Enzyme Kinetics and Regulation Notes

Enzymes: Kinetics and Regulation

Enzyme Uses

• Enzymes are utilized in various industries.
• Examples include the use of enzymes in denim production to create vintage looks via laser, sandpaper, and enzyme techniques, avoiding sandblasting.
• Lactaid is a pharmaceutical example, recommended for preventing gas, diarrhea, and bloating from digesting dairy.

Learning Objectives

• Monitor enzyme catalysis in the lab.
• Apply Michaelis-Menten kinetics to describe the rate of a reaction (v0) and calculate the constants Km, V{max}, and k{cat}.
• Classify different types of chemical reactions.
• Describe the effect of covalent and non-covalent regulation on an enzyme’s structure and function.
• Distinguish between reversible and irreversible inhibitors.
• Apply Michaelis-Menten kinetics to evaluate the type of inhibition.

Enzyme Mechanisms

• Carboxypeptidase A cleaves a tetrapeptide into V-E-R and Y fragments.
• Trypsin also generates these fragments but via different mechanisms.
• The difference is due to what non-covalent interactions form.

Binding Importance

• Biochemical interactions are vital for cellular processes.
• Binding affinity and kinetics help understand molecular interactions.
• Binding is saturable based on stoichiometry.
• Non-covalent interactions allow reversible binding, while covalent bonds lead to irreversible binding.
• Many drugs target enzymes to inhibit function, quantified via kinetics.
• Example: Ca^{2+}-ATPase, a membrane transporter and enzyme.

Active Site Specificity

• Enzymes' active sites bind specifically to a single substrate or a small subset of substrate molecules.
• Homologous enzymes evolve from a common ancestor, with mutations altering activity and binding specificity.
• Trypsin and chymotrypsin have similar tertiary structures but different primary sequences, leading to different specificities.
• Understanding protein structure aids in understanding its function.

Enzyme Effects

• Enzymes decrease:
  • Activation energy of a reaction
  • Time to reach equilibrium
• Enzymes increase:
  • The rate of the reaction

Enzyme-Catalyzed Reactions

• Enzymes are represented by the suffix '-ase'.
• They bind to a specific substrate or subset of substrates in an active site.
• Enzymes exist in small numbers relative to substrates.
• They remain unchanged after the reaction.
• Enzymes stabilize the transition state, lowering the activation energy.
• Enzymes must be controlled or regulated.

Proteolytic Cleavage for Activation

• Enzymes can be synthesized as inactive precursors called zymogens, activated when needed.
• Proteolytic cleavage converts a proenzyme precursor to the functional enzyme.
• Chymotrypsinogen, secreted by the pancreas, is activated in the small intestine to produce chymotrypsin.
• Proteolytic cleavage occurs in digestive enzymes, blood clotting, and hormone activation (e.g., insulin).

Enzyme Kinetics

• Enzyme kinetics measures substrate-to-product conversion to compare binding affinity and specificity and understand mechanisms, inhibition, and regulation.
• It studies the reaction rate, also known as the velocity (v_0).
• For simple enzymes, v_0 is measured before the substrate concentration decreases significantly and before significant reverse reaction occurs.
• Michaelis-Menten kinetics models simple enzymatic reactions.

Measuring Initial Rates

• The reaction rate indicates how fast substrate is converted to product expressed mathematically as:
  • v_0 = \frac{d[P]}{dt}
  • v_0 = -\frac{d[S]}{dt}
  • Where d = ‘change in’ or \Delta

Monitoring Enzyme Catalysis

• Chromogenic substrates generate colored products, useful for monitoring enzyme activity.
• N-Acetyl-L-phenylalanine-p-nitrophenyl ester is a chromogenic substrate for chymotrypsin.
• Absorbance is measured at 405 nm and converted to concentration using:
  • A = \epsilon cl
  • v_0 = \frac{[product]}{time}

Measuring Initial Rates - vo

• At low substrate concentrations, the reaction rate depends on substrate amount: v_0 = k[S].
• At high substrate concentrations, active sites saturate, and the reaction rate approaches V_{max}.
  • The rate is dependent on enzyme concentration: more enzyme = faster rate.
• Michaelis-Menten kinetics uses v_0 and [S] to understand binding.

