Biochemically detailed model of LTP and LTD in a cortical spine (Maki-Marttunen et al 2020)

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Accession:260971
"Signalling pathways leading to post-synaptic plasticity have been examined in many types of experimental studies, but a unified picture on how multiple biochemical pathways collectively shape neocortical plasticity is missing. We built a biochemically detailed model of post-synaptic plasticity describing CaMKII, PKA, and PKC pathways and their contribution to synaptic potentiation or depression. We developed a statistical AMPA-receptor-tetramer model, which permits the estimation of the AMPA-receptor-mediated maximal synaptic conductance based on numbers of GluR1s and GluR2s predicted by the biochemical signalling model. We show that our model reproduces neuromodulator-gated spike-timing-dependent plasticity as observed in the visual cortex and can be fit to data from many cortical areas, uncovering the biochemical contributions of the pathways pinpointed by the underlying experimental studies. Our model explains the dependence of different forms of plasticity on the availability of different proteins and can be used for the study of mental disorder-associated impairments of cortical plasticity."
Reference:
1 . Mäki-Marttunen T, Iannella N, Edwards AG, Einevoll GT, Blackwell KT (2020) A unified computational model for cortical post-synaptic plasticity. Elife [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Synapse;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Neocortex spiking regular (RS) neuron;
Channel(s): I Calcium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s): Glutamate; Norephinephrine; Acetylcholine;
Simulation Environment: NEURON; NeuroRD;
Model Concept(s): Long-term Synaptic Plasticity;
Implementer(s): Maki-Marttunen, Tuomo [tuomomm at uio.no];
Search NeuronDB for information about:  I Calcium; Acetylcholine; Norephinephrine; Glutamate;
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synaptic
L23PC
mechanisms
Ca_HVA.mod *
Ca_LVAst.mod *
CaDynamics_E2.mod *
epsp.mod *
Ih.mod *
Im.mod *
K_Pst.mod *
K_Tst.mod *
Nap_Et2.mod *
NaTa_t.mod *
NaTs2_t.mod *
ProbAMPANMDA_EMS.mod
ProbAMPANMDA_EMS_group.mod
ProbAMPANMDA_EMS_groupdet.mod
ProbAMPANMDA_EMST.mod
ProbAMPANMDA2.mod
ProbAMPANMDA2group.mod
ProbAMPANMDA2groupdet.mod
ProbGABAAB_EMS.mod
ProbGABAAB_EMS_group.mod
ProbUDFsyn2.mod *
ProbUDFsyn2group.mod *
ProbUDFsyn2groupdet.mod *
SK_E2.mod *
SKv3_1.mod *
                            
TITLE AMPA and NMDA receptor with presynaptic short-term plasticity 


COMMENT
AMPA and NMDA receptor conductance using a dual-exponential profile
presynaptic short-term plasticity based on Fuhrmann et al. 2002
Implemented by Srikanth Ramaswamy, Blue Brain Project, July 2009
Etay: changed weight to be equal for NMDA and AMPA, gmax accessible in Neuron

ENDCOMMENT


NEURON {

        POINT_PROCESS ProbUDFsyn2group  
        RANGE tau_r, tau_d, Nsyns
        RANGE Use, u, Dep, Fac, u0
        RANGE i, g, e, gmax
        NONSPECIFIC_CURRENT i
	POINTER rng
}

PARAMETER {

        tau_r = 0.2   (ms)  : dual-exponential conductance profile
        tau_d = 1.7    (ms)  : IMPORTANT: tau_r < tau_d
        Use = 1.0   (1)   : Utilization of synaptic efficacy (just initial values! Use, Dep and Fac are overwritten by BlueBuilder assigned values) 
        Dep = 100   (ms)  : relaxation time constant from depression
        Fac = 10   (ms)  :  relaxation time constant from facilitation
        e = 0     (mV)  : AMPA and NMDA reversal potential
    	gmax = .001 (uS) : weight conversion factor (from nS to uS)
    	u0 = 0 :initial value of u, which is the running value of Use
        Nsyns = 10 : How many synapses are there actually
}

COMMENT
The Verbatim block is needed to generate random nos. from a uniform distribution between 0 and 1 
for comparison with Pr to decide whether to activate the synapse or not
ENDCOMMENT
   
VERBATIM

#include<stdlib.h>
#include<stdio.h>
#include<math.h>

double nrn_random_pick(void* r);
void* nrn_random_arg(int argpos);

extern int ifarg(int iarg);
extern int vector_capacity(void* vv);
extern void* vector_arg(int iarg);

ENDVERBATIM
  

ASSIGNED {

        v (mV)
        i (nA)
	g (uS)
        factor
	rng
	weight_NMDA
        space       : A pointer to the vector containing the synapse times. Note that the underlying vector should not be touched after initialization by setVec().
}

STATE {
        A       : state variable to construct the dual-exponential profile - decays with conductance tau_r_AMPA
        B       : state variable to construct the dual-exponential profile - decays with conductance tau_d_AMPA
}

INITIAL{

  LOCAL tp
        
	A = 0
  B = 0
	
        
	tp = (tau_r*tau_d)/(tau_d-tau_r)*log(tau_d/tau_r) :time to peak of the conductance
	      
	factor = -exp(-tp/tau_r)+exp(-tp/tau_d) : Normalization factor - so that when t = tp, gsyn = gpeak
        factor = 1/factor
 
}

BREAKPOINT {

        SOLVE state METHOD cnexp
        g = gmax*(B-A) :compute time varying conductance as the difference of state variables B and A
        i = g*(v-e) :compute the driving force based on the time varying conductance, membrane potential, and reversal
}

