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traub_cond_multisyn_neuron.nestml
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traub_cond_multisyn_neuron.nestml
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"""
traub_cond_multisyn - Traub model according to Borgers 2017
###########################################################
Description
+++++++++++
Reduced Traub-Miles Model of a Pyramidal Neuron in Rat Hippocampus [1]_.
parameters got from reference [2]_ chapter 5.
AMPA, NMDA, GABA_A, and GABA_B conductance-based synapses with
beta-function (difference of two exponentials) time course corresponding
to "hill_tononi" model.
References
++++++++++
.. [1] R. D. Traub and R. Miles, Neuronal Networks of the Hippocampus,Cam- bridge University Press, Cambridge, UK, 1991.
.. [2] Borgers, C., 2017. An introduction to modeling neuronal dynamics (Vol. 66). Cham: Springer.
See also
++++++++
hh_cond_exp_traub
"""
model traub_cond_multisyn_neuron:
state:
V_m mV = -70. mV # Membrane potential
V_m_old mV = E_L # Membrane potential at previous timestep for threshold check
refr_t ms = 0 ms # Refractory period timer
is_refractory boolean = false
Act_m real = alpha_m_init / ( alpha_m_init + beta_m_init ) # Activation variable m for Na
Inact_h real = alpha_h_init / ( alpha_h_init + beta_h_init ) # Inactivation variable h for Na
Act_n real = alpha_n_init / ( alpha_n_init + beta_n_init ) # Activation variable n for K
g_AMPA real = 0
g_NMDA real = 0
g_GABAA real = 0
g_GABAB real = 0
g_AMPA$ real = AMPAInitialValue
g_NMDA$ real = NMDAInitialValue
g_GABAA$ real = GABA_AInitialValue
g_GABAB$ real = GABA_BInitialValue
equations:
recordable inline I_syn_ampa pA = -convolve(g_AMPA, AMPA) * nS * ( V_m - AMPA_E_rev )
recordable inline I_syn_nmda pA = -convolve(g_NMDA, NMDA) * nS * ( V_m - NMDA_E_rev ) / ( 1 + exp( ( NMDA_Vact - V_m ) / NMDA_Sact ) )
recordable inline I_syn_gaba_a pA = -convolve(g_GABAA, GABA_A) * nS * ( V_m - GABA_A_E_rev )
recordable inline I_syn_gaba_b pA = -convolve(g_GABAB, GABA_B) * nS * ( V_m - GABA_B_E_rev )
recordable inline I_syn pA = I_syn_ampa + I_syn_nmda + I_syn_gaba_a + I_syn_gaba_b
inline I_Na pA = g_Na * Act_m * Act_m * Act_m * Inact_h * ( V_m - E_Na )
inline I_K pA = g_K * Act_n * Act_n * Act_n * Act_n * ( V_m - E_K )
inline I_L pA = g_L * ( V_m - E_L )
V_m' = ( -( I_Na + I_K + I_L ) + I_e + I_stim + I_syn ) / C_m
# Act_n
inline alpha_n real = 0.032 * (V_m / mV + 52.) / (1. - exp(-(V_m / mV + 52.) / 5.))
inline beta_n real = 0.5 * exp(-(V_m / mV + 57.) / 40.)
Act_n' = ( alpha_n * ( 1 - Act_n ) - beta_n * Act_n ) / ms # n-variable
# Act_m
inline alpha_m real = 0.32 * (V_m / mV + 54.) / (1.0 - exp(-(V_m / mV + 54.) / 4.))
inline beta_m real = 0.28 * (V_m / mV + 27.) / (exp((V_m / mV + 27.) / 5.) - 1.)
Act_m' = ( alpha_m * ( 1 - Act_m ) - beta_m * Act_m ) / ms # m-variable
# Inact_h'
inline alpha_h real = 0.128 * exp(-(V_m / mV + 50.0) / 18.0)
inline beta_h real = 4.0 / (1.0 + exp(-(V_m / mV + 27.) / 5.))
