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BETSE, the BioElectric Tissue Simulation Engine.

Project description

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.. # ------------------( SYNOPSIS )------------------


**BETSE** (**B**\ io\ **E**\ lectric **T**\ issue **S**\ imulation **E**\ ngine)
is an open-source cross-platform `finite volume`_ simulator for 2D computational
multiphysics problems in the life sciences – including electrodiffusion_,
electro-osmosis_, galvanotaxis_, `voltage-gated ion channels`_, `gene regulatory
networks`_, and `biochemical reaction networks`_ (e.g., metabolism). BETSE is
associated with the `Paul Allen Discovery Center`_ at `Tufts University`_ and
supported by a `Paul Allen Discovery Center award`_ from the `Paul G. Allen
Frontiers Group`_.

BETSE is `portably implemented <codebase_>`__ in pure `Python 3`_, `continuously
stress-tested <testing_>`__ with GitLab-CI_ **×** Appveyor_ **+** py.test_, and
`permissively distributed <License_>`__ under the `BSD 2-clause license`_.


BETSEE_ (\ **BETSE E**\ nvironment) is the official open-source cross-platform
graphical user interface (GUI) for BETSE. BETSEE_ wraps the low-level
command-line interface (CLI) bundled with BETSE in a high-level interactive
modelling environment optimized for both new and advanced users alike.

Like BETSE, BETSEE_ is `portably implemented <BETSEE codebase_>`__ in `Python
3`_ and `permissively distributed <License_>`__ under the `BSD 2-clause
license`_. Unlike BETSE, BETSEE_ leverages the industry-standard PySide2_-based
`Qt 5 <Qt_>`_ application framework to deliver a modern scientific workflow.

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.. contents:: **Contents**

.. # ------------------( DESCRIPTION )------------------


BETSE currently supports **Linux**, **macOS**, and **Windows** out-of-the-box.


For new users, BETSE is portably installable as follows:

- [\ *Windows*\ ] Emulate **Ubuntu Linux** via the `Windows Subsystem for Linux
(WSL) <WSL_>`__. [#windows_not]_
- Install the **Python 3.x** [#python2_not]_ (e.g., 3.6) variant of Anaconda_.
- Open a **Bash terminal.** [#terminal]_
- Run the following commands.

- Enable conda-forge_.

.. code-block:: console

conda config --add channels conda-forge

- Install **BETSE.** [#conda_package]_

.. code-block:: console

conda install betse

- [\ *Optional*\ ] Test **BETSE.** [#test_command]_

.. code-block:: console

betse -v try

.. [#windows_not]
The `Windows Subsystem for Linux (WSL) <WSL_>`__ and – hence BETSE itself –
is *only* installable under **Windows 10.** Under older Windows versions,
BETSE may be installed from a `virtual Linux guest <VirtualBox_>`__.

.. [#python2_not]
Do *not* install the **Python 2.7** variant of Anaconda_. BETSE requires
**Python 3.x.**

.. [#anaconda_not]
If you prefer *not* to install Anaconda_, BETSE dependencies are also
`manually installable <Advanced_>`__ via your platform-specific package
manager (e.g., Homebrew_ on macOS, APT_ on Ubuntu Linux). Doing so is
non-trivial and, where performed incorrectly, could produce a
performance-crippled single-core installation of BETSE. Anaconda_ suffers no
such issues and is guaranteed to produce a performance-optimized multicore
installation of BETSE on *all* supported platforms. We strongly recommend
Anaconda_ – even when you think you know better.

.. [#terminal]
To open a `POSIX`_\ -compatible terminal under:

- **Windows:**

#. Install **Ubuntu Linux** via the `Windows Subsystem for Linux (WSL) <WSL_>`__.
#. Open an *Ubuntu Linux terminal.*

- **macOS:**

#. Open the *Finder*.
#. Open the *Applications* folder.
#. Open the *Utilities* folder.
#. Open **.

- **Ubuntu Linux:**

#. Type ``Ctrl``\ +\ ``Alt``\ +\ ``t``.

