pump mechanism
Posted: Tue Apr 25, 2017 2:30 pm
Hi,
generally, in the Hodgkin-Huxley style model, the Na/K ion-pump is not explicitly modeled, instead, it is assumed that the passive conductance restores the resting membrane potential.
I want to model the explicit effect that the Na/K pump has on the Na and K concentrations and then on membrane potential.
I considered a single compartment. I inserted the following HH mechanism which contains the voltage-gated K and Na channel mechanisms, the Na/K pump and ion accumulation mechanisms:
I would like to change the pump mechanism in order to obtain this: when I insert an IClamp stimulus with a certain duration and amplitude able to generate a spike, after a certain time v returns back to the resting membrane potential because the pump has been able to pump ions against the concentration gradients. Basically, if the voltage-gated channels moved a certain amount of Na (k) ions inside (outside) the cell (quickly), the pump in order to restore the equilibrium should pump in the opposite direction the same amount of ions on a different time scale (slowly). I would like to correctly count this amont of ions.
At the moment, of course, I have that the v is going below the resting potential because the currents generated by the pump is not balancing the current genereted by the the channels.
Here figures for the Na:
The ink is dependent on the change of ionic concentration (nai and ko). The change of ionic concentrations is own to the activated currents.
I think would be useful to keep track of the numbers of ions are moving in or out the cell, but how?
I think I should modify something in
ink= INaKmax/((1 + (Kmnai/nai)^1.5)*(1 + Kmko/ko))
but, in which direction to go?
Or I can use persistent Na and K channels inseatd?
Best
Menica
generally, in the Hodgkin-Huxley style model, the Na/K ion-pump is not explicitly modeled, instead, it is assumed that the passive conductance restores the resting membrane potential.
I want to model the explicit effect that the Na/K pump has on the Na and K concentrations and then on membrane potential.
I considered a single compartment. I inserted the following HH mechanism which contains the voltage-gated K and Na channel mechanisms, the Na/K pump and ion accumulation mechanisms:
Code: Select all
TITLE HH channels
:
: Fast Na+ and K+ currents responsible for action potentials
: Iterative equations
:
: Equations modified by Traub, for Hippocampal Pyramidal cells, in:
: Traub & Miles, Neuronal Networks of the Hippocampus, Cambridge, 1991
:
: range variable vtraub adjust threshold
:
: Written by Alain Destexhe, Salk Institute, Aug 1992
:
: Modifications by Arthur Houweling for use in MyFirstNEURON
: Modifications by Paulo Aguiar: vh changed from 5 to 6 - NOT ANYMORE: vh=5 as originally set
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX HH2
USEION na READ ena WRITE ina
USEION k READ ek WRITE ik
RANGE gnabar, gkbar, vtraub
RANGE m_inf, h_inf, n_inf
RANGE tau_m, tau_h, tau_n
RANGE m_exp, h_exp, n_exp
RANGE ik, ina
}
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
}
PARAMETER {
gnabar = .1 (mho/cm2)
gkbar = .06 (mho/cm2)
ena (mV)
ek (mV)
celsius (degC)
dt (ms)
v (mV)