Inact_h' = ( alpha_h * ( 1 - Inact_h ) - beta_h * Inact_h ) / ms # h-variable
#############
# Synapses
#############
kernel g_AMPA' = g_AMPA$ - g_AMPA / tau_AMPA_2,
g_AMPA$' = -g_AMPA$ / tau_AMPA_1
kernel g_NMDA' = g_NMDA$ - g_NMDA / tau_NMDA_2,
g_NMDA$' = -g_NMDA$ / tau_NMDA_1
kernel g_GABAA' = g_GABAA$ - g_GABAA / tau_GABAA_2,
g_GABAA$' = -g_GABAA$ / tau_GABAA_1
kernel g_GABAB' = g_GABAB$ - g_GABAB / tau_GABAB_2,
g_GABAB$' = -g_GABAB$ / tau_GABAB_1
parameters:
C_m pF = 100.0 pF # Membrane Capacitance
g_Na nS = 10000.0 nS # Sodium peak conductance
g_K nS = 8000.0 nS # Potassium peak conductance
g_L nS = 10 nS # Leak conductance
E_Na mV = 50. mV # Sodium reversal potential
E_K mV = -100. mV # Potassium reversal potentia
E_L mV = -67. mV # Leak reversal Potential (aka resting potential)
V_Tr mV = -20. mV # Spike Threshold
refr_T ms = 2 ms # Duration of refractory period
# Parameters for synapse of type AMPA, GABA_A, GABA_B and NMDA
AMPA_g_peak nS = 0.1 nS # peak conductance
AMPA_E_rev mV = 0.0 mV # reversal potential
tau_AMPA_1 ms = 0.5 ms # rise time
tau_AMPA_2 ms = 2.4 ms # decay time, Tau_1 < Tau_2
NMDA_g_peak nS = 0.075 nS # peak conductance
tau_NMDA_1 ms = 4.0 ms # rise time
tau_NMDA_2 ms = 40.0 ms # decay time, Tau_1 < Tau_2
NMDA_E_rev mV = 0.0 mV # reversal potential
NMDA_Vact mV = -58.0 mV # inactive for V << Vact, inflection of sigmoid
NMDA_Sact mV = 2.5 mV # scale of inactivation
GABA_A_g_peak nS = 0.33 nS # peak conductance
tau_GABAA_1 ms = 1.0 ms # rise time
tau_GABAA_2 ms = 7.0 ms # decay time, Tau_1 < Tau_2
GABA_A_E_rev mV = -70.0 mV # reversal potential
GABA_B_g_peak nS = 0.0132 nS # peak conductance
tau_GABAB_1 ms = 60.0 ms # rise time
tau_GABAB_2 ms = 200.0 ms # decay time, Tau_1 < Tau_2
GABA_B_E_rev mV = -90.0 mV # reversal potential for intrinsic current
# constant external input current
I_e pA = 0 pA
internals:
AMPAInitialValue real = compute_synapse_constant( tau_AMPA_1, tau_AMPA_2, AMPA_g_peak )
NMDAInitialValue real = compute_synapse_constant( tau_NMDA_1, tau_NMDA_2, NMDA_g_peak )
GABA_AInitialValue real = compute_synapse_constant( tau_GABAA_1, tau_GABAA_2, GABA_A_g_peak )
GABA_BInitialValue real = compute_synapse_constant( tau_GABAB_1, tau_GABAB_2, GABA_B_g_peak )
alpha_n_init real = 0.032 * (V_m / mV + 52.) / (1. - exp(-(V_m / mV + 52.) / 5.))
beta_n_init real = 0.5 * exp(-(V_m / mV + 57.) / 40.)
alpha_m_init real = 0.32 * (V_m / mV + 54.) / (1.0 - exp(-(V_m / mV + 54.) / 4.))
beta_m_init real = 0.28 * (V_m / mV + 27.) / (exp((V_m / mV + 27.) / 5.) - 1.)
alpha_h_init real = 0.128 * exp(-(V_m / mV + 50.0) / 18.0)
beta_h_init real = 4.0 / (1.0 + exp(-(V_m / mV + 27.) / 5.))
input:
AMPA <- spike
NMDA <- spike
GABA_A <- spike
GABA_B <- spike
I_stim pA <- continuous
output:
spike
update:
if is_refractory:
refr_t -= resolution()
V_m_old = V_m
integrate_odes()
onCondition(not is_refractory and V_m > V_Tr and V_m_old > V_m):
# threshold crossing and maximum
refr_t = refr_T # start of the refractory period
is_refractory = true
emit_spike()
onCondition(is_refractory and refr_t <= resolution() / 2):
# end of refractory period
refr_t = 0 ms
is_refractory = false
function compute_synapse_constant(Tau_1 ms, Tau_2 ms, g_peak real) real:
# Factor used to account for the missing 1/((1/Tau_2)-(1/Tau_1)) term
# in the ht_neuron_dynamics integration of the synapse terms.
# See: Exact digital simulation of time-invariant linear systems
# with applications to neuronal modeling, Rotter and Diesmann,
# section 3.1.2.
exact_integration_adjustment real = ( ( 1 / Tau_2 ) - ( 1 / Tau_1 ) ) * ms
t_peak real = ( Tau_2 * Tau_1 ) * ln( Tau_2 / Tau_1 ) / ( Tau_2 - Tau_1 ) / ms
normalisation_factor real = 1 / ( exp( -t_peak / Tau_1 ) - exp( -t_peak / Tau_2 ) )
return g_peak * normalisation_factor * exact_integration_adjustment