XPP model

This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6.

# XPP scripts for supplementary Figure S5A of
# Maex R, Grinevich VP, Grinevich V, Budygin E, Bencherif M, Gutkin B (2014)
# Understanding the role a7 nicotinic receptors play in dopamine efflux
# in nucleus accumbens. ACS Chemical Neuroscience 5, 1032-1040.
#
# Here I want to implement the facilitation of the receptor
# at very low (partial) agonist concentration, as described 
# by Smulders et al. (2005) and Prickaerts et al. (2012).

# The graph plots the fraction of open a7 channels across time.

# Naming conventions 
#
# V_      = membrane voltage of (neuron or neuron population)
# R_      = release of (transmitter)
# C_      = concentration of (transmitter)
# I_      = membrane current of (channel or receptor)
# P_      = presynatic membrane current of (receptor)
# tau_    = time-constant of
# tmin_ = minimum value of time-constant of
# tmax_ = maximum value of time-constant of
# inf_    = steady-state value of
# act_    = level of activation of (receptor)
# des_    = level of desensitisation of (receptor)
# w_      = weight of
# EC50_   = halfmax concentration of steady-state response
# Ktau_   = halfmax concentration of time-constant
# stim_   = stimulation by

# glu  = glutamate or glu-ergic neuron (population)
# dop  = dopamine or dopamine-ergic neuron (population)
# gab  = gaba or gaba-ergic neuron (population)
# ach  = acetylcholine
# nic  = nicotine
# a7   = alpha7-type nicACh receptor
# a4b2 = alpha4-beta2-type nicACh receptor
# bas  = basal
#


# Units 
# time seconds
# concentration micromolar


# Transfer functions (input-output) 
# sigmoid
f(x) = 1/(1 + exp(-x)) 
# halfwave rectification
hwr(x) = heav(x) * x    
# clipped at 0 and 1
clip(x) = (1 + (x-1) * (heav (1-x))) * heav(x) 
# Hill equation
# Hill(x,K,n) = 1 / (1 + (K/x)^n)
Hill(x,K,n) = x^n / (x^n + K^n) 
# competitive Hill 
compHill(x,y,z,wx,wy,wz,Kx,Ky,Kz,n) = \
  (wx * x^n/(x^n + Kx^n * (1 + (y/Ky)^n + (z/Kz)^n))) + \
  (wy * y^n/(y^n + Ky^n * (1 + (x/Kx)^n + (z/Kz)^n))) + \
  (wz * z^n/(z^n + Kz^n * (1 + (x/Kx)^n + (y/Ky)^n)))
# steady-state Hill function with cross-terms representing the effect of
# the simultaneous binding of two different compounds, for instance ACh and EVP 
Hillcross(x,y,z,wx,wy,wz,Kx,Ky,Kz,n,fxy,fyz,fxz) = \
  ((wx * (x/Kx)^n) + \
   (wy * (y/Ky)^n) + \
   (wz * (z/Kz)^n) + \
   (fxy * (x/Kx) * (y/Ky)) + \
   (fxz * (x/Kx) * (z/Kz)) + \
   (fyz * (y/Kz) * (z/Kz))) / (1 + (z/Kz)^n + (x/Kx)^n + (y/Ky)^n + \
                                   2 * (z/Kz) + 2 * (x/Kx) + 2 * (y/Ky) + \
                                   2 * (x/Kx) * (y/Ky) + \
                                   2 * (x/Kx) * (z/Kz) + \
                                   2 * (y/Ky) * (z/Kz) )
# rectangular pulse
rect_pulse(t,from,to,amp) = amp * (heav (t-from) - heav (t-to))



# THE MODEL 

# We now have two neuron populations sharing inputs from
# glu neurons (mostly a7-driven) and through a4b2 receptors.
# The parameter coefficients r and s specify the balance 
# between these inputs.

   par s=0.8,r=0.8


# the dynamics of the dopaminergic neuron population V_dop

   V_dop' = (-V_dop - I_gab + hwr (I_basDop + s*I_glu + r*I_b2)) / tau_Vdop

   par tau_Vdop=0.02,I_basDop=0.1
   aux aux_hwr=hwr (I_basDop + s*I_glu + r*I_b2)


