Single parameter global sensitivity analysis

[ftavella]

It would be great to have a function that given a particular protein interaction network and a particular parameter set, returns the period and amplitude values for a single parameter change. This will be used to replicate the results in Tsai et al. 2008, Figure 3. We can start from a known point in parameter set that oscillates and from there, span both directions to find the critical points where oscillations stop. Once we have both critical points, we can simulate parameters in-between to obtain the behavior of period and amplitude as a function of the changed parameter.

Functions that will be needed:

• find_critical_point(model, parameter_set, selected_parameter_name, direction; hyperparameters=DEFAULT_BISECTION_HYPERPARAMETERS)
• simulate_pin_from_parameter_sets(model, parameter_sets; hyperparameters=DEFAULT_PIN_HYPERPARAMETERS)
• pin_single_parameter_variation(model, parameter_set, parameter_name; hyperparameters=DEFAULT_PIN_HYPERPARAMETERS)

[ftavella]

We will also need a function that simulates a given model for a particular parameter set:
-simulate_pin_model(model, parameter_set; hyperparameters=DEFAULT, initial_condition=NaN, simulation_time=NaN)
In the future, this function can be used to eliminate duplicated code in our codebase.
This function will be different from simulate_ODEs() because it doesn't create an Ensemble of simulations but rather a single one.

[ftavella]

Another option is to use BifurcationKit.jl to get a bifurcation diagram and from there get the information we want. I'm currently trying to write up a minimal example of this to see if we could wrap BifurcationKit.jl nicely to provide an easy way for users to get a single parameter scan for a protein interaction network