.. [#conda_package]

This command installs both the `most recent stable release of BETSE <conda
package_>`__ *and* all mandatory and most optional dependencies of this
release. Older stable releases are installable in a similar manner (e.g.,
``conda install betse=0.7.0`` for BETSE 0.7.0). All `Anaconda packages`_ are
kindly hosted by the `non-profit conda-forge organization <conda-forge_>`__.

.. [#test_command]

This test command:

#. Enables verbosity with the ``-v`` option, simplifying issue reporting in
the event of an unexpected error.
#. Creates a ``sample_sim/`` subdirectory in the current directory, providing
the default simulation for this release of BETSE. This includes *all*
configuration files and resources referenced by these files.
#. Runs all simulation phases (e.g., seed, initialization) of this simulation.

When finished, you may safely either:

- Remove this subdirectory.
- Rename this subdirectory (e.g., to ``my_sim/``) to serve as a basis for
subsequent simulations.
- Preserve this subdirectory as is.


For developers and advanced users, *any* version of BETSE – including the live
repository and prior stable releases – is manually installable as follows:

#. Install **Python 3.x** and `all dependencies <dependencies_>`__ required by
BETSE. Under:

- **Linux,** install `these dependencies <dependencies_>`__ via your
distribution-specific package manager (e.g., APT_ under Debian-based
distributions). Do *not* use ``pip``.\ [#pip_not]_
- **macOS,** either:

- (\ *Recommended*\ ) Install the **Python 3.x** variant of Anaconda_.
- Or both:

#. Install a third-party package manager (e.g., Homebrew_, MacPorts_).
Apple does *not* provide a package manager out-of-the-box.
#. Install `these dependencies <dependencies_>`__ via that package
manager. Do *not* use ``pip``.\ [#pip_not]_

- **Windows,** install the **Python 3.x** variant of Anaconda_.\ [#windows]_

#. Open a **terminal.**
#. **Download** either:

- **The unstable BETSE repository** as follows:

#. Install Git_.
#. Clone the ``master`` branch of this repository.

.. code-block:: console

git clone

#. Prepare for installation.

.. code-block:: console

cd betse

- **Any stable BETSE release,** including the most recent, as follows:

#. Visit our `source tarball archive <tarballs_>`__.
#. Click the download icon to the right of the desired release and select
*Download tar.gz*.
#. Extract the downloaded tarball into the current directory.

.. code-block:: console

tar -xvzf betse-*.tar.gz

#. (\ *Optional*\ ) Remove this tarball.

.. code-block:: console

rm betse-*.tar.gz

#. Prepare for installation.

.. code-block:: console

cd betse-*

#. **Install BETSE** either:

- (\ *Recommended*\ ) **Editably,** installing a cross-platform symbolic link
to the current BETSE codebase. Modifications to this code are applied
immediately *without* requiring reinstallation.

.. code-block:: console

sudo python3 develop

- **Non-editably,** installing a physical copy of the current BETSE codebase.
Modifications to this code are ignored and thus require reinstallation.

.. code-block:: console

sudo python3 install

#. (\ *Optional*\ ) **Test BETSE,** running all modelling phases of a sample
simulation from a new directory.

.. code-block:: console

cd /tmp && betse try

.. [#pip_not]
Do *not* install scientific dependencies (e.g., NumPy_, SciPy_) with either
``pip`` or ``easy_install``; doing so typically degrades BETSE to single-core
performance. To optimize BETSE across multiple cores, *always* install these
dependencies with your platform-specific package manager (e.g., Homebrew_,

.. [#windows]
Unlike Linux and macOS, Anaconda_ is (\ *effectively*\ ) required under
Windows. Due to Microsoft's lack of support for `POSIX`_\ -compliant
toolchains, *no* reasonable alternatives for installing multicore-aware
scientific dependencies exist.



BETSE installs the ``betse`` command, a low-level command line interface (CLI)
designed for experienced users. The typical CLI-based workflow resembles:

#. Create a default simulation configuration in a new ``my_sim/`` subdirectory
of the current directory.

.. code-block:: console

betse config my_sim/sim_config.yml

#. [\ *Optional*\ ] Edit the new ``my_sim/sim_config.yml`` file with `your
favourite text editor <Atom_>`__.
#. Create a pseudo-random cell cluster from this simulation configuration.