# the dynamics of the gaba-ergic neuron population V_gab

   V_gab' = (-V_gab + hwr ((1-s)*I_glu + (1-r)*I_b2)) / tau_Vgab

   par tau_Vgab=0.02


# the (stationary) glutamatergic input I_glu to dopamine (and GABA)neurons

   I_glu = w_glu * clip (V_glu + P_glu)

   par w_glu=1,V_glu=0.1


# the (varying) gaba-ergic input I_gab to dopamine neurons

   I_gab = w_gab * clip (V_gab + I_basGab)
   aux auxI_gab=I_gab
 
   par w_gab=1.5
   par I_basGab=-0.05
   aux auxI_gab=I_gab


# the presynaptic facilitation of glu input to dopamine (and GABA) neurons

   P_glu = P_a7


# the dynamics of presynaptic a7 receptors (same single variable for 
# glu inputs to dopamine cells in VTA and medium spiny neurons in striatum)

   P_a7 = act_a7 * (1 - des_a7)

   aux auxP_a7=P_a7
   aux auxact_a7=act_a7
   aux auxsen_a7=1-des_a7

#   /* activation of alpha7 */

   act_a7' = (- act_a7 + inf_actA7) / tau_actA7

   inf_actA7 = Hillcross(C_ach + C_chol,        C_nic,        C_agA7, \
                                      1.0,   w_actNicA7,     w_actAgA7, \
                             EC50_A7ach,   EC50_A7nic,     EC50_A7ag, Hill_actA7, \
                                      0,            0,    crossactA7) 
   par crossactA7=0.3

   aux   ainf_actA7=inf_actA7

   par EC50_A7=80
   par EC50_A7ach=68
   par EC50_A7nic=13
   par Hill_actA7=1.73
   par EC50_A7ag=0.03 
   par w_actNicA7=0.8
   par w_actAgA7=0
   par tau_actA7=0.005


#   /* desensitisation of alpha7 */

   des_a7' = (- des_a7 + inf_desA7) / tau_desA7

   inf_desA7 = compHill(    0,      C_nic,      C_agA7, \
                            1,          1,           0, \
                            1, IC50_A7nic,   IC50_A7ag, Hill_desA7)

   par  crosssenA7=0

   aux ainf_desA7=inf_desA7

   par IC50_A7ach=1.3
   par IC50_A7nic=1.3
   par IC50_A7ag=0.002
   par Hill_desA7=2

   tau_desA7 = tmin_desA7 + \ 
               tmax_desA7 * (1 - inf_desA7)
   aux aux_tdA7=tau_desA7

   par tmin_desA7=0.05
   par tmax_desA7=120


# the dynamics of somatic a4b2 receptors on the soma/dendrite of dopamine neurons

   I_b2 = act_b2 * (1 - des_b2)

   aux auxI_b2=I_b2
   aux auxact_b2=act_b2
   aux auxsen_b2=1-des_b2

#   /* activation of alpha4beta2 */

   act_b2' = (- act_b2 + inf_actB2) / tau_actB2

   inf_actB2 = compHill(C_ach,      C_nic,        C_agB2, \
                            1, w_actNicB2,   w_actAgB2, \
                   EC50_B2ach, EC50_B2nic,   EC50_B2ag, Hill_actB2)


   par EC50_actB2=30
   par EC50_B2ach=30
   par EC50_B2ag=30
   par EC50_B2nic=0.23
   par Hill_actB2=1.05
   par w_actNicB2=2
   par w_actAgB2=1
   par tau_actB2=0.005

#   /* desensitisation */

   des_b2' = (- des_b2 + inf_desB2) / tau_desB2

   inf_desB2 = Hill (C_nic + C_agB2, EC50_desB2, Hill_desB2)

   tau_desB2 = tmin_desB2 + \ 
               tmax_desB2 * Hill (Ktau_desB2, C_nic + C_agB2, Htau_desB2)
   aux aux_tdB2=tau_desB2

   par EC50_desB2=0.061
   par Hill_desB2=0.5
   par tmin_desB2=0.5
   par tmax_desB2=600
   par Ktau_desB2=0.11
   par Htau_desB2=3


