ode2tn 1.0.0

A Python package to turn arbitrary polynomial ODEs into a transcriptional network simulating it.

ode-to-transcription-network

ode2tn is a Python package to turn arbitrary polynomial ODEs into a transcriptional network simulating it.

See this paper for details: TODO

Installation

Type pip install ode2tn at the command line.

Usage

See the notebook.ipynb for more examples of usage.

The functions ode2tn and plot_tn are the main elements of the package. ode2tn converts a system of arbitrary polynomial ODEs into another system of ODEs representing a transcriptional network as defined in the paper above. Each variable $x$ in the original ODEs is represented by a pair of variables $x^\top,x^\bot$, whose ratio $x^\top / x^\bot$ follows the same dynamics in the transcriptional network as $x$ does in the original ODEs. plot_tn does this conversion and then plots the ratios by default, although it can be customized what exactly is plotted; see the documentation for gpac.plot for a description of all options.

Here is a typical way to call each function:

from math import pi
import numpy as np
import sympy as sp
from transform import plot_tn, ode2tn

x,y = sp.symbols('x y')
odes = { # odes dict maps each symbol to an expression for its time derivative
    x: y-2,
    y: -x+2,
}
inits = { # inits maps each symbol to its initial value
    x: 2,
    y: 1,
}
gamma = 2 # uniform decay constant; should be set sufficiently large that ???
beta = 1 # constant introduced to keep values from going to infinity or 0
t_eval = np.linspace(0, 6*pi, 1000)
tn_odes, tn_inits, tn_ratios = ode2tn(odes, inits, gamma, beta)
for sym, expr in tn_odes.items():
    print(f"{sym}' = {expr}")
print(f'{tn_inits=}')
print(f'{tn_ratios=}')
plot_tn(odes, inits, gamma, beta, t_eval=t_eval)

This will print

x_t' = x_b*y_t/y_b - 2*x_t + x_t/x_b
x_b' = 2*x_b**2/x_t - 2*x_b + 1
y_t' = 2*y_b - 2*y_t + y_t/y_b
y_b' = -2*y_b + 1 + x_t*y_b**2/(x_b*y_t)
tn_inits={x_t: 2, x_b: 1, y_t: 1, y_b: 1}
tn_ratios={x: x_t/x_b, y: y_t/y_b}

showing that the variables x and y have been replace by pairs x_t,x_b and y_t,y_b, whose ratios x_t/x_b and y_t/y_b will track the values of the original variable x and y over time. The function plot_tn above does this conversion and then plots the ratios. Running the code above in a Jupyter notebook will print the above text and show this figure:

One could also hand the transcriptional network ODEs to gpac to integrate, if you want to directly access the data being plotted above. The OdeResult object returned by gpac.integrate_odes is the same returned by scipy.integrate.solve_ivp, where the return value sol has a field sol.y that has the values of the variables in the order they were inserted into tn_odes, which will be the same as the order in which the original variables x and y were inserted, with x_t coming before x_b:

t_eval = np.linspace(0, 2*pi, 5)
sol = gp.integrate_odes(tn_odes, tn_inits, t_eval)
print(f'times = {sol.t}')
print(f'x_y = {sol.y[0]}')
print(f'x_b = {sol.y[1]}')
print(f'y_t = {sol.y[2]}')
print(f'y_b = {sol.y[3]}')

which would print

times = [0.         1.57079633 3.14159265 4.71238898 6.28318531]
x_y = [2.         1.78280757 3.67207594 2.80592514 1.71859172]
x_b = [1.         1.78425369 1.83663725 0.93260227 0.859926  ]
y_t = [1.         1.87324904 2.14156469 2.10338162 2.74383426]
y_b = [1.         0.93637933 0.71348949 1.05261915 2.78279691]