2. (35 points) Use you program to investigative properties of a four step linear pathway. Just extend the model given in question 1 to include an additional two species x2 and x3. You can assume simple irreversible mass-action kinetic on each reaction. I recommend you use the following values for the rate constants: 1 = 0.6; k2 = 1.8; k3 = 0.5; k40.04. This will enable you to more easily answer the following questions. You can also assume that the input is the source X and you can set its value to one. You may find that the plot of the phase change at x3 is broken at -180 degrees because it wraps around. To avoid this you can use the method: phase = np.unwrap(phase) to make sure the phase plot is continuous. [10] i) Compute and show the Bode plots for x1, x2 and x3 with respect to the input Xo. [5] ii) Do you see a pattern with the maximum phase shifts as you move from x₁ to x3? [10] iii) Can you explain this pattern? [5] iv) What would you predict would be the maximum phase shift for a forth species x4 if it were added to the end of the pathway? [5] v) Do you see a pattern in the amplitude at low frequencies as you move from x₁ to x3. Do you see attenuation or amplification? Free Code The following is a method to compute the B matrix with complex entries. It requires a roadrunner object (the model) and a string to indicate the name of the input (eg 'Xo'). # This compute the B matrix given: # A roadrunner instance # The name of the input symbl (as a string) # eg B = getBMatrix (r, 'Xo') # Note B is already set up as a complex matrix def getBMatrix (r, inputSymbol): num Reactions = r.getNumReactions() reactionIds = r.getReactionIds(); #3 1 number of inputs dvdp = np.zeros((numReactions, 1), dtype=complex) for k in range (numReactions): val = r.getUnscaled ParameterElasticity (reactionIds (k), input Symbol); dvdp [k] = val+0j #3 It must be complex B = np.matmul (r.getFullStoichiometry Matrix(), dvdp) return np.array (B)
2. (35 points) Use you program to investigative properties of a four step linear pathway. Just extend the model given in question 1 to include an additional two species x2 and x3. You can assume simple irreversible mass-action kinetic on each reaction. I recommend you use the following values for the rate constants: 1 = 0.6; k2 = 1.8; k3 = 0.5; k40.04. This will enable you to more easily answer the following questions. You can also assume that the input is the source X and you can set its value to one. You may find that the plot of the phase change at x3 is broken at -180 degrees because it wraps around. To avoid this you can use the method: phase = np.unwrap(phase) to make sure the phase plot is continuous. [10] i) Compute and show the Bode plots for x1, x2 and x3 with respect to the input Xo. [5] ii) Do you see a pattern with the maximum phase shifts as you move from x₁ to x3? [10] iii) Can you explain this pattern? [5] iv) What would you predict would be the maximum phase shift for a forth species x4 if it were added to the end of the pathway? [5] v) Do you see a pattern in the amplitude at low frequencies as you move from x₁ to x3. Do you see attenuation or amplification? Free Code The following is a method to compute the B matrix with complex entries. It requires a roadrunner object (the model) and a string to indicate the name of the input (eg 'Xo'). # This compute the B matrix given: # A roadrunner instance # The name of the input symbl (as a string) # eg B = getBMatrix (r, 'Xo') # Note B is already set up as a complex matrix def getBMatrix (r, inputSymbol): num Reactions = r.getNumReactions() reactionIds = r.getReactionIds(); #3 1 number of inputs dvdp = np.zeros((numReactions, 1), dtype=complex) for k in range (numReactions): val = r.getUnscaled ParameterElasticity (reactionIds (k), input Symbol); dvdp [k] = val+0j #3 It must be complex B = np.matmul (r.getFullStoichiometry Matrix(), dvdp) return np.array (B)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Question
![2. (35 points) Use you program to investigative properties of a four step linear pathway. Just
extend the model given in question 1 to include an additional two species x2 and x3. You can
assume simple irreversible mass-action kinetic on each reaction.
I recommend you use the following values for the rate constants: 1 = 0.6; k2 = 1.8; k3 =
0.5; k40.04. This will enable you to more easily answer the following questions.
You can also assume that the input is the source X and you can set its value to one.
You may find that the plot of the phase change at x3 is broken at -180 degrees because it wraps
around. To avoid this you can use the method:
phase = np.unwrap(phase)
to make sure the phase plot is continuous.
[10] i) Compute and show the Bode plots for x1, x2 and x3 with respect to the input Xo.
[5] ii) Do you see a pattern with the maximum phase shifts as you move from x₁ to x3?
[10] iii) Can you explain this pattern?
[5] iv) What would you predict would be the maximum phase shift for a forth species x4 if it
were added to the end of the pathway?
[5] v) Do you see a pattern in the amplitude at low frequencies as you move from x₁ to x3. Do
you see attenuation or amplification?
Free Code
The following is a method to compute the B matrix with complex entries. It requires a roadrunner
object (the model) and a string to indicate the name of the input (eg 'Xo').
# This compute the B matrix given:
#
A roadrunner instance
#
The name of the input symbl (as a string)
#
eg B = getBMatrix (r, 'Xo')
# Note B is already set up as a complex matrix
def getBMatrix (r, inputSymbol):
num Reactions = r.getNumReactions()
reactionIds = r.getReactionIds();
#3 1 number of inputs
dvdp = np.zeros((numReactions, 1), dtype=complex)
for k in range (numReactions):
val = r.getUnscaled ParameterElasticity (reactionIds (k), input Symbol);
dvdp [k] = val+0j #3 It must be complex
B = np.matmul (r.getFullStoichiometry Matrix(), dvdp)
return np.array (B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f3e5576-0f79-4ac1-b31d-3e0bb619ebe7%2Fe3a45662-97de-4100-917b-cf044fae5fc4%2Fki217y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. (35 points) Use you program to investigative properties of a four step linear pathway. Just
extend the model given in question 1 to include an additional two species x2 and x3. You can
assume simple irreversible mass-action kinetic on each reaction.
I recommend you use the following values for the rate constants: 1 = 0.6; k2 = 1.8; k3 =
0.5; k40.04. This will enable you to more easily answer the following questions.
You can also assume that the input is the source X and you can set its value to one.
You may find that the plot of the phase change at x3 is broken at -180 degrees because it wraps
around. To avoid this you can use the method:
phase = np.unwrap(phase)
to make sure the phase plot is continuous.
[10] i) Compute and show the Bode plots for x1, x2 and x3 with respect to the input Xo.
[5] ii) Do you see a pattern with the maximum phase shifts as you move from x₁ to x3?
[10] iii) Can you explain this pattern?
[5] iv) What would you predict would be the maximum phase shift for a forth species x4 if it
were added to the end of the pathway?
[5] v) Do you see a pattern in the amplitude at low frequencies as you move from x₁ to x3. Do
you see attenuation or amplification?
Free Code
The following is a method to compute the B matrix with complex entries. It requires a roadrunner
object (the model) and a string to indicate the name of the input (eg 'Xo').
# This compute the B matrix given:
#
A roadrunner instance
#
The name of the input symbl (as a string)
#
eg B = getBMatrix (r, 'Xo')
# Note B is already set up as a complex matrix
def getBMatrix (r, inputSymbol):
num Reactions = r.getNumReactions()
reactionIds = r.getReactionIds();
#3 1 number of inputs
dvdp = np.zeros((numReactions, 1), dtype=complex)
for k in range (numReactions):
val = r.getUnscaled ParameterElasticity (reactionIds (k), input Symbol);
dvdp [k] = val+0j #3 It must be complex
B = np.matmul (r.getFullStoichiometry Matrix(), dvdp)
return np.array (B)
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