# the dynamics of dopamine release AND RE-UPTAKE

   R_dop' = (C_basDop * (1 + (V_dop-ss_Vdop) / ss_Vdop) - R_dop) / tau_Rdop - R_dop * Vmax_Rdop / (R_dop + EC50_Rdop)

   par tau_Rdop=0.2,P_a7bas=0.01
# the assumed basal DA production, denotated C_basDop, in the absence of re-uptake 
   par C_basDop=0.1
# the following values are from Chen and Budygin 2007
   par Vmax_Rdop=1.3
   par EC50_Rdop=0.2


# the physiological (ach) and pharmacological (nic) stimuli

#   /* acetylcoline HERE I USE CHOLINE BECAUSE THIS SELECTIVELY ACTIVATES THE A7s */
 
    C_ach' = (-C_ach + stim_ach) / 1

    stim_chol = bas_chol + rect_pulse (t, 1, 10, dose_chol)  + rect_pulse (t, 31, 35, dose_chol)  \
                    + rect_pulse (t, 61, 65, dose_chol)  \
         	    + rect_pulse (t, 91, 95, dose_chol)  \
		    + rect_pulse (t, 121, 125, dose_chol) \
		    + rect_pulse (t, 151, 155, dose_chol) \
		    + rect_pulse (t, 181, 185, dose_chol) \
		    + rect_pulse (t, 211, 215, dose_chol) \
		    + rect_pulse (t, 241, 245, dose_chol) \
		    + rect_pulse (t, 271, 275, dose_chol) \
		    + rect_pulse (t, 301, 305, dose_chol) \
                    + rect_pulse (t, 331, 335, dose_chol) \
		    + rect_pulse (t, 361, 365, dose_chol) \
                    + rect_pulse (t, 391, 395, dose_chol) \
		    + rect_pulse (t, 421, 425, dose_chol) \
                    + rect_pulse (t, 481, 485, dose_chol) \
                    + rect_pulse (t, 541, 545, dose_chol) \
                    + rect_pulse (t, 571, 575, dose_chol) \
                    + rect_pulse (t, 601, 605, dose_chol) \
                    + rect_pulse (t, 631, 635, dose_chol) 
 
    C_chol' = (-C_chol + stim_chol) / 1

    par bas_ach=0
    par bas_chol=0
    par dose_ach=0
    par stim_ach=0

# FOR THE UPPER PLOT PULSES OF 1 microM ARE APPLIED
    par dose_chol=1
# FOR THE LOWER PLOT PULSES OF 60 microM ARE APPLIED
#    par dose_chol=60


#   /* nicotine */
    stim_nic = bas_nic + rect_pulse (t, 66, 67, dose_Nic)

    par dose_Nic=0

# we now simulate an alpha function as a second-order ode
# the alpha-function is area normalized
# to calculate its peak, take amplitude and divide by 10*e

    C_nic_nic' = (-C_nic_nic + stim_nic)/tau1_nic
    C_nic' = (-C_nic + C_nic_nic)/tau2_nic

    par tau1_nic=10,tau2_nic=10,bas_nic=0 


#   /* alpha7 agonist */
    stim_a7 = rect_pulse (t, 170, 510, dose_Aga7)

    par dose_Aga7=0.003

    C_agA7A7' = (-C_agA7A7 + stim_a7) / tau1_agA7
    C_agA7' = (-C_agA7 + C_agA7A7) / tau2_agA7

    par tau1_agA7=10,tau2_agA7=10 


#   /* alpha4 beta2 agonist */
    stim_b2 = rect_pulse (t, 60, 61, 0)
    C_agB2' = (-C_agB2 + stim_b2) / tau_agB2

    par tau_agB2=10


# /* calculating the steady-states (in reverse order) */
    ss_Ib2 = compHill(   bas_ach,          0,           0, \
                            1, w_actNicB2,   w_actAgB2, \
                   EC50_B2ach, EC50_B2nic,   EC50_B2ag, Hill_actB2)
    ss_Pa7 = compHill(   bas_ach + bas_chol,          0,           0, \
                            1, w_actNicA7,   w_actAgA7, \
                   EC50_A7ach, EC50_A7nic,   EC50_A7ag, Hill_actA7)
    ss_Pglu = ss_Pa7
    ss_Iglu = w_glu * clip (V_glu + ss_Pglu)
    ss_Vgab = hwr ((1-s)*ss_Iglu + (1-r)*ss_Ib2)
    ss_Igab = w_gab * clip (ss_Vgab + I_basGab)
    ss_Vdop = - ss_Igab + hwr (I_basDop + s*ss_Iglu + r*ss_Ib2)
# aux auxss_Vdop=ss_Vdop


