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Homework_2 Solutions

# Homework_2 Solutions - BME 210 Homework 2 Receptor-Ligand...

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1 BME 210 – Homework 2 Receptor-Ligand 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 membrane-bound 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 receptor-ligand 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, in units of nMolar, while RL 1 and RL 2 denote the concentration (in nMolar) of the two receptor-ligand 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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Homework_2 Solutions - BME 210 Homework 2 Receptor-Ligand...

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