BME210
Spring2008
1
Homework 2
ReceptorLigand Kinetics
Solution – 100 points
Part 1 – Problem Setup
Introduction
An important goal of biomedical engineering is to understand cell behavior in terms of its molecular properties.
Central to this understanding is the knowledge of how cell membranebound receptors interact with ligands to
direct cell proliferation and protein synthesis (intercellular signaling). Moreover, receptors and their ligands are
ideal candidates for molecular manipulation, thereby allowing for the modification of receptorligand association
and dissociation rates and therefore intracellular signaling activities.
This homework assignment will explore the kinetics of the following receptor ligand interaction:
(1)
which represents a receptor model with one binding site and two conformational states. In Eq.(1), L and R
represent the concentration of ligand and receptor, respectively (unit:nMol). RL1 and RL2 denote the
concentration (in nMol) of the two receptorligand conformation states. The rate constants K1, K2, K3 and K4
are in units of 1/sec.
The 4 equations describing the mass balance of L, R, RL1 and RL2 in this reaction are as follows:
( )
2*
1( )
1*
( )*
( )
( )
2*
1( )
1*
( )*
( )
1( )
4*
2( )
(
2
3)*
1( )
1*
( )*
( )
2( )
3*
1( )
4*
2( )
dL t
K
RL
t
K
L t
R t
dt
dR t
K
RL
t
K
L t
R t
dt
dRL
t
K
RL
t
K
K
RL
t
K
L t
R t
dt
dRL
t
K
RL
t
K
RL
t
dt
=
−
=
−
=
−
+
+
=
−
One of the algorithms used to solve ordinary differential equations is RungeKutta 2
nd
order (RK2) algorithm.
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 Spring '07
 D'Argenio
 Biomedical Engineering, Cell Signaling, 1 %, Ligand Receptor RL1, Receptor RL1 RL2

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