Synaptic polarity of the interneuron circuit controlling C. elegans locomotion

Abstract

Caenorhabditis elegans is the only animal for which a detailed neural connectivity diagram has been constructed. However, synaptic polarities in this diagram, and thus, circuit functions are largely unknown. Here, we deciphered the likely polarities of seven pre-motor neurons implicated in the control of worm's locomotion, using a combination of experimental and computational tools. We performed single and multiple laser ablations in the locomotor interneuron circuit and recorded times the worms spent in forward and backward locomotion. We constructed a theoretical model of the locomotor circuit and searched its all possible synaptic polarity combinations and sensory input patterns in order to find the best match to the timing data. The optimal solution is when either all or most of the interneurons are inhibitory and forward interneurons receive the strongest input, which suggests that inhibition governs the dynamics of the locomotor interneuron circuit. From the five pre-motor interneurons, only AVB and AVD are equally likely to be excitatory, i.e., they have probably similar number of inhibitory and excitatory connections to distant targets. The method used here has a general character and thus can be also applied to other neural systems consisting of small functional networks.

Keywords: C. elegans; laser ablations; locomotion; locomotory interneurons; neural circuit modeling; optimization; synaptic polarity.

Figure 1

Schematic diagram of the interneuron locomotory circuit. (A) Intact circuit. ASH neuron is an upstream neuron that provides synaptic input to the locomotory interneurons. The output coming from the six neurons (five interneurons and DVA) feeds the activities of motor neurons, represented by E_f (controlling forward motion) and by E_b (controlling backward motion). Synaptic connections are shown as solid arrows (blue), and gap junctions are represented by dashed lines (red). The magnitude of an arrow and the width of a dashed line are indicators of the strength of synaptic and gap junction connections, respectively. (B) An example of an ablated circuit, in which ASH and AVB neurons are removed. Note that this leads to the removal of all connections (synaptic and electric) coming out from these neurons. Such ablations not only change the circuit architecture but also modify its activity output.

Figure 2

Comparison of the theory with the data for relative times spent in forward locomotion across different ablations. The theoretical values are for the winning polarity combination # 1, corresponding to all inhibitory neurons. Correlation between theoretical points (red triangles) and experimental (blue circles) is relatively high (R = 0.743) and statistically significant (p = 0.0004). The error bars for the experimental points were computed from SEM values of T_f and T_b given in Table 2. The optimal values of the free parameters are given in Table 3.

Figure 3

Dependence of the Euclidean Distance (ED) on the patterns of synaptic polarities and input strength. Neurons receiving a strong input are marked in orange. Inhibitory neurons are represented in red, while excitatory in blue. The smallest (optimal) value of ED is pinpointed by a pink arrow. Note that configurations with small ED are generally associated with mostly inhibitory connections and a moderate input strength (left part of the map), whereas large ED values occur for mostly excitatory configurations (right part of the map). The optimal parameters are the same as in Figure 2.

Figure 4

Distribution of synaptic polarities for each interneuron. The first 20 polarity combinations with the smallest Euclidean distance (ED) are shown, and they are associated with the optimal parameters given in Table 3. Note that the interneurons ASH, AVA, AVE, and PVC are inhibitory with a high probability. There are some non-zero likelihoods that AVB, AVD, and DVA neurons are excitatory (especially AVB and AVD), although the smallest ED values are associated with negative polarities. The optimal parameters are the same as in Figure 2.

Figure 5

Dependence of ED on synaptic and electric conductances. ED is optimal (minimal) for some range of values of q_s and q_e. Note that the changes in synaptic conductance (horizontal direction) are more critical for ED than the changes in q_e (vertical direction). The optimal values of other parameters are: σ = 8.0 mV, κ = 0.6, and η = 1.05 mV.

Figure 6

Dependence of ED on the system noise amplitude η. ED has a minimum for some optimal η, and this is essentially independent of the synaptic polarity configuration. Shown are synaptic configurations number 1 (solid line), 17 (dashed line), and 11 (dotted line). The optimal values of other parameters are: σ = 8.0 mV, κ = 0.6, and q_s = q_e = 0.1 nS.