Disentangling astroglial physiology with a realistic cell model in silico (Savtchenko et al 2018)

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"Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. ..."
1 . Savtchenko LP, Bard L, Jensen TP, Reynolds JP, Kraev I, Medvedev N, Stewart MG, Henneberger C, Rusakov DA (2018) Disentangling astroglial physiology with a realistic cell model in silico. Nat Commun 9:3554 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Glia;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s): Astrocyte;
Channel(s): I Calcium; I Potassium; Kir;
Gap Junctions: Gap junctions;
Transmitter(s): Glutamate;
Simulation Environment: NEURON; MATLAB; C or C++ program;
Model Concept(s): Calcium waves; Calcium dynamics; Potassium buffering; Volume transmission; Membrane Properties;
Implementer(s): Savtchenko, Leonid P [leonid.savtchenko at ucl.ac.uk];
Search NeuronDB for information about:  I Calcium; I Potassium; Kir; Glutamate;

The model of Glutamate  transporter.
is based on two papers, 

from the paper 

1. Zhang Z1, Tao Z, Gameiro A, Barcelona S, Braams S, Rauen T, Grewer C. 
Transport direction determines the kinetics of substrate transport by the glutamate transporter EAAC1.
Proc Natl Acad Sci U S A. 2007 Nov 13;104(46):18025-30. Epub 2007 Nov 8.

we determine the basic kinetic scheme for glutamate transporters, 

from the  paper
2. Bergles, D.E. & Jahr, C.E. 
Synaptic activation of glutamate transporters in hippocampal astrocytes. Neuron 19, 1297-1308 (1997).

we corrected the numerical values of the kinetic constants corresponding to the dynamics of glutamate transporters in astrocytes


    SUFFIX  GluTrans
    RANGE part, C1, C2, C3, C4, C5, C6
    GLOBAL k12, k21, k23, k32, k34, k43, k45, k54, k56, k65, k16, k61
    GLOBAL Nain, Naout, Kin, Kout, Gluin, charge 
    RANGE  itrans, Gluout, density, itransLog

    (l) = (liter)
    (nA) = (nanoamp)
    (mV) = (millivolt)
    (mA) = (milliamp)
    (pS) = (picosiemens)
    (umho) = (micromho)
    (mM) = (milli/liter)
    (uM) = (micro/liter)
    F = (faraday) (coulombs)
        PI      = (pi)       (1)

    : Rates

    k12 = 20           (l /mM /ms)
    k21 = 0.1          (/ms)
    k23 = 0.015       (l /mM /ms)
    k32 = 0.5          (/ms)
    k34 = 0.2          (/ms)
    k43 = 0.6          (/ms)
    k45 = 4            (/ms)
    k54 = 10           (l /mM /ms)
    k56 = 1            (/ms) 
    k65 = 0.1          (l /mM /ms) 
    k16 = 0.0016          (l /mM /ms)
    k61 =  2e-4        (l /mM /ms)

    Nain = 15        (mM/l)
    Naout = 150   (mM/l)
    Kin = 120       (mM/l)
    Kout = 3        (mM/l)
    Gluin = 0.3      (mM/l)
    Gluout = 20e-6	(mM/l)

    density =1e12  : (/cm2) : 10000 per um2
    charge = 1.6e-19 (coulombs)

    v	   (mV)		:  voltage
    itrans (mA/cm2)            : 
    surf   (cm2)
    volin  (liter)
    volout (liter)

    : Transporter  states (all fractions)
    C1	(/cm2)	:  
    C2	(/cm2)	:  
    C3	(/cm2)	: 
    C4	(/cm2)	: 
    C5	(/cm2)	: 
    C6  (/cm2)

    C1= 0.9074    
    C2= 0.0199    
    C3= 0.0435    
    C4= 0.0103    
    C5= 0.0142    
    C6= 0.0047
    volin = 1
    volout = 1
    surf = 1

    SOLVE kstates METHOD sparse
    itrans=-charge*density*(1e+006)*(0.6*(C1*k16*Kout*u(v,0.6)-C6*k61*Kin) -0.1*(C1*k12*Gluout*u(v,-0.1)-C2*k21)+0.5*(C2*k23*Naout*u(v,0.5)-C3*k32)+0.4*( C3*k34-C4*k43)+0.6*(C5*k56*u(v,0.6)-C6*k65*Nain) )
    : itransLog=log(-itrans*(1e+006))

    :itrans=-charge*density*(1e+006)*(0.6*(C1*k16*Kout*u(v,0.6)-C6*k61*Kin) +0.4*( C3*k34-C4*k43)+0.6*(C5*k56*u(v,0.6)-C6*k65*Nain) )	  

KINETIC kstates {
            COMPARTMENT volin { Nain Kin Gluin}
            COMPARTMENT volout { Naout Kout Gluout}
            : COMPARTMENT surf { C1 C2 C3 C4 C5 C6}
        : surf=1 : !!!!!!!
        ~ C1   <-> C2      (Gluout*k12*u(v,-0.1), k21)
        ~ C2  <-> C3       (Naout*k23*u(v,0.5),k32)
        ~ C3 <-> C4	       (k34*u(v,0.4),k43)
        ~ C4 <-> C5 	   (k45,k54*Gluin)
        ~ C5 <-> C6	       (k56*u(v,0.6),k65*Nain)
        ~ C6  <-> C1       (Kin*k61, k16*u(v,0.6)*Kout)
    CONSERVE C1+C2+C3+C4+C5+C6= 1

FUNCTION u(x(mV), th) {
    u = exp(th*x/(2*(26.7 (mV))))

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