Metadata-Version: 1.1
Name: betse
Version: 0.6.1
Summary: BETSE, the BioElectric Tissue Simulation Engine.
Home-page: https://gitlab.com/betse/betse
Author: Alexis Pietak, Cecil Curry, et al.
Author-email: alexis.pietak@gmail.com
License: 2-clause BSD
Download-URL: https://gitlab.com/betse/betse/repository/archive.tar.gz?ref=v0.6.1
Description: .. # ------------------( BADGES                             )------------------
        .. image::  https://gitlab.com/betse/betse/badges/master/build.svg
           :target: https://gitlab.com/betse/betse/pipelines
           :alt: Linux Build Status
        .. image::  https://ci.appveyor.com/api/projects/status/mow7y8k3vpfu30c6/branch/master?svg=true
           :target: https://ci.appveyor.com/project/betse/betse/branch/master
           :alt: Windows Build Status
        
        .. # ------------------( SYNOPSIS                           )------------------
        
        =====
        BETSE
        =====
        
        **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
        ======
        
        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.
        
        .. # ------------------( TABLE OF CONTENTS                  )------------------
        .. # Blank line. By default, Docutils appears to only separate the subsequent
        .. # table of contents heading from the prior paragraph by less than a single
        .. # blank line, hampering this table's readability and aesthetic comeliness.
        
        |
        
        .. # Table of contents, excluding the above document heading. While the
        .. # official reStructuredText documentation suggests that a language-specific
        .. # heading will automatically prepend this table, this does *NOT* appear to
        .. # be the case. Instead, this heading must be explicitly declared.
        
        .. contents:: **Contents**
           :local:
        
        .. # ------------------( DESCRIPTION                        )------------------
        
        Installation
        ============
        
        BETSE currently supports **Linux**, **macOS**, and **Windows** out-of-the-box.
        
        Simple
        --------
        
        For new users, BETSE is readily installable as follows:
        
        .. # FIXME: Commented out until we actually have a working Windows installation script.
        
        .. # - Under **Windows 10**:
        .. #
        .. #   #. Install **Ubuntu Linux** via the `Windows Subsystem for Linux (WSL) <WSL_>`__.
        .. #   #. Open an **Ubuntu Linux terminal.** [#terminal]_
        .. #   #. Run the following commands in this terminal.
        .. # 
        .. #      wget https://gitlab.com/betse/betse/raw/master/bin/install/windows/betsee_windows_10.bash && source betsee_windows_10.bash
        
        .. # FIXME: Create a BETSE-specific installer reduced from this BETSEE installer.
        
        - Under `Ubuntu Linux 16.04 (Xenial Xerus)`_ and newer:
        
          #. Open a **terminal.** [#terminal]_
          #. Run the following commands.
        
             .. code:: bash
        
                wget https://gitlab.com/betse/betsee/raw/master/bin/install/linux/betsee_ubuntu_16_04.bash && source betsee_ubuntu_16_04.bash
        
        - Under all other platforms: :sup:`(e.g., macOS, Windows)`
        
          #. Install the **Python 3.x** [#python2_not]_ (e.g., 3.6) variant of
             Anaconda_. [#anaconda_not]_
          #. Open a **terminal.** [#terminal]_
          #. Run the following commands.
          
             #. Install **mandatory dependencies.** [#why_dependencies]_
          
                .. code:: bash
          
                   conda install dill
                   conda install -c conda-forge imageio
          
             #. Install **BETSE.** [#pip3_not]_
          
                .. code:: bash
          
                   python3 -m pip install betse
          
             #. (\ *Optional*\ ) Install **recommended dependencies.** While *not*
                required for basic usage, the following third-party packages are required
                for advanced functionality (e.g., gene regulatory networks, animation
                video encoding).
          
                .. code:: bash
          
                   conda install -c anaconda graphviz && \
                   conda install -c conda-forge ffmpeg networkx && \
                   conda install -c rmg pydot
        
        - (\ *Optional*\ ) Test **BETSE.** Run all modelling phases of a sample
          simulation from the current directory.
        
          .. code:: bash
        
             betse try
        
        
        .. [#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 *Terminal.app*.
        
           - **Ubuntu Linux:**
        
             #. Type ``Ctrl``\ +\ ``Alt``\ +\ ``t``.
        
