From d3d7b46b61ef0e3a788047da26e8aecf5015c75a Mon Sep 17 00:00:00 2001
From: Jan Breuer <j.m.br@gmx.de>
Date: Tue, 20 Aug 2024 17:37:17 +0200
Subject: [PATCH] Add Michaelis Menten kinetic documentation

---
 doc/interface/reaction/index.rst              |  1 +
 .../reaction/michaelis_menten_kinetics.rst    | 41 +++++++++++++++++++
 doc/modelling/reaction/index.rst              |  1 +
 .../reaction/michaelis_menten_kinetics.rst    | 40 ++++++++++++++++++
 4 files changed, 83 insertions(+)
 create mode 100644 doc/interface/reaction/michaelis_menten_kinetics.rst
 create mode 100644 doc/modelling/reaction/michaelis_menten_kinetics.rst

diff --git a/doc/interface/reaction/index.rst b/doc/interface/reaction/index.rst
index fc80b2f21..5e00dd6d7 100644
--- a/doc/interface/reaction/index.rst
+++ b/doc/interface/reaction/index.rst
@@ -7,6 +7,7 @@ Reaction models
     :maxdepth: 2
 
     mass_action_law
+    michaelis_menten_kinetics
 
 Externally dependent reaction models
 ------------------------------------
diff --git a/doc/interface/reaction/michaelis_menten_kinetics.rst b/doc/interface/reaction/michaelis_menten_kinetics.rst
new file mode 100644
index 000000000..76884ea2e
--- /dev/null
+++ b/doc/interface/reaction/michaelis_menten_kinetics.rst
@@ -0,0 +1,41 @@
+.. _michaelis_menten_kinetics_config:
+
+Michaelis Menten kinetics
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+**Group /input/model/unit_XXX/reaction - REACTION_MODEL = MICHAELIS_MENTEN**
+
+``MM_STOICHIOMETRY_BULK``
+
+   Stochiometric matrix :math:`S`.
+   The substrate component :math:`c_S` is identified by the index of the first negative entry in the stoichiometry of the corresponding reaction.
+   Input as reaction index major.
+   
+   ================  =============================  ========================================================
+   **Type:** double  **Range:** :math:`\mathbb{R}`  **Length:** :math:`\texttt{NREACT} \cdot \texttt{NCOMP}`
+   ================  =============================  ========================================================
+   
+``MM_VMAX``
+
+	Limiting rate :math:`\mu_{\mathrm{max},j}` at saturation.
+   
+   ================  =============================  ===================================
+   **Type:** double  **Range:** :math:`\mathbb{R}`  **Length:** :math:`\texttt{NREACT}`
+   ================  =============================  ===================================
+
+``MM_KMM``
+
+	Michaelis constant :math:`k_{\mathrm{MM},j}`.
+   
+   ================  =============================  ===================================
+   **Type:** double  **Range:** :math:`\mathbb{R}`  **Length:** :math:`\texttt{NREACT}`
+   ================  =============================  ===================================
+
+``MM_KI``
+
+	Inhibition constant :math:`k_{\mathrm{I},j,i}` w.r.t component :math:`i` and reaction :math:`j`. If :math:`k_{\mathrm{I},j,i} <= 0`, the component does not inhibit the reaction.
+	Input as reaction index major.
+   
+   ================  =============================  ========================================================
+   **Type:** double  **Range:** :math:`\mathbb{R}`  **Length:** :math:`\texttt{NREACT} \cdot \texttt{NCOMP}`
+   ================  =============================  ========================================================
\ No newline at end of file
diff --git a/doc/modelling/reaction/index.rst b/doc/modelling/reaction/index.rst
index 504120518..172908182 100644
--- a/doc/modelling/reaction/index.rst
+++ b/doc/modelling/reaction/index.rst
@@ -9,6 +9,7 @@ reaction mechanism.
 CADET features one reaction type:
 
  - :ref:`mass_action_law_model` (most commonly used)
+ - :ref:`michaelis_menten_kinetics_model`
 
 
 .. _dependence-on-external-function_react:
diff --git a/doc/modelling/reaction/michaelis_menten_kinetics.rst b/doc/modelling/reaction/michaelis_menten_kinetics.rst
new file mode 100644
index 000000000..2efe7cc40
--- /dev/null
+++ b/doc/modelling/reaction/michaelis_menten_kinetics.rst
@@ -0,0 +1,40 @@
+.. _michaelis_menten_kinetics_model:
+
+Michaelis Menten kinetics
+-------------------------
+
+Implements liquid phase Michaelis-Menten reaction kinetics of the form
+
+.. math::
+
+    \begin{aligned}
+        f_\text{react} = S \mathbf{\nu},
+    \end{aligned}
+
+where :math:`S` is the stoichiometric matrix and the fluxes are given by
+
+.. math::
+
+    \begin{aligned}
+        \nu_j = \frac{\mu_{\mathrm{max},j} \, c_S}{k_{\mathrm{MM},j} + c_S},
+    \end{aligned}
+
+where
+
+- :math:`j` is the reaction index,
+- :math:`c_S` is the substrate component,
+- :math:`\mu_{\mathrm{max},j}`, is the limiting rate approached by the system at saturation,
+- :math:`k_{\mathrm{MM},j}` is the Michaelis constant, which is defined as the concentration of substrate at which the reaction rate is half ov :math:`\mu_{\mathrm{max},j}`.
+
+
+In addition, the reaction might be inhibited by other components.
+In this case, the flux has the form
+
+.. math::
+
+    \begin{aligned}
+        \nu_j = \frac{\mu_{\mathrm{max},j} \, c_S}{k_{\mathrm{MM},j} + c_S} \prod_i \frac{k_{\mathrm{I},j,i}}{k_{\mathrm{I},j,i} + c_{\mathrm{I},i}}.
+    \end{aligned}
+
+Here, :math:`k_{\mathrm{I},j,i}` is the inhibition constant w.r.t component :math:`i` and reaction :math:`j`.
+If :math:`k_{\mathrm{I},j,i} <= 0`, component :math:`i` does not inhibit the reaction.