Equations and Parameters for Glucose-Excited Neuron Model

Supplementary Material Equations and Parameters for Glucose-excited neuron model

Table S1. Abbreviations Parameters Descriptions

CFX dependency of ion“X”flux on Vm (constant field equation)

Cm membrane capacitance (pF)

Ex equilibrium potential for ion“X” (mV) F Faraday’s constant, 96.4867 C/mmol Gx conductance (pA/mV)

IaX ion X component of current Ia (pA/pF) k,α, β, λ rate constants (/msec)

Xi intracellular amount of substance X (amol)

Xo extracellular amount of substance X (amol)

[X]i intracellular concentration of substance X (mM)

[X]o extracellular concentration of substance X (mM) Px convert factor (pA/pF/mM) for CFX p(X) probability of state X in a scheme of multiple state transitions

Table S2. Calculation of ionic currents and glucose metabolism Constant Field Equation

CFX=zXFVm/R/T * ([X]i-[X]o)*exp(-zXFVm/R/T)/(1- exp(-zXFVm/R/T))

INKb: background non-selective cation current pINKb=0.00396; INKb,Na=pINKb*CFNa; INKb,K=2.525*pINKb*CFK; INKb=INKb,Na+INKb,K; 2+ Il(Ca): Ca -activated background cation current

Pl(Ca) = 0.0075; 2+ p(open)=1/(1+(0.0012/[Ca ]i)^3); Il(Ca)Na = Pl(Ca)*CFNa*p(open); Il(Ca)K = Pl(Ca)*CFK*p(open); Il(Ca) = Il(Ca),Na + Il(Ca),K; + IKATP: ATP-sensitive K current kdd=0.01; ktt=0.05; ktd=0.026; gKATP=2.31; pOatp=(0.08*(1+2*[MgADP]/kdd)+0.89*([MgADP]/kdd)^2)/(1+[MgADP]/kdd)^2/(1+0.45*[MgADP]/ktd+ [ATP]/ktt); IKATP=gKATP*pOatp*(Vm-EK); + IKDr : delayed rectifier K current(Including IKr and IKs) pKDr=2.1; αp=1/(33.07*exp(-(Vm)/8)+0.937*exp(-(Vm)/100)); βp=1/(22.73*exp(Vm/100)); αq=1/800; βq=1/(1000*exp(-Vm/8)+100*exp(-Vm/100)); dp_KDr/dt=(αp*(1-p_KDr)-βp*p_KDr); dq_KDr/dt =(αq*(1-q_KDr)-βq*q_KDr); IKDr=pKDr*p_KDr*(0.6*q_KDr+0.4)* CFK; + Ito : transient outward K current

GKto=2.13; αm=1/(13.65*exp(-Vm/20)); βm=1/(6.2*exp(Vm/60)); αh=1/(570*exp(Vm/500)); βh=1/(7.765*exp(-Vm/9)+4.076*exp(-Vm/1000)); dm_Kto/dt =(αm*(1-m_Kto)-βm*m_Kto); dh_Kto/dt =(αh*(1-h_Kto)-βh*h_Kto); IKto=GKto*m_Kto*h_Kto*(Vm-EK); 2+ ICaL : voltage-dependent Ca current (Including ICaL and ICaT)

RCaLNa=0.0000185; RCaLK=0.000367; PCaL=48.9; %voltage-dependent activation gate dα=1/(0.9344*exp(-(Vm)/50)+0.09045*exp(-(Vm)/600)); dβ=1/(4.2678*exp((Vm)/12)+1.1265*exp((Vm)/30)); VpOpen=d_CaL^2; dd_CaL/dt =(dα*(1-d_CaL)-dβ*d_CaL); %calcium-dependent inactivation gate

