Enzyme kinetics

Cytochrome P450 bound to

Its substrate camphor

L-serine + indole derivative produces L-tryptophan

Lock and key model

• Proposed by Emil Fischer in 1890

Induced fit model

𝑉 = 𝑘[𝐴]

𝑘

𝑉 = 𝑘 𝐴 [𝐵]

𝑉𝑜 = 𝑉𝑚𝑎𝑥[𝑆]

𝑆 + 𝐾𝑀

𝐾𝑀 =𝑘

− 1 + 𝑘2

𝑘1

K+1[E][S] = k-1 + k2[ES]

𝐸 [𝑆]

[𝐸𝑆]=

(k−1 + k2)

k+1= 𝐾𝑀

KM

• If,

• Then it is independent of both

– Substrate concentration

– Enzyme concentration

= (k−1 + k2)

k+1

𝐾𝑀

𝑉 = 𝑉𝑚𝑎𝑥

[𝑆]

𝑆 + 𝐾𝑚

𝑉 = 𝑉𝑚𝑎𝑥

[𝑆]

𝑆 + 𝐾𝑚

𝑉 =𝑉

𝑚𝑎𝑥

𝐾𝑚 [S]

X

𝑉 = 𝑉𝑚𝑎𝑥[𝑆]

𝑆 + 𝐾𝑚

𝑉 = 𝑉𝑚𝑎𝑥

X X X

𝑉 = 𝑉𝑚𝑎𝑥[𝑆]

𝑆 + 𝐾𝑀

𝐾𝑀 If = 𝑆

Then 𝑉 = 𝑉𝑚𝑎𝑥[𝑆]

𝑆 + [𝑆]

Thus V = Vmax/2

𝐾𝑀 = (k−1 + k2)

k+1=

𝐸 𝑆

[𝐸𝑆]

𝐾𝑀 = (k−1 + k2)

k+1=

𝐸 𝑆

[𝐸𝑆]

X

𝐾𝑀 = k−1k+1

=𝐸 𝑆

[𝐸𝑆]

Thus

Large KM weak binding, small KM strong binding

Under these conditions KM tells us the enzyme-substrate affinity

𝑉𝑚𝑎𝑥 = 𝑘2 𝐸 𝑇

Significance of Vmax

𝑉𝑚𝑎𝑥 = 𝑘2[𝐸𝑇] 𝑉 = 𝑉𝑚𝑎𝑥

[𝑆]

𝑆 + 𝐾𝑚

𝑉 =𝑘2

𝐾𝑀

𝐸𝑇 [𝑆]