The paddle controller
4.2 Models of Central Pattern Generators
In this section a compact overview of a number of models of CPGs will be given. It will focuss mainly upon aspects of the generation of oscillations in these models, and not delve into all the intricacies of how these oscillation are put to use. Let us start with a theoretical example.
4.2.1 A model pacemaker neurone
Beer (1990) describes a neuro-ethological model of a computational cockroach. This model includes a locomotion controller which drives the six legs of the animal, and which is based upon a model put forward by Pearson (1976). The controller contains six coupled oscillators that underly the rhythmic behaviour of the locomotion controller. Each of these oscillators controls the cycle (stanceZ swingZ stance) of one of the six individual legs. In Pearson’sproposal these six oscillators are modelled (based on empirical data) as small networks of four reciprocally inhibiting interneurones. Beer uses oscillatory neurones instead.
A neurone can be described as a simple leaky integrator that represents the neurone membrane potential as it results from inputs from other neurones. Input to a neurone is the postsynaptic current caused by, and assumed to be proportional to, the firing frequencies of the neurones projecting onto it. The output represents the firing frequency of the model neurone, and is a clipping function of the membrane potential. A model neurone can also display internal currents: hyper- or de-polarising currents that alter the response of the neurone to its inputs.
Intrinsic oscillatory activity in natural neurones can arise from coupled opening and closing of ion channels, resulting in alternating hyper- and depolarisation of the neurone. Llin´as (1990) describes this phenomenon for, among others, neurones from the inferior olive: these cells display both bursting and subthreshold (i.e. non-spiking) oscillations, resonating at 3-6 Hz and 9-12 Hz respectively.
A model neurone as described above (originally put forward by Beer (1990)) can be made into a pacemaker neurone by adding a depolarising (/\[
) and a hyperpolarising (/^]
) intrinsic current. Rhythmicity results when /?[
is activated for some fixed amount of time by depolarisation or termination of/^]
, which must be activated in its turn for a time period proportional to the steady state membrane potential at the termination of/\[
. This mechanism is similar to the mechanism of voltage dependant opening and closing of de- and hyper- polarising ion channels as described by Llin ´as. The resulting pacemaker cell exhibits the properties formulated by Kandel (1976), and is used in a number of neural controllers, among which the locomotion controller and thebite pacemaker which controls the mouth of the cockroach when feeding (Beer 1990).
4.2.2 Pacemaker networks
4.2.2 a The lamprey locomotion controller One of the CPG studied in most detail is the pacemaker network underlying swimming in the lamprey. This network, located in the spinal cord, has been studied extensively in vitro.84 CHAPTER4. THE PADDLE CONTROLLER
In a suitable saline bath containing excitatory amino acids, an isolated lamprey spinal cord is capable of generating burst patterns similar to those occuring in the intact animal.
The lamprey swims by propagating an undulatory wave along its body, travelling from head to tail. This wave is generated by a CPG that produces a corresponding wave of muscle contractions caused by periodic bursting in spinal motor neurones. The mechanism, an interneuronal network located in the spinal cord, that underlies this pattern has been uncovered using paired intracellular recordings (Grillner et al. 1991) and has been tested with simulations. EC EC RS RS CCIN LIN EIN MN MN EIN LIN CCIN EC EC Figure 4.1
Segmental oscillator of the lamprey CPG. The CPG is activated by the twoRSneurones that are located in the brain stem. After Grillneret al.1991.
The segmental oscillator that forms a building block of this network is shown in figure 4.1. It consists of two mutually contralateral half-centres. Each half-centre consists of several pools of interneurones. The excitatory interneurones (EIN) reciprocally inhibit each other through an excitatory projection onto a commissural pool of inhibitory interneurones (CCIN). This inhibition is excerted on all contralateral interneurone pools. An ipsilateral inhibition by an inhibitory interneurone pool (LIN) also excited byEINserves to terminate an ipsilateral burst by inhibiting CCIN, and thus dis-inhibiting the contralateral half-centre. The motor neurones which generate the actual swimming movements are innervated byEIN. Two pair of stretch-sensitive edge cells (EC) implement a local sensory feedback; stretching excites the ipsilateral half-centre and inhibits the contralateral one, thereby stabilising the wave pattern. Each of the approximately 100 segments of the animal has such an elementary oscillator. Intersegmental coordination and sensory feedback are responsible for a constant phase-lag between the segments (approximately 1% of the swim-cycle per segment), and thus for the direction of the wave. For faster speeds the undulatory wave needs to be propagated faster, requiring that the phase-lag between the segments expressedin seconds(instead of in cycles) be shorter.
The intersegmental coordination is partly accounted for by the inhibitory interneurone poolsCCINandLIN. Both pools have long caudally directed axons, providing more inhibition for more caudal segments.
4.2. MODELS OFCENTRALPATTERNGENERATORS 85