Assignment 3

# Assignment 3 - AMATH/BIOL 382 Assignment 3 Due 1 Consider...

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AMATH/BIOL 382 Assignment 3 Due February 12, 2010 1. Consider the metabolic chain indicated below. Take the reaction kinetics as v 3 S v 1 v 2 S 1 2 v 1 = V max 1 v 2 = V max 2 s 1 K m 2 + s 1 v 3 = V max 3 s 2 K m 3 + s 2 You will investigate the sensitivity of the steady state with respect to the parameter V max 2 . i) Take nominal parameter values of V max 1 = 1, V max 2 = 2, V max 3 = 4, K m 2 = 4, and K m 3 = 3. Find the corresponding steady state by simulating the system and observing the long-time behaviour. ii) Determine how sensitive the steady-state ( s ss 1 , s ss 2 ) is to the value of V max 2 by re-running the simulation for values of V max 2 just above and/or below the given nominal value and using those results to estimate the sensitivities. Report the relative as well as the absolute sensitivities. iii) Recall that the result in (ii) is local, in the sense that it is only valid at parameter values near the given nominal parameter set. To verify this, repeat steps (i-ii) with the alternative parameter set V max 1 = 0 . 25, V max 2 = 1, V max 3 = 1, K m 2 = 1, and K m 3 = 3. iv) A more complete analysis is provided by a continuation diagram showing the steady states as a function of the parameter value. Returning to the nominal parameter values given in (i), Generate such a diagram using XPP and AUTO, as follows (also refer to XPP AUTO notes online): 1) Run your simulation to steady state at the nominal parameter values given in (i) above. 2)

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## This note was uploaded on 04/11/2010 for the course CHEM 1101 taught by Professor Leroy during the Spring '10 term at University of Toronto.

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Assignment 3 - AMATH/BIOL 382 Assignment 3 Due 1 Consider...

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