vtraub = -55 (mV) : adjusts threshold
}
STATE {
m h n
}
ASSIGNED {
ina (mA/cm2)
ik (mA/cm2)
il (mA/cm2)
m_inf
h_inf
n_inf
tau_m
tau_h
tau_n
m_exp
h_exp
n_exp
tadj
}
BREAKPOINT {
SOLVE states
ina = gnabar * m*m*m*h * (v - ena)
ik = gkbar * n*n*n*n * (v - ek)
}
:DERIVATIVE states { : use this for exact Hodgkin-Huxley equations
: evaluate_fct(v)
: m' = (m_inf - m) / tau_m
: h' = (h_inf - h) / tau_h
: n' = (n_inf - n) / tau_n
:}
PROCEDURE states() { : this discretized form is more stable
evaluate_fct(v)
m = m + m_exp * (m_inf - m)
h = h + h_exp * (h_inf - h)
n = n + n_exp * (n_inf - n)
VERBATIM
return 0;
ENDVERBATIM
}
UNITSOFF
INITIAL {
:
: Q10 was assumed to be 3 for both currents
:
tadj = 3.0 ^ ((celsius-36)/ 10 )
evaluate_fct(v)
m= m_inf
h= h_inf
n= n_inf
}
PROCEDURE evaluate_fct(v(mV)) { LOCAL a,b,v2,vh
v2 = v - vtraub : convert to traub convention
vh = 5
a = 0.32 * (13-v2) / ( exp((13-v2)/4) - 1)
b = 0.28 * (v2-40) / ( exp((v2-40)/5) - 1)
tau_m = 1 / (a + b) / tadj
m_inf = a / (a + b)
:a = 0.128 * exp((17-v2)/18)
:b = 4 / ( 1 + exp((40-v2)/5) )
:tau_h = 1 / (a + b) / tadj
:h_inf = a / (a + b)
a = 0.128 * exp((17-v2-vh)/18)
b = 4 / ( 1 + exp((40-v2-vh)/5) )
tau_h = 1 / (a + b) / tadj
h_inf = a / (a + b)
a = 0.032 * (15-v2) / ( exp((15-v2)/5) - 1)
b = 0.5 * exp((10-v2)/40)
tau_n = 1 / (a + b) / tadj
n_inf = a / (a + b)
m_exp = 1 - exp(-dt/tau_m)
h_exp = 1 - exp(-dt/tau_h)
n_exp = 1 - exp(-dt/tau_n)
}
UNITSON
Code: Select all
TITLE sodium potassium pump
: from Lindblad et al Am J Physiol 1996 275:H1666
NEURON {
SUFFIX nkpump
USEION k READ ko, ki WRITE ik
USEION na READ nao, nai WRITE ina
RANGE ik, ina , INaKmax, ink, Kmko, Kmnai,inapump
GLOBAL dummy : prevent vectorization for use with CVODE
}
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
}
PARAMETER {
INaKmax = 2.18660e-3 (mA/cm2) <0,1e6>
Kmnai = 10 (mM) <0,1e6>
Kmko = 1.5 (mM) <0,1e6>
}
ASSIGNED {
celsius (degC)
v (mV)
ik (mA/cm2)
ina (mA/cm2)
ko (mM)
ki (mM)
nao (mM)
nai (mM)
ink (mA/cm2)
dummy
}
BREAKPOINT {
ink= INaKmax/((1 + (Kmnai/nai)^1.5)*(1 + Kmko/ko))
ina = 3*ink
ik = -2*ink
}
Code: Select all
NEURON {
SUFFIX nacumst
USEION na READ ina WRITE nai
RANGE tau, C0
}
UNITS {
(mA) = (milliamp)
(mol) = (1)
(molar) = (mol/liter)
(mM) = (millimolar)
(uM) = (micromolar)
(um) = (micrometer)
FARADAY = (faraday) (coulombs)
}
PARAMETER {
tau = 5 (ms) : AB soma; 300 ms for PD soma
C0 = 10 (mM)
}
ASSIGNED {
ina (mA/cm2)
diam (um)
}
STATE {
nai (mM)
}
INITIAL {
nai = C0
}
BREAKPOINT {
SOLVE states METHOD cnexp
}
DERIVATIVE states {
nai' = -(1e4)*2*ina/(FARADAY*diam) + (C0 - nai)/tau
}
At the moment, of course, I have that the v is going below the resting potential because the currents generated by the pump is not balancing the current genereted by the the channels.
Here figures for the Na:
The ink is dependent on the change of ionic concentration (nai and ko). The change of ionic concentrations is own to the activated currents.
I think would be useful to keep track of the numbers of ions are moving in or out the cell, but how?
I think I should modify something in
ink= INaKmax/((1 + (Kmnai/nai)^1.5)*(1 + Kmko/ko))
but, in which direction to go?
Or I can use persistent Na and K channels inseatd?
Best
Menica