def get_Izh_FS_component():
"""
Load Fast spiking Izhikevich XML definition from file and parse into
Abstraction Layer of Python API.
"""
izhi_fs = al.Dynamics(
name='IzhikevichFS',
parameters=[
al.Parameter('a', un.per_time),
al.Parameter('b', un.conductance / (un.voltage**2)),
al.Parameter('c', un.voltage),
al.Parameter('k', un.conductance / un.voltage),
al.Parameter('Vr', un.voltage),
al.Parameter('Vt', un.voltage),
al.Parameter('Vb', un.voltage),
al.Parameter('Vpeak', un.voltage),
al.Parameter('Cm', un.capacitance)
],
analog_ports=[
al.AnalogReducePort('iSyn', un.current, operator="+"),
al.AnalogReducePort('iExt', un.current, operator="+"),
al.AnalogSendPort('U', un.current),
al.AnalogSendPort('V', un.voltage)
],
event_ports=[al.EventSendPort("spikeOutput")],
state_variables=[
al.StateVariable('V', un.voltage),
al.StateVariable('U', un.current)
],
regimes=[
al.Regime('dU/dt = a * (b * pow(V - Vb, 3) - U)',
'dV/dt = V_deriv',
transitions=[
al.On('V > Vpeak',
do=['V = c',
al.OutputEvent('spikeOutput')],
to='subthreshold')
],
name="subthreshold"),
al.Regime('dU/dt = - U * a',
'dV/dt = V_deriv',
transitions=[al.On('V > Vb', to="subthreshold")],
name="subVb")
],
aliases=[
"V_deriv := (k * (V - Vr) * (V - Vt) - U + iExt + iSyn) / Cm"
]) # @IgnorePep8
return izhi_fs
def spiking_component_type_to_nineml(cls):
"""Return a 9ML ComponentClass describing the neuron model."""
iaf = al.ComponentClass(
name="iaf_tau",
regimes=[
al.Regime(
name="subthreshold_regime",
time_derivatives=["dv/dt = (v_rest - v)/tau_m + (i_offset + i_syn)/cm"],
transitions=al.On("v > v_thresh",
do=["t_spike = t",
"v = v_reset",
al.OutputEvent('spike_output')],
to="refractory_regime"),
),
al.Regime(
name="refractory_regime",
time_derivatives=["dv/dt = 0"],
transitions=[al.On("t >= t_spike + tau_refrac",
to="subthreshold_regime")],
)
],
state_variables=[
al.StateVariable('v'), #, dimension='[V]' # '[V]' should be an alias for [M][L]^2[T]^-3[I]^-1
al.StateVariable('t_spike'), #, dimension='[T]'
],
analog_ports=[al.AnalogSendPort("v"),
al.AnalogReducePort("i_syn", reduce_op="+"), ],
event_ports=[al.EventSendPort('spike_output'), ],
parameters=['cm', 'tau_refrac', 'tau_m', 'v_reset', 'v_rest', 'v_thresh', 'i_offset'] # add dimensions, or infer them from dimensions of variables
# in fact, we should be able to infer what are the parameters, without listing them
)
return iaf
def create_leaky_integrate_and_fire():
dyn = al.Dynamics(
name='LeakyIntegrateAndFire',
regimes=[
al.Regime('dv/dt = (i_synaptic*R - v)/tau',
transitions=[al.On('v > v_threshold',
do=[al.OutputEvent('spike_output'),
al.StateAssignment(
'refractory_end',
't + refractory_period'),
al.StateAssignment('v',
'v_reset')],
to='refractory')],
name='subthreshold'),
al.Regime(transitions=[al.On('t > refractory_end',
to='subthreshold')],
name='refractory')],
state_variables=[al.StateVariable('v', dimension=un.voltage),
