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Analysis of ODE models with focus on model selection and parameter estimation.

Project Description

S-timator is a Python library to analyse ODE-based models (also known as dynamic or kinetic models). These models are often found in many scientific fields, particularly in Physics, Chemistry, Biology and Engineering.

Features include:

  • A model description mini language: models can be input as plain text following a very simple and human-readable language.
  • Basic analysis: numerical solution of ODE’s, parameter scanning.
  • Parameter estimation and model selection: given experimental data in the form of time series and constrains on model operating ranges, built-in numerical optimizers can find parameter values and assist you in the experimental design for model selection.

S-timator is in an alpha stage: many new features will be available soon.


S-timator supports Python versions 2.6 and up, but support of 3.x is coming soon.

S-timator depends on the “scientific python stack”. The mandatory requirements for S-timator are the following libraries:

  • Python (2.6 or 2.7)
  • numpy
  • scipy
  • matplotlib
  • pip

One of the following “scientific python” distributions is recommended, as they all provide an easy installation of all requirements:

The installation of these Python libraries is optional, but strongly recommended:

  • sympy: necessary to compute dynamic sensitivities, error estimates of parameters and other symbolic computations.
  • IPython and all its dependencies: some S-timator examples are provided as IPython notebooks.
  • wxPython: although S-timator is a python library meant to be used for scripting or in IPython literate programming interface, a simple GUI is included. This interface requires wxPython.


After installing the required libraries, (Python, numpy, scipy, matplotlib and pip) the easiest way to install S-timator is with pip:

$ pip install stimator

The classical way also works, but is not recomended:

$ python install

Basic use: solution of ODE models

This is a warm-up example that illustrates model description, ODE numerical solving and plotting:

from stimator import read_model, solve, plot
import pylab as pl

mdl = """# Example file for S-timator
title Example 1

#reactions (with stoichiometry and rate)
vin  : -> x1     , rate = k1
v2   : x1 ->  x2 , rate = k2 * x1
vout : x2 ->     , rate = k3 * x2

#parameters and initial state
k1 = 1
k2 = 2
k3 = 1
init = state(x1=0, x2=0)

#filter what you want to plot
!! x1 x2"""

m = read_model(mdl)

print '========= model ========================================'
print mdl
print '--------------------------------------------------------'

s1 = solve(m, tf=5.0)

Parameter estimation

Model parameter estimation, based on experimental time-course data (run example

from stimator import *
from stimator.deode import DeODESolver
import pylab as pl

mdl = """# Example file for S-timator
title Example 2

vin  : -> x1     , rate = k1
v2   : x1 ->  x2 , rate = k2 * x1
vout : x2 ->     , rate = k3 * x2
k1 = 1
k2 = 2
k3 = 1
init = state(x1=0, x2=0)
!! x2
find k1  in [0, 2]
find k2 in [0, 2]
find k3 in [0, 2]

timecourse ex2data.txt
generations = 200   # maximum generations for GA
genomesize = 60     # population size in GA
m1 = read_model(mdl)
print mdl

optSettings={'genomesize':60, 'generations':200}
timecourses = readTCs(['ex2data.txt'], verbose=True)

solver = DeODESolver(m1,optSettings, timecourses)
print solver.reportResults()
fig1 = pl.figure()

m2 = m1.clone()
best = solver.optimum.parameters
best = [(n,v) for n,v,e in best]
s2 = solve(m2, tf=20.0)

This produces the following output:

11 time points for 2 variables read from file .../examples/ex2data.txt

Solving Example 2...
0   : 3.837737
1   : 3.466418
2   : 3.466418
...  (snip)
39  : 0.426056
refining last solution ...

Too many generations with no improvement in 40 generations.
best energy = 0.300713
best solution: [ 0.29399228  0.47824875  0.99081065]
Optimization took 8.948 s (00m 08.948s)

--- PARAMETERS           -----------------------------
k3      0.293992 +- 0.0155329
k2      0.478249 +- 0.0202763
k1      0.990811 +- 0.0384208

--- OPTIMIZATION         -----------------------------
Final Score 0.300713
generations 40
max generations     200
population size     60
Exit by     Too many generations with no improvement

--- TIME COURSES         -----------------------------
Name                Points          Score
ex2data.txt 11      0.300713

Model selection (experimental design)

One of the examples included in S-timator solves an experimental design problem: finding a feasible set of experimental conditions that lead to the clear selection between 2 models.

Run example

Summary of road map

  • Improve documentation
  • I/O to other model description formats (SBML, etc)

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