XPP model
This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6
.
# Code for article by N. Huebel and M. A. Dahlem: # "Dynamics from seconds to hours in Hodgkin–Huxley model with # time-dependent ion concentrations and buffer reservoirs" # PLoS Comp Biol (2014) # email: niklas.huebel@gmail.com # Oct. 7, 2014 # # # README # # This code computes time series like in Fig. 5. SD is # triggered either by current stimulation (dynamics of variable # "stim") or by pump interruption (dynamics of pump coefficient # "z"). Two regulation schemes for potassium are implemented: # glial buffering and diffusive coupling to the vascular system # (with a switch parameter "s", see below). For diffusive # coupling with elevated "k_bath" values the time series of Fig. 7 # can be simulated. # ################################## # RATE EQUATIONS FOR 5D SD MODEL # ################################## v' = 1000. * v_DOT n' = 1000. * n_DOT ki' = 1000. * ki_DOT cli' = 1000. * cli_DOT dk' = 1000. * dk_DOT ######################################################### # STIMULATE MEMBRANE WITH A 0.5sec DEPOLARIZING CURRENT # ######################################################### stim' = 0 global 1 1.000000000001*t - 20.0 {stim=Amp} global 1 1.000000000001*t - (20.0 + 0.5) {stim=0} par Amp=0. #par Amp=100. ##################################### # SWITCH PUMP OFF FOR delta SECONDS # ##################################### z' = 0 global 1 1.000000000001*t - 20.0 {z=0.0} global 1 1.000000000001*t - (20.0 + delta) {z=1.0} #par delta=0. par delta=9.5 ###################### # INITIAL CONDITIONS # ###################### init v=-67.193253 init n=0.069410823 init ki=129.25764 init cli=9.900239 init dk=0 init stim=0 init z=1 ######################### # REGULATION PARAMETERS # ######################### # s=0: glial buffering # s=1: diffusive coupling # k_bath is the bath concentration par k_bath=4 par s=0 ########## # GATING # ########## A_N = 0.01 * (v + 34.0) / (1.0 - exp(-0.1 * (v + 34.0))) B_N = 0.125 * exp(-(v + 44.0) / 80.0) A_M = 0.1 * (v + 30.0) / (1.0 - exp(-0.1 * (v + 30.0))) B_M = 4.0 * exp(-(v + 55.0) / 18.0) m = A_M / (A_M + B_M) h = 1 - 1. / (1 + exp(-6.5*(n-0.35))) ###################### # ION CONCENTRATIONS # ###################### par vol_i=2.16 par vol_e=0.72 par ki0=129.25764 par nai0=25.231485 par cli0=9.900239 par ke0=4. par nae0=125.30555 par cle0=123.2716 nai = nai0 + ki0 - ki - cli0 + cli nae = (nai0 * Vol_i + nae0 * vol_e - nai * vol_i) / vol_e cle = (cli0 * Vol_i + cle0 * vol_e - cli * vol_i) / vol_e ke = (ki0 * Vol_i + ke0 * vol_e - ki * vol_i) / vol_e + dk ##################### # NERNST POTENTIALS # ##################### EK = 26.64 * log(ke /ki) ENA = 26.64 * log(nae/nai) ECL =-26.64 * log(cle/cli) ############ # CURRENTS # ############ par G_NA_L=0.0175 par G_NA_G=100. par G_K_L=0.05 par G_K_G=40. par G_CL_L=0.02 par NA_PUMP=25 par K_PUMP=5.5 par MAX_PUMP=6.8 I_NA_L = G_NA_L * (v - ENA) I_NA_G = G_NA_G * m**3 * h * (v - ENA) I_K_L = G_K_L * (v - EK) I_K_G = G_K_G * n**4 * (v - EK) I_CL_L = G_CL_L * (v - ECL) IPUMP = MAX_PUMP / (1.0 + exp((NA_PUMP - NAI)/3.)) / (1. + exp(K_PUMP - ke)) * z ################# # FULL CURRENTS # ################# I_NA = I_NA_L + I_NA_G + 3. * IPUMP I_K = I_K_L + I_K_G - 2. * IPUMP ######################## # POTASSIUM REGULATION # ######################## par lambda=3.0e-05 par b0=500 par K_cr=15. par k1=5.e-8 J_DIFF = lambda * (k_bath - ke) dk_DOT_1 = J_DIFF k2 = k1 / (1 + exp((K_cr - ke) / 1.09)) dk_DOT_0 = -k1 * dk - k2 * ke * (B0 + dk) ############################# # RATE FUNCTIONS FOR SOLVER # ############################# par PHI=3 par C=1 par CONV=9.55589e-05 v_DOT = -1. / C * (I_CL_L + I_NA + I_K - stim) n_DOT = PHI * (A_N * (1 - n) - B_N * n) ki_DOT = -1. / Vol_i * CONV * I_K cli_DOT = 1. / Vol_i * CONV * I_CL_L dk_DOT = (1 - s) * dk_DOT_0 + s * dk_DOT_1 ############### # AUXILIARIES # ############### aux _nai = nai aux _nae = nae aux _cle = cle aux _ke = ke aux _EK = EK aux _ENA = ENA aux _ECL = ECL aux _I_NA_L = I_NA_L aux _I_NA_G = I_NA_G aux _I_K_L = I_K_L aux _I_K_G = I_K_G aux _I_CL_L = I_CL_L aux _IPUMP = IPUMP aux _I_NA = I_NA aux _I_K = I_K ######################## # INTEGRATION NUMERICS # ######################## @ meth=stiff @ dt=5e-2 @ maxstor=10000000, bounds=10000000 @ total=500 @ bell=0 ################ # PLOT OPTIONS # ################ @ xhi=500 @ nplot=4, yp1=v, yp2=_EK, yp3=_ENA, yp4=_ECL, ylo=-150, yhi=160 done
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Copyright © 2017 Matthias Koenig
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Model :
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type | FunctionDefinitions [4] | name | math | sbo | cvterm |
---|---|---|---|---|---|
FunctionDefinition | max
|
minimum | |||
FunctionDefinition | min
|
maximum | |||
FunctionDefinition | heav
|
heavyside | |||
FunctionDefinition | mod
|
modulo |
type | Parameters [80] | name | constant | value | unit | derived unit | sbo | cvterm |
---|---|---|---|---|---|---|---|---|
Parameter | amp
|
amp = 0. | F | 0.0 | None | |||
Parameter | delta
|
delta = 9.5 | F | 9.5 | None | |||
Parameter | v
|
v = -67.193253 | F | -67.193253 | None | |||
Parameter | n
|
n = 0.069410823 | F | 0.069410823 | None | |||
Parameter | ki
|
ki = 129.25764 | F | 129.25764 | None | |||
Parameter | cli
|
cli = 9.900239 | F | 9.900239 | None | |||
Parameter | dk
|
dk = 0 | F | 0.0 | None | |||
Parameter | stim
|
stim = 0 | F | 0.0 | None | |||
Parameter | z
|
z = 1 | F | 1.0 | None | |||
Parameter | k_bath
|
k_bath = 4 | F | 4.0 | None | |||
Parameter | s
|
s = 0 | F | 0.0 | None | |||
Parameter | vol_i
|
vol_i = 2.16 | F | 2.16 | None | |||
Parameter | vol_e
|
vol_e = 0.72 | F | 0.72 | None | |||
Parameter | ki0
|
ki0 = 129.25764 | F | 129.25764 | None | |||
Parameter | nai0
|
nai0 = 25.231485 | F | 25.231485 | None | |||
