Connectivities and Synchronous Firing in Cortical Neuronal Networks

Network connectivities ($\overline{k}$) of cortical neural cultures are studied by synchronized firing and determined from measured correlations between fluorescence intensities of firing neurons. The bursting frequency ($f$) during synchronized firing of the networks is found to be an increasing function of $\overline{k}$. With $f$ taken to be proportional to $\overline{k}$, a simple random model with a $\overline{k}$ dependent connection probability $p(\overline{k})$ has been constructed to explain our experimental findings successfully.

Figure 1

Time dependence of bursting rate for a culture with a plating density of $\rho ={10}^4\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{s}/{\mathrm{m}\mathrm{m}}^2$ in BSS($-$). Lower inset shows the time dependence of fluorescence intensity on 4 DIV and the upper inset shows the plating density dependence of the onset time of synchronous firings. Solid lines in the figure and the upper inset are fits of the data to forms described in the text. Error is estimated from two sets of data obtained from two different dissections.

Figure 2

Time dependence of the bursting rate of SF of a dying culture with a plating density of $\rho ={10}^4\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{s}/{\mathrm{m}\mathrm{m}}^2$ on 6 DIV in BSS($-$). More than ten samples have been observed to give similar results but the bursting rates of different samples can be different by as much as 30%. Inset shows the effects on the bursting rate as the neurons in the SF cluster are being killed in a similar sample.

Figure 3

Effect of $[{\mathrm{M}\mathrm{g}}^{2+}]$ on the bursting rate of SF for a culture with a plating density of $\rho ={10}^4\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{s}/{\mathrm{m}\mathrm{m}}^2$ on 10 DIV. The upper branch are the data obtained during the decrease of $[{\mathrm{M}\mathrm{g}}^{2+}]$, while the lower branch is obtained during the increase of $[{\mathrm{M}\mathrm{g}}^{2+}]$. More than five different dissections have been observed to give similar results. The inset displays the variation of the number of links of the neural network as $[{\mathrm{M}\mathrm{g}}^{2+}]$ is changed.

Figure 4

Connectivity structures constructed from correlation matrix for the experiment in Fig. 3 when $[{\mathrm{M}\mathrm{g}}^{2+}]$ equals (a)  0.0 mM, (b) 1.0 mM, (c)  5.0 mM, and (d)  back to 0.0 mM again. Location of the neurons are denoted by squares and the coordinates of the axis are distance in real space. Note that there is hysteresis in the structure.