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In the simulations there will be 50 E-cells and 50 I-cells. The Network will be "trained" to encode assemblies by running the weight producing algorithm on a set of patterns, each which represents a cell assembly (remember weights are only produced between the E-cells initially). There will be 8 patterns that contain 8 E-Cells in each. Each "event" or pattern will carry equal significance when the weighting algorithm runs. To help visualize the patterns look at the diagram below.
Below are tables with parameter that are given exactly from A Lansner and E Fransen.
Parameter | E-Cell | I-Cell |
${V}_{leak}$ (mV) | -50 | -70 |
${G}_{core}$ | 0.04 | 0.0638 |
${G}_{m}$ Soma $\left(\mu S\right)$ | 0.0032 | 0.0016 |
${C}_{m}$ Soma $\left(nF\right)$ | 0.032 | 0.016 |
${G}_{m}$ $\left(\mu S\right)$ Dentrites | 0.0096 | 0.0096 |
${C}_{m}$ Dentrites $\left(nF\right)$ | 0.288 | 0.288 |
${V}_{Na}$ | 40 | 50 |
${G}_{Na}$ $\left(\mu S\right)$ | 1.0 | 1.0 |
${V}_{K}$ | -70 | -90 |
${G}_{K}$ $\left(\mu S\right)$ | 0.5 | 1.0 |
${V}_{Ca}$ | 150 | 150 |
${G}_{Ca}$ $\left(\mu S\right)$ | 0 | 0 |
${G}_{K\left(Ca\right)}$ $\left(\mu S\right)$ | 0.0017 | 0.01 |
${\rho}_{AP}$ (mV ${}^{-1}$ ms ${}^{-1}$ ) | 4 | 0.013 |
${\delta}_{AP}$ ms ${}^{-1}$ | .075 | .02 |
m | h | n | q | p | ||
A (mV ${}^{-1}$ ms ${}^{-1}$ ) | 0.2 | 0.08 | 0.02 | 0.08 | 0.7 (ms ${}^{-1}$ ) | |
$\alpha $ | B (mV) | -40 | -40 | -15 | -25 | |
C (mV) | 1 | 1 | 0.8 | 1 | 17 | |
A (mV ${}^{-1}$ ms ${}^{-1}$ ) | 0.06 | 0.4 | 0.04 | 0.005 | 0.1 (ms ${}^{-1}$ ) | |
$\beta $ | B (mV) | -49 | -36 | -40 | -20 | |
C (mV) | 20 | 2 | 0.4 | 20 | 17 |
m | h | n | q | ||
A (mV ${}^{-1}$ ms ${}^{-1}$ ) | 0.2 | 0.08 | 0.02 | 0.08 | |
$\alpha $ | B (mV) | -30 | -30 | -21 | -15 |
C (mV) | 1 | 0.2 | 0.2 | 1 | |
A (mV ${}^{-1}$ ms ${}^{-1}$ ) | 0.06 | 0.4 | 0.02 | 0.005 | |
$\beta $ | B (mV) | -38 | -26 | -18 | -10 |
C (mV) | 20 | 0.2 | 0.2 | 20 |
${V}_{syn}$ Excitatory | 0 $mV$ |
${V}_{syn}$ Inhibitory | -85 $mV$ |
$s$ | variable |
${G}_{syn}$ E to E (AMPA) | ${w}_{ij}$ x ${w}_{E2E}$ |
${G}_{syn}$ E to I (AMPA) | ${w}_{ij}$ x ${w}_{E2I}$ |
${G}_{syn}$ I to E | ${g}_{I2E}$ |
${G}_{NMDA}$ E to E | ${G}_{syn}$ x ${w}_{NMDA}scalar$ |
${\rho}_{NMDA}$ E to E | ${G}_{syn}$ x ${\rho}_{NMDA}scalar$ |
${\delta}_{NMDA}$ $m{s}^{-1}$ | .02 |
There are a few parameters that remain to be given values. A Lanser and Fransen do not give exact values for these unknown parameters, but instead a desired range for EPSP's (Excitatory Post Synaptic Potentials) that the parameters help determine. By experimenting with a single neuron we can find the ideal range for these unknown parameters. Hence, we can then scale the resulting Weights from the algorithm so they are mapped to the ideal range. We need an overall weighting scale constant for connections from E to E cells (AMPA), ${w}_{E2E}$ . A weighting scale constant for E to I cells, ${w}_{E2I}$ Also, a scale general conductance constant for all I to E connections, ${g}_{I2E}$ . The NMDA connections will be proportional to the AMPA weight but scaled by a constant ${w}_{NMDA}scalar$ . The influx parameter ${\rho}_{NMDA}$ for the $\left[C{a}_{NMDA}\right]$ pool is also proportional to the AMPA weight. Lastly, the binary variable $s$ needs to be given a time duration to stay active for. This time duration may be chosen different for each type of connection class as well (meaning E to E, E to I, and I to E).
Most of these unfixed variables relate to the strength of connections between cells and the EPSPs or IPSPs they create. The reason they won't be fixed for all different size simulations is that the values should vary according to size of the networks and assemblies. For instance, if we model on large networks that have large assemblies we would desire that a cell would require synaptic input from more cells in order to fire, than when the network is small. By picking these numbers accordingly we will be able to roughly determine how many cells of an assembly need to be firing in order to fully activate the assembly.
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