Parameter | cli0
|
cli0 = 9.900239 | F | 9.900239 | None | |||
Parameter | ke0
|
ke0 = 4. | F | 4.0 | None | |||
Parameter | nae0
|
nae0 = 125.30555 | F | 125.30555 | None | |||
Parameter | cle0
|
cle0 = 123.2716 | F | 123.2716 | None | |||
Parameter | g_na_l
|
g_na_l = 0.0175 | F | 0.0175 | None | |||
Parameter | g_na_g
|
g_na_g = 100. | F | 100.0 | None | |||
Parameter | g_k_l
|
g_k_l = 0.05 | F | 0.05 | None | |||
Parameter | g_k_g
|
g_k_g = 40. | F | 40.0 | None | |||
Parameter | g_cl_l
|
g_cl_l = 0.02 | F | 0.02 | None | |||
Parameter | na_pump
|
na_pump = 25 | F | 25.0 | None | |||
Parameter | k_pump
|
k_pump = 5.5 | F | 5.5 | None | |||
Parameter | max_pump
|
max_pump = 6.8 | F | 6.8 | None | |||
Parameter | lambda
|
lambda = 3.0e-05 | F | 3e-05 | None | |||
Parameter | b0
|
b0 = 500 | F | 500.0 | None | |||
Parameter | k_cr
|
k_cr = 15. | F | 15.0 | None | |||
Parameter | k1
|
k1 = 5.e-8 | F | 5e-08 | None | |||
Parameter | phi
|
phi = 3 | F | 3.0 | None | |||
Parameter | c
|
c = 1 | F | 1.0 | None | |||
Parameter | conv
|
conv = 9.55589e-05 | F | 9.55589e-05 | None | |||
Parameter | a_n
|
F | 0.0 | dimensionless | None | |||
Parameter | b_n
|
F | 0.0 | dimensionless | None | |||
Parameter | a_m
|
F | 0.0 | dimensionless | None | |||
Parameter | b_m
|
F | 0.0 | dimensionless | None | |||
Parameter | m
|
F | 0.0 | dimensionless | None | |||
Parameter | h
|
F | 0.0 | dimensionless | None | |||
Parameter | nai
|
F | 0.0 | dimensionless | None | |||
Parameter | nae
|
F | 0.0 | dimensionless | None | |||
Parameter | cle
|
F | 0.0 | dimensionless | None | |||
Parameter | ke
|
F | 0.0 | dimensionless | None | |||
Parameter | ek
|
F | 0.0 | dimensionless | None | |||
Parameter | ena
|
F | 0.0 | dimensionless | None | |||
Parameter | ecl
|
F | 0.0 | dimensionless | None | |||
Parameter | i_na_l
|
F | 0.0 | dimensionless | None | |||
Parameter | i_na_g
|
F | 0.0 | dimensionless | None | |||
Parameter | i_k_l
|
F | 0.0 | dimensionless | None | |||
Parameter | i_k_g
|
F | 0.0 | dimensionless | None | |||
Parameter | i_cl_l
|
F | 0.0 | dimensionless | None | |||
Parameter | ipump
|
F | 0.0 | dimensionless | None | |||
Parameter | i_na
|
F | 0.0 | dimensionless | None | |||
Parameter | i_k
|
F | 0.0 | dimensionless | None | |||
Parameter | j_diff
|
F | 0.0 | dimensionless | None | |||
Parameter | dk_dot_1
|
F | 0.0 | dimensionless | None | |||
Parameter | k2
|
F | 0.0 | dimensionless | None | |||
Parameter | dk_dot_0
|
F | 0.0 | dimensionless | None | |||
Parameter | v_dot
|
F | 0.0 | dimensionless | None | |||
Parameter | n_dot
|
F | 0.0 | dimensionless | None | |||
Parameter | ki_dot
|
F | 0.0 | dimensionless | None | |||
Parameter | cli_dot
|
F | 0.0 | dimensionless | None | |||
Parameter | dk_dot
|
F | 0.0 | dimensionless | None | |||
Parameter | _nai
|
F | 0.0 | dimensionless | None | |||
Parameter | _nae
|
F | 0.0 | dimensionless | None | |||
