eberhard o. voit georgia techtemplate file with basic commands (see file aaatemplate) start with...
TRANSCRIPT
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Eberhard O. Voit Georgia Tech
Copyright: António E.N. Ferreira 2001-2012
An Introduction to
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Open File
Cut Copy Paste
Solve Steady State
Save File
Typical Windows Stuff Will be Your File Name
Download PLAS and Create Shortcut
Start by clicking Shortcut button to PLAS
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Mandatory
Definition of Differential Equations Definition of Initial Values Definition of Parameters
Optional
Title Comments Transformations “Show only” Option
Sometimes Mandatory
Definition of Independent Variables
Components of a PLAS File
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x
Arguments of functions in brackets
“Taboo” names: They must not be changed
Show z only!
Template File with Basic Commands (see File AAATemplate)
Start with AAATemplate, save under another name
Statements starting with // are comments
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Typical File Options
Typical Edit Options
Steady State Run
Solver Settings
Arrangement of Windows
Much is explained here!
Your File Name with Path
Typical Options
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Because of this command, only z is shown
Progress of solution is shown; often it is too fast to see
0 25 50
0
20
40z
A First Dynamic Solution: Click
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Under Results specify Phase Plot 2D
Because of this new command, x and y are shown (need to run the program again, before x and y show up)
0 2 4
0
2
4
x
y
Phase Plane Plot
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“Tiled” windows
Display Options
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Results can be selected and
right-click copied
Copied with
right-click “Copy”
Display Options for Comparison
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Internal PLAS Representation; Useful for Debugging
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z not listed, since it is a transformation Oscillations
Select and right-click
to copy
Display of Steady-State Features ( )
Stable
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Select and right-click
to copy
Hide insignificant
quantities
Display of Variable Sensitivities
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Comparative Simulation Studies
Save under a new name
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Specify ‘Merge from file’
to import saved graph
Comparative Simulation Studies (Cont’d)
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X 1
X 11
X 4
X 6
X 5
X 2
X 3
X 8
X 9
X 10
X 7
−
Glycogen
Phosphorylase a
Glucose-1-P
Phosphoglucomutase
Glucose-6-P
Phosphoglucose isomerase
Fructose-6-P
Phosphofructokinase
Glucokinase
Glucose
Pi
−
Independent Variables
Example: Initial Steps of Glycolysis and Glycogenolysis*
X .
1 = 0.077884314 X 4 0.66 X 6
− 1.062708258 X 1
1.53 X 2 -0.59 X 7
X .
2 = 0. 585012402 X 1 0.95 X 2
-0.41 X 5 0.32 X 7
0.62 X 10 0.38
− 7.93456 × 10 -4 X 2 3.97 X 3
-3.06 X 8
X .
3 = 7.93456 × 10 -4 X 2 3.97 X 3
-3.06 X 8 − 1.05880847 X 3 0.3 X 9
GMA Model
* Cascante and Torres (unpublished); see details and references in: Voit, E.O.: Computational Analysis of Biochemical Systems, Cambridge University Press, 2000.
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A Model of the First Steps of Glycolysis (Cascante and Torres)
X1' = .077884314 X4^0.66 X6 - 1.062708258 X1^1.53 X2^(-0.59) X7 X2' = .585012402 X1^0.95 X2^-0.41 X5^0.32 X7^0.62 X10^0.38 - >>
>> p X2^3.97 X3^(-3.06) X8 X3' = p X2^3.97 X3^(-3.06) X8 - 1.05880847 X3^0.3 X9
X1 = .067 X2 = .465 X3 = .15 X4= 10 X5= 5 X6= 3 X7= 40 X8= 136 X9= 2.86 X10 = 4
p= .000793456
&& X4 X5 X6 X7 X8 X9 X10
V7 = .077884314 X4^0.66 X6
V1 = 1.05880847 X3^0.3 X9 V5 = .038706421 X2^(-0.1) X5^.84 X10
t0 = 0 tf = .1 hr = 0.1
!! x y z
Independent variables; made explicit for
log gain computation
Use Symbol Instead of Number
Continuation Symbol
Define to report dynamics of these fluxes
PLAS File for Example
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Sensitivity Analysis for Example
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X4 X5 X6 X7 X8 X9 X10
-4
-3
-2
-1
0
1
2
Independent Variables
X3X2X1
Dependent
Variables
Loga
rithm
ic G
ain
Pick up Data from PLAS Import into Excel Create 3D Bar Graph
Import into PowerPoint
Representation of Sensitivities in Excel and PowerPoint
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e
Dynamics: Blue Sky Catastrophe
(see Chapter 2)
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Nice, stable oscillations!
Use of LSODA Solver for Stiff or Non-Power-Law Systems
Switch to LSODA Method
Test responses to changes in A;
start with 0.264
e
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A is Changed By under 1% !
100
Dynamics is Extremely Sensitive to Changes in Parameter A
e
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e
Dynamics is Extremely Sensitive to Changes in Initial Values
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e
Dynamics is Extremely Sensitive to Changes in Initial Values (Cont’d)
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Chaotic Dynamics is Extremely Sensitive (cont’d)
e
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Need both to compute phase plane plot
Phase-Plane Plot of Chaotic System
Under Results Specify Phase Plot 2D
e
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!! x y t
Pseudo-3D Plot of the Chaotic System
Create explicit variable for time (scaled)
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e
Pseudo-3D Plot of the Chaotic System
Under Results Specify Phase Plot 3D