Question

The enzyme known as chucknorrisase is a very power catalyst. A study was conducted that varied substrate concentration (in mM) and measured the corresponding rate (mM/min). The study used 180 nM enzyme. The resulting Lineweaver-Burke plot yielded a straight line with the linear equation y = 71.5 x + 999. What is the catalytic efficiency for this enzyme with its substrate?

77.8 M-1s-1
		7.69 x 10-4 M-1s-1
		1300 M-1s-1
		77,800 M-1s-1
		4.68 x 106 M-1s-1

Answer 1

Given that [E] = 180 nM = 180 x 10^-9 M

We know that

catalytic efficiency = Kcat/Km

Kcat = Vmax/[E]

Km = -1/ x-intercept

Vmax = 1/ y-intercept

Equation of straight line in intercept form is x/a + y/b = 1 where a = x -intercept , b = y-intercept

Given equation y = 71.5 x + 999

71.5x -y = -999

(71.5x/-999)+ ( -y/-999 )= 1

  (x/-999/71.5)+ ( y/999 )= 1

Hence, x-intercept = -999/71.5, y-intercept = 999

Then,

Km = -1/ x-intercept = -1/ (-999/71.5) = 71.5/999

Vmax = 1/ y-intercept = 1/999

Then,

Kcat = Vmax/[E] = (1/ 999 ) / (180 x 10^-9 ) = 1/ [999 x 180 x 10^-9 ]

Therefore,

catalytic efficiency = Kcat/Km

= 1/ [999 x 180 x 10^-9 ] / 71.5/999

= 1/ (71.5 x 180 x 10^-9 )

= 77700 M-1s-1

Therefore,

catalytic efficiency for this enzyme = 77700 M-1s-1