Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey

Abstract

Most previous models of the spinal central pattern generator (CPG) underlying locomotion in the lamprey have relied on reciprocal inhibition between the left and right side for oscillations to be produced. Here, we have explored the consequences of using self-oscillatory hemisegments. Within a single hemisegment, the oscillations are produced by a network of recurrently coupled excitatory neurons (E neurons) that by themselves are not oscillatory but when coupled together through N-methyl-d-aspartate (NMDA) and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid (AMPA)/kainate transmission can produce oscillations. The bursting mechanism relies on intracellular accumulation of calcium that activates Ca(2+)-dependent K(+). The intracellular calcium is modeled by two different intracellular calcium pools, one of which represents the calcium entry following the action potential, Ca(AP) pool, and the other represents the calcium inflow through the NMDA channels, Ca(NMDA) pool. The Ca(2+)-dependent K(+) activated by these two calcium pools are referred to as K(CaAP) and K(CaNMDA), respectively, and their relative conductances are modulated and increase with the background activation of the network. When changing the background stimulation, the bursting activity in this network can be made to cover a frequency range of 0.5-5.5 Hz with reasonable burst proportions if the adaptation is modulated with the activity. When a chain of such hemisegments are coupled together, a phase lag along the chain can be produced. The local oscillations as well as the phase lag is dependent on the axonal conduction delay as well as the types of excitatory coupling that are assumed, i.e. AMPA/kainate and/or NMDA. When the caudal excitatory projections are extended further than the rostral ones, and assumed to be of approximately equal strength, this kind of network is capable of reproducing several experimental observations such as those occurring during strychnine blockade of the left-right reciprocal inhibition. Addition of reciprocally coupled inhibitory neurons in such a network gives rise to antiphasic activity between the left and right side, but not necessarily to any change of the frequency if the burst proportion of the hemisegmental bursts is well below 50%. Prolongation of the C neuron projection in the rostrocaudal direction restricts the phase lag produced by only the excitatory hemisegmental network by locking together the interburst intervals at different levels of the spinal cord.

Emergence of coherent traveling waves controlling quadruped gaits in a two-dimensional spinal cord model

“…P com ¼ 0 throughout Otherwise, a moderate decrease in phase lag, by approximately 30% or 1/wavelength, would actually occur with a rise in frequency of approximately 50%. This contrasts with other simulations (Kotaleski et al 1999) that failed to produce a constant phase lag, but generated a phase lag that increased with frequency, in effect leading to a shorter wavelength.…”

“…In addition, the topological parameters of the network were chosen to be as general (or symmetric) as possible, but at the same time to incorporate essential features of the spinal cord anatomy. This symmetry conforms to the demonstrated anatomy (Roberts et al 1998), but contrasts with other models (Kotaleski et al 1999). Besides topological considerations, the following symmetry or invariance principles were incorporated into our model: the processing of synaptic inputs was independent of the location on the dendrite.…”

“…Further, SD may have no dynamic effects unless multiple spikes (i.e., bursts of the premotor neurons and spike doublets from inhibitory interneurons) are generated during a locomotor cycle. The implementation of such spiking behavior requires fairly sophisticated Hodgkin-Huxley models (Kotaleski et al 1999).…”

Travelling wave patterns in a model of the spinal pattern generator using spiking neurons

“…6). However, parameter domains of constant wavelength were smaller, pointing to the possibility that the excitability type of HodgkinHuxley-type neurons might be responsible for some problems of other models in producing a constant phase lag (Kotaleski et al 1999). In this context it may be interesting to note that the use of the theta neuron, claimed to be a canonical type I excitability neuron (Hoppenstead and Izhikevich 2002) allowed us to produce a wide range of two-dimensional travelling wave patterns (Osan and Ermentrout 2001).…”

“…The former requires that the pulse velocity increase linearly with the frequency. Previous models (Kotaleski et al 1999) actually struggled to obtain a constant phase lag. Our simulations In the spinal cord glutamate or NMDA (used for stimulation in in vitro experiments) is the main excitatory transmitter responsible for the excitatory synaptic coupling.…”