Berkeley Madonna User’s Guide Version 8.0 April 21, 2003 Robert Macey George Oster Tim Zahnley University of California Department of Molecular and Cellular Biology Berkeley, CA 94720 http://www.berkeleymadonna.com Table of Contents INTRODUCTION .............................................................................................................5 SYSTEM REQUIREMENTS................................................................................................5 BERKELEY MADONNA WINDOWS................................................................................5 THE EQUATION WINDOW................................................................................................5 THE FLOWCHART WINDOW.............................................................................................7 THE PARAMETER WINDOW.............................................................................................8 THE GRAPH WINDOW ....................................................................................................9 Creating Multiple Graph Windows.........................................................................9 Specifying Which Variables to View ......................................................................9 Changing Axis Settings .......................................................................................10 Creating Multiple Pages [Windows only] .............................................................11 Using Graph Buttons...........................................................................................11 Printing Graphs and Tables.................................................................................13 Exporting Graphs and Tables..............................................................................13 Customizing Background Colors [Macintosh only] ..............................................13 Oscilloscope Mode..............................................................................................13 Run Information...................................................................................................14 Readout...............................................................................................................14 Initial Conditions..................................................................................................14 Fast-Fourier Transform .......................................................................................15 THE DATASETS WINDOW .............................................................................................15 Importing Datasets ..............................................................................................15 Vector Datasets...................................................................................................16 Matrix Datasets ...................................................................................................16 Modifying and Removing Datasets......................................................................16 THE NOTES WINDOW...................................................................................................17 Embedding Pictures and Objects ........................................................................17 RUNNING MODELS ......................................................................................................17 SINGLE RUN ...............................................................................................................17 CONTINUE RUN [WINDOWS ONLY].................................................................................18 SLIDERS .....................................................................................................................18 BATCH RUNS ..............................................................................................................19 PARAMETER PLOT.......................................................................................................19 CHECK DT..................................................................................................................21 FLOATING-POINT EXCEPTIONS .....................................................................................21 EQUATION SYNTAX.....................................................................................................22 BASIC SYNTAX ............................................................................................................22 DIFFERENTIAL EQUATIONS ...........................................................................................23 DIFFERENCE EQUATIONS .............................................................................................24 DISCRETE EQUATIONS .................................................................................................24 Conveyors ...........................................................................................................25 Ovens..................................................................................................................25 -2- Queues................................................................................................................27 ROOT FINDER EQUATIONS ...........................................................................................28 Initial and Step Root Finders...............................................................................28 The Root Finder Algorithm ..................................................................................29 Multidimensional Root Finders ............................................................................29 LIMIT EQUATIONS ........................................................................................................30 OTHER EQUATION TYPES.............................................................................................30 METHOD Statement ...........................................................................................30 DISPLAY Statement............................................................................................30 RENAME Statement............................................................................................31 BUILT-IN SYMBOLS ......................................................................................................31 OPERATORS ...............................................................................................................32 BUILT-IN FUNCTIONS ...................................................................................................33 ARRAYSUM, ARRAYMEAN, ARRAYSTDDEV ..................................................35 BINOMIAL, NORMAL, POISSON, RANDOM......................................................35 DELAY ................................................................................................................35 NETFLOW...........................................................................................................35 STEPSIZE...........................................................................................................36 MAXINFLOW, OUTFLOW, OSTATE, QPOP, QPOPS .......................................36 ARRAY EQUATIONS......................................................................................................36 DATASET FUNCTIONS ..................................................................................................39 Plotting Matrix Datasets ......................................................................................39 REGIONAL SETTINGS [WINDOWS ONLY].........................................................................40 RUNNING STELLA MODELS ........................................................................................40 TIPS AND TECHNIQUES ................................................................................................41 Creating Periodic Functions ................................................................................41 Creating Piecewise-Linear Functions..................................................................42 Non-negative Reservoirs and Unidirectional Flows.............................................42 Simulating STELLA Conveyors, Ovens, and Queues .........................................43 INTEGRATION METHODS............................................................................................43 FIXED-STEPSIZE METHODS ..........................................................................................43 VARIABLE-STEPSIZE METHODS .....................................................................................44 USING DTOUT...........................................................................................................45 CUSTOM DT METHOD .................................................................................................46 OTHER FEATURES ......................................................................................................47 CHEMICAL REACTIONS.................................................................................................47 Adding Other Equations ......................................................................................49 CURVE FITTER ............................................................................................................50 Multiple Fits .........................................................................................................51 Specifying Initial Guesses ...................................................................................51 Floating-point