Parameter | _cle
|
F | 0.0 | dimensionless | None | |||
Parameter | _ke
|
F | 0.0 | dimensionless | None | |||
Parameter | _ek
|
F | 0.0 | dimensionless | None | |||
Parameter | _ena
|
F | 0.0 | dimensionless | None | |||
Parameter | _ecl
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_na_l
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_na_g
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_k_l
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_k_g
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_cl_l
|
F | 0.0 | dimensionless | None | |||
Parameter | _ipump
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_na
|
F | 0.0 | dimensionless | None | |||
Parameter | _i_k
|
F | 0.0 | dimensionless | None | |||
Parameter | t
|
model time | F | 0.0 | dimensionless | None |
type | Rules [53] | assignment | name | derived units | sbo | cvterm | |
---|---|---|---|---|---|---|---|
Rule | d v/dt
|
= | None | ||||
Rule | d n/dt
|
= | None | ||||
Rule | d ki/dt
|
= | None | ||||
Rule | d cli/dt
|
= | None | ||||
Rule | d dk/dt
|
= | None | ||||
Rule | d stim/dt
|
= | None | ||||
Rule | d z/dt
|
= | None | ||||
Rule | a_n
|
= | None | ||||
Rule | b_n
|
= | None | ||||
Rule | a_m
|
= | None | ||||
Rule | b_m
|
= | None | ||||
Rule | m
|
= | None | ||||
Rule | h
|
= | None | ||||
Rule | nai
|
= | None | ||||
Rule | nae
|
= | None | ||||
Rule | cle
|
= | None | ||||
Rule | ke
|
= | None | ||||
Rule | ek
|
= | None | ||||
Rule | ena
|
= | None | ||||
Rule | ecl
|
= | None | ||||
Rule | i_na_l
|
= | None | ||||
Rule | i_na_g
|
= | None | ||||
Rule | i_k_l
|
= | None | ||||
Rule | i_k_g
|
= | None | ||||
Rule | i_cl_l
|
= | None | ||||
Rule | ipump
|
= | None | ||||
Rule | i_na
|
= | None | ||||
Rule | i_k
|
= | None | ||||
Rule | j_diff
|
= | None | ||||
Rule | dk_dot_1
|
= | None | ||||
Rule | k2
|
= | None | ||||
Rule | dk_dot_0
|
= | None | ||||
Rule | v_dot
|
= | None | ||||
Rule | n_dot
|
= | None | ||||
Rule | ki_dot
|
= | None | ||||
Rule | cli_dot
|
= | None | ||||
Rule | dk_dot
|
= | None | ||||
Rule | _nai
|
= | None | ||||
Rule | _nae
|
= | None | ||||
Rule | _cle
|
= | None | ||||
Rule | _ke
|
= | None | ||||
Rule | _ek
|
= | None | ||||
Rule | _ena
|
= | None | ||||
Rule | _ecl
|
= | None | ||||
Rule | _i_na_l
|
= | None | ||||
Rule | _i_na_g
|
= | None | ||||
Rule | _i_k_l
|
= | None | ||||
Rule | _i_k_g
|
= | None | ||||
Rule | _i_cl_l
|
= | None | ||||
Rule | _ipump
|
= | None | ||||
Rule | _i_na
|
= | None | ||||
Rule | _i_k
|
= | None | ||||
Rule | t
|
= | None |
type | Events [4] | name | trigger | priority | delay | assignments | sbo | cvterm |
---|---|---|---|---|---|---|---|---|
Event | e0
|
initialValue = False persistent = True |
stim =
|
|||||
Event | e1
|
initialValue = False persistent = True |
stim =
|
|||||
Event | e2
|
initialValue = False persistent = True |
z =
|
|||||
Event | e3
|
initialValue = False persistent = True |
z =
|