Inhibited Enzyme Kinetics Inhibitors may bind to enzyme and reduce their activity. Enzyme inhibition...
Transcript of Inhibited Enzyme Kinetics Inhibitors may bind to enzyme and reduce their activity. Enzyme inhibition...
Inhibited Enzyme Kinetics
• Inhibitors may bind to enzyme and reduce their activity.
• Enzyme inhibition may be reversible or irreversible.
• For reversible enzyme inhibition, there are
-
-
-
Inhibited Enzyme Kinetics
• Competitive inhibitors (I)
- substrate analogs
- compete with substrate for the active site of the enzyme
K1
EPk
ES 2E+SK-1
+
I
EI
K I
Inhibited Enzyme Kinetics
• Competitive inhibitors (I)
Assume rapid equilibrium and with the definitions of
][][][]0[ EIESEE
][][
2ESk
dt
Pdv
][
]][[
1
1'ES
SE
k
kmK
][
]][[
EI
IEIK
Inhibited Enzyme Kinetics• Competitive inhibitors (I),
we can obtain,
][)/][1('
][
SIKImK
SmVv
][',
][
SappmK
SmVv
)/][1('', IKImKappmK When [I] =0, ''
, mKappmK
mV Remains that of Michaelis-Menten equation.
appmK , is .
Inhibited Enzyme Kinetics
• Noncompetitive inhibitors (I)
- not substrate analogs
- bind on .
EPk
ES 2E+S+
I
EI+S
K I
+
I
ESI
K IKm’
Km’
Inhibited Enzyme Kinetics
• Noncompetitive inhibitors (I)
Assume:
- rapid equilibrium
- same equilibrium constants of inhibitor binding to E and ES KI
- same equilibrium constants of substrate binding to E and EI Km’
Inhibited Enzyme Kinetics
• Noncompetitive inhibitors (I)
][][][][]0[ ESIEIESEE
][][
2ESk
dt
Pdv
][
]][[
][
]][[
1
1'ESI
SEI
ES
SE
k
kmK
][
]][[
][
]][[
ESI
IES
EI
IEIK
Inhibited Enzyme Kinetics• Noncompetitive inhibitors (I)
we can obtain,
])[')(/][1(
][
SmKIKI
SmVv
]['
][,
SmK
SappmVv
)/][1/(, IKImVappmV When [I] =0, mVappmV ,
appmV ,
remains in Michaelis-Menten equation.mK
is .
Inhibited Enzyme Kinetics
• Uncompetitive inhibitors (I)
- have no affinity for itself
- bind only to the .
Assume rapid equilibrium,
EPk
ES 2E+S+
I
ESI
K I
Km’
Inhibited Enzyme Kinetics
• Uncompetitive inhibitors (I)
][][][]0[ ESIESEE
][][
2ESk
dt
Pdv
][
]][[
1
1'ES
SE
k
kmK
][
]][[
ESI
IESIK
Inhibited Enzyme Kinetics• Uncompetitive inhibitors (I)
we can obtain,
][))/][1/('(
]))[/][1/((
SIKImK
SIKImVv
][,'
][,
SappmK
SappmVv
)/][1/(, IKImVappmV )/][1/('', IKImKappmK
mVmKappmVappmK /',/', - in Lineweaver-
Burk Plot
Inhibited Enzyme Kinetics
• Uncompetitive substrate inhibitors
- can cause inhibition at substrate concentration
- bind only to the .
Assume rapid equilibrium,
EPk
ES 2E+S+
S
ES2
K SI
Km’
Substrate Inhibition
Inhibited Enzyme Kinetics
• Uncompetitive substrate inhibitors (I)
][][][]0[ 2ESESEE
][][
2ESk
dt
Pdv
][
]][[
1
1'ES
SE
k
kmK
][
]][[
2ES
SESSIK
Inhibited Enzyme Kinetics• Uncompetitive substrate inhibitors (I)
we can obtain,
SIKSSmK
SmVv/2][]['
][
]['][
SmK
SmVv
At low substrate concentration SIKS /2][ <<1
SIKS
mVv/][1
At high substrate concentration 1]/[' SmK
Michaelis-Menten Equation
Inhibited Enzyme Kinetics• Uncompetitive substrate inhibitors (I)
The substrate concentration resulting in the maximum reaction rate can be determined by setting dv/d[S]=0, [S]max is given by
0][/)/2][]['
][(][/
Sd
SIKSSmK
SmVdSddv
2/1)'(max][ SIKmKS
2/1)'(max][
0/2]['
0)2)/2][]['(
/2]['
0)2)/2][]['(
)/][21]([)/2][]['((
0)2)/2][]['(
)/][21]([(
/2][]['
0][/)/2][]['
][(][/
SIKmKS
SIKSmVmKmV
SIKSSmK
SIKSmVmKmV
SIKSSmK
SIKSSmVSIKSSmKmV
SIKSSmK
SIKSSmV
SIKSSmK
mV
Sd
SIKSSmK
SmVdSddv
• Uncompetitive substrate inhibitors (I) Determine [S]max:
Inhibition Estimation
• Product formation rate v ~ [S]: v has a peak?
If yes, then it’s substrate inhibition. - get [S]max from the plot of v~[s].- at low substrate concentration, obtain Vm and Km’ graphically or through direct calculation.- calculate KI through
If no, then examine the data with and without inhibitors in 1/v ~ 1/[S] plot (Lineweaver-Burk Plot).
2/1)'(max][ SIKmKS
Estimation of Inhibited Enzyme Kinetics
Estimation of Inhibited Enzyme Kinetics
• Determine the type of inhibition.
• Determine the parameters for Michaelis-Menten equation without inhibition.
• Determine the parameter of KI for inhibited kinetics.
Summary of Inhibited Kinetics
• For reversible enzyme inhibition, there are
- competitive
- noncompetitive
- uncompetitive- substrate inhibition
• Determine parameters for all these types of inhibition kinetics.