Consider the following kinetic parameter for a given enzyme:
Km=4.7x10-5 M
Vmax= 22 nmol/min/mg
[i]=5x10-1 mM
[s]=2x10-4 M
Ki=3x10-4 M
Calculate the rate of product formation in the presence of a competitive inhibitor.
I know that I have to solve for Vo. I also know that I need to convert the concentrations so that they are all alike so they will work in the equation, but the Vmax concentration he gave me is confusing. On every problem we did he gave us moles/(volume)/(time) which is what it should be, and in this problem it is almost like he is giving the me the specific activity of the enzyme. How would i convert Vmax into something useable for the equation for inhibitors?
To calculate the rate of product formation (Vo) in the presence of a competitive inhibitor, you need to first understand how Vmax is used in the equation. Vmax represents the maximum velocity of the enzyme-catalyzed reaction when the enzyme is saturated with substrate. In this case, Vmax is given as 22 nmol/min/mg, which means it is expressed in terms of enzyme activity (nmol/min) per unit mass (mg).
To make Vmax compatible with the units used for the concentrations, you need to convert it to a molar quantity. Here's how you can do it:
1. Convert Vmax from nmol/min to mol/min:
Vmax = 22 nmol/min/mg * (1 mol/10^9 nmol) * (1 min/60 s)
= 2.2 × 10^-8 mol/s/mg
2. Convert Vmax from mol/s/mg to mol/min/mg:
Vmax = 2.2 × 10^-8 mol/s/mg * (60 s/1 min)
= 1.32 × 10^-6 mol/min/mg
Now that Vmax is in mol/min/mg, you can use it in the equation for competitive inhibition. The equation for Vo in the presence of a competitive inhibitor is:
Vo = (Vmax * [S]) / (Km * (1 + ([I] / Ki)))
Where [S] is the substrate concentration, [I] is the inhibitor concentration, Km is the Michaelis constant, and Ki is the inhibition constant.
Make sure to use the appropriate units when plugging in the values:
[S] = 2 x 10^-4 M
[I] = 5 x 10^-1 mM (convert to M by dividing by 1000)
Km = 4.7 x 10^-5 M
Ki = 3 x 10^-4 M
Vo = (1.32 × 10^-6 mol/min/mg * 2 x 10^-4 M) / (4.7 x 10^-5 M * (1 + (5 x 10^-1 mM / 3 x 10^-4 M)))
Now, substitute the values and calculate Vo.