SingleiCaL=0.0676*CFCa; Uα=0.0042*2; 2+ Uβ=0.1159*(-1.15*SingleiCaL*VpOpen+[Ca ]i)*2; %ultra-slow inactivation gate usα=1/(75000*exp(Vm/34)); usβ=1/(50000*exp(-Vm/19)+500*exp(-Vm/100)); RundownATP=1/(1+(1.4/[ATP]^3)); pO=(VpOpen*U_CaL*(0.4+0.6*fus))*RundownATP; dU_CaL/dt =(Uα*(1-U_CaL)-Uβ*U_CaL); dfus/dt =(usα*(1-fus)-usβ*fus);

ICaL,Na=RCaLNa*PCaL*pO*CFNa; ICaL,K=RCaLK*PCaL*pO*CFK; ICaL,Ca=PCaL*pO*CFCa; ICaL= ICaL,Na+ICaL,K+ICaL,Ca; 2+ IPMCA: plasma membrane Ca -ATPase

P_PMCA=1.56; K_PMCA=0.00014; 2+ 2+ IPMCA=P_PMCA*[Ca ]i ^2/([Ca ]i ^2+K_PMCA^2); IPMCA,Na= -IPMCA; IPMCA,Ca=2*IPMCA; + + INaK : Na /K pump current R=8.3143; Tem=310.15; Pii=1.9; Proton=0.0001; Kd_MgATP=0.6; Kd_Nao0=26.8; Kd_Nai0=5.0; Kd_Ko0=0.8; Kd_Ki0=18.8; delta_Nao=0.44; delta_Nai=-0.14; delta_Ko=0.23; delta_Ki=-0.14; k1_plus=1.253; k2_plus=0.139; k3_plus=6.96; k4_plus=0.52; k1_minus=0.139; k2_minus=0.0139; k3_minus=13900; k4_minus=0.348;

PNaK=350; fVm=F*Vm/(R*Tem); Kd_Nao=Kd_Nao0*exp(delta_Nao*fVm); Kd_Nai=Kd_Nai0*exp(delta_Nai*fVm); Kd_Ko=Kd_Ko0*exp(delta_Ko*fVm); Kd_Ki=Kd_Ki0*exp(delta_Ki*fVm); + Nai_=[Na ]i/Kd_Nai; + Naout_=[Na ]o/Kd_Nao; + Ki_=[K ]i /Kd_Ki; + Kout_=[K ]o /Kd_Ko; MgATP_=ATP(j)/Kd_MgATP; a1_plus_=(k1_plus*Nai_^3.0)/((1+Nai_)^3+(1+Ki_)^2-1); a2_plus_=k2_plus; a3_plus_=k3_plus*Kout_^2/((1+Naout_)^3+(1+Kout_)^2-1); a4_plus_=k4_plus*MgATP_/(1+MgATP_); a1_minus_=k1_minus*MgADP(j); a2_minus_=k2_minus*Naout_^3/((1+Naout_)^3+(1+Kout_)^2-1); a3_minus_=k3_minus*Pii*Proton/(1+MgATP_); a4_minus_=k4_minus*Ki_^2/((1+Nai_)^3+(1+Ki_)^2-1); denomi=(a1_minus_+a1_plus_)*a2_minus_*a3_minus_+a1_plus_*a2_plus_*(a3_plus_+a3_minus_) +a2_plus_*a3_plus_*(a4_plus_+a4_minus_)+(a2_plus_+a2_minus_)*a3_minus_*a4_minus_+ (a1_minus_+a1_plus_)*a3_plus_*a4_plus_+a1_minus_*(a3_plus_+a3_minus_)*a4_minus_+a1_plus_*(a2_plus _+a2_minus_)*a4_plus_+a1_minus_*a2_minus_*(a4_plus_+a4_minus_); numer=a1_plus_*a2_plus_*a3_plus_*a4_plus_-a1_minus_*a2_minus_*a3_minus_*a4_minus_; iglc=(0.4+0.6*exp(-[Glucose]/5.84)); vcyc=(numer/denomi); INaK=PNaK*vcyc*iglc; INaK,Na=3*INaK; INaK,K=-2*INaK; + 2+ INaCa: Na /Ca exchange current KdNao=87.5; KdCao=1.38; KdNai=20.75; KdCai=0.0184; k3=1; k4=1; AmpINaCa=204; RTF=R*Tem/F; + 2+ pE1Na=1/(1+(KdNai/[Na ]i)^3*(1+[Ca ]i /KdCai)); 2+ + pE1Ca=1/(1+(KdCai/[Ca ]i)*(1+([Na ]i /KdNai)^3)); + 2+ pE2Na=1/(1+(KdNao/[Na ]o)^3*(1+[Ca ]o /KdCao)); 2+ + pE2Ca=1/(1+(KdCao/[Ca ]o)*(1+([Na ]o /KdNao)^3)); k1=exp(0.32*Vm/RTF); k2=exp((0.32-1)*Vm/RTF); 2+ 2+ fCa=[Ca ]i /( [Ca ]i +0.004); α1=pE1Na*(fCa*0.002+(1-fCa)*0.0015); β1=fCa*0.0012+(1-fCa)*0.0000005; α2=fCa*0.00003+(1-fCa)*0.01; β2=fCa*0.09+(1-fCa)*0.0001; kf=k2*pE2Na+k4*pE2Ca; kb=k1*pE1Na+k3*pE1Ca; E2_tot=1-E1_tota-I1-I2; INaCa=AmpINaCa*(k1*pE1Na*E1_tota-k2*pE2Na*E2_tot); INaCa,Na=3*INaCa; INaCa,Ca=-2*INaCa; dE1_tota/dt =(E2_tot*kf+I1*β1+I2*β2-E1_tota*(kb+α1+α2)); dI1/dt =(E1_tota*α1-I1*β1); dI2/dt =(E1_tota*α2-I2*β2); 2+ 2+ ER calcium dynamics(IERCA:Ca uptake by SERCA, Irel:Ca release from ER)

