02d Basic equations effect of pH.pdf

What happens if the enzyme is active at alkaline, but not at acidic pH? ... Acid-base properties of amino acids side chains. Same pKa ... H+ in solution is H. 3. O+ ...
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Basic equations: effect of pH Analyzing the pH dependence of enzymatic reactions may be useful: To understand the mechanism To understand the enzyme’s function in the organism

Stomach pepsin

Liver Glucose-6-phosphatase

Basic equations: effect of pH The questions:

1. Which equation should we use to fit the experimental data?

The protonated enzyme is fully active

We call it E

2. What repreents the « pKa »? 100

Vi

80 60

The de-protonated enzyme is inactive

40

We call it EH

20

3

4

5

6

7 pH

8

9

10

pH +

S

ES H+

H+ Ka1

No reaction

80

Vi

E

100

60 40

Ka2

20 0 3

4

5

6

7 pH

EH +

S

k1

EHS

k2

E + products

k-1

How to derive the Michaelis equation? Usual hypothesis initial rates mass conservation (with [S] >>[E], so [S]total = [S]free) [E]total = sum of all forms of E Steady-state [ES]=constant NOTE THAT pH=-log of FREE |H+]

8

9

10

pH E+ S

ES H+

H+ Ka1 EH+ +

S

k1

No reaction

Ka2 EHS+

k2

k-1

[E]total = sum of all forms of E [E]total = [E] + [EH+] + [ES] + [ESH+] [H+] [E] Ka1= -----------[EH+] [H+]

[ES] Ka2= -----------[ESH+]

Ka1 [E] = [EH+] -----------[H+] Ka2 [ES] = [ESH+] -----[H+]

E + products

pH [E]total = [E] + [EH+] + [ES] + [ESH+] Ka1 [E] = [EH+] -----------[H+]

[H+] [E] Ka1= -----------[EH+] [H+]

[ES] Ka2= -----------[ESH+]

Ka2 [ES] = [ESH+] -----[H+]

Ka2 Ka1 +] [E]total = [EH+] -------- + [EH+] + [ESH+] -----+ [ESH +] + [H [H ]

[E]total =

[EH+]

Ka1 Ka2 + (-------- + 1)+ [ESH ] (------ + 1) [H+] [H+]

pH [E]total =

[EH+]

Ka2 Ka1 + (1+ -------)+ [ESH ] (1+ ------) [H+] [H+] X2

X1

[E]total = [EH+] X1 + [ESH+] X2 Next step: steady-state E + S H+

H+ Ka1 EH +

S

k1

ES

No reaction

Ka2 EHS

k2

k-1

k1 [EH] [S] = (k –1 + k 2) [EHS] [EH] = (k –1 + k 2)/ k1 [EHS]/[S]

E + products

pH [E]total = [EH+] X1 + [ESH+] X2 [EH] = (k –1 + k 2)/ k1 [EHS]/[S]

(k –1 + k 2)/ k1 = Km

[E]total = [ESH+] Km/[S] X1 + [ESH+] X2 V = k2 [EHS] k2 [E]total V = --------------------------Km/[S] X1 + X2 Vmax [S]/X2 V = --------------------------Km X1/X2 + /[S]

pH Vmax [S]/X2 V = --------------------------Km X1/X2 + /[S]

Vmaxapp =

Vmax

Vmaxapp [S] V = ----------------Kmapp + /[S]

1 ---------------Ka2 1 + -----[H+]

Ka1 1 + -----[H+] app Km = Km----------------Ka2 1 + -----[H+]

Vmaxapp Vmax 1 ----- = ------- -----------Kmapp 1 + Ka1 -----Km [H+]

Vmaxapp ------------ is a function of the Ka of the FREE enzyme (it can be Kmapp measured directly)

pH

Vmaxapp Vmax ----Kmapp

1

= ------- -----------Ka1 1 + -----Km [H+]

Vmaxapp =

Ka1 1 + -----[H+] Kmapp = Km----------------Ka2 1 + -----[H+]

Vmax

1 ---------------Ka2 1 + -----[H+]

Last step: verify that the equation describes our experiment: In acid medium [H+]>>Ka2 Vmaxapp = Vmax In alkaline medium, [H+]