        .. [#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
           installable <Advanced_>`__ with your platform-specific package manager (e.g.,
           Homebrew_ on macOS, APT_ on Ubuntu Linux). Doing so is non-trivial and, if
           performed incorrectly, could produce a performance-crippled single-core
           installation of BETSE – which would be bad. Anaconda_ suffers no such issues
           and is guaranteed to produce a performance-optimized multicore installation
           of BETSE on *all* supported platforms – which is good.
        
        .. [#why_dependencies]
           Most mandatory dependencies of BETSE (e.g., NumPy_, SciPy_) are already
           bundled by default with Anaconda_. Some (e.g., dill_, imageio_) are not.
           The latter require manual installation.
        
        .. [#pip3_not]
           Always run the ``python3 -m pip`` command to install Python packages into the
           active Anaconda_ environment. *Never* run the ``pip`` or ``pip3`` commands,
           which incorrectly refer to their non-\ Anaconda_ versions on some platforms
           (e.g., macOS), which prevents BETSE from finding packages installed with
           these commands – which is bad. The ``python3 -m pip`` command suffers no such
           issues and is guaranteed to install packages in a BETSE-aware manner on *all*
           supported platforms – which is good.
        
        Advanced
        --------
        
        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:: bash
        
                   git clone https://gitlab.com/betse/betse.git
        
             #. Prepare for installation.
        
                .. code:: bash
        
                   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:: bash
        
                   tar -xvzf betse-*.tar.gz
        
             #. (\ *Optional*\ ) Remove this tarball.
        
                .. code:: bash
        
                   rm betse-*.tar.gz
        
             #. Prepare for installation.
        
                .. code:: bash
        
                   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:: bash
        
                sudo python3 setup.py develop
        
           - **Non-editably,** installing a physical copy of the current BETSE codebase.
             Modifications to this code are ignored and thus require reinstallation.
        
             .. code:: bash
        
                sudo python3 setup.py install
        
        #. (\ *Optional*\ ) **Test BETSE,** running all modelling phases of a sample
           simulation from a new directory.
        
           .. code:: bash
        
              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_,
           APT_).
        
        .. [#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.
        
        Usage
        ============
        
        BETSE itself provides the ``betse`` command, a low-level command line interface
        (CLI) optimized for non-interactive scripting (e.g., for implementing `massively
        parallel genetic algorithms <genetic algorithms_>`_). See the following
        external documents for detailed usage instructions – 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.*\ )
        
        Alternately, our sister project BETSEE_ provides the ``betsee`` command, a
        high-level graphical user interface (GUI) optimized for interactive
        experimentation.
        
        Introduction
        ============
        
        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:
        
        Ions
        ----
        
        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
        cells.
        
        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`_.
        
        Validation
        ==========
        
        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
           potential_>`__.
        -  Bioelectrical signals at large-scale cellular wound sites.
        
        For details, see our recently published `introductory paper <Reference_>`__.
        
        License
        =======
        
        BETSE is open-source software `released <license_>`__ under the permissive `BSD
        2-clause license`_.
        
        Reference
        =========
        
        BETSE is formally described in our `introductory paper <2016 article_>`__.
        Third-party papers, theses, and other texts leveraging BETSE should (ideally)
        cite the following:
        
            `Pietak, Alexis`_ and `Levin, Michael`_, 2016. |2016 article name|_
            |2016 article supplement|_ [#supplement]_ |2016 journal name|_ *4*\ (55).
            :sup:`DOI: 10.3389/fbioe.2016.00055`
        
        Subsequent papers expanding the BETSE architecture with additional theory,
        experimental results, and comparative metrics include:
        
            `Pietak, Alexis`_ and `Levin, Michael`_, 2017. |2017 article name|_
            |2017 article supplement|_ [#supplement]_ |2017 journal name|_ *14*\ (134),
            p.20170425.  :sup:`DOI: 10.1098/rsif.2017.0425`
        
        .. # FIXME: Add an image thumbnail 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.
        
        Authors
        =======
        
        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/DEVELOP.md>`__, detailing development of the BETSE
           codebase – philosophy, workflow, and otherwise.
        -  `Testing <doc/md/TEST.md>`__, detailing testing of the BETSE codebase –
           `continuous integration`_, manual testing, and otherwise.
        -  `Freezing <doc/md/FREEZE.md>`__, detailing conversion of the BETSE codebase
           into redistributable platform-specific executable binaries.
        
