Lab 11 Comprehensive Study Notes on Enzyme Kinetics and Inhibition Mechanisms of Inhibition

Introduction to Alkaline Phosphatase and Enzyme Kinetics

• This section marks a complete departure from the previous focus on green and red fluorescent proteins; students are instructed to transition entirely to studying enzyme kinetics.

• The goal of this laboratory module is to provide students with the foundational experience of measuring enzyme kinetics, a skill essential for work in biochemistry laboratories.

• Enzyme Selection: The study utilizes alkaline phosphatase (AP), an enzyme students encountered earlier in the course.

  • AP typically catalyzes the hydrolysis of phosphate esters.

  • In biological contexts, it is commonly used with DNA to remove terminal phosphate groups.

Chemical Reaction and Spectroscopic Monitoring

• Substrate Choice: For this kinetic analysis, a synthetic substrate called para-nitrophenyl phosphate (pNPP) is used.

• Reaction Conditions: The reaction is conducted under alkaline conditions because the enzyme is most active in high pH environments.

• Reaction Equation:     $\text{para-nitrophenyl phosphate (pNPP)} + \text{H}_2\text{O} \rightarrow \text{para-nitrophenolate (pNP)} + \text{phosphate}$

• Spectroscopic Properties of Product:

  • The resulting product, p-nitrophenolate, has a $pKa$ of approximately $7.2$.

  • Under the alkaline conditions of the experiment, the product is almost completely unprotonated.

  • In its unprotonated state, it exhibits a strong absorption maximum at approximately $410\,\text{nm}$.

  • Extinction Coefficient ($\epsilon$): Approximately $15,000\,\text{M}^{-1}\,\text{cm}^{-1}$.

  • This high extinction coefficient allows even small amounts of product formation to be easily detected using UV-visible spectroscopy.

• Monitoring Method: The reaction rate is monitored by tracking the appearance of the product over time, which corresponds to an increase in absorbance.

Calculation of Concentration and Velocity

• Beer's Law Application:     $A = \epsilon \times c \times l$

  • In this experiment, students look at the change in absorbance ($\Delta A$).

  • Path Length ($l$): For a microplate, the path length is roughly $0.25\,\text{cm}$ per $100\,\mu\text{L}$ of solution.

  • Calculation Example: If the solution volume is $200\,\mu\text{L}$, the path length $l$ would be $0.5\,\text{cm}$.

• Velocity ($v$): Change in absorbance per unit time ($\Delta A / \Delta t$) is converted to change in product concentration per unit time ($\Delta [P] / \Delta t$).

Determination of Kinetic Parameters ($V_{\max}$ and $K_m$)

• Initial Velocity ($v_0$): Data analysis focuses on the linear portion of the absorbance vs. time plot. Nonlinear portions (usually occurring at later time points as substrate is depleted or product accumulates) must be discarded.

• Direct Plotting Method: Plotting velocity ($v$) vs. substrate concentration ($[S]$).

  • $V_{\max}$ Estimation: Identifying the asymptote of the curve (e.g., $100\,\mu\text{M/min}$).

  • $K_m$ Determination: Finding the substrate concentration at $\frac{1}{2}V_{\max}$. If $V_{\max}$ is $100\,\mu\text{M/min}$, $K_m$ is found at the substrate concentration where the rate is $50\,\mu\text{M/min}$ (approx. $20\,\mu\text{M}$ in the presented example).

• Double Reciprocal Plot (Lineweaver-Burk): A linearization of the Michaelis-Menten equation ($y = mx + b$).     $\frac{1}{v} = \frac{K_m}{V_{\max}} \left( \frac{1}{[S]} \right) + \frac{1}{V_{\max}}$

  • X-axis: $\frac{1}{[S]}$

  • Y-axis: $\frac{1}{v}$

  • Y-intercept: $\frac{1}{V_{\max}}$. This is used to calculate the actual $V_{\max}$.

  • Slope ($m$): $\frac{K_m}{V_{\max}}$. Once $V_{\max}$ is known, $K_m$ is calculated from the slope.

  • This method is more accurate as it does not require visual estimation of an asymptote.

Enzyme Inhibitors in the Lab

• Phosphate: Acting as a product inhibitor since it is a direct product of the alkaline phosphatase reaction.

• Phenylalanine: An amino acid that inhibits alkaline phosphatase, despite lacking obvious structural similarity to the substrate.

• Acetazolamide (Diamox):

  • Clinically used to treat altitude sickness.

