Gating Functions
================

.. module:: microscopic_gating.gating

This module implements gating functions that determine bridge probability
as a function of surface occupancy.

Symmetric Gating
----------------

.. autoclass:: SymmetricGating
   :members:
   :member-order: bysource
   :show-inheritance:

Asymmetric Gating
-----------------

.. autoclass:: AsymmetricGating
   :members:
   :member-order: bysource
   :show-inheritance:

Theory Background
-----------------

Symmetric Gating
~~~~~~~~~~~~~~~~

For symmetric binding where :math:`K_P \approx K_N \approx K_d`, the gating
function is:

.. math::

   G(\phi) = \theta(\phi)[1-\theta(\phi)]

This reaches a maximum of 1/4 at :math:`\phi = K`.

Asymmetric Gating
~~~~~~~~~~~~~~~~~

For asymmetric binding with different particle and network affinities:

.. math::

   G(\phi) = \theta_P(\phi)[1-\theta_N(\phi)]

This accounts for different binding strengths on the particle versus network sides.