# the initial conditions
act_a7(0)=0
des_a7(0)=0
act_b2(0)=0
des_b2(0)=0
V_dop(0)=0
V_gab(0)=0
C_nic(0)=bas_nic
C_nic_nic(0)=bas_nic


# the numerical parameters
@ MAXSTOR=500000
@ BOUNDS=1e+8
@ DT=0.005
@ TOTAL=700
@ xlo=0
@ xhi=700
@ ylo=0
@ yhi=0.001
@ METHOD=rk
@ NJP=200
@ YP=auxP_a7

done

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Copyright © 2017 Matthias Koenig

Redistribution and use of any part of this model, with or without modification, are permitted provided that the following conditions are met:

  1. Redistributions of this SBML file must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in a different form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
This model is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.


Model :

id
name
time
substance
extent
volume
area
length
Access SBML model  L3V1

FunctionDefinitions [11] name math sbo cvterm
max minimum x y x x y y
min maximum x y x x y y
heav heavyside x 0 x 0 0.5 x 0 1 x 0 0
mod modulo x y x y x y x 0 y 0 x y x y
f x 1 1 x
hwr x heav x x
clip x 1 x 1 heav 1 x heav x
hill x k n x n x n k n
comphill x y z wx wy wz kx ky kz n wx x n x n kx n 1 y ky n z kz n wy y n y n ky n 1 x kx n z kz n wz z n z n kz n 1 x kx n y ky n
hillcross x y z wx wy wz kx ky kz n fxy fyz fxz wx x kx n wy y ky n wz z kz n fxy x kx y ky fxz x kx z kz fyz y kz z kz 1 z kz n x kx n y ky n 2 z kz 2 x kx 2 y ky 2 x kx y ky 2 x kx z kz 2 y ky z kz
rect_pulse t from to amp amp heav t from heav t to