        .. # ------------------( LINKS ~ betse                      )------------------
        .. _author list:
           doc/md/AUTHORS.md
        .. _codebase:
           https://gitlab.com/betse/betse/tree/master
        .. _contributors:
           https://gitlab.com/betse/betse/graphs/master
        .. _dependencies:
           doc/md/INSTALL.md
        .. _license:
           LICENSE
        .. _testing:
           https://gitlab.com/betse/betse/pipelines
        .. _tarballs:
           https://gitlab.com/betse/betse/tags
        
        .. # ------------------( LINKS ~ betse : docs               )------------------
        .. _BETSE 0.4 documentation:
           https://www.dropbox.com/s/n8qfms2oks9cvv2/BETSE04_Documentation_Dec1st2016.pdf?dl=0
        .. _BETSE 0.3 documentation:
           https://www.dropbox.com/s/fsxhjpipbiog0ru/BETSE_Documentation_Nov1st2015.pdf?dl=0
        
        .. # ------------------( LINKS ~ betsee                     )------------------
        .. _BETSEE:
           https://gitlab.com/betse/betsee
        .. _BETSEE codebase:
           https://gitlab.com/betse/betsee/tree/master
        
        .. # ------------------( LINKS ~ academia                   )------------------
        .. _Pietak, Alexis:
           https://www.researchgate.net/profile/Alexis_Pietak
        .. _Levin, Michael:
           https://ase.tufts.edu/biology/labs/levin
        .. _Channelpedia:
           http://channelpedia.epfl.ch
        .. _Paul Allen Discovery Center:
           http://www.alleninstitute.org/what-we-do/frontiers-group/discovery-centers/allen-discovery-center-tufts-university
        .. _Paul Allen Discovery Center award:
           https://www.alleninstitute.org/what-we-do/frontiers-group/news-press/press-resources/press-releases/paul-g-allen-frontiers-group-announces-allen-discovery-center-tufts-university
        .. _Paul G. Allen Frontiers Group:
           https://www.alleninstitute.org/what-we-do/frontiers-group
        .. _Tufts University:
           https://www.tufts.edu
        
        .. # ------------------( LINKS ~ paper ~ 2016               )------------------
        .. _2016 article:
           http://journal.frontiersin.org/article/10.3389/fbioe.2016.00055/abstract
        
        .. |2016 article name| replace::
           **Exploring instructive physiological signaling with the bioelectric tissue
           simulation engine (BETSE).**
        .. _2016 article name:
           http://journal.frontiersin.org/article/10.3389/fbioe.2016.00055/abstract
        
        .. |2016 article supplement| replace::
           **(**\ *Supplement*\ **).**
        .. _2016 article supplement:
           https://www.frontiersin.org/articles/file/downloadfile/203679_supplementary-materials_datasheets_1_pdf/octet-stream/Data%20Sheet%201.PDF/1/203679
        
        .. |2016 journal name| replace::
           *Frontiers in Bioengineering and Biotechnology,*
        .. _2016 journal name:
           http://journal.frontiersin.org/journal/bioengineering-and-biotechnology
        
        .. # ------------------( 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:
           http://rsif.royalsocietypublishing.org/content/14/134/20170425
        
        .. |2017 article supplement| replace::
           **(**\ *Supplement*\ **).**
        .. _2017 article supplement:
           https://figshare.com/collections/Supplementary_material_from_Bioelectric_gene_and_reaction_networks_computational_modelling_of_genetic_biochemical_and_bioelectrical_dynamics_in_pattern_regulation_/3878404
        
        .. |2017 journal name| replace::
           *Journal of The Royal Society Interface,*
        .. _2017 journal name:
           http://rsif.royalsocietypublishing.org
        
