Fitting SBML Models with Tellurium

This repo provides easy-to-use tools for doing parameter fitting using the Tellurium simulator. The project is named after the stoat, an animal that has superb skills at fitting into small places. SBstoat provides the following:

• Parameter fitting for a single model and for model suites (collections of models with overlapping parameters). The user can select any optimization method or combinations of methods that are available in scipy.optimize.
• A variety of plots to assess the quality of parameter fits.
• Cross validation to assess model quality.
• Bootstrapping for estimating confidence intervals for parameters.
• Multiprocess implementation for increased performance and scaling.

A Jupyter Notebook of detailed examples can be found here. Below is a summary.

The main module is modelFitter. A typically parameter fitting session is shown below. For convenience, the model is expressed using the Antimony modeling language. However, SBML models can be loaded into tellurium, and a tellurium object can be used in place of the antimony model.

ANTIMONY_MODEL = """ 
# Reactions   
J1: S1 -> S2; k1*S1
J2: S2 -> S3; k2*S2
J3: S3 -> S4; k3*S3
J4: S4 -> S5; k4*S4
J5: S5 -> S6; k5*S5;
# Species initializations
S1 = 10; S2 = 0; S3 = 0; S4 = 0; S5 = 0; S6 = 0;
k1 = 1; k2 = 2; k3 = 3; k4 = 4; k5 = 5;
"""

Now suppose we have the data file tst_data.txt. To fit this model to these data and see a report on the fit:

# Fit parameters to ts1
from SBstoat.modelFitter import ModelFitter
fitter = ModelFitter(ANTIMONY_MODEL, "tst_data.txt", ["k1", "k2", "k3", "k4", "k5"])
fitter.fitModel()
print(fitter.reportFit())

The output is:

[Fit Statistics]]
# fitting method   = leastsq
# function evals   = 49
# data points      = 180
# variables        = 5
chi-square         = 73.2546170
reduced chi-square = 0.41859781
Akaike info crit   = -151.822803
Bayesian info crit = -135.858019

[[Variables]]
k1:  0.95579053 +/- 0.03816186 (3.99%) (init = 5)
k2:  2.24079567 +/- 0.19847112 (8.86%) (init = 5)
k3:  2.96763525 +/- 0.35879852 (12.09%) (init = 5)
k4:  3.07652723 +/- 0.39858904 (12.96%) (init = 5)
k5:  5.90802238 +/- 1.43620318 (24.31%) (init = 5)

[[Correlations]] (unreported correlations are < 0.100)
C(k4, k5) = -0.248
C(k3, k4) = -0.226
C(k2, k3) = -0.218
C(k3, k5) = -0.211
C(k2, k4) = -0.189
C(k1, k2) = -0.179
C(k2, k5) = -0.178
C(k1, k3) = -0.147
C(k1, k5) = -0.144
C(k1, k4) = -0.141

You can also get bootstrap estimates of parameter values. Because bootstrapping is computationally intensive, SBstoat uses multiple processes on your machine.

# Get estimates of parameters
fitter.bootstrap(numIteration=2000, reportInterval=500)
fitter.reportBootstrap()

Here is the output:

**Running bootstrap for 2000 iterations with 4 processes.
bootstrap completed 500 iterations.
bootstrap completed 1000 iterations.
bootstrap completed 1500 iterations.
Completed bootstrap process 2.
Completed bootstrap process 3.
Completed bootstrap process 4.
bootstrap completed 2000 iterations.
Completed bootstrap process 1.

Bootstrap Report.
Total iterations: 2000
Total simulation: 2000
k1
  mean: 0.9666458789599315
  std: 0.03984278523619386
  [2.5, 97.55] Percentiles: [0.89206257 1.04470717]
k2
  mean: 2.1808554007110637
  std: 0.17819579282363782
  [2.5, 97.55] Percentiles: [1.85917689 2.56348925]
k3
  mean: 3.233849345953018
  std: 0.4074066158009789
  [2.5, 97.55] Percentiles: [2.57874824 4.12921803]
k4
  mean: 3.1037923601143054
  std: 0.38872479522475384
  [2.5, 97.55] Percentiles: [2.46792396 4.06937082]
k5
  mean: 5.9285194938461565
  std: 1.0301263970600283
  [2.5, 97.55] Percentiles: [4.42373341 8.44386604]

More details of the features of SBstoat can be found in this tutorial.

Installation and validation

1. pip install SBstoat

2. Verify the installation

   1. git clone https://github.com/sys-bio/SBstoat.git to get the repository
   2. cd SBstoat
   3. nosetests tests

Release Notes

Release 1.14

• Support for suites of models. A suite is a collection of models with overlapping sets of parameters. A common use case is having model variants (e.g., different initial concentrations of floating species or gene knock-outs) that reflect different experimental conditions. Parameter fitting requires simultaneously fitting all models in the suite. See the class SuiteFitter.
• Cross validation. Provides a way to assess model quality and estimates of parameter variance. Once you have an instance of ModelFitter, invoke the method crossValidate(numFold), where numFold is the number of folds.
• Progress bar. Long running activities have a progress bar. In this release, only bootstrapping has a progress bar. Future releases will extend this.
• Random restarts for fitting. The quality of a fit often depends on the initial values used for parameters. The optional keyword numRestart for constructing ModelFitter indicates the number of random restarts to use in a fit.

Release 1.16

• Breaking change: The interface to SuiteFitter has changed. See the tutorial for details. You can retain the old functionality (with exactly the same arguments) by using SBstoat.mkSuiteFitter instead of the constructor SBstoat.SuiteFitter.
• Benchmark for SuiteFitter, benchmarkSuiteFitter.py.
• Improved performance of SuiteFitter by a factor of 7.
• Parallel implementation of Cross Validation
• Cross validation for SuiteFitter; runs in parallel for each fold.
• Speedup of bootstrap by a factor of 5 by reducing the volume and complexity of data transferred by BootstrapRunner.

Developer Notes

1. run tests as follows:

   1. change to this directory

   2. set the environment variable PYTHONPATH to the absolute path of this directory.

      • Windows
      • Linux and Mac
      • PYTHONPATH=<current directory>
      • export PYTHONPATH

   3. nosetests tests