% # iGABAB_TC_TRN_NN: % % SCALED synaptic GABA-B-ergic inhibitory current % This is, very slightly, an original formulation of the GABA-B current. % The state variable [R] for GABAB is 'customized' here, in that, rather % than the popular formulation of a 0.5 mM box 0.3 ms long for the % transmitter amount, inherited from (Destexhe 1996), the VERY similar % 2 * (1 + tanh( V / 4) ) method of calculating transmitter concentration % from (Olufsen 2003) is used. 0.3 ms is about as long as a neuron's % voltage is above 0 mV, the latter being the definition of when this % voltage-sensitive transmitter concentration is non-zero. The same % concentration amplitude was used since I had already seen a long time % of realistic results with GABAA responding to it, and GABAB's effect % obviously has a much more malleable effector in its maximal conductance. % In many ways, this is a simplified version of the GABA-B current from (Vijayan % 2012): instead of a fixed spike of transmitter concentration when the % presynaptic cell spikes, we use the same GABA concentration calculation % method from the GABA-A current. % % References: % - Destexhe, A., Bal, T., McCormick, D. A., & Sejnowski, T. J. (1996). Ionic % mechanisms underlying synchronized oscillations and propagating waves in a % model of ferret thalamic slices. Journal of Neurophysiology, 76(3), 2049–2070. % - Olufsen, M. S., Whittington, M. A., Camperi, M., & Kopell, N. (2003). New % roles for the gamma rhythm: population tuning and preprocessing for the beta % rhythm. Journal of Computational Neuroscience, 14(1), 33–54. % - Vijayan, S., & Kopell, N. J. (2012). Thalamic model of awake alpha % oscillations and implications for stimulus processing. Proceedings of the % National Academy of Sciences, 109(45), 18553–18558. % doi:10.1073/pnas.1215385109 % % From (Destxhe 1996), % K1 = 0.5 mM^{-1} ms^{-1} % K2 = 0.0012 ms^{-1} % K3 = 0.18 ms^{-1} % K4 = 0.034 ms^{-1} % % Tags: synapse, connection, inhibition %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Parameters gGABAB = 0.001 EGABAB = -95 rGABABIC = 0 rGABABNoiseIC= 0.1 sGABABIC = 0 sGABABNoiseIC= 0.1 % Connectivity % Connective radius, aka how many target cells each source cell connects % to, from the source's perspective. radius = 10 % Remove autapses to the dendrite corresponding to this soma removeRecurrentBool = 0 % We also need to normalize the conductance in mS/cm^2 by the number of % connections each target cell is receiving on average, so that the TOTAL % sum of their conductive inputs adds to our overall maximal conductance % above. normalizingFactor = min(((2*radius + (1-removeRecurrentBool)) / (N_post/N_pre)), N_pre) % Note that what is passed is 2x the radius netcon = netconNearestNeighbors(2*radius, N_pre, N_post, removeRecurrentBool) % Functions iGABAB_TC_TRN_NN(X,sGABAB) = -gGABAB/N_pre.*((sGABAB.^4./(sGABAB.^4 + 100))*netcon).*(X-EGABAB) % This way we record the synaptic currents! monitor iGABAB_TC_TRN_NN % ODEs and ICs rGABAB' = 0.5.*(2.*(1 + tanh(X_pre./4))).*(1-rGABAB) - 0.0012.*rGABAB rGABAB(0) = rGABABIC+rGABABNoiseIC.*rand(1,Npre) sGABAB' = 0.18.*rGABAB - 0.034.*sGABAB sGABAB(0) = sGABABIC+sGABABNoiseIC.*rand(1,Npre) % Linker @current += iGABAB_TC_TRN_NN(X_post,sGABAB)