.. code-block:: console

betse seed my_sim/sim_config.yml

#. [\ *Optional*\ ] Export all enabled plots, animations, and comma-separated
value (CSV) files from this cell cluster.

.. code-block:: console

betse plot seed my_sim/sim_config.yml

#. Initialize (i.e., calculate steady-state concentrations for) this cell cluster.

.. code-block:: console

betse init my_sim/sim_config.yml

#. [\ *Optional*\ ] Export all enabled plots, animations, and comma-separated
value (CSV) files from this initialization.

.. code-block:: console

betse plot init my_sim/sim_config.yml

#. Simulate this initialized cell cluster.

.. code-block:: console

betse sim my_sim/sim_config.yml

#. [\ *Optional*\ ] Export all enabled plots, animations, and comma-separated
value (CSV) files from this simulation.

.. code-block:: console

betse plot sim my_sim/sim_config.yml

Also note that our sister project BETSEE_ installs the ``betsee`` command, a
high-level graphical user interface (GUI) designed for *all* users – regardless
of prior experience or familiarity with the command line.


BETSE provides a variety of command-line options and subcommands in addition to
those synopsized above. The standalone ``betse`` and ``betse --help`` commands
describe these options and subcommands as follows:

.. code-block:: console

usage: betse [-h] [-v] [-V] [--log-file LOG_FILENAME]
[--log-level {all,debug,info,warning,error,critical,none}]
[--profile-type {none,call,size}]
[--profile-file PROFILE_FILENAME]
[--matplotlib-backend MATPLOTLIB_BACKEND_NAME]
{config,seed,init,sim,sim-grn,plot,info,try} ...

The BioElectric Tissue Simulation Engine (BETSE) is a finite volume simulator
for 2D computational multiphysics problems in the life sciences -- including
electrodiffusion, electro-osmosis, galvanotaxis, voltage-gated ion channels,
gene regulatory networks, and biochemical reaction networks.

optional arguments:
-h, --help show this help message and exit
-v, --verbose print and log all messages verbosely
-V, --version print program version and exit
--log-file LOG_FILENAME
file to log to (defaults to
--log-level {all,debug,info,warning,error,critical,none}
minimum level of messages to log to "--log-file"
(defaults to "info") [overridden by "--verbose"]
--profile-type {none,call,size}
type of profiling to perform (defaults to "none"):
* "none", disabling profiling
* "call", profiling callables (functions, methods)
* "size", profiling object sizes (requires "pympler")
--profile-file PROFILE_FILENAME
file to profile to unless "--profile-type=none"
(defaults to "/home/leycec/.betse/")
--matplotlib-backend MATPLOTLIB_BACKEND_NAME
name of matplotlib backend to use (see: "betse info")

Exactly one of the following subcommands must be passed:

config create a default config file for BETSE simulations
seed seed a new cell cluster for a config file
init initialize a seeded cell cluster for a config file
sim simulate an initialized cell cluster for a config file
sim-grn simulate a gene regulatory network for a config file
plot plot an initialized or simulated simulation
info print metadata synopsizing BETSE and current system
try create, init, simulate, and plot a sample simulation

subcommand help:

For help with a specific subcommand, pass the "-h" or "--help" option to that
subcommand. For example, for help with the "config" subcommand, run:

betse config --help


BETSE also provides external documentation optimized for offline reading –
complete with explanatory examples, sample plots, and ample screenshots:

- Official `BETSE 0.4 documentation`_. (\ *PDF format; 72 pages.*\ )
- Official `BETSE 0.3 documentation`_. (\ *PDF format; 77 pages.*\ )


BETSE simulates biorealistic electrochemical phenomena in `gap junction`_\
-networked 2D cellular collectives. To predict `bioelectric patterns
<bioelectricity_>`__ and their spatio-temporal dynamics, BETSE:

- Models `ion channel`_ and `gap junction`_ activity.
- Tracks changes in ion concentration and net ionic charge.
- Calculates endogenous voltages and currents.
- Accepts simulation parameters, variables, and options as human-readable,
well-commented configuration files in YAML_ format.
- Exports simulation results to a variety of output formats, including:

- Publication-quality:

- Plots, charts, and animations driven by Matplotlib_, the industry
standard for open-source plot visualization.
- `Directed graphs`_ (i.e., networks) driven by Graphviz_, the industry
standard for open-source graph visualization.