PCaER=0.096; KCarp=0.0005; Pleak=0.46; 2+ 2+ IERCA =PCaER*[Ca ]i ^2/([Ca ]i ^2+KCarp^2); 2+ Irel =Pleak*( - [Ca ]i); Glycolysis And Oxidative phospholylation(ATP, MgADP, Re) Nt=10; totalATP=5; KmATP=0.5; hgl=2.5; Kg=13; Pop=0.0005; Kop=0.02; KRe=0.000126; Kfa=0.0000063; Stoichi=2.5; Rvol=2.5; kATPCa=0.187; kATP=0.000062; kADPf=0.0002; kADPb=0.00002; fGlu=[ATP]/(KmATP+[ATP])*[Glucose]^hgl/(Kg^hgl+[Glucose]^hgl); JOP=Pop*[Re]*[MgADP]^2/([MgADP]^2+Kop^2); ADPb=totalATP-[ATP]-[MgADP]/0.55; 2+ d[ATP]/dt=(JOP-((INaK+IPMCA/F+Jserca/2)/voli-(kATP+kATPCa*[Ca ]i)*[ATP]); 2+ d[MgADP]/dt=(-0.55*(JOP-((INaK+IPMCA)/F+Jserca/2)/voli-(kATP+kATPCa*[Ca ]i)*[ATP])+0.55*kADPb*ADPb- kADPf*[MgADP]); d[Re]/dt=((KRe*fGlu+Kfa)*(Nt-[Re])-JOP*Rvol/Stoichi);

Table S3. Initial values of related variables Variables Initial values

Vm -69.8663703359279 + [Na ]i 5.80400 + [K ]i 126.776 2+ [Ca ]i 0.000306139 [ATP] 3.5 [MgADP] 0.6 [Re] 0.641950 d_CaL 0.0305677246684658

U_CaL 0.97136209316892 fus 0.0234849 p_KDr 5.50634588785556E-05 q_KDr 0.999871116432097 m_Kto 0.00429094440645993 h_Kto 0.973579888263364 E1_tota 0.0995446568706361 I1 0.347091674662305 I2 0.552654630410071