A kinetic model unifying presynaptic short-term facilitation and depression (Lee et al. 2009)

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"... Here, we propose a unified theory of synaptic short-term plasticity based on realistic yet tractable and testable model descriptions of the underlying intracellular biochemical processes. Analysis of the model equations leads to a closed-form solution of the resonance frequency, a function of several critical biophysical parameters, as the single key indicator of the propensity for synaptic facilitation or depression under repetitive stimuli. This integrative model is supported by a broad range of transient and frequency response experimental data including those from facilitating, depressing or mixed-mode synapses. ... the model provides the reasons behind the switching behavior between facilitation and depression observed in experiments. ..."
1 . Lee CC, Anton M, Poon CS, McRae GJ (2009) A kinetic model unifying presynaptic short-term facilitation and depression. J Comput Neurosci 26:459-73 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Synapse;
Brain Region(s)/Organism:
Cell Type(s): Hippocampus CA1 pyramidal GLU cell; Cerebellum Purkinje GABA cell; Auditory nerve;
Channel(s): I Calcium;
Gap Junctions:
Receptor(s): AMPA;
Transmitter(s): Glutamate;
Simulation Environment: MATLAB; Simulink;
Model Concept(s): Synaptic Plasticity; Facilitation; Depression; Calcium dynamics;
Implementer(s): Lee, Chuang-Chung [chchlee at alum.mit.edu]; Anton, Mihai [mianton at mit.edu]; Poon, Chi-Sang [cpoon at mit.edu]; McRae, Gregory [mcrae at mit.edu];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; Cerebellum Purkinje GABA cell; AMPA; I Calcium; Glutamate;
function depression_freq

% ========================================================================
% This file is part of the Supplemental Codes of the manuscript 
% entitled "A Kinetic Model Unifying Presynaptic Short-Term Facilitation 
% and Depression" accepted by Journal of Compuational Neuroscience.  
% (Manucript No. #JCNS583R2).
% Authors: Chuang-Chung J. Lee, Mihai Anton, Chi-Sang Poon, Gregory McRae 
% Created by Chuang-Chung J. Lee 
% Created in Oct. '07.
% Latest modified in Oct. '08.
% ========================================================================

% ------------------------------------------------------------------------
% This function calculates the steady state frequency response of 
% synapses under depression and plots both experimental & simulated
% results.  The Probability of release and Ratio of realeasable vehsicle
% resposes are also output.  
% Equations used: Eq. (8) - (11)

% Experimental Data source: Henrique von Gersdorff et al. (1997) J. 
% Neurosci., 17(21):8137–8146

% Output: Figure 4A and 4B.  Responses of depressing synapses. A, The 
% frequency response of EPSC in the rat calyx of Held synapse. Data are 
% shown as mean ± standard error of the mean (SEM). B, The frequency 
% response of vesicle ratio and release probability by model.
% ------------------------------------------------------------------------

% -----------Plot the experimental frequency response first---------------
close all
freq_ex=[0.2 0.5 1.0 2.0 5.0 10.0];
EPSCss_norm=[0.89 0.69 0.47 0.42 0.34 0.28];
EPSCss_std=[0.09 0.07 0.09 0.08 0.11 0.14];

errorbar(freq_ex, EPSCss_norm, EPSCss_std,'ks', 'Markersize', 7)
hold on

xlabel('Frequency (Hz)','FontSize', 14);
ylabel ('Normalized EPSC_s_s','FontSize', 14);
axis([0 12 0 1])

% ---------Then Calculate and plot the model frequency response ----------
freq=linspace(0.001,12,50); % frequency range in the units of Hz
freqkHz=freq/1000; % frequency in the units of kHz
Ca0=0.02e2*4/1.5; % initial calcium concentration
krecov0=1E-4; % recovery rate constants
Prelmax=0.57; % release probability

for i=1:50
   krecov(i) = krecov0+(krecovmax-krecov0)*Ca(i)/(Ca(i)+Krecov);
sim_EPSC=sim_EPSC/sim_EPSC(1); % normalize EPSPs wrt the lowest freq 

% Plot the EPSC response 

% Plot the response of Rrel and Prel 
axis([0 12 0 1])
ylabel ('R_r_e_l (r)','FontSize', 14);

axis([0 12 0 1])
xlabel('Frequency (Hz)','FontSize', 14);
ylabel ('P_r_e_l (r)','FontSize', 14);