1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
|
How to plot functions
=====================
Models of synapses and neurons are typically composed of a series of functions.
To affirm their correct implementation a plot is often helpful.
Consider the following membrane voltage dependent Hodgkin-Huxley equations::
from brian2 import *
VT = -63*mV
eq = Equations("""
alpha_m = 0.32*(mV**-1)*4*mV/exprel((13*mV-v+VT)/(4*mV))/ms : Hz
beta_m = 0.28*(mV**-1)*5*mV/exprel((v-VT-40*mV)/(5*mV))/ms : Hz
alpha_h = 0.128*exp((17*mV-v+VT)/(18*mV))/ms : Hz
beta_h = 4./(1+exp((40*mV-v+VT)/(5*mV)))/ms : Hz
alpha_n = 0.032*(mV**-1)*5*mV/exprel((15*mV-v+VT)/(5*mV))/ms : Hz
beta_n = .5*exp((10*mV-v+VT)/(40*mV))/ms : Hz
tau_n = 1/(alpha_n + beta_n) : second
tau_m = 1/(alpha_m + beta_m) : second
tau_h = 1/(alpha_h + beta_h) : second
""")
We can do the following to plot them as function of membrane voltage::
group = NeuronGroup(100, eq + Equations("v : volt"))
group.v = np.linspace(-100, 100, len(group))*mV
plt.plot(group.v/mV, group.tau_m[:]/ms, label="tau_m")
plt.plot(group.v/mV, group.tau_n[:]/ms, label="tau_n")
plt.plot(group.v/mV, group.tau_h[:]/ms, label="tau_h")
plt.xlabel('membrane voltage / mV')
plt.ylabel('tau / ms')
plt.legend()
.. image:: images/function_plot.png
Note that we need to use ``[:]`` for the ``tau_...`` equations, because Brian cannot
resolve the external constant ``VT`` otherwise. Alternatively we could have supplied
the constant in the namespace of the `NeuronGroup`, see :doc:`/advanced/namespaces`.
|
