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Appendix


Neuron model equations

\begin{eqnarray*} C_m \frac{dV}{dt} & =& I_{syn}-I_{Na}-I_{Ca}-I_K-I_{K(Ca)}-I_... ...\infty}(V)-B}{\tau_{_B}},\\ \frac{dC}{dt} &=& K_p(-I_{Ca})-RC \end{eqnarray*}



where:

\begin{eqnarray*} \tau_{_W}(V) &=& \frac {1}{\lambda}\left(e^{a^{(W)} (V-V_{1/... ... -2a^{(P)}(V-{V_{1/2}^{(P)}})}\right)^{-1},~ for~P=W,m,X,A,B, \end{eqnarray*}



$V$ is the membrane potential, $W$ is the recovery variable, $C$ is the intracellular calcium concentration $X$ and $B$ are respectively the calcium channel activation variable and transient potassium channel inactivation variable. The steady-state functions $m_{\infty}$ , $A_{\infty}$ , $W_{\infty}$ , $X_{\infty}$ , and $B_{\infty}$ are modeled as sigmoidal curves, determined by two parameters: the half maximum voltage $V_{1/2}$ (values are -31, -20, -35, -45 and -70 $mV$ respectively) and a slope $a$ of the curve at this point (values are 0.065, 0.02, 0.055, 2.0, and -0.095 respectively). $K_p=0.0002$ is the conversion factor from calcium current to concentration and $R=0.006$ is the removal rate constant of the intracellular calcium concentration. $C_m=1~\mu F/cm^2$ is the membrane capacitance. $\tau_{_W}$ is the relaxation time function, and $\tau_{_X}=25~msec$ and $\tau_{_B}=10~msec$ are relaxation time constants for recovery $W$ , calcium activation $X$ , and potassium transients inactivation $B$ variables. Ion currents $I_i$ are described by the product of three terms: the maximal conductance $\overline{g}_i$ , the activation and inactivation variable or function, and the driving force $(V-V_i)$ .

\begin{eqnarray*} I_{Na} & = & \overline{g}_{Na}m_{\infty}^3(V)(1-W)(V-V_{Na})\... ..._A A_{\infty}(V)B(V-V_K)\\ I_L & = & \overline{g}_L(V-V_L)\\ \end{eqnarray*}



where: $\bar{g}_{Na}=120~ mS/cm^2$ , $\bar{g}_{Ca}=1.0 ~mS/cm^2$ , $\bar{g}_K=15~ mS/cm^2$ , $\bar{g}_A=12.5~ mS/cm^2$ , $\bar{g}_L=0.3~ mS/cm^2$ , $\bar{g}_{K(Ca)}$ in the range 0.5-3.5 $mS/cm^2$ are maximum conductances for the respective channels and $V_{Na}=-50~mV$ , $V_{Ca}=124~mV$ , $V_{K}=-72~mV$ , and $V_L=-50~mV$ are values of the reversal potentials for the respective ions and leak current. $K_d=0.5$ and $K_C=2$ are the calcium concentration function constants.

Synaptic model equations

\begin{eqnarray*} I_{syn} &=& \sum_{j=1}^{N_{syn}}w_j g_j(t) (V-E_{syn})\\ g(... ...c{-\Delta t_i}{\tau_d}}-e^{\frac{-\Delta t_i}{\tau_o}}\right) \end{eqnarray*}



where $i$ denotes summation over past action potentials and $j$ over the number of input synapses. $\overline{g}_{syn}=0.0112~mS/cm^2$ , is the synaptic conductance constant, $g_j(t)$ is the conductance function and $E_{syn}$ is a synaptic reversal potential equal $-10~mV$ for excitatory and $-120~mV$ for inhibitory synapse. $\tau_d=3~ms$ and $\tau_o=0.5~ms$ represent respectively decay time and onset time constants of a PSP. Synaptic weight $w_j$ was modeled as an integer in the range $0~-~120$ . $\Delta t_i$ denotes time elapsed since $i$ -th action potential arrival on synapse, $N$ is the number of past action potentials with significant contribution to the sum and $N_{syn}$ is the number of synaptic inputs, in these simulations $N_{syn}=4$ (2 excitatory and 2 inhibitory inputs). The ordinary differential equations were solved numerically using forward Euler method with a time step of 0.01 $msec$ .
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