Example: Degradable buffer

Calcium is heavily buffered in cells, as it is a major second messenger molecule.

Calbindin D28K dynamics

The calcium buffering protein Calbindin D28K has 6 EF-hands, four of which are active calcium ion binding sites. These sites are not equally active. A calcium ion is not free to bind to any of the sites equally. Instead, calcium ions are bound in sequence: 1, 4, 5, 3 with the last binding having the lowest affinity. (Venters et al., 2003.)

(To be clear, these dynamics are not representative of all calcium buffers; Parvalbumin and Calbindin D9K show little conformational change when carrying calcium.)

\[\mathrm{Ca} + \mathrm{Calbindin_0} \rightleftharpoons \mathrm{Calbindin_1}\]
\[\mathrm{Ca} + \mathrm{Calbindin_1} \rightleftharpoons \mathrm{Calbindin_{14}}\]
\[\mathrm{Ca} + \mathrm{Calbindin_{14}} \rightleftharpoons \mathrm{Calbindin_{145}}\]
\[\mathrm{Ca} + \mathrm{Calbindin_{145}} \rightleftharpoons \mathrm{Calbindin_{1453}}\]

A model

For our model, let us suppose that instead of calbindin D28K specifically, which has its own very specific binding affinities, we have some arbitrary buffer buf that also has 4 binding sites that load sequentially.

from neuron import h, rxd
# where
soma = h.Section(name="soma")
cyt = rxd.Region([soma], nrn_region="i")
# who
ca = rxd.Species(cyt, name="ca", charge=2, initial=1e-4)
buf = rxd.Species(cyt, name="buf", initial=1e-4)
cabuf = rxd.Species(cyt, name="cab2uf", initial=0)
# what
buffering = rxd.Reaction(2 * ca + buf, cabuf, 1e6, 1e-2)
degradation = rxd.Rate(buf, -1e-3 * buf)

For versions of NEURON before 7.7, we need to initialize the simulation here to enable using pointers for

Let’s set up some recording:

t = h.Vector()
ca_vec = h.Vector()
buf_vec = h.Vector()

A more realistic model would include