controlSBML 0.2.6

Control analysis and design for SBML Models.

controlSBML

The Systems Biology Markup Language (SBML) is a community standard for representing simulations of biological models, especially chemical reaction networks. controlSBML is a package that does control analysis and design of SBML models using the CalTech control package.

controlSBML uses the following "systems characterization" of an SBML model:

• state variables are floating species;
• inputs are reaction fluxes;
• outputs are a subset of the state variables.

We note that reaction fluxes cannot be manipulated directly. Thus,implementation requires a mapping from a reaction flux to an effector, typically a chemical species such as an enzyme that is specific to the reaction. The keyword effector_dct refers to a python dictionary that does this mapping. (See the makeNonlinearIOSystem method of ControlSBML.)

controlSBML interfaes to the control package by creating two kinds of control objects for an SBML model:

• NonlinearIOSystem, which wraps the actual simulation of the SBML model; and
• StateSpace, which is a linear MIMO model approximation of the SBML model at a specified time in the simulation.

These objects can be used in combination with other control objects to analyze system properties, design controllers, and construct closed loop systems.

controlSBML also provides analyses of SBML models as well as a means to manipulate elements of the SBML model.

Installation

pip install controlSBML

To find the current version:

import controlSBML as ctl
ctl.__version__

Installing slycot (optional)

To get the full set of capabilities from the control package, you need to install slycot, a package that addresses requirements for more sophisticated manipulation of MIMO models (e.g., solving algebraic Ricotti equations).

The best way is to install slycot is from binaries using anaconda. However, at the present time, anaconda is difficult to set up on Google Collaboratory.

Otherwise, you need to install from source. Below are the instructions for Ubuntu.

• install cmake: pip install cmake --upgrade
• install sikit-build: pip install scikit-build
• install fortran: sudo apt-get install gfortran
• provide path to fortran: export FC=`which gfortran
• install BLAS: sudo apt-get install libatlas-base-dev
• clone Sylcot: git clone --recurse-submodules https://github.com/python-control/Slycot.git
• cd Slycot
• python setup.py install

Constructing ControlSBML

ctlsb = ControlSBML(model_reference)

where model_referencecan be any of the following:

• path to a local file with the extension .ant or .xml
• a python string for an SBML or Antimony model representation
• a URL to an XML file

Technical Summary

ControlSBML

Properties

• roadrunner is the roadrunner object for the SBML model.
• jacobian_df is the full Jacobian of the model at the current simulation time. Changes to roadrunner can change this property.
• antimony is the antimony representation of the model.
• A_df is the ${\bf A}$ matrix in the linear system represented as a pandas DataFrame.
• B_df is the ${\bf B}$ matrix in the linear system represented as a pandas DataFrame.
• C_df is the ${\bf C}$ matrix in the linear system represented as a pandas DataFrame.
• state_names is a list of floating species that constitute the state vector.
• input_names is a list of reaction names that specify the input vector.
• output_names is a list of floating species that constitute the output vector.

Methods

• setTime(new_time) resets roadrunner and runs a simulation from time zero to the time specified.
• makeStateSpace() creates a control state space object using the Jacobian of the model at the current simulation time.
• makeNonlinearIOSystem() creates a NonlinearIOSystem object that simulates the SBML model.
• plotTrueModel plots a roadrunner simulation.
• plotLinearApproximation plots the linear approximation provided by an ${\bf A}$ matrix. The default ${\bf A}$ matrix is the Jacobian of the current RoadRunner instance. You can either specify a different ${\bf A}$ or set the RoadRunner instance to a different time.
• plotBode constructs bode plots for the SISO systems formed by all combinations of inputs and outputs.

Other Functions

• makeTS creates a time series object from an array. A time series object is a DataFrame whose index in time (in integer milliseconds), and the columns are variable names.
• simulateSystem provides a simplified way to simulate a system (which may be an interconnect) by creating the times and initial, returns a time series DataFrame.
• plotOneTS plots a single time series DataFrame.
• plotManyTS plots multiple time series DataFrames structured so that each column is a separate plot that compares the different times series.

Example

This notebook provides a simple example of using controlSBML.

Developer Notes

1. The package works with and without slycot. So two virtual environments are needed for testing: ctl includes slycot and ctl_tst does not. Note that continuous integration is done only without slycot.

Version History

• 0.2.6
  • Default for constructor: is_reduced=False
  • makeTransferFunction
• 0.2.5 4/8/2022
  • Improve performance by not recalculating Jacobian
  • Fix bugs related to implementation of is_reduced as applied on NonlinearIOSystem
• 0.2.4 3/31/2024 - Create reduced A matrix
  • mat2Df - fixed bug with printing column names
  • Create reduced A matrix for makeStateSpace so that A is non-singular Default output_names is all floating species
• 0.2.3, 3/22/2022 - Bug fix for mat2DF
• 0.2.2, 3/22/2022 - Bug fix
• 0.2.1, 3/22/2022 - Bug fix
• 0.2.0, 3/22/2022 - Version for class
  • ppMat - pretty print a matrix
  • plotMat - display a heatmap for a matrix
  • mat2TS - convert a matrix to a timeseries
  • mat2DF - convert a matrix to a dataframe
• 0.1.6, 3/16/2022
  • Using-Control-SBML.ipynb has an example of doing feedback control design with controlSBML.
  • control.NonlinearIOSystem wraps an SBML model. Can be used in the construction of systems using control.interconnect and in simulations using control.input_output_response. One caveat is that this may work poorly for models implemented as SBML rate rules.
• 0.1.5, 3/5/2022.
  • More options for plotting and simulations
  • plotBode
  • Inputs are identified by reaction Ids
• 0.1.3, 2/13/2022. First release.