Determine the Michaelis constant (K_M) and maximum catalytic velocity (V_max) for alkaline phosphatase-catalyzed hydrolysis of 4-nitrophenyl phosphate using initial-rate spectrophotometry at 405 nm and Lineweaver-Burk double-reciprocal regression analysis. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
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Adjust substrate concentration V, then weigh the dispensed aliquot.
Mass observations are determined by the high-precision thermodynamic equation of state for pure liquid water. Readings reflect thermal equilibrium and analytical balance force restoration.
The spectrophotometric determination of Michaelis-Menten kinetic parameters using the Lineweaver-Burk double-reciprocal transformation is subject to distinct systematic, physical, and mathematical boundary constraints: (1) Reciprocal Error Amplification: The linear inversion 1/v₀ vs 1/[S] distorts homoscedastic Gaussian experimental errors into heteroscedastic distributions, causing data points at the lowest substrate concentrations to carry disproportionate statistical leverage in ordinary least-squares regression; (2) Product Inhibition Threshold: Alkaline phosphatase is subject to potent competitive feedback inhibition by its enzymatic cleavage product, inorganic orthophosphate (P_i, K_i ≈ 1.0–2.0 mM). If initial rate tracking extends beyond 5% substrate turnover, accumulating phosphate depresses the measured velocity, leading to an artificially elevated apparent K_M; (3) Buffer and Ionic Strength Effects: Alkaline phosphatase catalytic velocity depends strongly on ionic strength and the chemical nature of the buffer system; transphosphorylation can occur in certain amine buffers (e.g., diethanolamine), elevating observed velocities relative to inert non-nucleophilic buffers like Tris; (4) Substrate Solubility and Inactivation: At extreme substrate concentrations ([S] > 10 mM), high ionic strength can alter protein conformation or cause substrate inhibition; and (5) Enzyme Thermal and Proteolytic Inactivation: Purified alkaline phosphatase is susceptible to trace proteolytic contaminants or thermal denaturation if kept at room temperature for extended periods, necessitating cold storage of enzyme stocks until seconds before assay initiation. Alkaline Phosphatase (EC 3.1.3.1) | Substrate: 4-Nitrophenyl Phosphate (4-NPP) | Product: 4-Nitrophenolate (ε₄₀₅ = 18,500 L·mol⁻¹·cm⁻¹ at pH 9.80) | K_M = 0.500 mM, V_max = 40.0 μM/min (0.0400 mM/min)
Provides monochromatic radiation at λ = 405 nm with a peltier-controlled thermostated cuvette holder regulated to 25.00 ± 0.05 °C and photometric absorbance stability better than ± 0.0002 AU/hr.
Contains reference buffer blank and active reaction cocktail with verified pathlength tolerance of ± 0.005 cm and optical transmittance matching within 0.1% across the near-UV and visible spectra.
Dispenses micro-volumes of substrate (4-NPP), magnesium cofactor, and enzyme stock solution with systematic volumetric inaccuracies strictly below 0.35% and CV < 0.2%.
Provides highly purified calf intestinal alkaline phosphatase formulated at 0.050 mg/mL in 0.050 M Tris-HCl buffer (pH 9.80) containing 1.0 mM MgCl₂ and 0.1 mM ZnCl₂ metallo-cofactors.
Supplies pure substrate solutions prepared across a dynamic range from 0.200 mM to 3.000 mM in 0.050 M Tris-HCl buffer (pH 9.80 at 25.0 °C).
Records real-time continuous optical absorbance data at 10 Hz, executes automated baseline subtraction, and determines linear initial reaction rates (dA/dt) over the initial 30–60 seconds prior to substrate depletion.
Determine the Michaelis constant (K_M) and maximum catalytic velocity (V_max) for alkaline phosphatase-catalyzed hydrolysis of 4-nitrophenyl phosphate using initial-rate spectrophotometry at 405 nm and Lineweaver-Burk double-reciprocal regression analysis. Suggested independent volumetric settings: 0.2, 0.35, 0.5, 0.8, 1.5, 3.0 mM.
Power on the UV-Vis spectrophotometer and allow deuterium and halogen lamp sources to stabilize for 30 minutes. Configure the monochromator to λ = 405 nm with a spectral bandwidth of 1.0 nm. Fill both sample and reference matched quartz cuvettes with 0.050 M Tris-HCl buffer (pH 9.80) containing 1.0 mM MgCl₂. Insert into the peltier cell holder equilibrated to 25.00 ± 0.05 °C and perform automatic zero absorbance and 100% transmittance autozero calibrations.
From a freshly prepared 20.00 mM stock solution of 4-nitrophenyl phosphate disodium hexahydrate in 0.050 M Tris-HCl (pH 9.80), prepare a series of six graded substrate assay solutions using calibrated volumetric micro-dispensers: 0.200, 0.350, 0.500, 0.800, 1.500, and 3.000 mM. Maintain all substrate vials in an insulated thermal block at 25.0 °C and verify absence of non-enzymatic spontaneous hydrolysis by verifying baseline absorbance A₄₀₅ < 0.005 AU.
For each concentration level, transfer 2.900 mL of pre-warmed substrate-buffer solution into the sample cuvette. Place the cuvette in the spectrophotometer cell chamber and allow 120 seconds for precise thermal equilibration. Rapidly initiate the reaction by injecting exactly 100 μL of standardized alkaline phosphatase enzyme stock using a positive-displacement micropipette, quickly cap the cuvette, invert three times to establish homogeneous mixing within 2 seconds, and immediately close the chamber lid.
Initiate automated data acquisition at 100 ms intervals for a total duration of 120 seconds. Monitor the continuous absorbance evolution at 405 nm as colorless 4-NPP converts to bright yellow 4-nitrophenolate. Inspect the progression curve for the initial linear steady-state window (typically 10 to 60 s post-mixing), verify that total substrate conversion remains strictly below 5% of [S]₀ to prevent product inhibition, and compute the linear regression slope (dA/dt) in AU/min.
Convert the measured absorbance rate (dA/dt) into the true initial reaction velocity v₀ (in μmol·L⁻¹·min⁻¹ or μM/min) applying the Beer-Lambert law: v₀ = [(dA/dt) / (ε₄₀₅ · l)] · 10⁶, utilizing the certified molar absorptivity of the 4-nitrophenolate dianion at pH 9.80 (ε₄₀₅ = 18,500 L·mol⁻¹·cm⁻¹) and optical pathlength l = 1.000 cm. Repeat triplicate trials for each substrate concentration and calculate mean initial velocities.
Tabulate reciprocal substrate concentrations x = 1/[S] (in mM⁻¹) and reciprocal initial velocities y = 1/v₀ (in min·mM⁻¹). Perform unweighted linear least-squares regression: y = m · x + b. Extract the maximum velocity V_max = 1/b (in mM/min or μM/min), calculate the Michaelis constant K_M = m · V_max = m / b (in mM), determine the catalytic turnover frequency k_cat = V_max / [E]₀, and compute the second-order catalytic efficiency specificity constant k_cat / K_M.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
| # | Substrate concentration [S] (mM) (mM) | Initial reaction velocity v₀ (μM/min) | Reciprocal substrate concentration 1/[S] (mM⁻¹) | Reciprocal initial velocity 1/v₀ (min·mM⁻¹) | Remove |
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