hw2solution _1

hw2solution _1 - BME210 Spring 2009 Receptor-Ligand...

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BME210 Spring 2009 1 Receptor-Ligand Kinetics Solutions - 100 points Part 1: Report Summary The N-methly-D-aspartate (NMDA) receptor for the excitatory neurotransmitter glutamate is the primary neurotransmitter in the central nervous system. Its kinetics of a simplified receptor-ligand 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 receptor-ligand 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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BME210 Spring 2009 2 The differential equation can be solved byseveral different numerical methods such as Euler method, Runge-Kutta 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.

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hw2solution _1 - BME210 Spring 2009 Receptor-Ligand...

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