al.StateVariable('refractory_end',
dimension=un.time)],
parameters=[al.Parameter('R', un.resistance),
al.Parameter('refractory_period', un.time),
al.Parameter('v_reset', un.voltage),
al.Parameter('v_threshold', un.voltage),
al.Parameter('tau', un.time)],
analog_ports=[al.AnalogReducePort('i_synaptic', un.current,
operator='+'),
al.AnalogSendPort('refractory_end', un.time),
al.AnalogSendPort('v', un.voltage)])
return dyn
def create_izhikevich():
subthreshold_regime = al.Regime(
name="subthreshold_regime",
time_derivatives=[
"dV/dt = alpha*V*V + beta*V + zeta - U + Isyn / C_m",
"dU/dt = a*(b*V - U)",
],
transitions=[
al.On("V > theta",
do=["V = c", "U = U+ d",
al.OutputEvent('spike')],
to='subthreshold_regime')
])
ports = [
al.AnalogSendPort("V", un.voltage),
al.AnalogReducePort("Isyn", un.current, operator="+")
]
parameters = [
al.Parameter('theta', un.voltage),
al.Parameter('a', un.per_time),
al.Parameter('b', un.per_time),
al.Parameter('c', un.voltage),
al.Parameter('d', old_div(un.voltage, un.time)),
al.Parameter('C_m', un.capacitance),
al.Parameter('alpha', old_div(un.dimensionless,
(un.voltage * un.time))),
al.Parameter('beta', un.per_time),
al.Parameter('zeta', old_div(un.voltage, un.time))
]
state_variables = [
al.StateVariable('V', un.voltage),
al.StateVariable('U', old_div(un.voltage, un.time))
]
c1 = al.Dynamics(name="Izhikevich",
parameters=parameters,
state_variables=state_variables,
regimes=[subthreshold_regime],
analog_ports=ports)
return c1
def create_hodgkin_huxley():
"""A Hodgkin-Huxley single neuron model.
Written by Andrew Davison.
See http://phobos.incf.ki.se/src_rst/
examples/examples_al_python.html#example-hh
"""
aliases = [
"q10 := 3.0**((celsius - qfactor)/tendegrees)", # temperature correction factor @IgnorePep8
"m_alpha := m_alpha_A*(V-m_alpha_V0)/(exp(-(V-m_alpha_V0)/m_alpha_K) - 1.0)", # @IgnorePep8
"m_beta := m_beta_A*exp(-(V-m_beta_V0)/m_beta_K)",
"mtau := 1.0/(q10*(m_alpha + m_beta))",
"minf := m_alpha/(m_alpha + m_beta)",
"h_alpha := h_alpha_A*exp(-(V-h_alpha_V0)/h_alpha_K)",
"h_beta := h_beta_A/(exp(-(V-h_beta_V0)/h_beta_K) + 1.0)",
"htau := 1.0/(q10*(h_alpha + h_beta))",
"hinf := h_alpha/(h_alpha + h_beta)",
"n_alpha := n_alpha_A*(V-n_alpha_V0)/(exp(-(V-n_alpha_V0)/n_alpha_K) - 1.0)", # @IgnorePep8
"n_beta := n_beta_A*exp(-(V-n_beta_V0)/n_beta_K)",
"ntau := 1.0/(q10*(n_alpha + n_beta))",
"ninf := n_alpha/(n_alpha + n_beta)",
"gna := gnabar*m*m*m*h",
"gk := gkbar*n*n*n*n",
"ina := gna*(ena - V)",
"ik := gk*(ek - V)",
"il := gl*(el - V )"
]
hh_regime = al.Regime("dn/dt = (ninf-n)/ntau",
"dm/dt = (minf-m)/mtau",
"dh/dt = (hinf-h)/htau",
"dV/dt = (ina + ik + il + isyn)/C",
transitions=al.On("V > v_threshold",
do=al.SpikeOutputEvent()))
state_variables = [
al.StateVariable('V', un.voltage),
al.StateVariable('m', un.dimensionless),
al.StateVariable('n', un.dimensionless),
al.StateVariable('h', un.dimensionless)
]
