Kinetic Diagram Analysis

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.

Examples

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 NxNarray 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:

Installation

Development version from source

To install the latest development version from source, run

git clone [email protected]:Becksteinlab/kda.git
cd kda
python setup.py install

Citation

When using Kinetic Diagram Analysis in published work, please cite the following paper:

• N. C. Awtrey and O. Beckstein. Kinetic Diagram Analysis: A Python Library for Calculating Steady-State Observables of Biochemical Systems Analytically. J. Chem. Theory Comput. (2024). doi: 10.1021/acs.jctc.4c00688

Copyright

Copyright (c) 2020, Nikolaus Awtrey

Acknowledgements

Project based on the Computational Molecular Science Python Cookiecutter version 1.2.