- Internet-friendly compressed video driven by any of various popular
open-source video encoders, including FFmpeg_, Libav_, and MEncoder_.
- Post-processable tabular data (e.g., `comma-separated values (CSV)
<comma-separated values_>`__).

- Imports bitmask images defining the shapes of:

- Cell clusters.
- Cell cluster regions localizing `ion channel`_ activity, typically
signifying disparate types of adjacent tissue.

To assemble simple concepts into complex simulations, BETSE supplies a richly
configurable, highly scalable biological toolset consisting of:


Simulations may enable arbitrary combinations of the principal ions implicated
in bioelectrical signaling – including:

- Sodium_ (*Na*\ :sup:`+`).
- Potassium_ (*K*\ :sup:`+`).
- Chloride_ (*Cl*\ :sup:`-`).
- Calcium_ (*Ca*\ :sup:`2+`).
- Hydrogen_ (*H*\ :sup:`+`).
- `Anionic proteins`_ (*P*\ :sup:`-`).
- Bicarbonate_ (*HCO*\ :sup:`-`\ :sub:`3`).

Ion Channels

Individual cells in simulations may enable arbitrary combinations of
`voltage-gated ion channels`_, each implementing the `Hodgkin-Huxley (HH)
formalism`_ with experimentally-derived parameters sourced from reputable
`knowledge-based systems`_ (e.g., Channelpedia_). Explicitly supported channel
types include:

- HCN1_, HCN2_, and HCN4_.
- `L-type Ca`_, `T-type Ca`_, and |P/Q-type Ca|_.
- Kir2.1_.
- Kv1.1_, Kv1.2_, Kv1.5_. Kv3.3_, and Kv3.4_.
- Nav1.2_, Nav1.3_, and Nav1.6_.
- `Leak <leak channels_>`__ and `ligand-gated channels`_, including:

- |Calcium-gated K+ channels|_.

Custom ion channels parametrized by user-selected constants may be trivially
defined in the same manner (e.g., via a YAML_\ -formatted configuration file).

Ion Pumps and Exchangers

For fine-grained control over cell dynamics, notable ion pumps and exchangers
may also be selectively enabled – including:

- |Ca2+-ATPase|_.
- |H+/K+-ATPase|_.
- |Na+/K+-ATPase|_.
- V-ATPase_.

Custom ion pumps and exchangers parametrized by user-selected constants may be
trivially defined in the same manner (e.g., via a YAML_\ -formatted
configuration file).

Extracellular Space

Cells form interconnected intracellular networks via voltage-sensitive `gap
junction connections <gap junction_>`__ embedded within an `extracellular
environment`_, maintained by `tight junctions`_ at the cell cluster periphery.
Simulation of this environment enables exploration of `local field
potentials`_, `transepithelial potential`_, and `ephaptic coupling`_ between

Biological Networks

Simulation of `gene regulatory <gene regulatory networks_>`__ and `biochemical
reaction networks`_ at both the cellular and mitochondrial level supports deep
spatial analysis of otherwise intractable biological processes. Metabolism,
disease, aging, and other `genetic <genetics_>`__ and `epigenetic
<epigenetics_>`__ phenomena commonly associated with quasi-`Big Data`_ are all
valid targets for exhaustive study with BETSE.

To integrate these potent control systems with bioelectrical signaling, the
`activity <enzyme activity_>`__-modulated interaction between `gene products`_
and similar biochemicals is fully integrated with `ion channels <ion
channel_>`__, `ion pumps`_, and `gap junctions`_.