# the rest are not "parameters" but aliases, assigned vars, state vars,
# indep vars, analog_analog_ports, etc.
parameters = [
al.Parameter('el', un.voltage),
al.Parameter('C', un.capacitance),
al.Parameter('ek', un.voltage),
al.Parameter('ena', un.voltage),
al.Parameter('gkbar', un.conductance),
al.Parameter('gnabar', un.conductance),
al.Parameter('v_threshold', un.voltage),
al.Parameter('gl', un.conductance),
al.Parameter('celsius', un.temperature),
al.Parameter('qfactor', un.temperature),
al.Parameter('tendegrees', un.temperature),
al.Parameter('m_alpha_A',
old_div(un.dimensionless, (un.time * un.voltage))),
al.Parameter('m_alpha_V0', un.voltage),
al.Parameter('m_alpha_K', un.voltage),
al.Parameter('m_beta_A', old_div(un.dimensionless, un.time)),
al.Parameter('m_beta_V0', un.voltage),
al.Parameter('m_beta_K', un.voltage),
al.Parameter('h_alpha_A', old_div(un.dimensionless, un.time)),
al.Parameter('h_alpha_V0', un.voltage),
al.Parameter('h_alpha_K', un.voltage),
al.Parameter('h_beta_A', old_div(un.dimensionless, un.time)),
al.Parameter('h_beta_V0', un.voltage),
al.Parameter('h_beta_K', un.voltage),
al.Parameter('n_alpha_A',
old_div(un.dimensionless, (un.time * un.voltage))),
al.Parameter('n_alpha_V0', un.voltage),
al.Parameter('n_alpha_K', un.voltage),
al.Parameter('n_beta_A', old_div(un.dimensionless, un.time)),
al.Parameter('n_beta_V0', un.voltage),
al.Parameter('n_beta_K', un.voltage)
]
analog_ports = [
al.AnalogSendPort("V", un.voltage),
al.AnalogReducePort("isyn", un.current, operator="+")
]
dyn = al.Dynamics("HodgkinHuxley",
parameters=parameters,
state_variables=state_variables,
regimes=(hh_regime, ),
aliases=aliases,
analog_ports=analog_ports)
return dyn
def get_HH_component():
"""A Hodgkin-Huxley single neuron model.
Written by Andrew Davison.
See http://phobos.incf.ki.se/src_rst/
examples/examples_al_python.html#example-hh
"""
aliases = [
"q10 := 3.0**((celsius - qfactor)/tendegrees)", # temperature correction factor @IgnorePep8
"alpha_m := alpha_m_A*(V-alpha_m_V0)/(exp(-(V-alpha_m_V0)/alpha_m_K) - 1.0)", # @IgnorePep8
"beta_m := beta_m_A*exp(-(V-beta_m_V0)/beta_m_K)",
"mtau := 1.0/(q10*(alpha_m + beta_m))",
"minf := alpha_m/(alpha_m + beta_m)",
"alpha_h := alpha_h_A*exp(-(V-alpha_h_V0)/alpha_h_K)",
"beta_h := beta_h_A/(exp(-(V-beta_h_V0)/beta_h_K) + 1.0)",
"htau := 1.0/(q10*(alpha_h + beta_h))",
"hinf := alpha_h/(alpha_h + beta_h)",
"alpha_n := alpha_n_A*(V-alpha_n_V0)/(exp(-(V-alpha_n_V0)/alpha_n_K) - 1.0)", # @IgnorePep8
"beta_n := beta_n_A*exp(-(V-beta_n_V0)/beta_n_K)",
"ntau := 1.0/(q10*(alpha_n + beta_n))",
"ninf := alpha_n/(alpha_n + beta_n)",
"gna := gnabar*m*m*m*h",
"gk := gkbar*n*n*n*n",
"ina := gna*(ena - V)",
"ik := gk*(ek - V)",
"il := gl*(el - V )"
]
hh_regime = al.Regime("dn/dt = (ninf-n)/ntau",
"dm/dt = (minf-m)/mtau",
"dh/dt = (hinf-h)/htau",
"dV/dt = (ina + ik + il + Isyn)/C",
transitions=al.On("V > theta",
do=al.SpikeOutputEvent()))
state_variables = [
al.StateVariable('V', un.voltage),
al.StateVariable('m', un.dimensionless),
al.StateVariable('n', un.dimensionless),
al.StateVariable('h', un.dimensionless)
]
