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

TL;DR: In this paper, the conditional firing probability (CFPi,j[τ]) is calculated as the probability of an action potential at electrode j at t = τ, given that one was detected at electrode i at 0.

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 (CFPi,j[τ]) as the probability of an action potential at electrode j at t = τ, given that one was detected at electrode i at t = 0. If a CFPi,j[τ] 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 × SD/mean) around 25% in periods of ≈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.