Reaction Diffusion#

In this example we consider a model where calcium ions interact with a buffer. We also add calcium extrusion.

[1]:

import sinaps as sn

Initialization#

Creating a sample neuron:

[2]:

nrn = sn.Neuron([(0,1),(1,2),(1,3),(3,4)])
nrn.plot()

Calculating layout...[OK]

[2]:

Settings channels: note that the Hodgkin_Huxley_Ca channel needs to be added to account for calcium entry through voltage-gated calcium channels. The Hodgkin_Huxley channels only contains sodium, potassium and leak channels.

[3]:

nrn[0].clear_channels()#Reset all channels, useful if you re-run this cell (does nothing the first time)
nrn[0].add_channel(sn.channels.PulseCurrent(500,2,3),0)
nrn[0].add_channel(sn.channels.Hodgkin_Huxley())
nrn[0].add_channel(sn.channels.Hodgkin_Huxley_Ca(gCa=14.5,V_Ca=115))

[4]:

sim = sn.Simulation(nrn,dx=10)

[5]:

sim.run((0,100))

100%|██████████| 100.0/100 [00:02<00:00, 36.65ms/s]

[6]:

sim.plot()

[6]:

Chemical reactions#

Ion species can be added to the model via the function add_species

nrn.add_species(sn.Species.Ca)

Chemical reactions are defined with the reaction equation and the reaction rates:

\[Ca + Bf \rightleftharpoons_{k_2}^{k_1} BfCa\]

Reactions are simulated during the electrodiffusion simulation.

Note that Species are automatically added to the neuron if they are not already present.

[7]:

#Reset reaction / not useful the first time
nrn.reactions=[]

[8]:

#shortcuts
Ca=sn.Species.Ca
BF=sn.Species.Buffer
BFB=sn.Species.Buffer_Ca

[9]:

nrn.add_reaction(
    {Ca:1,
     BF:1},
    {BFB:1},
    k1=0.2,
    k2=0.1)

The calcium extrusion is modeled using the equation:

\[Ca \rightleftharpoons^{k_1} \emptyset\]
[10]:

#Calcium extrusion
nrn.add_reaction(
    {Ca:1},
    {},
    k1=0.05,k2=0)

Initial concentrations can be set:

[11]:

#Calcium initial concentration
for s in nrn.sections:
    s.C0[Ca]=10**(-4)
    s.C0[BF]=2*10**(-3)

Running electro diffusion simulatiom#

[12]:

sim.run_diff(max_step=1)

100%|██████████| 100.0/100 [00:02<00:00, 37.03ms/s]

Plotting results#

[13]:

sim.plot.C(Ca)

[13]:

[14]:

sim.plot.C(BFB)

[14]:

[15]:

(sim.plot.V().opts(width=900,height=200)
 + sim.plot.C(Ca) .opts(width=900,height=200)
 + sim.plot.C(BFB).opts(width=900,height=200)
).cols(1).opts(plot={'shared_axes':False})

WARNING:param.OverlayPlot08807: responsive mode could not be enabled because fixed width and height were specified.
WARNING:param.OverlayPlot09244: responsive mode could not be enabled because fixed width and height were specified.
WARNING:param.OverlayPlot09680: responsive mode could not be enabled because fixed width and height were specified.

[15]:

[16]:

sim.plot.C_field(Ca)

[16]:

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