{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 1

# Assignment 1 - AMATH/BIOL 382 Problem Set 1 Due 1 Notes...

This preview shows pages 1–3. Sign up to view the full content.

AMATH/BIOL 382 Problem Set 1 Due January 22, 2010 1. Notes, chapter 1: Exercise 1.1.11. 2. Consider the chemical reaction network indicated in Figure 1 with rate constants as shown. A B C D E F k k k 1 3 2 Figure 1: Closed Network a) Write a set of six differential equations describing the evolution of the concentrations of the species from an arbitrary initial concentration profile. b) Use mass conservations to reduce the system description to three differential equations and three algebraic equations. c) Determine the system steady state as a function of the initial concentrations. (Note, the answer is rather trivial since the system is closed). d) Verify your result in (c) by simulating the system behaviour from initial condition ([A], [B], [C], [D], [E], [F]) = (1 , 1 , 1 2 , 0 , 0 , 0). For the simulation take k 1 = 3, k 2 = 1, k 3 = 4. Submit a printout. e) Repeat (a-d) for the open system in Figure 2. There will be fewer structural conservations. The input rate v is constant. For the simulation, take k 1 = 3, k 2 = 1, k 3 = 4, k 4 = 1, k 5 = 5, v = 0 . 5, and the same initial condition. k 2 A B C D E F k k 1 3 k 5 k 4 v Figure 2: Open Network f) Why is there no (physical) steady state if we choose v = 5? 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. Notes, chapter 1: Exercise 1.2.1 4. Consider the system described in Figure 3 below. Take S and P as boundary species with fixed concentrations and suppose the reaction constants are given (in units of s - 1 ) as k 1 = 1 , k 2 = 11 , k - 2 = 8 , k 3 = 0 . 2 and take S = 1 mM.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Assignment 1 - AMATH/BIOL 382 Problem Set 1 Due 1 Notes...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online