Before running a parameter estimation task, you must specify the experimental
dataset that COPASI will use to fit the parameters. This dataset can be provided
in one or more data files. Supported data files are delimited text files, usually
either TSV or CSV files. A <tab> will be assumed initially, but you can specify
the delimiter your files uses.
Each file may contain one or more experiments, and each experiment consists of one or more data columns. All data points from all columns and experiments contribute to the objective function, which is defined as a weighted sum of squared differences:
\[E(P) = \sum_{i, j} \omega_j \cdot (x_{i, j} - y_{i, j}(P))^2\]Here, $P$ represents the current set of parameters being tested. $x_{i, j}$ is a measured data point from the dataset, and $y_{i, j}(P)$ is the corresponding simulated value. The indices $i$ and $j$ refer to the row (data point) and column (data series) in the dataset, respectively. The weight $\omega_j$ is assigned for each data column, and can either be specified by the user or automatically calculated by COPASI. In the user interface, weights calculated by COPASI are displayed in brackets.
Weights are designed to adjust the contribution of each data column to the overall objective function, so that ideally data points from all columns contribute equally. COPASI offers three main methods for calculating weights, each based on a different assumption about how the residual error relates to the data values. You can select the method using a dropdown in the user interface; the available options are described in the table below. Depending on whether the Normalize Weights per Experiment checkbox is checked, COPASI will either scale the weights so that the largest weight among all columns in the dataset is $1$, or scale the largest weight in each experiment separately to $1$.
If you wish to adjust weight values manually, simply type new values directly in the table.
| Name | Formula | Comment |
|---|---|---|
| Mean | $\omega_{j}=\frac{1}{<x_{j}>^{2}}$ | Assumes the error scales with the mean of the data points in a column |
| Mean Square | $\omega_{j}=\frac{1}{<x_{j}^{2}>}$ | Assumes the error scales with the mean square of the data points in a column |
| Standard Deviation | $\omega_{j}=\frac{1}{<x_{j}^{2}> - <x_{j}> <x_{j}>}$ | Assumes the error scales with the standard deviation of the data points in a column |
| Value Scaling | --- | The Value Scaling option in the drop down menu selects an alternative scaling behaviour: In this case the contribution of each data point is scaled by the inverse of the data value, assuming a multiplicative error model. |
To specify the experimental data you click on the Experimental Data button at the top right of the parameter estimation dialog. A new dialog opens that lets you enter experimental data.
 |
| Experimental Data Dialog |
To load a data file, click the open button next to the File label at the top of the dialog, and choose a file containing experimental data. The data file should include experimental data grouped into experiments. For COPASI to automatically detect where each experiment begins, experiments must be separated by one or more empty lines. Manual definition of experiments is also supported.
Each experiment’s data must be arranged in a table, with columns separated by a
user-definable delimiter. The default and recommended delimiter is the <tab>
character. By default, the first line of each experiment is treated as the header
row containing column names. However, you can choose which row serves as the
header, and it may appear anywhere in the file. Including a header row is not
mandatory; if your data lacks a header, uncheck the box indicating a header is
present.
After COPASI loads a data file, you must provide additional information for each experiment included in the file. Select an experiment from the selection box on the right. The first property to define is whether the experiment data is for a steady-state analysis or a time course simulation.
Next, you need to associate each input data column with elements of the model.
Use the ... button in each row to open a selection dialog and choose the
corresponding model object. COPASI requires that the type of each data column is
specified. Each column can be one of four types:
The last column in each line of your experimental data file contains the weight assigned to that data point. If COPASI calculates this value automatically (using one of the available modes), it will be shown surrounded by brackets. To specify your own weight, simply remove the brackets and enter the desired value. If you want COPASI to return to automatic calculation, delete the contents of the box entirely, and COPASI will once again compute the weight for you.
If you only wish to use part of an experiment’s dataset rather than the entire set, you can indicate the start and end lines for the desired subset. You may also remove experiments altogether. When you do this, the New Document button will become enabled. Clicking this button adds the first unused experiment from the currently active file. Often, all experimental data within a file shares the same structure. COPASI makes it easy to copy experimental data information from one experiment to another—use the from previous or to next options to duplicate information as needed. If COPASI detects that two experimental data sections are identical, it will automatically check the from previous option and lock editing for the current experiment. To make changes, simply uncheck this box.
If you have several data files, you can load each additional file and process it in the same way. Once you’re satisfied with your dataset definitions, close the data dialog with the OK button. Before starting the parameter estimation process, choose the desired fitting method and, if necessary, adjust method parameters. In most cases, the default settings are sufficient. Select the method from the drop-down list at the bottom of the dialog. For further details on the available methods, please refer to the methods section.