Michaelis-Menten Kinetics

• Michaelis-Menten kinetics describes simple reactions where enzyme and substrate form an ES complex, lowering the activation energy.

• Assumptions:

  1. Measuring the initial rate: [P] << [S], negligible P \rightarrow S and no k_{-2}
  2. Rate of ES formation = rate of ES breakdown

• The Michaelis constant K_M describes the enzyme-substrate interaction:

  • KM = \frac{k{-1} + k2}{k1}

Michaelis-Menten Equation

• The Michaelis-Menten equation describes the initial reaction velocity as a function of substrate concentration:

Enzyme-Substrate Binding

• For a simple enzyme-substrate pair, Km indicates the substrate concentration at half of V{max}, when half the active sites are bound to substrate (50% binding).
• For receptor-ligand pairs, the dissociation constant K_d is the concentration when 50% of sites are bound to the ligand.
• Binding depends on non-covalent interactions between protein and binding partner.
• Low Km and Kd values indicate tighter binding.
• Cellular concentrations near Km (or Kd) allow a protein to adapt to metabolite level changes.

Binding Affinities Examples

• Serotonin receptor (5-HT2A) binding affinities:
  • Serotonin: 11 nM
  • Psilocin: 180 nM
  • Psilocybin: 10,000 nM
  • LSD: 0.33 nM

KM Values

• Some enzymes are highly specific to certain molecules.
• Other enzymes might have multiple substrates for a single reaction or non-specific general affinity.
• Km is independent of the amount of enzyme present (i.e., [E]{total}).

Michaelis-Menten Kinetics

• The Michaelis-Menten equation relies on steady-state kinetics.
• Reactions are set up to measure v0 at varying substrate concentrations to determine constants V{max} and K_m.
• As substrate concentration increases, the reaction rate increases hyperbolically, approaching V_{max}.
• Km defines substrate binding affinity and is the substrate concentration at 1/2 V{max}.
• The Lineweaver-Burk transformation is used to accurately determine V{max} and Km because the Michaelis-Menten curve is a rectangular hyperbola.

Lineweaver-Burk Plot

• Lineweaver-Burk plot equation:
  • y = mx + b

Penicillinase Example

• Penicillinase (beta-lactamase) breaks down and inactivates penicillin in resistant bacteria.
• Given data on penicillin concentration and amount hydrolyzed, V{max} and Km for penicillinase can be determined.

Michaelis-Menten vs. Lineweaver-Burk Plot

• Displays the differences between the two graphs.

Turnover Number, k_{cat}

• Enzyme efficiency is described using V{max} or k{cat}.
• k_{cat} is the rate constant when the enzyme is 100% saturated.
• k{cat} = \frac{V{max}}{[E]_{total}}
• Larger k_{cat} means faster product production.

Penicillinase kcat Calculation

• Penicillinase is a monomeric 30 kDa protein with 1 active site per molecule.
• k_{cat} can be determined when 1 ng of protein is used in each assay.

Enzyme Parameters Influenced by Enzyme Concentration

• The following are affected by a change in enzyme concentration:
  • v_0
  • V_{max}

Enzyme Classification

1. Oxidoreductases: oxidation-reduction reactions (e.g., prolyl hydroxylase).
2. Transferases: group transfer between molecules (e.g., protein kinase A).
3. Hydrolases: hydrolysis reactions (e.g., sucrase, ATPases, trypsin).
4. Lyases: addition or cleavage reactions, often involving double bonds/cyclization (e.g., carbonic anhydrase, adenylyl cyclase).
5. Isomerases: group transfer within a molecule (e.g., phosphoglucomutase).
6. Ligases: joining two molecules using nucleotides (e.g., biotin protein ligase).
7. Translocases: movement of ions/molecules across a membrane (e.g., flippases, Ca^{2+}-ATPase).

Alcohol Dehydrogenase

• Enzyme classification.
• Contains 2 Zn^{2+} ions, but only 1 is involved in catalysis.
• Dimeric structure, with each monomer functioning independently.
• K_m ADH-ethanol: 0.05 mM
• K_m ADH-methanol: 10.4 mM
• The difference in K_m is based on active site specificity

Enzyme Classification Examples

• Carbonic Anhydrase:
  • CO2 + H2O \rightleftharpoons H2CO3
• Phosphoglucomutase:
  • glucose 6-phosphate \rightleftharpoons glucose 1-phosphate

Classify Enzyme-Catalyzed Reaction

• Type of enzyme is a transferase.