BETSE is peer-reviewed software receiving continual evidence-based scrutiny.
Simulation output is reproducibly synchronized with experimental observations on
`membrane permeability`_, `resting potential`_, ion concentration, and similar
real-world biophysical quantities. Predictable outcomes have been demonstrated
for such well-known cases as:

- `Transmembrane voltage changes <transmembrane voltage_>`__ on perturbations
to single cell membrane states and environmental ion concentrations.
- `Transepithelial potential differences (TEPD) <transepithelial
- Bioelectrical signals at large-scale cellular wound sites.


BETSE is formally described in our `introductory paper <2016 article_>`__.
Third-party papers, theses, and other texts leveraging BETSE should ideally
cite the following:

`Alexis Pietak`_ and `Michael Levin`_, 2016. |2016 article name|_
|2016 article supplement|_ [#supplement]_ |2016 journal name|_ *4*\ (55).

Subsequent papers expanding the BETSE architecture with additional theory,
experimental results, and comparative metrics include:

* `Alexis Pietak`_ and `Michael Levin`_, 2017. |2017 article name|_
|2017 article supplement|_ [#supplement]_ |2017 journal name|_ *14*\ (134),
p.20170425. :sup:``
* Vaibhav P. Pai, `Alexis Pietak`_, Valerie Willocq, Bin Ye, Nian-Qing Shi,
and `Michael Levin`_, 2018. |2018 hcn2 article name|_ |2018 hcn2 article
supplement|_ [#supplement]_ |2018 hcn2 journal name|_ *9*\ (1), p.998.
* Javier Cervera, `Alexis Pietak`_, `Michael Levin`_, and Salvador Mafe,
2018. |2018 coupling article name|_ |2018 coupling journal name|_ *128*,
pp.45—61. :sup:``
* `Alexis Pietak`_ and `Michael Levin`_, 2018. |2018 review article name|_
|2018 review journal name|_

.. # FIXME: Add an image thumbnail for the first article above displaying the
.. # cover image selected by the prior journal for that edition's cover article.

.. # Note that, for unknown reasons, this footnote *MUST* be refenced above and
.. # defined here rather than in the supplement replacements defined below.

.. [#supplement]
This article's supplement extends the cursory theory presented by this
article with a rigorous treatment of the mathematics, formalisms, and
abstractions required to fully reproduce this work. If theoretical questions
remain after completing the main article, please consult this supplement.


To contact `Dr. Pietak`_, the principal developer of the BETSE codebase and
first or second author of all above papers, cordially direct correspondence to

* The `anonymous contact form <Organic Mechanics Contact_>`__ at `Organic
Mechanics`_, the personal archives of all material published to date by
`Dr. Pietak`_ – including papers, presentations, textbooks, and additional
theoretical work.
* The personal e-mail account of `Dr. Pietak`_: [#e-mail]_

* *Username:* **alexis** ``{dot}`` **pietak**
* *Hostname:* **gmail** ``{dot}`` **com**

To report a software issue (e.g., bug, crash, or other unexpected behaviour)
*or* request a new feature in BETSE, consider `submitting a new issue <issue
submission_>`__ to our `issue tracker`_. Thanks in advance; it's only through
generous user contributions that your user experience can continue to improve.

.. [#e-mail]
To protect Dr. Pietak's e-mail address against `automated harvesting <e-mail
harvesting_>`__, this address has been intentionally obfuscated. Reconstruct
the original address by:

* Replacing the ``{dot}`` substring with the ``.`` charecter.
* Concatenating the username and hostname strings with the ``@`` character.

For this reason, consider directing correspondence to the `anonymous contact
form <Organic Mechanics Contact_>`__ at `Organic Mechanics`_ instead.


BETSE comes courtesy a dedicated community of `authors <author list_>`__ and
contributors_ – without whom this project would be computationally impoverished,
biologically misaligned, and simply unusable.

**Thanks, all.**

See Also

For prospective users:

- `Installation <dependencies_>`__, detailing BETSE's installation with
exhaustive platform-specific instructions.

For prospective contributors:

- `Development <doc/md/>`__, detailing development of the BETSE
codebase – philosophy, workflow, and otherwise.
- `Testing <doc/md/>`__, detailing testing of the BETSE codebase –
`continuous integration`_, manual testing, and otherwise.
- `Freezing <doc/md/>`__, detailing conversion of the BETSE codebase
into redistributable platform-specific executable binaries.


