Conditional firing probabilities in cultured neuronal networks: a stable underlying structure in widely varying spontaneous activity patterns

Abstract

To properly observe induced connectivity changes after training sessions, one needs a network model that describes individual relationships in sufficient detail to enable observation of induced changes and yet reveals some kind of stability in these relationships. We analyzed spontaneous firing activity in dissociated rat cortical networks cultured on multi-electrode arrays by means of the conditional firing probability. For all pairs (i, j) of the 60 electrodes, we calculated conditional firing probability (CFP(i,j)[tau]) as the probability of an action potential at electrode j at t = tau, given that one was detected at electrode i at t = 0. If a CFP(i,j)[tau] distribution clearly deviated from a flat one, electrodes i and j were considered to be related. For all related electrode pairs, a function was fitted to the CFP-curve to obtain parameters for 'strength' and 'delay' (i.e. maximum and latency of the maximum of the curve) of each relationship. In young cultures the set of identified relationships changed rather quickly. At 16 days in vitro (DIV) 50% of the set changed within 2 days. Beyond 25 DIV this set stabilized: during a week more than 50% of the set remained intact. Most individual relationships developed rather gradually. Moreover, beyond 25 DIV relational strength appeared quite stable, with coefficients of variation (100 x SD/mean) around 25% in periods of approximately 10 h. CFP analysis provides a robust method to describe the underlying probabilistic structure of highly varying spontaneous activity in cultured cortical networks. It may offer a suitable basis for plasticity studies, in the case of changes in the probabilistic structure. CFP analysis monitors all pairs of electrodes instead of just a selected one. Still, it is likely to describe the network in sufficient detail to detect subtle changes in individual relationships.

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

“…Intracellular experiments showed that presynaptic spikes that precede postsynaptic firing by up to ∼30 ms lead to long-term potentiation of the connecting synapse (Bi and Poo 1998;Zhang et al 1998;Song et al 2000). Functional connections between neurons that have a latency in this range also tend to become strengthened in spontaneously active cultured cortical networks (le Feber et al 2007(le Feber et al , 2009). This adds justification to our assumption that neurons with ongoing activity have relatively strong synapses (intense neurons).…”

Network bursts in cortical cultures are best simulated using pacemaker neurons and adaptive synapses

“…In particular, during the second week in vitro they become wider and higher in firing rate. The third week is usually characterized by reduction and stabilization of NB firing rate and NB width (Van Pelt et al 2004a;Wagenaar et al 2006;Le Feber et al 2007;Stegenga et al 2008).…”

Functional Connectivity of Neural Network in Dissociated Hippocampal Culture Grown on Microelectrode Array

“…We used the term 'connection delay' to denote the time delay corresponding to the maximum of cross-correlation function which was regarded as connection strength. If connection delay was longer than 3 ms (Figure 2), the pair of electrodes was treated as synaptically connected [17]. Connectivity map characterized by connection strength and connection delay was constructed for each 20-or 60-minutes raster.…”

“…Functional connectivity was estimated by crosscorrelation analysis of spiking patterns of spontaneous network activity recorded through different microelectrodes (by analogy with [17]). The paper by le Feber [12] demonstrates that the integral indicator of neuronal network connectivity reorganization (Euclidean space between connectivity strength matrices for all pairs of recording electrodes before and after stimulation) changes after electrical stimulation.…”

“…We hypothesized that changes in functional connectivity of the network were induced by synaptic plasticity. Functional connectivity was estimated by cross-correlation analysis of spiking patterns of spontaneous network activity recorded through different microelectrodes (by analogy with [17]). Connectivity changes induced by electrical stimulation were found on the time scale of 20 min.…”