STDP and BDNF in CA1 spines (Solinas et al. 2019)

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Storing memory traces in the brain is essential for learning and memory formation. Memory traces are created by joint electrical activity in neurons that are interconnected by synapses and allow transferring electrical activity from a sending (presynaptic) to a receiving (postsynaptic) neuron. During learning, neurons that are co-active can tune synapses to become more effective. This process is called synaptic plasticity or long-term potentiation (LTP). Timing-dependent LTP (t-LTP) is a physiologically relevant type of synaptic plasticity that results from repeated sequential firing of action potentials (APs) in pre- and postsynaptic neurons. T-LTP is observed during learning in vivo and is a cellular correlate of memory formation. T-LTP can be elicited by different rhythms of synaptic activity that recruit distinct synaptic growth processes underlying t-LTP. The protein brain-derived neurotrophic factor (BDNF) is released at synapses and mediates synaptic growth in response to specific rhythms of t-LTP stimulation, while other rhythms mediate BDNF-independent t-LTP. Here, we developed a realistic computational model that accounts for our previously published experimental results of BDNF-independent 1:1 t-LTP (pairing of 1 presynaptic with 1 postsynaptic AP) and BDNF-dependent 1:4 t-LTP (pairing of 1 presynaptic with 4 postsynaptic APs). The model explains the magnitude and time course of both t-LTP forms and allows predicting t-LTP properties that result from altered BDNF turnover. Since BDNF levels are decreased in demented patients, understanding the function of BDNF in memory processes is of utmost importance to counteract Alzheimer’s disease.
1 . Solinas SMG, Edelmann E, Leßmann V, Migliore M (2019) A kinetic model for Brain-Derived Neurotrophic Factor mediated spike timing-dependent LTP. PLoS Comput Biol 15:e1006975 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Synapse; Dendrite;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s): Hippocampus CA1 pyramidal GLU cell;
Channel(s): I Na,t; I_KD; I K; I h; I A; I Calcium;
Gap Junctions:
Receptor(s): AMPA; NMDA;
Transmitter(s): Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Facilitation; Long-term Synaptic Plasticity; Short-term Synaptic Plasticity; STDP;
Implementer(s): Solinas, Sergio [solinas at]; Migliore, Michele [Michele.Migliore at];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; AMPA; NMDA; I Na,t; I A; I K; I h; I Calcium; I_KD; Glutamate;
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na3n.mod *
naxn.mod *
netstims.mod *
Two state kinetic scheme synapse described by rise time taur,
and decay time constant taud. The normalized peak condunductance is 1.
Decay time MUST be greater than rise time.

The solution of A->G->bath with rate constants 1/taur and 1/taud is
A = a*exp(-t/taur) and
G = a*taud/(taud-taur)*(-exp(-t/taur) + exp(-t/taud))
where taur < taud

If taud-taur -> 0 then we have a alphasynapse.
and if taur -> 0 then we have just single exponential decay.

The factor is evaluated in the
initial block such that an event of weight 1 generates a
peak conductance of 1.

Because the solution is a sum of exponentials, the
coupled equations can be solved as a pair of independent equations
by the more efficient cnexp method.


    POINT_PROCESS ghknmda
    USEION na WRITE ina
    USEION ca READ cai, cao WRITE ica
    USEION glut READ gluti VALENCE 0
    RANGE taur, taud
    RANGE inmda
    RANGE P, mg, Pmax
    RANGE  mgb, ica, Area, mgb_k, mg_ref

    (nA) = (nanoamp)
    (mV) = (millivolt)
    (uS) = (microsiemens)
    (molar) = (1/liter)
    (mM) = (millimolar)
    FARADAY = (faraday) (coulomb)
    R = (k-mole) (joule/degC)

    taur=5 (ms) <1e-9,1e9>
    taud = 50 (ms) <1e-9,1e9>
    cai = 100e-6(mM)	: 100nM
    cao = 2		(mM)
    nai = 18	(mM)	: Set for a reversal pot of +55mV
    nao = 140	(mM)
    ki = 140	(mM)	: Set for a reversal pot of -90mV
    ko = 5		(mM)
    celsius		(degC)
    mg = 1		(mM) : 2 mM in the Johnston et al. 2010, extracellula [MgCl2] = 1 mM in Edelman et al. 2015
    Pmax=1e-6   (cm/s)	: According to Canavier, PNMDAs default value is
    : 1e-6 for 10uM, 1.4e-6 cm/s for 30uM of NMDA
    Area = 1 (cm2)
    mgb_k = 0.062 (/mV)
    mg_ref = 3.57 (mM)

    ina     (nA)
    ik      (nA)
    ica     (nA)
    v (mV)
    P (cm/s)
    mgb	(1)
    inmda	(nA)
    gluti (mM)

    A (cm/s)
    B (cm/s)

    LOCAL tp
    if (taur/taud > .9999) {
	taur = .9999*taud
    A = 0
    B = 0
    tp = (taur*taud)/(taud - taur) * log(taud/taur)
    factor = -exp(-tp/taur) + exp(-tp/taud)
    factor = 1/factor
    : Area=1

    SOLVE state METHOD cnexp
    mgb = mgblock(v)
    : Area is just for unit conversion of ghk output
    ina = P*mgb*ghk(v, nai, nao,1)*Area	
    ica = P*10.6*mgb*ghk(v, cai, cao,2)*Area
    ik = P*mgb*ghk(v, ki, ko,1)*Area
    inmda = ica + ik + ina
    : printf("nmda%g\t",gluti)
    : printf("nmdaP %g\t",P)

    A' = -A/taur
    B' = -B/taud

FUNCTION ghk(v(mV), ci(mM), co(mM),z) (0.001 coul/cm3) {
    LOCAL arg, eci, eco
    arg = (0.001)*z*FARADAY*v/(R*(celsius+273.15))
    eco = co*efun(arg)
    eci = ci*efun(-arg)
    ghk = (0.001)*z*FARADAY*(eci - eco)

FUNCTION efun(z) {
    if (fabs(z) < 1e-4) {
	efun = 1 - z/2
	efun = z/(exp(z) - 1)

FUNCTION mgblock(v(mV)) (1){
    DEPEND mg
    FROM -140 TO 80 WITH 1000 
    : from Jahr & Stevens, JNS, 1990
    mgblock = 1 / (1 + exp(mgb_k * -v) * (mg / mg_ref)) 
    : remove the background activation at -70 mV
    : if (mgblock < 0.036 ) {
    : 	mgblock = 0
    : }

NET_RECEIVE(weight (uS)) { 	: No use to weight, can be used instead of Pmax,
    : if you want NetCon access to the synaptic
    : conductance.
    : printf("nmda_sp%g\t",gluti)
    if (flag == 0 ) {
    if (flag == 2 ) {
	A = A + Pmax*factor * gluti
	B = B + Pmax*factor * gluti