#D.P.Dougherty 2010 #Spiking model of mouse ORN #This is a multi-scale extension of the model in Dougherty et al 2005. PNAS 102(30):10415-10420 #which includes cilium, dendrite, and soma compartments. # #The XPP file is configured to demonstrate a dual-pulse stimulation protocol #with whole cell suction pipette recording showing the slow transduction #current and fast action potentials generated. # #Alphabetically sorted listing of all model parameters (descriptions given below). param cap=0.0035 param cc1lin=0.6362 param cc2=20.9869 param ck1lin=10.3615 param ck2=0.5833 param clmax=0.8294 param cnmax=3.6417 param ef=7.9725 param gl=15.4267 param hmc1=1.5965 param hmc2=7.6415 param inf=1.4654 param inhmax=0.98 param k1=2.2748 param k2lin=42.0896 param kI=16.5304 param kinh=1.3875 param kinhcng=0.2242 param n1=5.6384 param n2=3.4161 param ninh=0.4067 param ninhcng=0.6306 param pd=15.4669 param r1=9.4574 param r2=12.5485 param smax=63.0987 param vcl=-7.3248 param vcng=0.4641 param vl=-69.6653 #Spiking aspect of the model -- dendrite and soma parameters. param ge1=70.244 param ge2=20.245 param tau_soma=6100 param epsilon=0.09 param beta=0.092 param beta_cap=0.95 param cap_max=400.5 param cap_off=-75 param gamma=43.92 param VSspike=-58.23 param VSamp=14.36 param vd=0.05 #Parameters descriptions with their units. # #cap #Capacitance of ORN ciliary membrane# nF #cc1lin #Rate at which Ca2+ associates with CaM to form CaCaM # s^-1 #cc2 #Rate at which CaCaM dissociates to Ca2+ and CaM # s^-1 #ck1lin #Rate at which CaCaM activates CaMK # s^-1 #ck2 #Rate at which active CaMK deactivates # s^-1 #clmax #Maximal conductance of ANO2 Cl(Ca) channels # nS #cnmax #Maximal conductance of CNG channels # nS #ef #Maximum calcium efflux (assumed sodium & potassium independent) #s^-1 #gl #Maximum leak (generic) conductance # nS #hmc1 #Concentration of cAMP needed to achieve half-maximal activation (K1/2) of the CNG channel # uM #hmc2 #Concentration of Ca2+ needed to achieve half-maximal activation (K1/2) of the Cl(Ca) channel| # uM #inf #Net calcium inward flux via CNG channel # uM*pC^-1 #inhmax #Maximum inhibition of CNG by CaCAM # unitless #k1 #Receptor affinity for ligand # (um*s)^-1 #k2lin #Rate of G-protein activation per bound receptor complex # s^-1 #kinh #Concentration of aCaMK needed for half-maximal inhibition (IC50) of cAMP production # uM #kinhcng #Concentration of CaCaM needed for half-maximal inhibition of the CNG channel # uM #n1 #Hill coefficient of the CNG channel activation function # unitless #n2 #Hill coefficient of the Cl(Ca) channel activation function # unitless #ninh #Steepness of the decreasing sigmoid representing aCaMK-mediated inhibition of cAMP synthesis # unitless #ninhcng #Steepness of the sigmoid inhcng representing inhibition of CNG channel by CaCaM # unitless #pd #Rate at which a cAMP molecule is degraded by phosphodiesterase # s^-1 #r1 #Rate of unbinding of odorant from receptor # s^-1 #r2 #Rate at which a G-protein becomes deactivate rate # s^-1 #smax #Maximal (uninhibited) rate of cAMP production by adenylyl cyclase per active G-protein # uM*s^-1 #vcl #Reversal potential of Cl(Ca) channels # mV #vcng #Reversal potential of CNG channels # mV #vl #Effective reversal potential for leak current # mV #ge1 #Coupling strength between cilia and dendrite compartments # s^-1 #ge2 #Coupling strength between dendrite and soma compartments # mV^-1 #tau_soma #Relative time scale of soma to cilia dynamics #s^-1 #epsilon #Relative time scale of Na and K channel dynamics to voltage dynamics in soma #Unitless #beta #Sharpness of Na and K channel response to voltage # mV #beta_cap #Sharpness of soma capacitance dependence on voltage # mV #cap_max #Maximum soma capacitance # nF #cap_off #Voltage at which soma capacitance is half maximal #mV #gamma #Na and K channel activation rate (sets height of channel manifold) #unitless #VSspike #Reference voltage for action potentials by soma # mV #VSamp #Sharpness of soma voltage response #mV #vd #Diffusive dendritic voltage leak/loss. #s^-1 #Now parameters related to the experimental design: #Micromolar concentration of odorant at full concentration #Feel free to play with this!! param ostim=100 #hv defines a heaviside-like pulse but with adjustable steepness parameter. #Use this to describe a "smeared" square wave odorant plume reaching the neuron. #Sharpness of odorant plume param SHARPNESS=0.0001 hv(x,s)=1/(1+exp(-x/s)) #Pulse comes on for 1s at t=1 then on again for 1s at t=5. PULSE(t)=(hv(t-1,SHARPNESS) - hv(t-2,SHARPNESS) + (hv(t-5,SHARPNESS) - hv(t-6,SHARPNESS))) OD(t) = ostim*PULSE(t) #The vertebrate ORN model has 3 compartments i) Cilia, ii) Dendrite, and iii) Soma. #### Cilia Compartment #### dbLR/dt = k1*OD(t)*(1-bLR)-r1*bLR daG/dt = k2lin*bLR*(1-aG) - r2*aG dcAMP/dt = (aG*smax)/(1 + ((CAMK/kinh)^ninh)) - pd*cAMP dCa/dt = inf*Icng(cAMP,Vcilia) - ef*Ca + (-cc1lin*Ca + cc2*CaCAM) dCaCAM/dt = cc1lin*Ca - cc2*CaCAM dCAMK/dt = ck1lin*CaCAM - ck2*CAMK dVcilia/dt = (1/cap)*(Icng(cAMP,Vcilia) + Icacl(Ca,Vcilia) + Il(Vcilia)) #### Dendrite Compartment #### dVdend/dt = ge1*(Vcilia-Vdend) - vd*Vdend #### Soma Compartment #### dVsoma/dt = VOLTAGE(V(Vsoma),Vcilia,Vdend) dNaKXsoma/dt = tau_soma*(epsilon*(gamma*(1+tanh(V(Vsoma)/beta))-NaKXsoma)) Input(x,y) = ge2*(x-y) V(x) = (x-VSspike)/(0.5*VSamp) VOLTAGE(x,y,z) = tau_soma*(3*x - x^3 + 2 - NaKXsoma + Input(y,z)) inhcng(CaCAM) = 1+(inhmax-1)*((CaCAM^ninhcng)/(CaCAM^ninhcng + kinhcng^ninhcng)) #Current models: Icng(cAMP,Vcilia) = ((cnmax*cAMP^n1)/(cAMP^n1 + (inhcng(CaCAM)*hmc1)^n1))*(vcng-Vcilia) Icacl(Ca,Vcilia) = ((clmax*Ca^n2)/(Ca^n2 + hmc2^n2))*(vcl-Vcilia) Il(Vcilia) = gl*(vl-Vcilia) cap_soma(Vcilia) = cap_max*(1+tanh((cap_off-Vcilia)/beta_cap)) Isoma(x,y,z) = cap_soma(Vcilia)*VOLTAGE(x,y,z) #These auxilliary functions simply model what is actually measured by suction pipette recording #from whole cell. aux Icilia=-(Icng(cAMP,Vcilia) + Icacl(Ca,Vcilia)) aux WholeCell=Isoma(V(Vsoma),Vcilia,Vdend) -(Icng(cAMP,Vcilia) + Icacl(Ca,Vcilia)) aux Odorant=100*PULSE(t) #The number 100 is used above simply to give the odorant pulses a nice magnitude when plotted in the #same axes as the currrents. Unfortunately XPP does not have real double y-axis plots. #Anyway, at least you can see the odorant pulses now! #Initial conditions. Note that we actually run the model to steady-state in the absence #of odorant for 1s before simulation of the experiment. See T0 option below. # init bLR=1.e-8 init aG=1.e-8 init cAMP=1.e-8 init Ca=1.e-8 init CaCAM=1.e-8 init CAMK=1.e-8 init Vcilia=vl init Vdend=vl init Vsoma=vl init NaKXsoma=3.e-8 @ BUT=RunModel:ig,BUT=FitAxes:wf,MAXSTOR=2000000,T0=-1,TOTAL=8.0,BOUND=1000000 @ meth=cvode,TOL=1e-5,ATOL=1e-5,T0=-1,DT=0.00001,DTMIN=0.0001,DTMAX=0.001 @ XLO=0,XHI=8,YLO=-250,YHI=150 @ NPLOT=2,YP=WholeCell,YP2=Odorant done