Biochemistry Enzyme Kinetics - Tutorial Notes (Tutorial #3)

Enzyme Kinetics Tutorial Notes

• Scope and context

  • Tutorial 3 covers content from lectures 7 to 10 and focuses on enzyme kinetics and related thermodynamics, catalysis mechanisms, active-site features, and enzyme inhibition.
  • Learning objectives include understanding thermodynamic features of enzyme-catalysed reactions, roles of cofactors, active-site interactions, how enzymes reduce ΔG to accelerate reactions, and how to compare enzymes using KM, Vmax, kcat, and kcat/KM. Also covers reversible vs irreversible inhibition and competitive vs non-competitive inhibition.

• Core definition of enzymes and related terms

  • Enzymes: proteins that act as biological catalysts to speed up biochemical reactions.
  • Enzyme-catalysed reactions characteristics:
  • Much faster reaction times (billions to trillions of times faster).
  • Operation under milder conditions (physiological pH and temperature).
  • Reaction specificity (substrates brought together correctly).
  • Tight regulation (timely substrates availability).
  • Key terms:
  • Active Site: region of the enzyme where the reaction happens and where substrate/transition state binds; a relatively small portion of the protein.
  • Cofactors: non-protein helpers inside the active site essential for the reaction; include metal ions and coenzymes.
  • Substrate(s): molecules acted upon by the enzyme (start of the reaction).
  • Transition State: the high-energy, unstable intermediate between substrate and product; has the highest free energy in the reaction.
  • Product(s): molecules formed after the reaction.
  • Free Energy: the potential energy/work required for the reaction, encompassing substrates, transition state, and products.
  • ΔG: change in free energy from substrate to product.
  • ΔG‡: activation energy, the free-energy difference between substrate and the transition state.

• Enzyme–substrate interactions and binding

  • Interaction at the enzyme active site occurs mainly through non-covalent interactions:
  • Ionic bonds
  • Hydrogen bonds
  • Van der Waals interactions
  • Covalent bonds can occur, but are rare
  • Product formation results in release of the product, breaking non-covalent interactions to free the product from the active site.

• Transition state concept

  • Transition State: a chemical species intermediate in structure between substrate and product.
  • Enzymes stabilize the transition state, with the tightest binding often to the transition state itself.
  • Transition-state analogues can serve as ideal competitive inhibitors.

• Gibbs Free Energy and thermodynamics

  • Gibbs Free Energy (G): measure of the maximum work obtainable in a thermodynamic system at constant temperature and pressure.
  • ΔG = Gproducts − Gsubstrates (change in Gibbs Free Energy from substrate to product).
  • Sign conventions:
  • ΔG < 0: spontaneous (energy released).
  • ΔG > 0: non-spontaneous (energy required).
  • ΔG = 0: at equilibrium.
  • Activation energy: ΔG‡ is the energy barrier between substrates and transition state.

• Reaction coupling and energy management

  • Reactions with ΔG > 0 require energy input; reactions with ΔG < 0 release energy.
  • Coupling allows energy release from one reaction to drive another; the overall ΔG is the sum of the two ΔGs:
  • Overall ΔG = ΔG1 + ΔG2, and the overall ΔG must be negative for both reactions to proceed.
  • Coupling often involves a shared intermediate; product of one reaction is used as the substrate for the next.

• How enzymes catalyse reactions (thermodynamics and mechanism)

  • Enzymes lower the energy of the transition state (lower ΔG‡) but do not change the free energy levels of reactants or products.
  • Mechanisms by which enzymes lower ΔG‡:
  • Ground state destabilisation: destabilizing the substrate when bound in the active site.
  • Transition state stabilisation: stabilizing the transition state to accelerate the reaction.
  • Alternate reaction pathway: enabling multiple smaller steps to reach the same product more efficiently.
  • The transition state is the critical target of catalysis; stabilizing it speeds up the reaction.

• Enzyme structure and active sites

  • Active Site characteristics:
  • A relatively small region within the enzyme where substrates bind.
  • Substrate binding is via weak non-covalent interactions (mostly).
  • Can bind via covalent bonds in covalent catalysis.
  • Active sites are clefts or crevices; amino acid side chains project into the site to participate in binding and catalysis.
  • Active site determines reaction specificity via geometric (shape) and stereospecific (chirality) constraints.
  • Binding models:
  • Lock and Key: substrate and active site are perfectly complementary without substantial enzyme movement; assumes no conformational change.
  • Induced Fit: enzyme undergoes a conformational change upon substrate binding to better accommodate the transition state.

