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BME210
Spring 2009
1
ReceptorLigand Kinetics
Solutions  100 points
Part 1: Report Summary
The NmethlyDaspartate (NMDA) receptor for the excitatory neurotransmitter
glutamate is the primary neurotransmitter in the central nervous system. Its kinetics of
a simplified receptorligand model works like following diagram.
Fig.1 kinetics of NMDA model
Using the principle of mass action assuming first order kinetics, we can derive
the differential equations of the receptor ligand kinetics.
LD
K
LR
K
dt
dLD
P
LR
dt
dP
LR
K
LD
K
LR
P
LR
K
LR
L
K
dt
dLR
LR
K
LR
L
K
LR
L
K
R
L
K
dt
dLR
LR
L
K
R
L
K
dt
dR
LR
K
LR
L
K
LR
L
K
R
L
K
dt
dL
r
d
open
open
d
r
open
off
on
off
on
off
on
off
on
off
on
off
on
−
=
⋅
−
⋅
=
−
+
⋅
−
⋅
+
−
⋅
=
+
⋅
−
⋅
−
⋅
=
⋅
+
⋅
−
=
+
⋅
−
⋅
+
⋅
−
=
2
2
2
2
2
2
2
2
2
2
2
2
2
2
β
α
(1)
Where L and R represent the concentration of ligand and receptor, LR and LR2 denote
the concentration of the two receptorligand conformation states,
LD desensitized
form of LR2 and P
oepn
is proportional to the probability of channel opening (units:
micro molar
M
μ
)
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View Full Document BME210
Spring 2009
2
The differential equation can be solved byseveral different numerical methods
such as Euler method, RungeKutta Method of order 2 (RK2) etc. In this project, RK2
algorithm is utilized to approximate the solution of multiple differential equations.
The RK2 method approximates the value of the function x at time t+h through the
value of the function x at time t and slope at time t+h/2, as depicted in Fig. 2.
Fig.2 RK2 method
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This note was uploaded on 04/12/2009 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.
 Spring '07
 D'Argenio

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