Development of input connections in neural cultures

We introduce a novel approach for the quantitative assessment of the connectivity in neuronal cultures, based on the statistical mechanics of percolation on a graph. This allows us to follow the development of the culture and see the emergence of connectivity in the network. The culture becomes fully connected at a time equivalent to full term. The spontaneous bursting activity that characterizes cultures develops in parallel with the connectivity. The average number of inputs per neuron can be quantitatively determined in units of $m_0$, the number of activated inputs needed to excite the neuron. For $m_0\sim 10$ we find that hippocampal neurons have on average $\sim 40-80$ inputs while cortical neurons have $\sim 50-100$, depending on neuronal density. The ratio of excitatory to inhibitory neurons is determined using the GABA$_\text{A}$ antagonist bicuculine. This ratio changes during development and reaches the final value at day $7-8$, coinciding with the expected time of the GABA switch. For hippocampal cultures the inhibitory cells comprise about $30\%$ of the neurons in the culture while for cortical cultures they are about $20\%$. Such detailed global information on the connectivity of networks in neuronal cultures is at present inaccessible by any electrophysiological or other technique.