inhibited enzyme kinetics inhibitors may bind to enzyme and reduce their activity. enzyme inhibition...
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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.