On the number of states of the neuronal sources

In a previous paper (Proceedings of the World Congress on Neuroinformatics (2001)) the authors applied the so-called Lempel-Ziv complexity to study neural discharges (spike trains) from an information-theoretical point of view. Along with other results, it is shown there that this concept of complexity allows to characterize the responses of primary visual cortical neurons to both random and periodic stimuli. To this aim we modeled the neurons as information sources and the spike trains as messages generated by them. In this paper, we study further consequences of this mathematical approach, this time concerning the number of states of such neuronal information sources. In this context, the state of an information source means an internal degree of freedom (or parameter) which allows outputs with more general stochastic properties, since symbol generation probabilities at every time step may additionally depend on the value of the current state of the neuron. Furthermore, if the source is ergodic and Markovian, the number of states is directly related to the stochastic dependence lag of the source and provides a measure of the autocorrelation of its messages. Here, we find that the number of states of the neurons depends on the kind of stimulus and the type of preparation ( in vivo versus in vitro recordings), thus providing another way of differentiating neuronal responses. In particular, we observed that (for the encoding methods considered) in vitro sources have a higher lag than in vivo sources for periodic stimuli. This supports the conclusion put forward in the paper mentioned above that, for the same kind of stimulus, in vivo responses are more random (hence, more difficult to compress) than in vitro responses and, consequently, the former transmit more information than the latter.