A thermodynamics problem. Please provide legible, reproducible soln so I can try

Question

A thermodynamics problem.

Please provide legible, reproducible soln so I can try solving it on my own learning from yours.

Many thanks in advance,

2. Prostaglandins (PGs) are molecules associated with inflammation, fevers, and pain. PGs are produced from precursor molecules via the action of an enzyme known as prostaglandin endoperoxide synthase (PES). PES is a member of the cyclooxygenase family of enzymes, which are major drug targets for the treatment of pain. Some kinetic data for PG synthesis by a particular PES are given ISI (mM) Rate of formation of PG (mMImin) Rate of formation of PG with 10 mg/mL ibuprofen (mM/min 23.5 16.67 0.5 25.25 32.2 30.49 36.9 37.04 2.5 41.8 440 38.91 3.5

Explanation / Answer

Michelis- Menten kinetics is V=Vmax*S/(KM+S)

The above equatino can be written as

1/V= (KM/Vmax)1/S+ 1/Vmax . This plot is known as Lineweaver–Burk plot

the data on 1/V vs 1/S in the presence and absence of inhibitor is drawn and shown below

In the absence of inhibitor 1/Vmax ( intercept) = 0.019, Vmax= 1/0.019= 52.63 mM/min

Slope is Km/Vmax= 0.011, KM= 52.63*0.011 =0.5789 mM

since the intercept in the presence of inhibitor remains the same, this is called competitive inhibition.

in case of competitive inhibition

1/V= (KMapp/Vmax)*1/S +1/Vmax where Vmax= 52.63 mM/min

KMapp/Vmax ( slope of 1/V vs 1/S in presence of ibuprofen)= 0.020

KMapp =0.020*52.63=1.053

KMapp = (1+I/KI)= 1.053

I/KI= 0.053

KI= 10mg/ml/ 0.053 = 188.7 mg/ml

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