        .. # ------------------( LINKS ~ science                    )------------------
        .. _bioelectricity:
           https://en.wikipedia.org/wiki/Bioelectromagnetics
        .. _biochemical reaction networks:
           http://www.nature.com/subjects/biochemical-reaction-networks
        .. _electrodiffusion:
           https://en.wikipedia.org/wiki/Nernst%E2%80%93Planck_equation
        .. _electro-osmosis:
           https://en.wikipedia.org/wiki/Electro-osmosis
        .. _enzyme activity:
           https://en.wikipedia.org/wiki/Enzyme_assay
        .. _ephaptic coupling:
           https://en.wikipedia.org/wiki/Ephaptic_coupling
        .. _epigenetics:
           https://en.wikipedia.org/wiki/Epigenetics
        .. _extracellular environment:
           https://en.wikipedia.org/wiki/Extracellular
        .. _finite volume:
           https://en.wikipedia.org/wiki/Finite_volume_method
        .. _galvanotaxis:
           https://en.wiktionary.org/wiki/galvanotaxis
        .. _gap junction:
        .. _gap junctions:
           https://en.wikipedia.org/wiki/Gap_junction
        .. _gene products:
           https://en.wikipedia.org/wiki/Gene_product
        .. _gene regulatory networks:
           https://en.wikipedia.org/wiki/Gene_regulatory_network
        .. _genetics:
           https://en.wikipedia.org/wiki/Genetics
        .. _genetic algorithms:
           https://en.wikipedia.org/wiki/Genetic_algorithm
        .. _Hodgkin-Huxley (HH) formalism:
           https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model
        .. _local field potentials:
           https://en.wikipedia.org/wiki/Local_field_potential
        .. _membrane permeability:
           https://en.wikipedia.org/wiki/Cell_membrane
        .. _resting potential:
           https://en.wikipedia.org/wiki/Resting_potential
        .. _tight junctions:
           https://en.wikipedia.org/wiki/Tight_junction
        .. _transmembrane voltage:
           https://en.wikipedia.org/wiki/Membrane_potential
        .. _transepithelial potential:
           https://en.wikipedia.org/wiki/Transepithelial_potential_difference
        
        .. # ------------------( LINKS ~ science : ions             )------------------
        .. _anionic proteins:
           https://en.wikipedia.org/wiki/Ion#anion
        .. _bicarbonate: https://en.wikipedia.org/wiki/Bicarbonate
        .. _calcium:     https://en.wikipedia.org/wiki/Calcium_in_biology
        .. _chloride:    https://en.wikipedia.org/wiki/Chloride
        .. _hydrogen:    https://en.wikipedia.org/wiki/Hydron_(chemistry)
        .. _sodium:      https://en.wikipedia.org/wiki/Sodium_in_biology
        .. _potassium:   https://en.wikipedia.org/wiki/Potassium_in_biology
        
        .. # ------------------( LINKS ~ science : channels         )------------------
        .. _ion channel:
           https://en.wikipedia.org/wiki/Ion_channel
        .. _leak channels:
           https://en.wikipedia.org/wiki/Leak_channel
        .. _ligand-gated channels:
           https://en.wikipedia.org/wiki/Ligand-gated_ion_channel
        .. _voltage-gated ion channels:
           https://en.wikipedia.org/wiki/Voltage-gated_ion_channel
        
        .. |calcium-gated K+ channels| replace::
           Calcium-gated K\ :sup:`+` channels
        .. _calcium-gated K+ channels:
           https://en.wikipedia.org/wiki/Calcium-activated_potassium_channel
        
        .. # ------------------( LINKS ~ science : channels : type  )------------------
        .. _HCN1:   http://channelpedia.epfl.ch/ionchannels/61
        .. _HCN2:   http://channelpedia.epfl.ch/ionchannels/62
        .. _HCN4:   http://channelpedia.epfl.ch/ionchannels/64
        .. _Kir2.1: http://channelpedia.epfl.ch/ionchannels/42
        .. _Kv1.1:  http://channelpedia.epfl.ch/ionchannels/1
        .. _Kv1.2:  http://channelpedia.epfl.ch/ionchannels/2
        .. _Kv1.5:  http://channelpedia.epfl.ch/ionchannels/5
        .. _Kv3.3:  http://channelpedia.epfl.ch/ionchannels/13
        .. _Kv3.4:  http://channelpedia.epfl.ch/ionchannels/14
        .. _Nav1.2: http://channelpedia.epfl.ch/ionchannels/121
        .. _Nav1.3: http://channelpedia.epfl.ch/ionchannels/122
        .. _Nav1.6: http://channelpedia.epfl.ch/ionchannels/125
        .. _L-type Ca:   http://channelpedia.epfl.ch/ionchannels/212
        .. _T-type Ca:   https://en.wikipedia.org/wiki/T-type_calcium_channel
        
        .. |P/Q-type Ca| replace:: :sup:`P`\ /\ :sub:`Q`-type Ca
        .. _P/Q-type Ca:
           http://channelpedia.epfl.ch/ionchannels/78
        
        .. # ------------------( LINKS ~ science : pumps : type     )------------------
        .. _ion pumps:
           https://en.wikipedia.org/wiki/Active_transport
        
