Enzyme kinetics and Kcat

[MedGen]

I've been given this question as a part of a revision tutorial. I've already done the calculations but was wondering if anyone could point out any glaring errors. This is not an assessed piece of work, so strictly not homework per se.

 

The turnover number of carbonic anhydrase:

Carbonic anhydrase of erythrocytes (Mr 30,000) has one of the highest turnover numbers among known enzymes, it catalyses the reversible reaction of CO2:

 

H2O + CO2 -> H2CO3

This is an important process in the transport of CO2 from the tissues to the lungs.

If 10μg of pure carbonic anhydrase catalyses the hydration of 0.30g of CO2 in 1min at 37°C at Vmax, and the reaction volume is 1ml. What is the turnover number (Kcat) of carbonic anhydrase expressed in units of per min and per sec)? Mr of CO2 is 44.

 

 

So here are my calculations:

Kcat = Vmax/[E]t, where [E]t is the total enzyme concentration in M or mol/ltr.

Vmax is the at which all active sites are fully saturated. This is given as 0.30g after 1mins.

 

Reaction volume=1ml

Protein content = 10μg

Therefore [E]t is 10μg/ml, this needs to be expressed as M or mol/ltr.

M=g/ltr x mol/g

 

So carbonic anhydrase Mr = 30,000 or 30,000g/mol. Take the reciprocal = 1/30,000 = 3.3E-05.

There are 10μg/ml of volume, so convert to g/ltr = 0.01,.

Now [E]t = 0.01 x 3.3E-05

=3.3E-07 mol/ltr or M

 

Vmax= 0.30g in 1mins in 1ml.

Mr CO2 = 44, [CO2] = same base calculations as [E]t. (calculating mol/ltr)

=0.068mM

 

So Kcat=Vmax/[E]t

=0.068mM/3.3E-04mM

=204 mM per sec and

=12240 mM per min.