Parameters [106] name constant value unit derived unit sbo cvterm
s s = 0.8 0.8 None
r r = 0.8 0.8 None
tau_vdop tau_vdop = 0.02 0.02 None
i_basdop i_basdop = 0.1 0.1 None
tau_vgab tau_vgab = 0.02 0.02 None
w_glu w_glu = 1 1.0 None
v_glu v_glu = 0.1 0.1 None
w_gab w_gab = 1.5 1.5 None
i_basgab i_basgab = -0.05 -0.05 None
crossacta7 crossacta7 = 0.3 0.3 None
ec50_a7 ec50_a7 = 80 80.0 None
ec50_a7ach ec50_a7ach = 68 68.0 None
ec50_a7nic ec50_a7nic = 13 13.0 None
hill_acta7 hill_acta7 = 1.73 1.73 None
ec50_a7ag ec50_a7ag = 0.03 0.03 None
w_actnica7 w_actnica7 = 0.8 0.8 None
w_actaga7 w_actaga7 = 0 0.0 None
tau_acta7 tau_acta7 = 0.005 0.005 None
crosssena7 crosssena7 = 0 0.0 None
ic50_a7ach ic50_a7ach = 1.3 1.3 None
ic50_a7nic ic50_a7nic = 1.3 1.3 None
ic50_a7ag ic50_a7ag = 0.002 0.002 None
hill_desa7 hill_desa7 = 2 2.0 None
tmin_desa7 tmin_desa7 = 0.05 0.05 None
tmax_desa7 tmax_desa7 = 120 120.0 None
ec50_actb2 ec50_actb2 = 30 30.0 None
ec50_b2ach ec50_b2ach = 30 30.0 None
ec50_b2ag ec50_b2ag = 30 30.0 None
ec50_b2nic ec50_b2nic = 0.23 0.23 None
hill_actb2 hill_actb2 = 1.05 1.05 None
w_actnicb2 w_actnicb2 = 2 2.0 None
w_actagb2 w_actagb2 = 1 1.0 None
tau_actb2 tau_actb2 = 0.005 0.005 None
ec50_desb2 ec50_desb2 = 0.061 0.061 None
hill_desb2 hill_desb2 = 0.5 0.5 None
tmin_desb2 tmin_desb2 = 0.5 0.5 None
tmax_desb2 tmax_desb2 = 600 600.0 None
ktau_desb2 ktau_desb2 = 0.11 0.11 None
htau_desb2 htau_desb2 = 3 3.0 None
tau_rdop tau_rdop = 0.2 0.2 None
p_a7bas p_a7bas = 0.01 0.01 None
c_basdop c_basdop = 0.1 0.1 None
vmax_rdop vmax_rdop = 1.3 1.3 None
ec50_rdop ec50_rdop = 0.2 0.2 None
bas_ach bas_ach = 0 0.0 None
bas_chol bas_chol = 0 0.0 None
dose_ach dose_ach = 0 0.0 None
stim_ach stim_ach = 0 0.0 None
dose_chol dose_chol = 1 1.0 None
dose_nic dose_nic = 0 0.0 None
tau1_nic tau1_nic = 10 10.0 None
tau2_nic tau2_nic = 10 10.0 None
bas_nic bas_nic = 0 0.0 None
dose_aga7 dose_aga7 = 0.003 0.003 None
tau1_aga7 tau1_aga7 = 10 10.0 None
tau2_aga7 tau2_aga7 = 10 10.0 None
tau_agb2 tau_agb2 = 10 10.0 None
act_a7 act_a7 = 0 0.0 None
des_a7 des_a7 = 0 0.0 None
act_b2 act_b2 = 0 0.0 None
des_b2 des_b2 = 0 0.0 None
v_dop v_dop = 0 0.0 None
v_gab v_gab = 0 0.0 None
c_nic c_nic 0.0 None
c_nic_nic c_nic_nic 0.0 None
r_dop 0.0 dimensionless None
c_ach 0.0 dimensionless None
c_chol 0.0 dimensionless None
c_aga7a7 0.0 dimensionless None
c_aga7 0.0 dimensionless None
c_agb2 0.0 dimensionless None
aux_hwr 0.0 dimensionless None
i_glu 0.0 dimensionless None
i_gab 0.0 dimensionless None
auxi_gab 0.0 dimensionless None
p_glu 0.0 dimensionless None
p_a7 0.0 dimensionless None
auxp_a7 0.0 dimensionless None
auxact_a7 0.0 dimensionless None
auxsen_a7 0.0 dimensionless None
inf_acta7 0.0 dimensionless None
ainf_acta7 0.0 dimensionless None
inf_desa7 0.0 dimensionless None
ainf_desa7 0.0 dimensionless None
tau_desa7 0.0 dimensionless None
aux_tda7 0.0 dimensionless None
i_b2 0.0 dimensionless None
auxi_b2 0.0 dimensionless None
auxact_b2 0.0 dimensionless None
auxsen_b2 0.0 dimensionless None
inf_actb2 0.0 dimensionless None
inf_desb2 0.0 dimensionless None
tau_desb2 0.0 dimensionless None
aux_tdb2 0.0 dimensionless None
stim_chol 0.0 dimensionless None
stim_nic 0.0 dimensionless None
stim_a7 0.0 dimensionless None
stim_b2 0.0 dimensionless None
ss_ib2 0.0 dimensionless None
ss_pa7 0.0 dimensionless None
ss_pglu 0.0 dimensionless None
ss_iglu 0.0 dimensionless None
ss_vgab 0.0 dimensionless None
ss_igab 0.0 dimensionless None
ss_vdop 0.0 dimensionless None
t model time 0.0 dimensionless None

InitialAssignments [2] name assignment derived units sbo cvterm
c_nic = bas_nic None
c_nic_nic = bas_nic None

