Eberhard O. Voit Georgia Tech

Copyright: António E.N. Ferreira 2001-2012

An Introduction to

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

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

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

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

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

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

“Tiled” windows

Display Options

Results can be selected and

right-click copied

Copied with

right-click “Copy”

Display Options for Comparison

Internal PLAS Representation; Useful for Debugging

z not listed, since it is a transformation Oscillations

Select and right-click

to copy

Display of Steady-State Features ( )

Stable

Select and right-click

to copy

Hide insignificant

quantities

Display of Variable Sensitivities

Comparative Simulation Studies

Save under a new name

Specify ‘Merge from file’

to import saved graph

Comparative Simulation Studies (Cont’d)

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* Cascante and Torres (unpublished); see details and references in: Voit, E.O.: Computational Analysis of Biochemical Systems, Cambridge University Press, 2000.

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

Sensitivity Analysis for Example

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

e

Dynamics: Blue Sky Catastrophe

(see Chapter 2)

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

A is Changed By under 1% !

100

Dynamics is Extremely Sensitive to Changes in Parameter A

e

e

Dynamics is Extremely Sensitive to Changes in Initial Values

e

Dynamics is Extremely Sensitive to Changes in Initial Values (Cont’d)

Chaotic Dynamics is Extremely Sensitive (cont’d)

e

Need both to compute phase plane plot

Phase-Plane Plot of Chaotic System

Under Results Specify Phase Plot 2D

e

!! x y t

Pseudo-3D Plot of the Chaotic System

Create explicit variable for time (scaled)

e

Pseudo-3D Plot of the Chaotic System

Under Results Specify Phase Plot 3D