Terminology

 

Reactants, Products, and Modifiers

 

The left figure shows a single reaction from a reactant to a product, enzymatically triggered by a so called modifier. The right figure displays the corresponding set of differential equations, which are determined automatically by PottersWheel using the PottersWheel chemical compiler. The enzyme concentration is constant.

Symbols

A dynamical model
An experimental or synthetic data set
A model-data couple
An assembly comprising several model-data-couples

The main PottersWheel user interface comprises two lists. The upper one is called the couple-list and stores all models and data sets that will potentially be used for fitting. In order to fit a set of couples, they have to be combined into an assembly, represented by the lower list.

Observables

Most systems are only partially observed, i.e. not all system players can be measured. In the example on the left the observable y measures the sum of B, C, and D. The measurements are then compared with the trajectory calculated by the mathematical model as shown on the right.

Driving input functions

 

Driving input functions characterize the experimental setting, e.g. the dose level or the duration of a pulsed stimulation.

 

Fitting

 

During parameter calibration, a set of parameters is changed systematically until the distance between model and measurements is minimized.

 

Trajectory

In a dynamical system, the graph of a state variable drawn over time is called a trajectory. This could be the concentration of a measured or internal species.

Difference between experiments and stimuli

Two stimuli of the same experiment have

  • the same initial values for all species,
  • the same kinetic and scaling parameters,
  • the same units for the observables,
  • maybe different driving input functions.

Two experiments may be different in all aspects. Each initial value, kinetic and scaling parameter can individually be forced to have the same value for all experiments if the fit setting is global. One data file per experiment is required, which may comprise one or more stimuli.

Abbreviations

Reaction R
Dynamical variable X
Observable Y
Derived variable Z
Driving input U
Dynamic parameter K
Initial value x0
Scaling parameter S
Derived parameter P
Algebraic equation (also called assignment rule) A