Evaluating performance of neural codes in model neural communication networks

Information needs to be appropriately encoded to be reliably transmitted over a physical media. Similarly, neurons have their own codes to convey information in the brain. Even though it is well-know that neurons exchange information using a pool of several protocols of spatial-temporal encodings, the suitability of each code and their performance as a function of the network parameters and external stimuli is still one of the great mysteries in Neuroscience. This paper sheds light into this problem considering small networks of chemically and electrically coupled Hindmarsh-Rose spiking neurons. We focus on the mathematical fundamental aspects of a class of temporal and firing-rate codes that result from the neurons' action-potentials and phases, and quantify their performance by measuring the Mutual Information Rate, aka the rate of information exchange. A particularly interesting result regards the performance of the codes with respect to the way neurons are connected. We show that pairs of neurons that have the largest rate of information exchange using the interspike interval and firing-rate codes are not adjacent in the network, whereas the spiking-time and phase codes promote large exchange of information rate from adjacent neurons. This result, if possible to extend to larger neural networks, would suggest that small microcircuits of fully connected neurons, also known as cliques, would preferably exchange information using temporal codes (spiking-time and phase codes), whereas on the macroscopic scale, where typically there will be pairs of neurons that are not directly connected due to the brain's sparsity, the most efficient codes would be the firing rate and interspike interval codes, with the latter being closely related to the firing rate code.