BETSE is open-source software `released <license_>`__ under the permissive `BSD
2-clause license`_.

The logo prominently displayed on this `project page <project_>`__ is a flat
`Noun Project`_ icon entitled `"Cow," <Cows collection_>`__ `kindly released
<Noun Project license_>`__ under the permissive `BSD-compatible <license
compatibility_>`__ `CC BY 3.0 license`_ by `Maxim Kulikov`_.

.. # ------------------( LINKS ~ betse )------------------
.. _author list:
.. _codebase:
.. _conda package:
.. _contributors:
.. _dependencies:
.. _issue submission:
.. _issue tracker:
.. _license:
.. _project:
.. _testing:
.. _tarballs:

.. # ------------------( LINKS ~ betse : docs )------------------
.. _BETSE 0.4 documentation:
.. _BETSE 0.3 documentation:

.. # ------------------( LINKS ~ betsee )------------------
.. _BETSEE codebase:

.. # ------------------( LINKS ~ academia )------------------
.. _Michael Levin:
.. _Levin, Michael:
.. _Channelpedia:
.. _Paul Allen Discovery Center:
.. _Paul Allen Discovery Center award:
.. _Paul G. Allen Frontiers Group:
.. _Tufts University:

.. # ------------------( LINKS ~ academia : ally )------------------
.. _Alexis Pietak:
.. _Pietak, Alexis:
.. _Dr. Pietak:
.. _Organic Mechanics:
.. _Organic Mechanics Contact:

.. # ------------------( LINKS ~ paper : 2016 )------------------
.. _2016 article:

.. |2016 article name| replace::
**Exploring instructive physiological signaling with the bioelectric tissue
simulation engine (BETSE).**
.. _2016 article name:

.. |2016 article supplement| replace::
**(**\ Supplement\ **).**
.. _2016 article supplement:

.. |2016 journal name| replace::
*Frontiers in Bioengineering and Biotechnology,*
.. _2016 journal name:

.. # ------------------( LINKS ~ paper ~ 2017 )------------------
.. |2017 article name| replace::
**Bioelectric gene and reaction networks: computational modelling of genetic, biochemical and bioelectrical dynamics in pattern regulation.**
.. _2017 article name:

.. |2017 article supplement| replace::
**(**\ Supplement\ **).**
.. _2017 article supplement:

.. |2017 journal name| replace::
*Journal of The Royal Society Interface,*
.. _2017 journal name:

.. # ------------------( LINKS ~ paper ~ 2018 : hcn2 )------------------
.. |2018 hcn2 article name| replace::
**HCN2 rescues brain defects by enforcing endogenous voltage pre-patterns.**
.. _2018 hcn2 article name:

.. |2018 hcn2 article supplement| replace::
**(**\ Supplement\ **).**
.. _2018 hcn2 article supplement:

.. |2018 hcn2 journal name| replace::
*Nature Communications.*
.. _2018 hcn2 journal name:

.. # ------------------( LINKS ~ paper ~ 2018 : coupling )------------------
.. |2018 coupling article name| replace::
**Bioelectrical coupling in multicellular domains regulated by gap junctions: A conceptual approach.**
.. _2018 coupling article name:

.. |2018 coupling journal name| replace::
.. _2018 coupling journal name:

.. # ------------------( LINKS ~ paper ~ 2018 : review )------------------
.. |2018 review article name| replace::
**Bioelectrical control of positional information in development and regeneration: A review of conceptual and computational advances.**
.. _2018 review article name:

.. |2018 review journal name| replace::
*Progress in Biophysics and Molecular Biology.*
.. _2018 review journal name:

.. # ------------------( LINKS ~ science )------------------
.. _bioelectricity:
.. _biochemical reaction networks:
.. _electrodiffusion:
.. _electro-osmosis:
.. _enzyme activity:
.. _ephaptic coupling:
.. _epigenetics:
.. _extracellular environment:
.. _finite volume:
.. _galvanotaxis:
.. _gap junction:
.. _gap junctions:
.. _gene products:
.. _gene regulatory networks:
.. _genetics:
.. _genetic algorithms:
.. _Hodgkin-Huxley (HH) formalism:
.. _local field potentials:
.. _membrane permeability:
.. _resting potential:
.. _tight junctions:
.. _transmembrane voltage:
.. _transepithelial potential:

