Examples
============

The following interactive Jupyter notebook examples demonstrate the capabilities
of the jLM Python interface for `Lattice Microbes <https://lattice-microbes.org>`_.
These examples cover both Chemical Master Equation (CME) and Reaction-Diffusion 
Master Equation (RDME) simulations, showcasing various biochemical systems and
modeling approaches.

Basic Chemical Kinetics
-----------------------

**Bimolecular Reactions**

The bimolecular reaction examples demonstrate fundamental chemical kinetics:

* `bimol.html <_static/bimol.html>`_ - Basic bimolecular reaction :math:`A + B \to C`
* `bimolConc.html <_static/bimolConc.html>`_ - Bimolecular reactions with concentration effects
* `bimol-pp.html <_static/bimol-pp.html>`_ - Post-processing analysis of bimolecular systems

**Enzymatic Reactions**

* `MichaelisMenten.html <_static/MichaelisMenten.html>`_ - Classic Michaelis-Menten enzyme kinetics

.. math::
    E + S &\rightleftharpoons ES \\
    ES &\to E + P

where :math:`E` is enzyme, :math:`S` is substrate, :math:`ES` is the enzyme-substrate
complex, and :math:`P` is the product.

Population Dynamics
-------------------

**Predator-Prey Systems**

* `LotkaVolterra.html <_static/LotkaVolterra.html>`_ - Classic Lotka-Volterra predator-prey dynamics

The Lotka-Volterra system models population oscillations:

.. math::
    X &\to 2X \\
    X + Y &\to 2Y \\
    Y &\to \emptyset

where :math:`X` represents prey and :math:`Y` represents predators.

Gene Regulation and Cellular Processes
--------------------------------------

**Gene Expression Models**

* `rnaprotein.html <_static/rnaprotein.html>`_ - RNA transcription and protein translation dynamics
* `lac2state.html <_static/lac2state.html>`_ - Two-state lac operon gene regulation model

**Developmental Biology**

* `minde.html <_static/minde.html>`_ - MinDE system for bacterial cell division dynamics

The MinDE system demonstrates protein oscillations crucial for proper cell division
positioning in bacteria.


Advanced Simulation Techniques  
-----------------------------

**Model Extension and Customization**

* `extendcme.html <_static/extendcme.html>`_ - Extending CME simulations with custom solvers
* `extendrdme.html <_static/extendrdme.html>`_ - Extending RDME simulations for spatial systems


Getting Started
--------------

**Interactive Documentation**

* `notebook.html <_static/jLM-doc.html>`_ - General jLM documentation and tutorial notebook

This comprehensive notebook provides an introduction to the jLM interface,
covering basic concepts, simulation setup, and result analysis workflows.

Running the Examples
-------------------

To run these examples locally, ensure you have jLM installed with Jupyter support:

.. code-block:: bash

    # Install jLM with notebook dependencies
    pip install jLM[notebook]
    
    # Start Jupyter notebook server
    jupyter notebook

The HTML files provided here are static exports of interactive Jupyter notebooks.
For the full interactive experience with live code execution, download the 
corresponding ``.ipynb`` files from the jLM examples repository.

Each example includes:

* **Model definition** using jLM's Python API
* **Simulation parameter setup** including solver selection and runtime options  
* **Result visualization** with matplotlib and other plotting libraries
* **Analysis workflows** demonstrating post-processing techniques

For spatial simulations (RDME), examples also demonstrate:

* **Geometric region construction** using jLM's RegionBuilder tools
* **Species placement and diffusion** parameter specification
* **Spatial visualization** of concentration profiles and particle trajectories