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* Cascante and Torres (unpublished); see details and references in: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