• Cofactors and their roles

  • Cofactors: non-protein components essential for enzyme function.
  • Two main classes:
  • Metal ions (e.g., Mg^{2+}, Zn^{2+}, Fe^{2+/3+}); provide substrate orientation, act as Lewis acids, and serve as sites for electron transfer.
  • Coenzymes: small organic molecules often derived from vitamins.
  • Cofactors reside in or near the active site, enabling catalytic activity.

• Enzyme catalytic mechanisms (categories)

  • Preferential binding of the transition state: enzymes bind the transition state most tightly to lower ΔG‡.
  • Geometric effects (proximity and orientation): bring substrates into close proximity and proper orientation to react.
  • Acid-base catalysis: transfer of protons via acid-base interactions; involves ionisable amino acids (e.g., Glu, Asp, Lys, His, Cys) or cofactors; Histidine is particularly well suited as a donor/acceptor.
  • Covalent catalysis: formation of a short-lived covalent intermediate between enzyme and substrate via nucleophilic attack on an electrophile.
  • Redox and radical catalysis (often involving metal ions): electron transfer processes that facilitate reactions.

• Specific catalytic concepts in more detail

  • Preferential binding
  • Optimal binding is to the transition state, which lowers the activation energy and drives progression toward product.
  • Effects on ΔG‡: decreases or lowers the activation energy barrier; product and enzyme become easier to separate once the reaction proceeds.
  • Geometric effects
  • Substrate proximity and orientation are crucial for reaction: close spatial arrangement and correct angular alignment enable reaction to occur.
  • Acid-base catalysis
  • Proton transfer between donors and acceptors facilitates bond-making/breaking.
  • Involves ionisable amino acids (e.g., Glu, Asp, Lys, His, Cys) or cofactors; Histidine is versatile as a proton donor/acceptor.
  • Metal ion catalysis
  • Metals provide substrate orientation via specific coordination geometries, act as Lewis acids, and serve as sites for electron transfer.
  • Common metal cofactors: Mg^{2+}, Zn^{2+}, Fe^{2+/3+}.
  • Covalent catalysis
  • Involves formation of a reactive, short-lived intermediate covalently attached to the enzyme.
  • Often includes nucleophilic attack on an electrophile.

• Enzyme kinetics: KM, Vmax, and kcat

  • KM (Michaelis constant): the substrate concentration needed to reach half of Vmax; reflects how well a substrate binds to the enzyme.
  • Vmax: the maximum velocity of an enzyme-catalysed reaction; assumes enzyme is saturated with substrate; represents a theoretical maximum that is difficult to reach in practice.
  • kcat (turnover number): how fast substrate is converted to product when the enzyme is saturated; intrinsic rate constant for the catalytic step.
  • Practical interpretation: a good (efficient) enzyme tends to have a high kcat and a low KM.
  • Common shorthand relationships:
  • v =
    ( \dfrac{V{\max} [S]}{KM + [S]} )
    (Michaelis–Menten equation)
  • For inhibitors and plotting, see below.

• Experimental progress curves and initial velocity

  • Progress Curve: a plot of product appearance (or substrate disappearance) over time.
  • Purpose: to determine the initial velocity v0 from the linear portion of the curve at early time.
  • As the reaction proceeds, curvature increases because substrate concentration decreases, making the rate slower.

• Substrate concentration versus rate: the V vs [S] curve

  • The V0 vs [S] curve shows how the reaction rate depends on substrate concentration.
  • Early phase: linear increase when [S] is high and enzyme active sites are available.
  • Later phase: rate plateaus at Vmax as all enzyme active sites become occupied.
  • From this curve, two key kinetic parameters can be determined: KM and Vmax.

• Linearization: Lineweaver–Burk plots

  • Lineweaver–Burk is a double-reciprocal plot that linearizes v0 vs [S] data for better parameter estimation.
  • Equation:
  • ( \dfrac{1}{v0} = \dfrac{KM}{V{\max}} \cdot \dfrac{1}{[S]} + \dfrac{1}{V{\max}} )
  • Benefits: allows more accurate estimation of KM and Vmax from experimental data.

• Relating the three graph types and experimental workflow

  • To generate a V vs [S] curve, perform multiple experiments with constant enzyme concentration and varying [S], each yielding a progress curve to estimate v0.
  • For each experiment, plot v0 versus [S].
  • To generate a Lineweaver–Burk plot, convert the collected data into reciprocals (1/[S] and 1/v0) and plot a straight line.

• Physiological relevance and substrate ranges

  • In physiological conditions, it is desirable that small changes in substrate concentration drive a controlled increase in enzymatic work without substrate buildup.
  • Therefore, cellular [S] is often kept below KM to regulate the rate and prevent bottlenecks or substrate accumulation.

