Mathematical model for windup (Aguiar et al. 2010)

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Accession:128559
"Windup is characterized as a frequency-dependent increase in the number of evoked action potentials in dorsal horn neurons in response to electrical stimulation of afferent C-fibers. ... The approach presented here relies on mathematical and computational analysis to study the mechanism(s) underlying windup. From experimentally obtained windup profiles, we extract the time scale of the facilitation mechanisms that may support the characteristics of windup. Guided by these values and using simulations of a biologically realistic compartmental model of a wide dynamic range (WDR) neuron, we are able to assess the contribution of each mechanism for the generation of action potentials windup. ..."
Reference:
1 . Aguiar P, Sousa M, Lima D (2010) NMDA channels together with L-type calcium currents and calcium-activated nonspecific cationic currents are sufficient to generate windup in WDR neurons. J Neurophysiol 104:1155-66 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Wide dynamic range neuron;
Channel(s): I Na,p; I Na,t; I L high threshold; I N; I K; I K,Ca;
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; MATLAB;
Model Concept(s): Activity Patterns; Action Potentials;
Implementer(s):
Search NeuronDB for information about:  GabaA; AMPA; NMDA; I Na,p; I Na,t; I L high threshold; I N; I K; I K,Ca;
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WDR-Model
readme.html
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TITLE Slow Ca-dependent potassium current
:
:   Ca++ dependent K+ current IC responsible for slow AHP
:   Differential equations
:
:   Model based on a first order kinetic scheme
:
:       + n cai <->     (alpha,beta)
:
:   Following this model, the activation fct will be half-activated at 
:   a concentration of Cai = (beta/alpha)^(1/n) = cac (parameter)
:
:   The mod file is here written for the case n=2 (2 binding sites)
:   ---------------------------------------------
:
:   This current models the "slow" IK[Ca] (IAHP): 
:      - potassium current
:      - activated by intracellular calcium
:      - NOT voltage dependent
:
:   A minimal value for the time constant has been added
:
:   Ref: Destexhe et al., J. Neurophysiology 72: 803-818, 1994.
:   See also: http://www.cnl.salk.edu/~alain , http://cns.fmed.ulaval.ca
:   modifications by Yiota Poirazi 2001 (poirazi@LNC.usc.edu)
:   taumin = 0.5 ms instead of 0.1 ms	

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
    SUFFIX iKCa
    USEION k READ ek WRITE ik
    USEION ca READ cai
    RANGE gk, gbar, m_inf, tau_m
    GLOBAL beta, cac
}


UNITS {
    (mA) = (milliamp)
    (mV) = (millivolt)
    (molar) = (1/liter)
    (mM) = (millimolar)
}


PARAMETER {
    v                 (mV)
    celsius = 36      (degC)
    ek      = -80     (mV) 
    cai     = 50.0e-6 (mM)            : initial [Ca]i
    gbar    = 0.01    (mho/cm2)
    beta    = 0.03    (1/ms)          : backward rate constant
    :cac     = 0.025   (mM)            : middle point of activation fct    
    cac     = 0.001   (mM)            : middle point of activation fct    
    taumin  = 0.1     (ms)            : minimal value of the time cst
    gk
}


STATE {m}        : activation variable to be solved in the DEs       

ASSIGNED {       : parameters needed to solve DE 
    ik      (mA/cm2)
    m_inf
    tau_m   (ms)
    tadj
}
BREAKPOINT { 
    SOLVE states METHOD derivimplicit
    gk = gbar*m*m*m     : maximum channel conductance
    ik = gk*(v - ek)    : potassium current induced by this channel
}

DERIVATIVE states { 
    evaluate_fct(v,cai)
    m' = (m_inf - m) / tau_m
}

UNITSOFF
INITIAL {
    :
    :  activation kinetics are assumed to be at 22 deg. C
    :  Q10 is assumed to be 3
    :
    tadj = 3 ^ ((celsius-22.0)/10) : temperature-dependent adjastment factor
    evaluate_fct(v,cai)
    m = m_inf
}

PROCEDURE evaluate_fct(v(mV),cai(mM)) {  LOCAL car
    car = (cai/cac)^2
    m_inf = car / ( 1 + car )      : activation steady state value
    tau_m =  1 / beta / (1 + car) / tadj
    if(tau_m < taumin) { tau_m = taumin }   : activation min value of time cst
}
UNITSON

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