.. # ------------------( LINKS ~ science : ions )------------------
.. _anionic proteins:
.. _bicarbonate:
.. _calcium:
.. _chloride:
.. _hydrogen:
.. _sodium:
.. _potassium:

.. # ------------------( LINKS ~ science : channels )------------------
.. _ion channel:
.. _leak channels:
.. _ligand-gated channels:
.. _voltage-gated ion channels:

.. |calcium-gated K+ channels| replace::
Calcium-gated K\ :sup:`+` channels
.. _calcium-gated K+ channels:

.. # ------------------( LINKS ~ science : channels : type )------------------
.. _HCN1:
.. _HCN2:
.. _HCN4:
.. _Kir2.1:
.. _Kv1.1:
.. _Kv1.2:
.. _Kv1.5:
.. _Kv3.3:
.. _Kv3.4:
.. _Nav1.2:
.. _Nav1.3:
.. _Nav1.6:
.. _L-type Ca:
.. _T-type Ca:

.. |P/Q-type Ca| replace:: :sup:`P`\ /\ :sub:`Q`-type Ca
.. _P/Q-type Ca:

.. # ------------------( LINKS ~ science : pumps : type )------------------
.. _ion pumps:

.. # ------------------( LINKS ~ science : pumps : type )------------------
.. _V-ATPase:

.. |Ca2+-ATPase| replace:: Ca\ :sup:`2+`-ATPase
.. _Ca2+-ATPase:

.. |H+/K+-ATPase| replace:: H\ :sup:`+`/K\ :sup:`+`-ATPase
.. _H+/K+-ATPase:

.. |Na+/K+-ATPase| replace:: Na\ :sup:`+`/K\ :sup:`+`-ATPase
.. _Na+/K+-ATPase:

.. # ------------------( LINKS ~ science : computer )------------------
.. _Big Data:
.. _comma-separated values:
.. _continuous integration:
.. _directed graphs:
.. _e-mail harvesting:
.. _genenic algorithms:
.. _knowledge-based systems:

.. # ------------------( LINKS ~ os : linux )------------------
.. _APT:
.. _POSIX:
.. _Ubuntu:
.. _Ubuntu Linux:
.. _Ubuntu Linux 16.04 (Xenial Xerus):

.. # ------------------( LINKS ~ os : macos )------------------
.. _Homebrew:
.. _MacPorts:

.. # ------------------( LINKS ~ os : windows )------------------
.. _WSL:

.. # ------------------( LINKS ~ software )------------------
.. _Appveyor:
.. _Atom:
.. _dill:
.. _FFmpeg:
.. _Git:
.. _GitLab-CI:
.. _Graphviz:
.. _imageio:
.. _Libav:
.. _Matplotlib:
.. _NumPy:
.. _MEncoder:
.. _Python 3:
.. _py.test:
.. _SciPy:
.. _VirtualBox:
.. _YAML:

.. # ------------------( LINKS ~ software : conda )------------------
.. _Anaconda:
.. _Anaconda packages:
.. _conda-forge:

.. # ------------------( LINKS ~ software : pyside2 )------------------
.. _PySide2:
.. _PySide2 5.6:
.. _PySide2 installation:
.. _PySide2 PPA:
.. _Qt:
.. _Qt 5.6:

.. # ------------------( LINKS ~ software : icons )------------------
.. _Cows collection:
.. _Maxim Kulikov:
.. _Noun Project:
.. _Noun Project license:

.. # ------------------( LINKS ~ software : licenses )------------------
.. _license compatibility:
.. _BSD 2-clause license:
.. _CC BY 3.0 license:

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Filename, size & hash SHA256 hash help File type Python version Upload date
betse-0.9.0-py3-none-any.whl (1.7 MB) Copy SHA256 hash SHA256 Wheel py3
betse-0.9.0.tar.gz (1.7 MB) Copy SHA256 hash SHA256 Source None

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