [S] + Vmax y = slope (x) + y-intcp Lineweaver-Burk Plot

Enzyme Inhibition

Enzyme Inhibition Competitive inhibition: Substrate Enzyme Enzyme inhibitor Substrate Enzyme Enzyme -- inhibitor binds to part or all of the active site -- blocks substrate binding.

Michaelis-Menten: Competitive Inhibition Km (app) Michaelis-Menten: Competitive Inhibition (red: no inhibitor; green: inhibitor) -- apparent Km higher: S must compete with I to fill 50% of active sites -- Vmax not affected: S can outcompete I at high concentrations

Noncompetitive Inhibition: Substrate Enzyme Substrate Noncompetitive Inhibitor Enzyme -- binds to an allosteric site -- affects the active site -- enzyme can’t catalyze the reaction (ESI complex nonproductive) (lowers ES; decreases Vmax) -- substrate still binds; Km not changed

Michaelis-Menten: Noncompetitive Inhibition Vmax (app) (red: no inhibitor; blue: inhibitor) -- Km not affected: S does not compete with I at the active site -- Vmax decreases (to Vmax (app))

( ) ( ) Michaelis-Menten Equations for Inhibition Competitive: 1 + 1 + [ I ] Ki ( ) Km v = [S] + Vmax = Km (app) Noncompetitive: 1 + [ I ] Ki + ( ) Km v = [S] Vmax = Vmax (app) Ki is the EI dissociation constant

Enzyme Inhibitors in Medicine: Examples