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BME 210 – Homework 2
ReceptorLigand Kinetics
Solutions  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 (intracellular 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 receptorligand 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, in units of nMolar, while
RL
1 and
RL
2
denote the concentration (in nMolar) of the two receptorligand conformation states. The rate constants
k
1
,
k
2
, k
3
, and
k
4
are in units of 1/sec.
R = K
1
*R*L  K
6
*R*L + K
2
*RL1 + K
5
*RL2
(2)
L = K
1
*R*L  K
6
*R*L + K
2
*RL1 + K
5
*RL2
(3)
RL1 = K
1
*R*L  K
2
*R*L + K
4
*RL2  K
3
*RL1
(4)
RL2 = K
7
*RL2  K
4
* RL2
 K
5
* RL2 + K
3
* RL1 + K
6
* L * R
(5)
where the variables are sharing the same names as in Eq.(1).
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2
One of the algorithms solving ordinary differential equations is the Euler’s method, which
provides a procedure for approximating the value of the function
x
at time
t+h (i.e. x(t+h))
given a value of
the function x at time
t (i.e. x(t)): x(t+h)=x(t)+h*f(x(t))
where
h
is the step size of the approximating
propagation, and
f(x)
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 Spring '07
 D'Argenio
 Biomedical Engineering, steady state values, run2

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