Frequency-dependent coupling between rhythmically active neurons in the leech

Contribution of motoneuron intrinsic properties to fictive motor pattern generation

Previously, we reported a canonical ensemble model of the heart motoneurons that underlie heartbeat in the medicinal leech. The model motoneurons contained a minimal set of electrical intrinsic properties and received a synaptic input pattern based on measurements performed in the living system. Although the model captured the synchronous and peristaltic motor patterns observed in the living system, it did not match quantitatively the motor output observed. Because the model motoneurons had minimal intrinsic electrical properties, the mismatch between model and living system suggests a role for additional intrinsic properties in generating the motor pattern. We used the dynamic clamp to test this hypothesis. We introduced the same segmental input pattern used in the model to motoneurons isolated pharmacologically from their endogenous input in the living system. We show that, although the segmental input pattern determines the segmental phasing differences observed in motoneurons, the intrinsic properties of the motoneurons play an important role in determining their phasing, particularly when receiving the synchronous input pattern. We then used trapezoidal input waveforms to show that the intrinsic properties present in the living system promote phase advances compared with our model motoneurons. Electrical coupling between heart motoneurons also plays a role in shaping motoneuron output by synchronizing the activity of the motoneurons within a segment. These experiments provide a direct assessment of how motoneuron intrinsic properties interact with their premotor pattern of synaptic drive to produce rhythmic output.

Using a model to assess the role of the spatiotemporal pattern of inhibitory input and intrasegmental electrical coupling in the intersegmental and side-to-side coordination of motor neurons by the leech heartbeat central pattern generator

Previously we presented a quantitative description of the spatiotemporal pattern of inhibitory synaptic input from the heartbeat central pattern generator (CPG) to segmental motor neurons that drive heartbeat in the medicinal leech and the resultant coordination of CPG interneurons and motor neurons. To begin elucidating the mechanisms of coordination, we explore intersegmental and side-to-side coordination in an ensemble model of all heart motor neurons and their known synaptic inputs and electrical coupling. Model motor neuron intrinsic properties were kept simple, enabling us to determine the extent to which input and electrical coupling acting together can account for observed coordination in the living system in the absence of a substantive contribution from the motor neurons themselves. The living system produces an asymmetric motor pattern: motor neurons on one side fire nearly in synchrony (synchronous), whereas on the other they fire in a rear-to-front progression (peristaltic). The model reproduces the general trends of intersegmental and side-to-side phase relations among motor neurons, but the match with the living system is not quantitatively accurate. Thus realistic (experimentally determined) inputs do not produce similarly realistic output in our model, suggesting that motor neuron intrinsic properties may contribute to their coordination. By varying parameters that determine electrical coupling, conduction delays, intraburst synaptic plasticity, and motor neuron excitability, we show that the most important determinant of intersegmental and side-to-side phase relations in the model was the spatiotemporal pattern of synaptic inputs, although phasing was influenced significantly by electrical coupling.

Neuronal integrative analysis of the "Dumbbell" model for passive neurons

We analyze the so called "Dumbbell" model of Jackson (J. Neurophysiol. 69 (1993) pp. 464) for a single neuron consisting of a patch-clamped cell body attached to dendritic cable of finite length terminating in an oblique derivative ("natural termination") boundary condition representing a dendritic swelling or a natural ending sealed by a continuous surface of the cell membrane. The model is solved analytically via the Green's function method. Large and small time asymptotic behavior of the membrane potential is developed when there is a somatic voltage-clamp imposed. We discuss the difference in the voltage distribution if a sealed-end (Neumann) termination is used instead of the natural termination boundary condition. If the access resistance is large the differences between the potentials corresponding to the two boundary conditions are small at the soma, but can vary significantly near the dendritic termination. This discrepancy is amplified at the soma if there is a synaptic stimulus introduced between the soma and dendritic tip.

Frequency domain analysis of electrotonic coupling between leech Retzius cells

Transfer functions of the input impedance Z(f) and coupling ratio H(f) were measured from the paired Retzius cells of leech segmental ganglia, using sinusoidal and pseudorandom test test currents. The data were compared with two classes of linear electric circuit models of electrotonic coupling, one with a purely resistive junction, and the other with a finite equivalent cable coupling the two somata. Model simulations suggested the phase behavior of the coupling ratio as a sensitive discriminator between these two cases. For resistive coupling, the phase of the coupling ratio asymptotically approaches -90 degrees at high frequencies, while for a cable segment, at least 0.5 length constants in length, it crosses -90 degrees with a definite negative slope and continues to more negative values. Measured phase lags of the coupling ratio in Retzius cell preparations consistently exceeded -90 degrees at frequencies above 50 Hz, and phase plots crossed -90 degrees with significantly negative slopes. We conclude therefore that a significant cable segment contributes to the coupling between Retzius cell somata.