Rules [49]   assignment name derived units sbo cvterm
d v_dop/dt = v_dop i_gab hwr i_basdop s i_glu r i_b2 tau_vdop None
d v_gab/dt = v_gab hwr 1 s i_glu 1 r i_b2 tau_vgab None
d act_a7/dt = act_a7 inf_acta7 tau_acta7 None
d des_a7/dt = des_a7 inf_desa7 tau_desa7 None
d act_b2/dt = act_b2 inf_actb2 tau_actb2 None
d des_b2/dt = des_b2 inf_desb2 tau_desb2 None
d r_dop/dt = c_basdop 1 v_dop ss_vdop ss_vdop r_dop tau_rdop r_dop vmax_rdop r_dop ec50_rdop None
d c_ach/dt = c_ach stim_ach 1 None
d c_chol/dt = c_chol stim_chol 1 None
d c_nic_nic/dt = c_nic_nic stim_nic tau1_nic None
d c_nic/dt = c_nic c_nic_nic tau2_nic None
d c_aga7a7/dt = c_aga7a7 stim_a7 tau1_aga7 None
d c_aga7/dt = c_aga7 c_aga7a7 tau2_aga7 None
d c_agb2/dt = c_agb2 stim_b2 tau_agb2 None
aux_hwr = hwr i_basdop s i_glu r i_b2 None
i_glu = w_glu clip v_glu p_glu None
i_gab = w_gab clip v_gab i_basgab None
auxi_gab = i_gab None
p_glu = p_a7 None
p_a7 = act_a7 1 des_a7 None
auxp_a7 = p_a7 None
auxact_a7 = act_a7 None
auxsen_a7 = 1 des_a7 None
inf_acta7 = hillcross c_ach c_chol c_nic c_aga7 1 w_actnica7 w_actaga7 ec50_a7ach ec50_a7nic ec50_a7ag hill_acta7 0 0 crossacta7 None
ainf_acta7 = inf_acta7 None
inf_desa7 = comphill 0 c_nic c_aga7 1 1 0 1 ic50_a7nic ic50_a7ag hill_desa7 None
ainf_desa7 = inf_desa7 None
tau_desa7 = tmin_desa7 tmax_desa7 1 inf_desa7 None
aux_tda7 = tau_desa7 None
i_b2 = act_b2 1 des_b2 None
auxi_b2 = i_b2 None
auxact_b2 = act_b2 None
auxsen_b2 = 1 des_b2 None
inf_actb2 = comphill c_ach c_nic c_agb2 1 w_actnicb2 w_actagb2 ec50_b2ach ec50_b2nic ec50_b2ag hill_actb2 None
inf_desb2 = hill c_nic c_agb2 ec50_desb2 hill_desb2 None
tau_desb2 = tmin_desb2 tmax_desb2 hill ktau_desb2 c_nic c_agb2 htau_desb2 None
aux_tdb2 = tau_desb2 None
stim_chol = bas_chol rect_pulse t 1 10 dose_chol rect_pulse t 31 35 dose_chol rect_pulse t 61 65 dose_chol rect_pulse t 91 95 dose_chol rect_pulse t 121 125 dose_chol rect_pulse t 151 155 dose_chol rect_pulse t 181 185 dose_chol rect_pulse t 211 215 dose_chol rect_pulse t 241 245 dose_chol rect_pulse t 271 275 dose_chol rect_pulse t 301 305 dose_chol rect_pulse t 331 335 dose_chol rect_pulse t 361 365 dose_chol rect_pulse t 391 395 dose_chol rect_pulse t 421 425 dose_chol rect_pulse t 481 485 dose_chol rect_pulse t 541 545 dose_chol rect_pulse t 571 575 dose_chol rect_pulse t 601 605 dose_chol rect_pulse t 631 635 dose_chol None
stim_nic = bas_nic rect_pulse t 66 67 dose_nic None
stim_a7 = rect_pulse t 170 510 dose_aga7 None
stim_b2 = rect_pulse t 60 61 0 None
ss_ib2 = comphill bas_ach 0 0 1 w_actnicb2 w_actagb2 ec50_b2ach ec50_b2nic ec50_b2ag hill_actb2 None
ss_pa7 = comphill bas_ach bas_chol 0 0 1 w_actnica7 w_actaga7 ec50_a7ach ec50_a7nic ec50_a7ag hill_acta7 None
ss_pglu = ss_pa7 None
ss_iglu = w_glu clip v_glu ss_pglu None
ss_vgab = hwr 1 s ss_iglu 1 r ss_ib2 None
ss_igab = w_gab clip ss_vgab i_basgab None
ss_vdop = ss_igab hwr i_basdop s ss_iglu r ss_ib2 None
t = time None