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ODE solvers |
  
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ODE solvers |
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The process of model simulation and its adjustment can be demonstrated on the example of the cell cycle model (DGR0068 in BMOND/Biopath; Gardner et al., 1998).
After you opened a diagram-model you will see the view like this:
The upper right part of the window contains the scheme of the model with proteins, biochemical interactions (arrows) and set initial values of protein (or something else) concentrations.
The model consists of variables (protein concentrations), constants (the constants of included biochemical reactions), and various additional conditions (events, mathematical functions, etc not shown in this model). Values of variables and constants can be observed in the menu Variables and Parameters (a range of panels at the bottom of the lower right part of the window), respectively.
By clicking those menus you will get the list of desirable entities with respective values (as it is shown below for variables of this model).
The column "Name" contains database IDs of the components of the model that have to be used in all formulas and equations describing the dynamics of the concentration changes. Initial values of variables can be changed by clicking of respective table cell and input of desirable value using keyboard. "Boundary condition" can be used by ticking respective table cell to fix the concentration of a variable in the process of model simulation. "Units" contains dimension data. "Show in plot" allows to regulate how many graphs (and variables, respectively) should be demonstrated during simulation on the plot. The same logic is used for "Parameters" menu (see below).
Biochemical formulas are one of the important components of the model. You can add them during creation of biochemical reactions using BioUML tools or add/edit by clicking a dot on an existing arrow (as it is shown on the example of the reaction number 9) and using "Edit" menu of the lower left part of the window like it is shown below. In the chapter "Kinetic law" you will see the formula or can add new one if there is no any formula. Newly entered variables and constants will be added to the respective lists "Variables" and "Parameters" automatically.
After all values were inputted and all components of the model were confirmed you can go to the menu "Java" containing tools for adjustment of simulation procedure.
You will see the window like demonstrated below containing info about predefined parameters of simulation process:
"Output dir" – the destination folder for saving simulation results.
"Initial time" (set 0.0) – here you can choose the time point starting from you will see the results of simulation as graphs.
"Completion time" – the time period for which you will simulate the changes of protein concentrations, etc. (may be given in seconds, minutes, etc according to the dimensionality of constants).
"Time increment" – the delta for time; the less increment the more calculations will be made by a solver to get values of variables (and the graph will be smoother), but it is time consuming. The bigger increment, the faster calculations and the graph will be rough. Default value is 1.0, you can use 0.1, for example.
"Absolute tolerance" and "Relative tolerance" – these parameters are used to select the time interval for calculations.
"Solver name" – here you can select a solver for calculations and simulation of results.
"Needed plot simulation" – if selected then you will see a plot with simulation results on it in the regime of real time.
After you confirmed all parameters, you can start simulation process by clicking button "Play" (as it is shown below).
In new window you will see a plot with graphs reflecting changes of variable values in time.
Clicking buttons depicted below (red) will allow to save results (calculated values for each time point regarding to the time increment value) and show the window with plot to modify output graphs (remove undesirable and so on).
For solving ordinary differential equation initial value problem next solvers were applied in BioUML: