hh_moto_5ht

hh_moto_5ht_nestml - a motor neuron model in HH formalism with 5HT modulation

Description

hh_moto_5ht is an implementation of a spiking motor neuron using the Hodgkin-Huxley formalism according to [2]. Basically this model is an implementation of the existing NEURON model [1].

The parameter that represents 5HT modulation is g_K_Ca_5ht. When it equals 1, no modulation happens. An application of 5HT corresponds to its decrease. The default value for it is 0.6. This value was used in the Neuron simulator model. The range of this parameter is (0, 1] but you are free to play with any value.

Post-synaptic currents and spike detection are the same as in hh_psc_alpha.

References

[1]

Muscle spindle feedback circuit by Moraud EM and Capogrosso M. https://senselab.med.yale.edu/ModelDB/showmodel.cshtml?model=189786

[2]

Compartmental model of vertebrate motoneurons for Ca2+-dependent spiking and plateau potentials under pharmacological treatment. Booth V, Rinzel J, Kiehn O. http://refhub.elsevier.com/S0896-6273(16)00010-6/sref4

[3]

Repository: https://github.com/research-team/hh-moto-5ht

See also

hh_psc_alpha

Parameters

Name	Physical unit	Default value	Description
refr_T	ms	2ms	Duration of refractory period
g_Na	nS	5000.0nS	Sodium peak conductance
g_L	nS	200.0nS	Leak conductance
g_K_rect	nS	30000.0nS	Delayed Rectifier Potassium peak conductance
g_Ca_N	nS	5000.0nS
g_Ca_L	nS	10.0nS
g_K_Ca	nS	30000.0nS
g_K_Ca_5ht	real	0.6	modulation of K-Ca channels by 5HT. Its value 1.0 == no modulation.
Ca_in_init	mmol	0.0001mmol	Initial inside Calcium concentration
Ca_out	mmol	2.0mmol	Outside Calcium concentration. Remains constant during simulation.
C_m	pF	200.0pF	Membrane capacitance
E_Na	mV	50.0mV
E_K	mV	-80.0mV
E_L	mV	-70.0mV
R_const	real	8.314472	Nernst equation constants
F_const	real	96485.34
T_current	real	309.15	36 Celcius
tau_syn_ex	ms	0.2ms	Rise time of the excitatory synaptic alpha function
tau_syn_in	ms	2.0ms	Rise time of the inhibitory synaptic alpha function
I_e	pA	0pA	Constant current
V_m_init	mV	-65.0mV
hc_tau	ms	50.0ms
mc_tau	ms	15.0ms
p_tau	ms	400.0ms
alpha	mmol / pA	1e-05mmol / pA

State variables

Name	Physical unit	Default value	Description
V_m	mV	V_m_init	Membrane potential
V_m_old	mV	V_m_init	Membrane potential
refr_t	ms	0ms	Refractory period timer
is_refractory	boolean	false
Ca_in	mmol	Ca_in_init	Inside Calcium concentration
Act_m	real	alpha_m(V_m_init) / (alpha_m(V_m_init) + beta_m(V_m_init))
Act_h	real	h_inf(V_m_init)
Inact_n	real	n_inf(V_m_init)
Act_p	real	p_inf(V_m_init)
Act_mc	real	mc_inf(V_m_init)
Act_hc	real	hc_inf(V_m_init)

Equations

\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-(I_{Na} + I_{K} + I_{L} + I_{Ca,N} + I_{Ca,L} + I_{K,Ca}) + I_{stim} + I_{e} + I_{syn,inh} + I_{syn,exc}) } \right)\]

\[\frac{ dInact_{n} } { dt }= \frac{ (\text{n_inf}(V_{m}) - Inact_{n}) } { \text{n_tau}(V_{m}) }\]

\[\frac{ dAct_{m} } { dt }= \text{alpha_m}(V_{m}) \cdot (1.0 - Act_{m}) - \text{beta_m}(V_{m}) \cdot Act_{m}\]

\[\frac{ dAct_{h} } { dt }= \frac{ (\text{h_inf}(V_{m}) - Act_{h}) } { \text{h_tau}(V_{m}) }\]

\[\frac{ dAct_{p} } { dt }= \frac 1 { p_{\tau} } \left( { (\text{p_inf}(V_{m}) - Act_{p}) } \right)\]

\[\frac{ dAct_{mc} } { dt }= \frac 1 { mc_{\tau} } \left( { (\text{mc_inf}(V_{m}) - Act_{mc}) } \right)\]

\[\frac{ dAct_{hc} } { dt }= \frac 1 { hc_{\tau} } \left( { (\text{hc_inf}(V_{m}) - Act_{hc}) } \right)\]

\[\frac{ dCa_{in} } { dt }= (\frac{ 0.01 } { \mathrm{s} }) \cdot (-\alpha \cdot (I_{Ca,N} + I_{Ca,L}) - 4.0 \cdot Ca_{in})\]

Source code

The model source code can be found in the NESTML models repository here: hh_moto_5ht.

Characterisation