Regulating Protein Function

• Cells respond to external stimuli via stimulating or inhibiting enzyme activity.
• Proteins are regulated at gene expression and degraded by the proteasome or lysosome.
• Membrane proteins require endocytosis before degradation.
• Protein and enzyme function can be regulated by structural changes via cleavage, non-covalent, or covalent interactions (phosphorylation, methylation, acetylation).

Trypsin Activity

• Reasons why purified enzyme may not be functioning properly:
  1. The enzyme may not be folded properly.
  2. The zymogen may not have been cleaved to activate the enzyme.

Inhibiting Enzyme Function

• Zymogens are inactive precursors activated by proteolytic cleavage.
• Phosphorylation regulates protein function: kinases transfer a phosphate from ATP, causing conformational changes. Dephosphorylation by a phosphatase can re-activate the enzyme.
• Irreversible inhibition occurs when a molecule binds covalently to the enzyme and cannot be removed; overcoming this requires synthesizing a new enzyme.

Irreversible Inhibition Example

• Aspirin acetylates Serine 529 in COX1, leading to irreversible inhibition.

Simple, Reversible Inhibition

• Reversible inhibition involves non-covalent interactions and can be:
  • Competitive: the inhibitor binds to the active site.
  • Uncompetitive: the inhibitor can only bind to the ES complex.
  • Non-competitive: the inhibitor binds to the enzyme or ES complex.
• Michaelis-Menten kinetics and the Lineweaver-Burk plot compare these inhibition types.

Enzyme Kinetics and Reversible Inhibition Types

• Shows the different graphs for competitive, uncompetitive, and non-competitive inhibition.

Competitive Inhibition

• The inhibitor binds to the active site of the enzyme, preventing substrate binding.

Un-competitive Inhibition

• The inhibitor binds only to the enzyme-substrate (ES) complex.

Non-competitive Inhibition

• The inhibitor binds to either the enzyme or the enzyme-substrate complex.

Allosteric Regulation

• Proteins are regulated by molecules that bind to allosteric sites distant from the active site.
• Allosteric effectors can be stimulatory or inhibitory.
• Binding of allosteric regulators results in conformational changes that affect ligand binding.
• Conformations are described as Tense/Taut (T) and Relaxed (R).
• Allosteric enzymes display sigmoidal kinetics, indicating cooperativity in binding of substrates to adjacent active sites.

Michaelis-Menten vs. Allosteric Enzyme Kinetics

• Michaelis-Menten enzymes are hyperbolic, while allosteric enzymes are sigmoidal.

Cooperativity

• Allosteric enzymes show cooperativity where the binding of one substrate molecule increases the affinity for subsequent substrate molecules

Inhibition Type Problem

• Based on the data provided, pentamidine inhibition of hVAP-1 cannot be determined.

Oxygen Binding

• Myoglobin is a monomer that binds O2 tightly with a P{50} of 2 torr.
• Hemoglobin is a tetramer that displays allosteric cooperativity upon O_2 binding.
• Upon O2 binding, an \alpha1\beta_1 dimer rotates 15˚ to convert from the T → R state.
• Hemoglobin releases oxygen at higher pO_2 to allow the tissues to use the oxygen.

2,3-BPG as Allosteric Regulator

• 2,3-bisphosphoglycerate binds to deoxyhemoglobin to stabilize the T state, facilitate O_2 release, and prevent rebinding.
• 2,3-BPG binds to a pocket via ionic bonds.

Irreversible Enzyme Regulatory Mechanism?

• Activation of a zymogen

Key Messages

• Enzymes increase the rate of metabolite turnover but do not affect the chemical equilibrium. The amino acids in an active site dictate its specificity and affinity.
• Substrate binding is saturable at high concentrations, and the rate depends on the number of active sites present.
• Simple enzymes can be described using Michaelis-Menten kinetics and the Lineweaver-Burk Plot, and the type of reversible inhibition can be determined using kinetics.
• Enzymes are classified based on 7 different categories, depending on the main reaction catalyzed.