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
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
|
#!/usr/bin/env python3
"""
Fig. 1 from:
M. Tsodyks, K. Pawelzik, H. Markram
Neural Networks with Dynamic Synapses
Neural Computation 10, 821–835 (1998)
https://doi.org/10.1162/089976698300017502
Sebastian Schmitt, 2022
"""
import numpy as np
import matplotlib.pyplot as plt
from brian2 import (
NeuronGroup,
Synapses,
SpikeGeneratorGroup,
SpikeMonitor,
StateMonitor,
)
from brian2 import ms, mV, pA, Mohm, Gohm, Hz
from brian2 import run
def get_neuron(tau_mem, R_in):
"""
tau_mem -- membrane time constant
R_in -- input resistance
"""
neuron = NeuronGroup(1,
"""
tau_mem : second
I_syn : ampere
R_in : ohm
dv/dt = -v/tau_mem + (R_in*I_syn)/tau_mem : volt
""",
method="exact")
neuron.tau_mem = tau_mem
neuron.R_in = R_in
return neuron
def get_synapses(stimulus, neuron, tau_inact, A_SE, U_SE, tau_rec, tau_facil=None):
"""
stimulus -- input stimulus
neuron -- target neuron
tau_inact -- inactivation time constant
A_SE -- absolute synaptic strength
U_SE -- utilization of synaptic efficacy
tau_rec -- recovery time constant
tau_facil -- facilitation time constant (optional)
"""
synapses_eqs = """
dx/dt = z/tau_rec : 1 (clock-driven) # recovered
dy/dt = -y/tau_inact : 1 (clock-driven) # active
A_SE : ampere
U_SE : 1
tau_inact : second
tau_rec : second
z = 1 - x - y : 1 # inactive
I_syn_post = A_SE*y : ampere (summed)
"""
if tau_facil:
synapses_eqs += """
du/dt = -u/tau_facil : 1 (clock-driven)
tau_facil : second
"""
synapses_action = """
u += U_SE*(1-u)
y += u*x # important: update y first
x += -u*x
"""
else:
synapses_action = """
y += U_SE*x # important: update y first
x += -U_SE*x
"""
synapses = Synapses(stimulus,
neuron,
model=synapses_eqs,
on_pre=synapses_action,
method="exponential_euler")
synapses.connect()
# start fully recovered
synapses.x = 1
synapses.tau_inact = tau_inact
synapses.A_SE = A_SE
synapses.U_SE = U_SE
synapses.tau_rec = tau_rec
if tau_facil:
synapses.tau_facil = tau_facil
return synapses
def get_stimulus(start, stop, frequency):
"""
start -- start time of stimulus
stop -- stop time of stimulus
frequency -- frequency of stimulus
"""
times = np.arange(start / ms, stop / ms, 1 / (frequency / Hz) * 1e3) * ms
stimulus = SpikeGeneratorGroup(1, [0] * len(times), times)
return stimulus
parameters = {
"A": {
"neuron": {"tau_mem": 40 * ms,
"R_in": 100*Mohm},
"synapse": {
"tau_inact": 3 * ms,
"A_SE": 250 * pA,
"tau_rec": 800 * ms,
"U_SE": 0.6, # 0.5 from publication does not match plot
},
"stimulus": {"start": 100 * ms,
"stop": 1100 * ms,
"frequency": 20 * Hz},
"simulation": {"duration": 1200 * ms},
"plot": {
"title": "A) D - 20 Hz",
"ylim": [0, 1],
"xlim": [0, 1200],
"xtickstep": 200,
},
},
"B": {
"neuron": {"tau_mem": 60 * ms,
"R_in": 1*Gohm},
"synapse": {
"tau_inact": 1.5 * ms,
"A_SE": 1540 * pA,
"tau_rec": 130 * ms,
"U_SE": 0.03,
"tau_facil": 530 * ms,
},
"stimulus": {"start": 100 * ms,
"stop": 1100 * ms,
"frequency": 20 * Hz},
"simulation": {"duration": 1200 * ms},
"plot": {
"title": "B) F - 20 Hz",
"ylim": [0, 14.9],
"xlim": [0, 1200],
"xtickstep": 200,
},
},
"C": {
"neuron": {"tau_mem": 60 * ms,
"R_in": 1*Gohm},
"synapse": {
"tau_inact": 1.5 * ms,
"A_SE": 1540 * pA,
"tau_rec": 130 * ms,
"U_SE": 0.03,
"tau_facil": 530 * ms,
},
"stimulus": {"start": 100 * ms,
"stop": 375 * ms,
"frequency": 70 * Hz},
"simulation": {"duration": 500 * ms},
"plot": {
"title": "C) F - 70 Hz",
"ylim": [0, 20],
"xlim": [0, 500],
"xtickstep": 50,
},
},
}
fig, axes = plt.subplots(3)
for ax, (panel, p) in zip(axes, parameters.items()):
neuron = get_neuron(**p["neuron"])
stimulus = get_stimulus(**p["stimulus"])
synapses = get_synapses(stimulus, neuron, **p["synapse"])
state_monitor_neuron = StateMonitor(neuron, ["v"], record=True)
run(p["simulation"]["duration"])
ax.plot(
state_monitor_neuron.t / ms,
state_monitor_neuron[0].v / mV,
label=p["plot"]["title"],
)
ax.set_xlim(*p["plot"]["xlim"])
ax.set_ylim(*p["plot"]["ylim"])
ax.set_ylabel("mV")
ax.set_xlabel("Time (ms)")
ax.set_xticks(
np.arange(
p["plot"]["xlim"][0],
p["plot"]["xlim"][1] + p["plot"]["xtickstep"],
p["plot"]["xtickstep"],
)
)
ax.legend()
plt.show()
|