  • Inhibits both alkaline phosphatase and carbonic anhydrase (the latter helps humans adjust to high altitudes).

Classification of Inhibition Types

Competitive Inhibition

• Mechanism: The inhibitor ($I$) and substrate ($[S]$) compete for the same active site on the free enzyme ($E$).

• Characteristics:

  • $V_{\max}$ remains unchanged because high substrate concentrations can outcompete the inhibitor (the y-intercept on a Lineweaver-Burk plot does not change).

  • $K_m$ appears to increase (the x-intercept shifts closer to the origin).

• Dissociation Constant ($K_i$): Describes the affinity between enzyme and inhibitor. A lower $K_i$ indicates stronger binding.

• Calculation: The slope of the inhibited line is $\frac{K_m}{V_{\max}} \times \left( 1 + \frac{[I]}{K_i} \right)$.

Noncompetitive Inhibition

• Mechanism: Substrate and inhibitor bind to different sites. The inhibitor can bind to the free enzyme ($E$) or the enzyme-substrate complex ($ES$).

• Characteristics:

  • $V_{\max}$ decreases (the y-intercept increases).

  • $K_m$ remains unchanged (the x-intercept remains the same).

• Special Case: Pure noncompetitive inhibition occurs when the inhibitor has identical affinity ($K_i$) for both $E$ and $ES$. In this case, $\alpha = \alpha'$.

• Calculation: Either the slope ($\frac{K_m}{V_{\max}} \times (1 + \frac{[I]}{K_i})$) or the y-intercept ($\frac{1}{V_{\max}} \times (1 + \frac{[I]}{K_i})$) can be used to calculate $K_i$.

Uncompetitive Inhibition

• Mechanism: The inhibitor binds only to the enzyme-substrate ($ES$) complex at a site distinct from the active site. This typically requires a two-substrate reaction.

• Characteristics:

  • Both $V_{\max}$ and $K_m$ decrease.

  • The degree of decrease is proportional, resulting in a Lineweaver-Burk plot with parallel lines (slopes are identical).

Mixed Inhibition

• Mechanism: The inhibitor can bind to both $E$ and $ES$ but with different affinities ($K_i \neq K_i'$).

• Characteristics:

  • In a Lineweaver-Burk plot, the lines intersect at a point that is neither on the x-axis nor the y-axis.

  • Competitive-like: If the intersection is closer to the y-axis, the inhibitor favors binding the free enzyme.

  • Noncompetitive-like: If the intersection is closer to the x-axis, the inhibitor favors binding the $ES$ complex.

Case Study: Roundup (Glyphosate)

• Enzyme Target: EPSP synthase, found in plants and bacteria.

• Reaction: Converts shikimate-3-phosphate (S3P) and phosphoenolpyruvate (PEP) to EPSP and phosphate.

• Mechanism of Action:

  • Glyphosate mimics PEP.

  • It acts as an uncompetitive inhibitor with respect to shikimate-3-phosphate because it can only bind after S3P has already bound to the enzyme.

  • It acts as a competitive inhibitor with respect to PEP because it sits in the PEP binding site.

• Biological Impact: Plants cannot produce essential aromatic amino acids (Tyrosine, Phenylalanine, Tryptophan), leading to protein deficiency and death.

Case Study: Invertase and Substrate Inhibition

• Enzyme Task: Hydrolyzes sucrose (table sugar) into glucose and fructose.

• Inhibition Mechanism: High concentrations of sucrose cause a second molecule of sucrose to bind to the enzyme, blocking the catalytic reaction.

• Kinetic Signature: This represents a form of uncompetitive/substrate inhibition. At very high substrate concentrations, the activity actually decreases, causing the Lineweaver-Burk plot to curve upward.

Structural Flowchart for Inhibition Identification

1. Is there a change in $V_{\max}$?

   • No: Likely competitive inhibition (Confirm: $K_m$ should increase).

   • Yes: Proceed to compare $K_m$ values.

2. Compare $K_m$ and $K_m\text{-inhibited}$:

   • If $K_m = K_m\text{-inhibited}$, it is noncompetitive.

   • If $K_m > K_m\text{-inhibited}$ (a decrease), ask if slopes are equal:

     • Slopes equal: Purely uncompetitive.

     • Slopes not equal: Somewhere between noncompetitive and uncompetitive.

   • If $K_m < K_m\text{-inhibited}$ (an increase) but $V_{\max}$ decreased, it is in the mixed region between competitive and noncompetitive.