• Enzyme inhibition: basics and classifications

  • Definition: Inhibitors are molecules that bind to enzymes and reduce catalytic efficiency.
  • Two broad classes:
  • Irreversible inhibitors
  • Reversible inhibitors (can be further categorized as competitive, non-competitive, or mixed)
  • Within reversible inhibitors:
  • Competitive inhibitors bind at the active site, competing with substrate.
  • Non-competitive inhibitors bind at an allosteric site, distinct from the active site.
  • Mixed inhibitors bind at an allosteric site but affect KM, Vmax, or both in different ways.

• Competitive inhibitors

  • Mechanism: occupy the active site, preventing substrate binding (temporarily).
  • Effect on kinetic parameters:
  • Increases KM (apparent binding affinity is reduced) because more substrate is required to reach half-maximal velocity.
  • Vmax is unchanged at high substrate concentrations because excess substrate can outcompete the inhibitor.
  • Conceptual takeaway: competitive inhibitors mimic the substrate and are overcome by high substrate concentrations.

• Pure non-competitive inhibitors

  • Mechanism: bind to an allosteric (non-active) site; binding does not prevent substrate binding at the active site.
  • Effect on kinetic parameters:
  • KM remains unchanged (substrate binding affinity is not directly affected).
  • Vmax is lowered because catalytic turnover is reduced even when substrate is bound.
  • Conceptual takeaway: non-competitive inhibition reduces the catalytic efficiency without affecting substrate binding.

• Mixed non-competitive inhibitors

  • Mechanism: bind to an allosteric site but influence the active site to alter substrate binding.
  • Effect on kinetic parameters:
  • KM is changed (either increased or decreased) depending on how inhibitor binding affects substrate affinity.
  • Vmax is lowered because the enzyme’s overall catalytic capacity is reduced.
  • Conceptual takeaway: mixed inhibitors impact both substrate binding and catalytic turnover to varying extents.

• Practical and conceptual links

  • The best enzyme characteristics: high kcat and low KM, enabling fast turnover at low substrate concentrations.
  • Transition-state analogs provide strong inhibition by closely mimicking the transition state, often serving as competitive inhibitors.
  • Cofactors expand the catalytic repertoire, enabling diverse reaction chemistries (e.g., metal ions for orientation and electron transfer, coenzymes for redox reactions, etc.).

• Essential equations and constants to remember

  • Michaelis–Menten relationship:
  • $v = \frac{V<em>{\max} [S]}{K</em>M + [S]}$
  • Lineweaver–Burk linear form:
  • $\frac{1}{v} = \frac{K<em>M}{V</em>{\max}} \cdot \frac{1}{[S]} + \frac{1}{V_{\max}}$
  • Relative effects of inhibitors (qualitative):
  • Competitive: increases KM, leaves Vmax unchanged.
  • Non-competitive: keeps KM unchanged, decreases Vmax.
  • Mixed: changes KM and decreases Vmax.
  • Transition state and catalysis concepts:
  • Transition-state stabilization lowers activation energy: $\Delta G^{\ddagger}<em>{\text{enzyme}} < \Delta G^{\ddagger}</em>{\text{uncatalyzed}}$
  • Energetics:
  • Ground-state destabilisation and transition-state stabilization contribute to lowering the activation barrier.
  • Coupled reactions: overall ΔG = ΔG1 + ΔG2; the sum must be negative for the coupled process to proceed.

• Quick glossary recap

  • Active site: region where binding/catalysis occurs; defines specificity.
  • Cofactor: non-protein helper (metal ions or coenzymes).
  • Transition state: high-energy intermediate; enzymes stabilize it.
  • Vmax: maximum rate at enzyme saturation.
  • KM: substrate concentration at 0.5 Vmax; indicator of substrate binding affinity.
  • kcat: turnover number at saturation; rate per enzyme molecule.
  • Inhibitors: molecules reducing enzyme activity; include competitive, non-competitive, and mixed types.

• Practical takeaway for exam preparation

  • Be able to explain how enzymes lower ΔG‡ via ground-state destabilisation, transition-state stabilisation, and alternative pathways.
  • Be able to describe the differences between competitive, non-competitive, and mixed inhibitors, including predicted changes to KM and Vmax.
  • Be able to interpret progress curves, V vs [S] curves, and Lineweaver–Burk plots, and to extract KM, Vmax, and kcat from data.
  • Remember the role of cofactors (metal ions and coenzymes) in enzyme catalysis and how they can influence catalytic strategies (acid-base, covalent, metal-ion catalysis).