# the rest are not "parameters" but aliases, assigned vars, state vars,
# indep vars, analog_analog_ports, etc.
parameters = [
al.Parameter('el', un.voltage),
al.Parameter('C', un.capacitance),
al.Parameter('ek', un.voltage),
al.Parameter('ena', un.voltage),
al.Parameter('gkbar', un.conductance),
al.Parameter('gnabar', un.conductance),
al.Parameter('theta', un.voltage),
al.Parameter('gl', un.conductance),
al.Parameter('celsius', un.temperature),
al.Parameter('qfactor', un.temperature),
al.Parameter('tendegrees', un.temperature),
al.Parameter('alpha_m_A', un.dimensionless / (un.time * un.voltage)),
al.Parameter('alpha_m_V0', un.voltage),
al.Parameter('alpha_m_K', un.voltage),
al.Parameter('beta_m_A', un.dimensionless / un.time),
al.Parameter('beta_m_V0', un.voltage),
al.Parameter('beta_m_K', un.voltage),
al.Parameter('alpha_h_A', un.dimensionless / un.time),
al.Parameter('alpha_h_V0', un.voltage),
al.Parameter('alpha_h_K', un.voltage),
al.Parameter('beta_h_A', un.dimensionless / un.time),
al.Parameter('beta_h_V0', un.voltage),
al.Parameter('beta_h_K', un.voltage),
al.Parameter('alpha_n_A', un.dimensionless / (un.time * un.voltage)),
al.Parameter('alpha_n_V0', un.voltage),
al.Parameter('alpha_n_K', un.voltage),
al.Parameter('beta_n_A', un.dimensionless / un.time),
al.Parameter('beta_n_V0', un.voltage),
al.Parameter('beta_n_K', un.voltage)
]
analog_ports = [
al.AnalogSendPort("V", un.voltage),
al.AnalogReducePort("Isyn", un.current, operator="+")
]
c1 = al.Dynamics("HodgkinHuxley",
parameters=parameters,
state_variables=state_variables,
regimes=(hh_regime, ),
aliases=aliases,
analog_ports=analog_ports)
return c1
def get_aeIF_component():
"""
Adaptive exponential integrate-and-fire neuron as described in
A. Destexhe, J COmput Neurosci 27: 493--506 (2009)
Author B. Kriener (Jan 2011)
## neuron model: aeIF
## variables:
## V: membrane potential
## w: adaptation variable
## parameters:
## C_m # specific membrane capacitance [muF/cm**2]
## g_L # leak conductance [mS/cm**2]
## E_L # resting potential [mV]
## Delta # steepness of exponential approach to threshold [mV]
## V_T # spike threshold [mV]
## S # membrane area [mum**2]
## trefractory # refractory time [ms]
## tspike # spike time [ms]
## tau_w # adaptation time constant
## a, b # adaptation parameters [muS, nA]
"""
aeIF = al.Dynamics(
name="aeIF",
parameters=[
al.Parameter('C_m', un.capacitance),
al.Parameter('g_L', un.conductance),
al.Parameter('E_L', un.voltage),
al.Parameter('Delta', un.voltage),
al.Parameter('V_T', un.voltage),
al.Parameter('S'),
al.Parameter('trefractory', un.time),
al.Parameter('tspike', un.time),
al.Parameter('tau_w', un.time),
al.Parameter('a', un.dimensionless / un.voltage),
al.Parameter('b')
],
state_variables=[
al.StateVariable('V', un.voltage),
al.StateVariable('w')
],
regimes=[
al.Regime(
name="subthresholdregime",
time_derivatives=[
"dV/dt = -g_L*(V-E_L)/C_m + Isyn/C_m + g_L*Delta*exp((V-V_T)/Delta-w/S)/C_m", # @IgnorePep8
"dw/dt = (a*(V-E_L)-w)/tau_w",
],
transitions=al.On(
"V > V_T",
do=["V = E_L", "w = w + b",
al.OutputEvent('spikeoutput')],
to="refractoryregime")),
al.Regime(name="refractoryregime",
transitions=al.On("t>=tspike+trefractory",
to="subthresholdregime"))
],
analog_ports=[al.AnalogReducePort("Isyn", un.current, operator="+")])
return aeIF
],
to="refractory"),
),
al.Regime(
name="refractory",
transitions=[al.On("t > refractory_end", to="subthreshold")],
)
],
state_variables=[
al.StateVariable('v', dimension=voltage),
al.StateVariable('refractory_end', dimension=time)
],
analog_ports=[
al.AnalogSendPort("v", dimension=voltage),
al.AnalogSendPort("refractory_end", dimension=time),
al.AnalogReducePort("i_synaptic", operator="+", dimension=current)
],
event_ports=[
al.EventSendPort('spike_output'),
],
parameters=[
al.Parameter('tau', time),
al.Parameter('v_threshold', voltage),
al.Parameter('refractory_period', time),
al.Parameter('v_reset', voltage),
al.Parameter('R', resistance)
])
if __name__ == "__main__":
import nineml
filename = __file__[0].upper() + __file__[1:].replace(".py", ".xml")
