Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey I. Segmental oscillations dependent on reciprocal inhibition

Factors contributing to the production of a phase lag along chains of oscillatory networks consisting of Hodgkin-Huxley type neurons are analyzed by means of simulations. Simplified network configurations are explored consisting of the basic building blocks of the spinal central pattern generator (CPG) generating swimming in the lamprey. It consists of reciprocally coupled crossed inhibitory C interneurons and ipsilateral excitatory E interneurons that activate C neurons and other E neurons. Oscillatory activity in the model network can, in the simplest case, be produced by a pair of reciprocally coupled C interneurons oscillating through an escape mechanism. Different levels of tonic excitation drive the network over a wide burst frequency range. In this type of network, powerful frequency-regulating factors are the effective inhibition produced by the active side, in combination with the tendency of the inactive side to escape from the inhibition. These two mechanisms can be affected by several factors, e.g. spike frequency adaptation (calcium-dependent K+ channels): N-methyl-D-aspartate membrane properties as well as presence of low-voltage activated calcium channels. A rostrocaudal phase lag can be produced either by extending the contralateral inhibitory projections or the ipsilateral excitatory projections relatively more in the caudal than the rostral direction, since both an increased inhibition and a phasic excitation slow down the receiving network. The phase lag becomes decreased if the length of the intersegmental projections is increased or if the projections are extended symmetrically in both the rostral and the caudal directions. The simulations indicate that the conditions in the ends of an oscillator chain may significantly affect sign, magnitude and constancy of the phase lag. Also, with short and relatively weak intersegmental connections, the network remains robust against perturbations as well as intrinsic frequency differences along the chain. The phase lag (percentage of cycle duration) increases, however, with burst frequency also when the coupling strength is comparatively weak. The results are discussed and compared with previous "phase pulling" models as well as relaxation oscillators.