Homework_2_solution - BME210 Spring2008 Homework 2...

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BME210 Spring2008 1 Homework 2 Receptor-Ligand 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 membrane-bound 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 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 (unit:nMol). RL1 and RL2 denote the concentration (in nMol) of the two receptor-ligand 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* ( )* ( ) 4* 2( ) ( 2 3)* 2( ) 3* 1( ) 2( ) dL t KR L tK L t R t dt dR t L L t R t dt dRL t L t K K R L L t R t dt dRL t L tKR L t dt =− ++ One of the algorithms used to solve ordinary differential equations is Runge-Kutta 2 nd order (RK2) algorithm.
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Homework_2_solution - BME210 Spring2008 Homework 2...

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