Python package used for the analysis of biochemical kinetic diagrams using the diagrammatic approach developed by T.L. Hill.
WARNING: this software is in flux and is not API stable.
KDA has a host of capabilities, all beginning with defining the connections and reaction rates (if desired) for your system. This is done by constructing an NxN
array with diagonal values set to zero, and off-diagonal values (i, j)
representing connections (and reaction rates) between states i
and j
. If desired, these can be the edge weights (denoted kij
), but they can be specified later.
The following is an example for a simple 3-state model with all nodes connected:
import numpy as np
import kda
# define matrix with reaction rates set to 1
K = np.array(
[
[0, 1, 1],
[1, 0, 1],
[1, 1, 0],
]
)
# create a KineticModel from the rate matrix
model = kda.KineticModel(K=K, G=None)
# get the state probabilities in numeric form
model.build_state_probabilities(symbolic=False)
print("State probabilities: \n", model.probabilities)
# get the state probabilities in expression form
model.build_state_probabilities(symbolic=True)
print("State 1 probability expression: \n", model.probabilities[0])
The output from the above example:
$ python example.py
State probabilities:
[0.33333333 0.33333333 0.33333333]
State 1 probability expression:
(k21*k31 + k21*k32 + k23*k31)/(k12*k23 + k12*k31 + k12*k32
+ k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
As expected, the state probabilities are equal because all edge weights are set to a value of 1.
Additionally, the transition fluxes (one-way or net) can be calculated from the KineticModel
:
# make sure the symbolic probabilities have been generated
model.build_state_probabilities(symbolic=True)
# iterate over all edges
print("One-way transition fluxes:")
for (i, j) in model.G.edges():
flux = model.get_transition_flux(state_i=i+1, state_j=j+1, net=False, symbolic=True)
print(f"j_{i+1}{j+1} = {flux}")
The output from the above example:
$ python example.py
One-way transition fluxes:
j_12 = (k12*k21*k31 + k12*k21*k32 + k12*k23*k31)/(k12*k23 + k12*k31 + k12*k32 + k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
j_13 = (k13*k21*k31 + k13*k21*k32 + k13*k23*k31)/(k12*k23 + k12*k31 + k12*k32 + k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
j_21 = (k12*k21*k31 + k12*k21*k32 + k13*k21*k32)/(k12*k23 + k12*k31 + k12*k32 + k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
j_23 = (k12*k23*k31 + k12*k23*k32 + k13*k23*k32)/(k12*k23 + k12*k31 + k12*k32 + k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
j_31 = (k12*k23*k31 + k13*k21*k31 + k13*k23*k31)/(k12*k23 + k12*k31 + k12*k32 + k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
j_32 = (k12*k23*k32 + k13*k21*k32 + k13*k23*k32)/(k12*k23 + k12*k31 + k12*k32 + k13*k21 + k13*k23 + k13*k32 + k21*k31 + k21*k32 + k23*k31)
Continuing with the previous example, the KDA plotting
module can be leveraged to display the diagrams that lead to the above probability expression:
import os
from kda import plotting
# generate the directional diagrams
model.build_directional_diagrams()
# get the current working directory
cwd = os.getcwd()
# specify the positions of all nodes in NetworkX fashion
node_positions = {0: [0, 1], 1: [-0.5, 0], 2: [0.5, 0]}
# plot and save the input diagram
plotting.draw_diagrams(model.G, pos=node_positions, path=cwd, label="input")
# plot and save the directional diagrams as a panel
plotting.draw_diagrams(
model.directional_diagrams,
pos=node_positions,
path=cwd,
cbt=True,
label="directional_panel",
)
This will generate two files, input.png
and directional_panel.png
, in your current working directory:
input.png
directional_panel.png
NOTE: For more examples (like the following) visit the KDA examples repository:
To install the latest development version from source, run
git clone git@github.com:Becksteinlab/kda.git
cd kda
python setup.py install
When using Kinetic Diagram Analysis in published work, please cite the following paper:
Copyright (c) 2020, Nikolaus Awtrey
Project based on the Computational Molecular Science Python Cookiecutter version 1.2.