The Lineweaver-Burk

To analyze the activity of alkaline phosphatase at different substrate concentrations, a continuous assay was conducted, where the absorbance (at 400 nm) of the enzyme-substrate solution was monitored and recorded over the course of 70 seconds at 10 second increments. This assay was used to determine the rate at which alkaline phosphatase can dephosphorylate p-nitrophenyl phosphate to p-nitrophenol, which then dissociates to phenolate ion, which causes the solution to turn yellow in a solution at a pH of 9.0 (assumed optimum pH) (McCollam-Guilani, p.71). The color change causes the change in absorbance measured by the spectrophotometer.

The rate (V0) was calculated by plotting the absorbance against time, where the slope of the line indicates

the rate in Δ Absorbance/second. This was done for different concentrations of p-nitrophenyl phosphate. The equation: c = A/εb, was used to convert the rate to have units of concentration/second.
A Lineweaver-Burk plot was created using the inverse of the substrate concentrations and the inverse of the rates (in μmol/sec.), to determine the Km¬ and Vmax¬. From the calculated linear regression line, the y-intercept (1/Vmax) was used to determine the value of Vmax, and the slope of the line (Km/Vmax¬) was used to determine the Km ¬value. The Km and Vmax values were also determined by fitting the collected data to a Michaelis-Menten plot (non-linear regression) though the use of the Solver program in Excel, which was done to minimize the error present in a Lineweaver-Burk plot.
The Vmax is the maximal rate at which the enzyme can function and catalyze a reaction.

The Vmax values, as determined from the Lineweaver-Burk plot, for the uninhibited, half uninhibited, and inhibited enzymes were, 0.3647, 0.1262, and 0.3087 μmol/min respectively. The non-linear regression V¬max¬ values for the same enzyme were 0.3343 (9.09% error as compared to Lineweaver-Burk plot), 0.1264 (0.16% error), and 0.2694 μmol/min (14.6% error) respectively. The differences in the values are due to the presence of error introduced by a Lineweaver-Burk plot, where data points at higher and lower substrate concentrations are weighed differently (Tymoczko, p.115). This error is the reason why a Michaelis-Menten plot is preferred.

The Vmax for the inhibited reaction was lower than the Vmax for the normal uninhibited reaction, because Orthophosphate inhibitor prevented the enzyme from dephosphorylating the p-nitrophenyl, decreasing the maximal rate of reaction. The Vmax¬ for the reaction where only half of the original enzyme was present was the lowest, because there was less enzyme available. In the Michaelis-Menten plot, the line for the half enzyme uninhibited reaction is the furthest to the right and the curve does not extend as far up, because there is less available enzyme that can be saturated by the

substrate.
Km is the substrate concentration at which half the maximal velocity is reached. A higher Km indirectly indicates that a higher concentration of substrate is required for the reaction to reach half its Vmax¬ (McCollam-Guilani, p.75) The Km values determined from the Lineweaver-Burk plot, for the uninhibited, half uninhibited, and inhibited enzymes were, 0.1768, 0.0827, 0.4193 mM respectively. The non-linear regression Km¬ values for the enzyme were 0.1504 (17.6% error), 0.0827 (0% error), and 0.3433 mM (22.1% error) respectively. Just as with the Vmax¬ values, there is variability due to error. Both the normal uninhibited and inhibited enzymes had a higher Km¬, indicating that a higher substrate concentration was needed to reach Vmax¬/2.
The Kcat is the “number of substrate molecules that an enzyme can convert into product per unit time when the enzyme is fully saturated with substrate” (Tymoczko, p.

116). Catalytic efficiency deals with how efficiently an enzyme can encounter the substrate and cause the reaction to proceed to products. The Kcat’s for the uninhibited, half uninhibited, and inhibited enzymes were calculated to be 1528.2, 1155.7, and 1231.5 min-1 and the catalytic efficiencies were calculated to be 10161.1, 13974.1, and 3587.4 min¬¬-1 mM-1. The turnover number (K¬¬cat) for the half uninhibited and inhibited reactions were smaller than that of the normal uninhibited alkaline phosphatase, because there was less functional enzyme present, which prohibited the formation of more product and therefore a less intense color change. The catalytic efficiency of the half uninhibited enzyme was higher than the normal uninhibited enzyme, because the likelihood of the enzyme encountering the enzyme was higher, since the ratio of enzyme to substrate decreased. The catalytic efficiency for the inhibited enzyme was lower, because the concentration of enzyme stayed the same and the inhibitor blocked the

reaction.
The Orthophosphate inhibitor acts as a competitive inhibitor. Looking at the Lineweaver-Burk plot, the point of intersection on the y-axis for the uninhibited and inhibited enzyme is around the same point. The calculated Km values differ a lot from one another, which is represented on the plot (x-intercepts are far apart). This is based on the basic definition of a competitive inhibitor, where the Km increases, and Vmax stays the same (or relatively the same in this case due to slight error).
One possible source of error could be the assumption that the optimal pH is 9. If this is not the optimal pH, the enzyme’s catalytic efficiency and overall functional will not be at its maximal potential. Another source of error could be due to ineffective mixing of the solution upon addition of the enzyme. This would result in a lower absorbance reading.
Catalytic inhibition is clinically important when it comes to antibiotic use. Penicillin, for example, inhibits the enzyme transpeptidase in gram positive bacteria. Due to suicide inhibition, the bacteria can no longer function properly as a pathogen and reproduce sufficiently. Without the production of a cell wall, the bacteria can be more readily targeted by immune cells, which would then eliminate the pathogen from the body (Yocum, 1980).