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Python implementation of the kinetic model of neuromuscular transmission dynamics.

Project description

Dynamics of Neuromuscular Transmission Reproduced by Calcium-Dependent and Reversible Serial Transitions in the Vesicle Fusion Complex

KiNeuron: Python implementation of the kinetic model of neuromuscular transmission dynamics.

KiNeuron is an open-source implementation of our mechanistic kinetic model of neuromuscular transmission based on sequential maturation transitions in the molecular fusion complex.

KiNeuron is:

  • Simple -- It is possible to simulate an alternative kinetic model with a few lines of code. This way, you can focus on the key parts of the problem that really matter.
  • Flexible -- It is possible to customise the kinetic model by adjusting the number of transition states, the kinetic transitions between states, as well as the rate constants. Further, KiNeuron allows the addition of a stimulation protocol.


KiNeuron requires:

  • python >= 3.6
  • graphviz >= 0.19.1
  • matplotlib >= 3.3.4
  • numpy >= 1.19.5
  • pandas >= 1.1.5
  • tqdm >= 4.62.3

To use the graph display functions of the model, it is necessary to install Graphviz backend for your OS as described in following documentation.


There are two ways to install KiNeuron:

  1. Via PyPI repository (recommended):

    • In your local workspace, create a new Python Virtual Environment with venv or conda.
    • Install KiNeuron as follow:
    $ python -m pip install -U kineuron
    • All dependencies are downloaded and installed. To verify that it has been installed correctly, you can check the following output:
    $ python -c "import kineuron; print(kineuron.__version__)"
  2. Via GitHub:

    • Clone this project repository to your local workspace.
    • Create a new Python Virtual Environment with venv or conda.
    • Install the required libraries from the file requeriments.txt into your virtual environment as follow:
    $ python -m pip install -r requeriments.txt

You are ready to use KiNeuron.

Usage Example

Creating a Model

Create a file and import the following classes:

from kineuron import (KineticModel, RateConstant, Solver, Stimulation,
                      Transition, TransitionState)

Then, instantiate the model objects as follows:

model = KineticModel(name='my-model', vesicles=100)

docked = TransitionState(name='Docked')
fusion = TransitionState(name='Fusion')

alpha = RateConstant(name="α", value=0.3, calcium_dependent=True)
beta = RateConstant(name="β", value=15)

transition1 = Transition(name='Transition 1',
transition2 = Transition(name='Transition 2',

Add all objects to the model as follow:

model.add_transition_states([docked, fusion])
model.add_transitions([transition1, transition2])

Finally, initialize the model:


Likewise, a stimulation protocol should be defined (if the experiment expects it) as follows:

protocol = Stimulation(
     name="Custom Stimulation Protocol")

The following lines show the time profile of the stimulation protocol:

import numpy as np

t = np.arange(0, 0.5, 0.0001)

Stimulation protocol

Model Information (Optional)

The general model information can be obtained as follows:


and run the file

$ python

==============  MODEL INFORMATION  ===============
MODEL NAME:                   my-model
TOTAL VESICLES:               100
RESTING STATE:                False

- Docked:                     100
- Fusion:                     0
NAME TRANSITION:              Transition 1
RATE CONSTANT VALUE:          0.3 s⁻¹
CALCIUM-DEPENDENT:            True
ORIGIN:                       Docked
DESTINATION:                  Fusion
NAME TRANSITION:              Transition 2
RATE CONSTANT VALUE:          15 s⁻¹
CALCIUM-DEPENDENT:            False
ORIGIN:                       Fusion
DESTINATION:                  Docked

The following lines allow you to visualize the graph of the model:

graph = model.get_graph()

Graph Model

Run It

The Solver object that simulates the time evolution of the model must be instantiated. Here, we use an implementation of the Gillespie Stochastic Algorithm (1977).

experiment = Solver(model=model, stimulation=protocol)

Before initiating the simulation, make sure to obtain the resting state of the model, from which all repetitions of the experiment are starting. This is achieved as follows:


With the following lines the experiment is ran. The results can be obtained and saved in a .csv file for further analysis.
results = experiment.get_results(mean=True)
results.to_csv("results.csv", index=True)

Finally, the file should be executed to perform the complete simulation:

$ python


  • 0.1.2
    • Added an option to include the individual events of the transitions in the results.
    • A quantitative criterion was added to find the resting state automatically.
    • Added the ability to include an external custom function when instantiating the Stimulation object.
  • 0.1.1
    • Added a progress bar when simulations are running.
    • Fixed compatibility with pandas >=1.3.0 versions.
    • Simplification of adding objects to the model. It is not necessary to explicitly declare KineticModel.add_rate_constants() method.
    • Added a AssertionError if the model is not initialized.
    • Bug fixed in the number of vesicles when calling two or more times KineticModel.init() method.
  • 0.1.0
    • Stable version released.
  • 0.0.1
    • Work in progress.


  • If you are interested in contributing to the project, please follow these guidelines:

    1. Fork it (
    2. Create your feature branch:
    $ git checkout -b feature/fooBar
    1. Commit your changes:
    $ git commit -am 'Add some fooBar'
    1. Push to the branch:
    $ git push origin feature/fooBar
    1. Create a new Pull Request.
  • If you want to report a bug, please create a new issue here describing the error as clearly as possible.


Author: Alejandro Martínez-Valencia



If you use our code for your research or scientific publication, we kindly ask you to refer to our work as follows:

  • Martínez-Valencia A., Ramírez-Santiago G. and De-Miguel F.F. (2022) Dynamics of Neuromuscular Transmission Reproduced by Calcium-Dependent and Reversible Serial Transitions in the Vesicle Fusion Complex. Front. Synaptic Neurosci. 13:785361. DOI: 10.3389/fnsyn.2021.785361


Distributed under the GNU General Public License. See LICENSE for more information.

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