DERIVATIVE state{

        A' = -A/tau_r
        B' = -B/tau_d
}


NET_RECEIVE (weight, Pv, Pr, u, myInd, tsyn (ms), Pv_tmp){
	
        INITIAL{
                Pv=1
                u=u0
                tsyn=t
            }

        :Randomize which of the synapses is activated. Note that an additional random number is generated by rand() - this may interfere with the random number order in parallel simulations.
        VERBATIM
          void** vv = (void**)(&space);
          double *x;
          int nx = vector_instance_px(*vv, &x);
          int myInd = rand()%((int)Nsyns);
          _args[4] = myInd;
          _args[5] = x[myInd];                //tsyn
          _args[1] = x[myInd+(int)Nsyns];     //Pv
          _args[3] = x[myInd+2*((int)Nsyns)]; //u
        ENDVERBATIM
        ::printf("NET_RECEIVE_beg: Pv = %g, Pr = %g, u = %g, myInd = %g, tsyn = %g, t = %g\n", Pv, Pr, u, myInd, tsyn, t)
        :printf("NET_RECEIVE_beg:  myInd = %g/%g, Pv = %g, u = %g, tsyn = %g, t = %g. ", myInd, Nsyns, Pv, u, tsyn, t)

        : calc u at event-
        if (Fac > 0) {
          u = u*exp(-(t - tsyn)/Fac) :update facilitation variable if Fac>0 Eq. 2 in Fuhrmann et al.
        } else {
          u = Use  
        } 
        if(Fac > 0){
          u = u + Use*(1-u) :update facilitation variable if Fac>0 Eq. 2 in Fuhrmann et al.
        }    

        
        Pv_tmp  = 1 - (1-Pv) * exp(-(t-tsyn)/Dep) :Probability Pv for a vesicle to be available for release, analogous to the pool of synaptic
                                                  :resources available for release in the deterministic model. Eq. 3 in Fuhrmann et al.
        Pr  = u * Pv_tmp                          :Pr is calculated as Pv * u (running value of Use)
        Pv_tmp  = Pv_tmp - u * Pv_tmp             :update Pv as per Eq. 3 in Fuhrmann et al.
        :printf("Pv = %g\n", Pv)
        :printf("Pr = %g\n", Pr)
                
	if (erand() < Pr){
          tsyn = t
          Pv = Pv_tmp
          A = A + weight*factor
          B = B + weight*factor
          ::printf ( "Released! value = %g, Pr = %g\n" , erand(), Pr )
          :printf ( "R! Pr = %g\n" , Pr )
        } else {
          ::printf("Not released! value = %g, Pr = %g\n", erand(), Pr )
          :printf ( "NR! Pr = %g\n" , Pr )
        }
        VERBATIM
          x[myInd] = _args[5];
          x[myInd+(int)Nsyns] = _args[1];
          x[myInd+2*((int)Nsyns)] = _args[3];
        ENDVERBATIM
}

PROCEDURE setRNG() {
VERBATIM
    {
        /**
         * This function takes a NEURON Random object declared in hoc and makes it usable by this mod file.
         * Note that this method is taken from Brett paper as used by netstim.hoc and netstim.mod
         * which points out that the Random must be in negexp(1) mode
         */
        void** pv = (void**)(&_p_rng);
        if( ifarg(1)) {
            *pv = nrn_random_arg(1);
        } else {
            *pv = (void*)0;
        }
    }
ENDVERBATIM
}

FUNCTION erand() {
VERBATIM
	    //FILE *fi;
        double value;
        if (_p_rng) {
                /*
                :Supports separate independent but reproducible streams for
                : each instance. However, the corresponding hoc Random
                : distribution MUST be set to Random.negexp(1)
                */
                value = nrn_random_pick(_p_rng);
		        //fi = fopen("RandomStreamMCellRan4.txt", "w");
                //fprintf(fi,"random stream for this simulation = %lf\n",value);
                //printf("random stream for this simulation = %lf\n",value);
                return value;
        }else{
ENDVERBATIM
                : the old standby. Cannot use if reproducible parallel sim
                : independent of nhost or which host this instance is on
                : is desired, since each instance on this cpu draws from
                : the same stream
                erand = exprand(1)
VERBATIM
        }
ENDVERBATIM
        :erand = value :This line must have been a mistake in Hay et al.'s code, it would basically set the return value to a non-initialized double value.
                       :The reason it sometimes works could be that the memory allocated for the non-initialized happened to contain the random value
                       :previously generated. However, here we commented this line out.
}

PROCEDURE setVec() {    : Sets the times of firing of each synapse. This should be done only once for each ProbAMPANMDA2group,
                        : before the running of the simulation, and the underlying vector should be untouched after that.
  VERBATIM
  void** vv;
  vv = (void**)(&space);
  *vv = (void*)0;
  if (ifarg(1)) {
    *vv = vector_arg(1);
    Nsyns = vector_capacity(*vv)/3;
  }
  ENDVERBATIM
}

PROCEDURE printVec() { : Prints the previous times of firing of each synapse.
VERBATIM
    void** vv = (void**)(&space);
    double *x;
    int nx = vector_instance_px(*vv, &x);
    int i1;
    for (i1=0; i1<Nsyns;i1++) {
      printf("tsyns[%i] = %g, Pv[%i] = %g, u[%i] = %g\n", i1, x[i1], i1, x[i1+(nx/3)], i1, x[i1+2*(nx/3)]);
    }
ENDVERBATIM
}

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