        .. # ------------------( LINKS ~ science : pumps : type     )------------------
        .. _V-ATPase: https://en.wikipedia.org/wiki/V-ATPase
        
        .. |Ca2+-ATPase| replace:: Ca\ :sup:`2+`-ATPase
        .. _Ca2+-ATPase: https://en.wikipedia.org/wiki/Calcium_ATPase
        
        .. |H+/K+-ATPase| replace:: H\ :sup:`+`/K\ :sup:`+`-ATPase
        .. _H+/K+-ATPase: https://en.wikipedia.org/wiki/Hydrogen_potassium_ATPase
        
        .. |Na+/K+-ATPase| replace:: Na\ :sup:`+`/K\ :sup:`+`-ATPase
        .. _Na+/K+-ATPase: https://en.wikipedia.org/wiki/Na%2B/K%2B-ATPase
        
        .. # ------------------( LINKS ~ science : computer         )------------------
        .. _Big Data:
           https://en.wikipedia.org/wiki/Big_data
        .. _comma-separated values:
           https://en.wikipedia.org/wiki/Comma-separated_values
        .. _continuous integration:
           https://en.wikipedia.org/wiki/Continuous_integration
        .. _directed graphs:
           https://en.wikipedia.org/wiki/Directed_graph
        .. _genenic algorithms:
           https://en.wikipedia.org/wiki/Genetic_algorithm
        .. _knowledge-based systems:
           https://en.wikipedia.org/wiki/Knowledge-based_systems
        
        .. # ------------------( LINKS ~ os : linux                 )------------------
        .. _APT:
           https://en.wikipedia.org/wiki/Advanced_Packaging_Tool
        .. _POSIX:
           https://en.wikipedia.org/wiki/POSIX
        .. _Ubuntu:
        .. _Ubuntu Linux:
           https://www.ubuntu.com
        .. _Ubuntu Linux 16.04 (Xenial Xerus):
           http://releases.ubuntu.com/16.04
        
        .. # ------------------( LINKS ~ os : macos                 )------------------
        .. _Homebrew:
           http://brew.sh
        .. _MacPorts:
           https://www.macports.org
        
        .. # ------------------( LINKS ~ os : windows               )------------------
        .. _WSL:
           https://msdn.microsoft.com/en-us/commandline/wsl/install-win10
        
        .. # ------------------( LINKS ~ software                   )------------------
        .. _Anaconda:
           https://www.continuum.io/downloads
        .. _Appveyor:
           https://ci.appveyor.com/project/betse/betse/branch/master
        .. _BSD 2-clause license:
           https://opensource.org/licenses/BSD-2-Clause
        .. _dill:
           https://pypi.python.org/pypi/dill
        .. _FFmpeg:
           https://ffmpeg.org
        .. _Git:
           https://git-scm.com/downloads
        .. _GitLab-CI:
           https://about.gitlab.com/gitlab-ci
        .. _Graphviz:
           http://www.graphviz.org
        .. _imageio:
           https://imageio.github.io
        .. _Libav:
           https://libav.org
        .. _Matplotlib:
           http://matplotlib.org
        .. _NumPy:
           http://www.numpy.org
        .. _MEncoder:
           https://en.wikipedia.org/wiki/MEncoder
        .. _Python 3:
           https://www.python.org
        .. _py.test:
           http://pytest.org
        .. _SciPy:
           http://www.scipy.org
        .. _YAML:
           http://yaml.org
        
        .. # ------------------( LINKS ~ software : pyside2         )------------------
        .. _PySide2:
           https://wiki.qt.io/PySide2
        .. _PySide2 5.6:
           https://code.qt.io/cgit/pyside/pyside.git/log/?h=5.6
        .. _PySide2 installation:
           https://wiki.qt.io/PySide2_GettingStarted
        .. _PySide2 PPA:
           https://launchpad.net/~thopiekar/+archive/ubuntu/pyside-git
        .. _Qt:
           https://www.qt.io
        .. _Qt 5.6:
           https://wiki.qt.io/Qt_5.6_Release
        
Keywords: biology,multiphysics,science,simulator
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: Environment :: Console
Classifier: Environment :: MacOS X
Classifier: Environment :: Win32 (MS Windows)
Classifier: Environment :: X11 Applications
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: BSD License
Classifier: Natural Language :: English
Classifier: Operating System :: OS Independent
Classifier: Topic :: Scientific/Engineering :: Bio-Informatics
Classifier: Programming Language :: Python :: 3.4
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: 3.7
