A dynamic network simulation of the nematode tap withdrawal circuit: predictions concerning synaptic function using behavioral criteria

Abstract

The nematode tap withdrawal reflex demonstrates several forms of behavioral plasticity. Although the neural connectivity that supports this behavior is identified (Integration of mechanosensory stimuli in Caenorhabditis elegans, Wicks and Rankin, 1995, J Neurosci 15:2434-2444), the neurotransmitter phenotypes, and hence whether the synapses in the circuit are excitatory or inhibitory, remain uncharacterized. Here we use a novel strategy to predict the polarity configuration, i.e., the array of excitatory and inhibitory connections, of the nematode tap withdrawal circuit using an anatomically and physiologically justifiable dynamic network simulation of that circuit. The output of the modeled circuit was optimized to the behavior of animals, which possessed circuits altered by surgical ablation by exhaustively enumerating an array of synaptic signs that constituted the modeled circuit. All possible polarity configurations were then compared, and a statistical analysis was used to determine whether, for a given synaptic class, a particular polarity was associated with a good fit to behavioral data. The results from four related experiments were used to predict the polarities of seven of the nine cell classes of the tap withdrawal circuit. In addition, the model was used to assess possible roles for two novel mechanosensory integration neurons: DVA and PVD.

Fig. 1.

The complete connectivity of the tap withdrawal circuit. The circuit consists of seven sensory neurons (shaded circles), nine interneurons (unshaded circles), and two motorneuron pools (not shown), which produce forward and backward locomotion (triangles). Chemical connections are indicated by arrows, with the number of synaptic contacts being to the width of the arrow. Gap junctions are indicated bydotted lines. Every connection represented in this figure was also represented in the model. This representation is useful for identifying connection asymmetries, which might underlie the origin of oscillations that control locomotion and are hidden in simpler views of the circuitry.

Fig. 2.

Mean response magnitudes of the tap withdrawal reflex of seven groups of animals. These data were used to optimize the array of underlying functional polarities of the modeled circuit. Some ablations (for example, the removal of PLM) resulted in larger reversal responses than in control animals; other ablations resulted in consistent accelerations in response to tap (indicated by a negative reversal magnitude for the ALM− and AVMALM− groups). Note that the acceleration measure is a change in velocity, whereas the reversal measure is a distance; these are not directly comparable. Thus, the ordinate represents a number that is proportional to the amount of forward or backward locomotion. It was assumed that the pattern of response represented on this figure was dictated partially by the array of synaptic signs, which constituted the underlying circuitry (see Materials and Methods, Strategy for neuron polarity determination). These data are adapted from Wicks and Rankin (1995a).

Fig. 3.

Two different response profiles from experiment 1—one representing a good fit and one representing a poor fit—along with the empirical data to which they were compared. These data sets are expressed as three sets of standardized Z-scores used to evaluate the relative modulation by ablation of three behavioral measures:REVERSAL MAGNITUDE, ACCELERATION MAGNITUDE, andRESPONSE TYPE. The first set of Z-scores incorporates those ablation configurations that result in a reversal response in the empirical data set shown in Figure 2. It was used to determine the error associated with the relative modulation of reversal magnitude as a result of ablation between that data set and each polarity configuration from the model. The second set of Z-scores similarly assessed the error associated with the relative modulation of acceleration magnitude as a result of ablation. A third set of Z-scores evaluated the qualitative fit between the model and the empirical profiles with respect to response type. It assessed whether the gearbox output (Eq. 25) was lower, on average, for the acceleration profile than for the reversal profile, as was assumed to be the case for the intact animal. The fitness of a given configuration was calculated by summing the least-squared error between the model and empirical profiles for each of these three sets of standardized data. It is clear that the fitness of the modeled circuit to the behavioral data can be strongly modified by altering the array of underlying polarities in the modeled circuit.

Fig. 4.

Sample polarity configurations. The top 50 polarity configurations sorted according to error from experiment 1 are shown. This circuit did not include the DVA interneuron, and hence there were 256 possible configurations (2⁶) in the complete sorted list. Thus, the top 10% of the list reported in Table 3A consists of the top 26 polarity configurations shown in this figure. The PVD sensory neuron class was not externally stimulated during this run. A polarity consistent with that which resulted from statistical considerations is shown as a lightly shaded box; a polarity that is not consistent is shown in an unshaded box. No polarity predictions were made for the AVA or DVA neurons. These columns are darkly shaded. In this experiment, the tenth and sixteenth configurations are entirely consistent with the consensus configuration predicted in this report.

Fig. 5.

Fitness frequency distributions from four experiments. The 256 possible configurations in experiments 1 and 3 and the 512 possible configurations from experiments 2 and 4 were sorted according to the fitness measure described in Materials and Methods. The y-axis represents the number of configurations with a given error in each of 24 error bins. The frequency distributions are multimodal. The fraction of the sorted list of configurations that corresponds to the α level (>1 SD below the mean of the distribution) lies to the left of the indicated α level in each case. The mean of each distribution is also indicated.

Fig. 6.

Simplified circuit with predicted polarities. The circuit that mediates the nematode tap withdrawal reflex consists of seven sensory neurons (squares), nine interneurons (circles), and two motorneuron pools (not shown), which produce forward and backward locomotion (triangles). All cells represent bilateral classes of cells except AVM and DVA, which are single cells. Chemical connections are indicated byarrows, with the number of synaptic contacts proportional to the width of the arrow. Gap junctions are indicated bydotted lines. This circuit has been simplified for ease of presentation in two ways: the bilateral symmetry of the circuit has been collapsed, and only classes of connections with an average of greater than five synaptic contacts are shown. The consensus polarities of the neurons in this circuit, which were derived from four experiments, are also shown. Neurons that are predicted to make excitatory connections are darkly shaded, whereas neurons that are predicted to make inhibitory connections are lightly shaded. Two neurons (AVA and DVA) did not possess polarities that clustered at above chance levels in any of the experiments presented in this report.

Fig. 7.

Mean consensus configuration fit. The best fit profiles from four experiments are shown in comparison to the empirical data to which they were compared for those configurations that were consistent with the consensus configuration in Figure 6. These data sets are each expressed as Z-scores around the mean of that data set, because only changes relative to the intact condition are interpretable. All four simulated data sets differ from the intact condition in two consistent ways. First, the PVD ablation had a large effect on the reversal magnitude of real animals, but had little effect on the modeled response. Second, the relative effects of touch-cell ablations in the model are not consistent with the changes produced by ablations in worms. Specifically, the relative effects of the AVM and PLM ablations are reversed in the model as compared with the worm. This may be attributable to mechanical processes that affect the transduction efficiencies of these touch cells. Error bars indicate SEM.