Abstract
We studied how a neuronal circuit composed of two neuron types connected by chemical and electrical synapses maintains constant its integrative capacities as neurons grow. For this we combined electrophysiological experiments with mathematical modeling in pairs of electrically-coupled Retzius neurons from postnatal to adult leeches. The electrically-coupled dendrites of both Retzius neurons receive a common chemical input, which produces excitatory postsynaptic potentials (EPSPs) with varying amplitudes. Each EPSP spreads to the soma, but also crosses the electrical synapse to arrive at the soma of the coupled neuron. The leak of synaptic current across the electrical synapse reduces the amplitude of the EPSPs in proportion to the coupling ratio. In addition, summation of EPSPs generated in both neurons generates the baseline action potentials of these serotonergic neurons. To study how integration is adjusted as neurons grow, we first studied the characteristics of the chemical and electrical connections onto the coupled dendrites of neuron pairs with soma diameters ranging from 21 to 75 μm. Then by feeding a mathematical model with the neuronal voltage responses to pseudorandom noise currents we obtained the values of the coupling ratio, the membrane resistance of the soma (rm ) and dendrites (r dend), the space constant (λ) and the characteristic dendritic length (L = l/λ). We found that the EPSPs recorded from the somata were similar regardless on the neuron size. However, the amplitude of the EPSPs and the firing frequency of the neurons were inversely proportional to the coupling ratio of the neuron pair, which also was independent from the neuronal size. This data indicated that the integrative constancy relied on the passive membrane properties. We show that the growth of Retzius neurons was compensated by increasing the membrane resistance of the dendrites and therefore the λ value. By solely increasing the dendrite resistance this circuit maintains constant its integrative capacities as its neurons grow.