timeseries.rst

Running Time Series

First generate a model

import os
from pycotools3 import model, tasks


model_string = """
model model1()

    R1:   => A ; k1*S;
    R2: A =>   ; k2*A;
    R3:   => B ; k3*A;
    R4: B =>   ; k4*B*C; //feedback term
    R5:   => C ; k5*B;
    R6: C =>   ; k6*C;

    S = 1;
    k1 = 0.1;
    k2 = 0.1;
    k3 = 0.1;
    k4 = 0.1;
    k5 = 0.1;
    k6 = 0.1;

    A = 0;
    B = 0;
    C = 0;
    APlusB := A + B;
end
"""

# when running from a script you can use the special __file__ variable
if os.path.isfile(__file__):
    copasi_file = os.path.join(os.path.dirname(__file__), 'copasi_file.cps')
else:
    copasi_file = os.path.join(os.path.abspath(''), 'copasi_file.cps')

# create a copasi model
mod = model.loada(model_string, copasi_file)
assert isinstance(mod, model.Model)

To run a time course simulation use:

>>> # from 0 to 100 by step size of 0.1 >>> mod.simulate(0, 100, 0.1, variables='m') A B C Time 0 0.000000 0.000000 0.000000 1 0.095163 0.004837 0.000159 2 0.181269 0.018730 0.001208 3 0.259182 0.040810 0.003882 4 0.329680 0.070277 0.008766 5 0.393469 0.106377 0.016316 6 0.451188 0.148384 0.026874 7 0.503415 0.195577 0.040682 8 0.550671 0.247230 0.057889 9 0.593430 0.302596 0.078559 10 0.632121 0.360899 0.102679

The output is a :py:class:`pandas.DataFrame <https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html>`_.

Note

The variables argument is 'm' by default.

This gives you the time series of all the metabolites. If you also want global quantities (or even local parameters - though they are constants anyway) you can use 'g' or 'l'.

For instance:

Return time series for global variables

>>> mod.simulate(0, 100, 0.1, variables='g')

APlusB S k1 k2 k3 k4 k5 k6

Time 0 0.000000 1 0.1 0.1 0.1 0.1 0.1 0.1 1 0.100000 1 0.1 0.1 0.1 0.1 0.1 0.1 2 0.199999 1 0.1 0.1 0.1 0.1 0.1 0.1 3 0.299992 1 0.1 0.1 0.1 0.1 0.1 0.1 4 0.399957 1 0.1 0.1 0.1 0.1 0.1 0.1 5 0.499847 1 0.1 0.1 0.1 0.1 0.1 0.1 6 0.599572 1 0.1 0.1 0.1 0.1 0.1 0.1 7 0.698992 1 0.1 0.1 0.1 0.1 0.1 0.1 8 0.797901 1 0.1 0.1 0.1 0.1 0.1 0.1 9 0.896026 1 0.1 0.1 0.1 0.1 0.1 0.1 10 0.993020 1 0.1 0.1 0.1 0.1 0.1 0.1

Return time series for metabolites and global variables

>>> mod.simulate(0, 100, 0.1, variables='mg')

A APlusB B C S ... k2 k3 k4 k5 k6

Time ... 0 0.000000 0.000000 0.000000 0.000000 1 ... 0.1 0.1 0.1 0.1 0.1 1 0.095163 0.100000 0.004837 0.000159 1 ... 0.1 0.1 0.1 0.1 0.1 2 0.181269 0.199999 0.018730 0.001208 1 ... 0.1 0.1 0.1 0.1 0.1 3 0.259182 0.299992 0.040810 0.003882 1 ... 0.1 0.1 0.1 0.1 0.1 4 0.329680 0.399957 0.070277 0.008766 1 ... 0.1 0.1 0.1 0.1 0.1 5 0.393469 0.499847 0.106377 0.016316 1 ... 0.1 0.1 0.1 0.1 0.1 6 0.451188 0.599572 0.148384 0.026874 1 ... 0.1 0.1 0.1 0.1 0.1 7 0.503415 0.698992 0.195577 0.040682 1 ... 0.1 0.1 0.1 0.1 0.1 8 0.550671 0.797901 0.247230 0.057889 1 ... 0.1 0.1 0.1 0.1 0.1 9 0.593430 0.896026 0.302596 0.078559 1 ... 0.1 0.1 0.1 0.1 0.1 10 0.632121 0.993020 0.360899 0.102679 1 ... 0.1 0.1 0.1 0.1 0.1

Return time series for metabolites, global variables and local parameters (though remember there are none in this current topology)

>>> mod.simulate(0, 100, 0.1, variables='mgl')

A B C

Time 0 1.000000 1.000000 1.00000 1 0.082146 0.072788 2.81673 2 0.069317 0.062367 2.83276 3 0.068980 0.062080 2.82647 4 0.068817 0.061934 2.81989 5 0.068657 0.061789 2.81332 6 0.068497 0.061645 2.80677 7 0.068337 0.061502 2.80023 8 0.068178 0.061358 2.79371 9 0.068019 0.061215 2.78720 10 0.067861 0.061073 2.78071

Alternative simulation methods

Copasi supports several model simulation algorithms. PyCoTools supports most of these, including:

• deterministic (the default)
• direct
• gibson_bruck
• tau_leap
• adaptive_tau_leap
• hybrid_runge_kutta
• hybrid_lsoda
• hybrid_rk45

To use one of these alternative methods, ensure your model is adequate for the simulation you are performing (i.e. no reversible reactions and low enough copy numbers for stochastic simulation) and use the method argument to :pypycotools3.model.Model.simulate

Note

The example model above is not suitable to stochastic simulation

>>> mod.simulate(0, 100, 0.1, variables='m', method='direct')

Plotting

If you have used :pypycotools3.model.Model.simulate() then you will have a :pypandas.DataFrame. In this case, you might as well use either pandas plotting facilities or matplotlib with seaborn. You could also use plotly, plotly with dash or bokeh.

There are also some inherent plotting facilities in pycotools.

With PyCoTools

Visualisation in pycotools works by passing a plotter class an instance of a task. In this case we need a handle to the TimeCourse task.

>>> from pycotools3 import tasks, viz >>> tc = tasks.TimeCourse(model=mod, start=0, end=10, step_size=1) >>> viz.PlotTimeCourse(tc, savefig=True, show=True)

Since the inherent plotting module is basically just a wrapper around matplotlib and seaborn, it might be a good idea to use these tools instead.

Here's an example.

With matplotlib

Here's a very simple example using matplotlib.

import matplotlib.pyplot as plt
import seaborn as sns

sns.set_context('talk')

df = mod.simulate(0, 100, 0.1, variables='m')

for i in df:
    if i != 'Time:
        fig = plt.plot(df['Time'], df[i], label=i)
        seaborn.despine(fig=fig, top=True, right=True)
        plt.legend()
        plt.xlabel('Time')
        plt.ylabel('concentration')