A silicon model of the Hirudo swim oscillator

An implementation of a simple neuron model in field programmable analog arrays

A minimal neuron model, the Morris-Lecar model, is implemented on field programmable analog arrays (FPAAs). Our approach is to solve the differential equation describing the model in a similar way a computer solves the same problem: numerically integrate the differential equation by making arithmetic operations on voltage mode circuits of the FPAAs. The results demonstrate that biologically relevant dynamics can be observed from the electronic neuron despite limitations on the configurability of the FPAAs. Such models can be run accurately in real-time or many orders of magnitude faster than real-time. FPAAs are feasible candidates for implementation of neuron models using off-the-shelf software-reconfigurable analog circuit elements.

Neuronal control of leech behavior

The medicinal leech has served as an important experimental preparation for neuroscience research since the late 19th century. Initial anatomical and developmental studies dating back more than 100 years ago were followed by behavioral and electrophysiological investigations in the first half of the 20th century. More recently, intense studies of the neuronal mechanisms underlying leech movements have resulted in detailed descriptions of six behaviors described in this review; namely, heartbeat, local bending, shortening, swimming, crawling, and feeding. Neuroethological studies in leeches are particularly tractable because the CNS is distributed and metameric, with only 400 identifiable, mostly paired neurons in segmental ganglia. An interesting, yet limited, set of discrete movements allows students of leech behavior not only to describe the underlying neuronal circuits, but also interactions among circuits and behaviors. This review provides descriptions of six behaviors including their origins within neuronal circuits, their modification by feedback loops and neuromodulators, and interactions between circuits underlying with these behaviors.

A dye mixture (Neurobiotin and Alexa 488) reveals extensive dye-coupling among neurons in leeches; physiology confirms the connections

Although the neuronal circuits that generate leech movements have been studied for over 30 years, the list of interneurons (INs) in these circuits remains incomplete. Previous studies showed that some motor neurons (MNs) are electrically coupled to swim-related INs, e.g., rectifying junctions connect IN 28 to MN DI-1 (dorsal inhibitor), so we searched for additional neurons in these behavioral circuits by co-injecting Neurobiotin and Alexa Fluor 488 into segmental MNs DI-1, VI-2, DE-3 and VE-4. The high molecular weight Alexa dye is confined to the injected cell, whereas the smaller Neurobiotin molecules diffuse through gap junctions to reveal electrical coupling. We found that MNs were each dye-coupled to approximately 25 neurons, about half of which are likely to be INs. We also found that (1) dye-coupling was reliably correlated with physiologically confirmed electrical connections, (2) dye-coupling is unidirectional between MNs that are linked by rectifying connections, and (3) there are novel electrical connections between excitatory and inhibitory MNs, e.g. between excitatory MN VE-4 and inhibitory MN DI-1. The INs found in this study provide a pool of novel candidate neurons for future studies of behavioral circuits, including those underlying swimming, crawling, shortening, and bending movements.

A multiconductance silicon neuron with biologically matched dynamics

We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).

Model for intersegmental coordination of leech swimming: central and sensory mechanisms

Sensory feedback as well as the coupling signals within the CNS are essential for leeches to produce intersegmental phase relationships in body movements appropriate for swimming behavior. To study the interactions between the central pattern generator (CPG) and peripheral feedback in controlling intersegmental coordination, we have constructed a computational model for the leech swimming system with physiologically realistic parameters. First, the leech swimming CPG is simulated by a chain of phase oscillators coupled by three channels of coordinating signals. The activity phase, the projection direction, and the phase response curve (PRC) of each channel are based on the identified intersegmental interneuron network. Output of this largely constrained model produces stable coordination in the simulated CPG with average phase lags of 8-10 degrees/segment in the period range from 0.5 to 1.5 s, similar to those observed in isolated nerve cords. The model also replicates the experimental finding that shorter chains of leech nerve cords have larger phase lags per segment. Sensory inputs, represented by stretch receptors, were subsequently incorporated into the CPG model. Each stretch receptor with its associated PRC, which was defined to mimic the experimental results of phase-dependent phase shifts of the central oscillator by the ventral stretch receptor, can alter the phase of the local central oscillator. Finally, mechanical interactions between the muscles from neighboring segments were simulated by PRCs linking adjacent stretch receptors. This model shows that interactions between neighboring muscles could globally increase the phase lags to the larger value required for the one-wavelength body form observed in freely swimming leeches. The full model also replicates the experimental observation that leeches with severed nerve cords have larger intersegmental phase lags than intact animals. The similarities between physiological and simulation results demonstrate that we have established a realistic model for the central and peripheral control of intersegmental coordination of leech swimming.

Analysis of oscillations in a reciprocally inhibitory network with synaptic depression

We present and analyze a model of a two-cell reciprocally inhibitory network that oscillates. The principal mechanism of oscillation is short-term synaptic depression. Using a simple model of depression and analyzing the system in certain limits, we can derive analytical expressions for various features of the oscillation, including the parameter regime in which stable oscillations occur, as well as the period and amplitude of these oscillations. These expressions are functions of three parameters: the time constant of depression, the synaptic strengths, and the amount of tonic excitation the cells receive. We compare our analytical results with the output of numerical simulations and obtain good agreement between the two. Based on our analysis, we conclude that the oscillations in our network are qualitatively different from those in networks that oscillate due to postinhibitory rebound, spike-frequency adaptation, or other intrinsic (rather than synaptic) adaptational mechanisms. In particular, our network can oscillate only via the synaptic escape mode of Skinner, Kopell, and Marder (1994).