Fig 1.
Connectome of a small pre-motor neural network controlling locomotion in C. elegans.
The strengths of synaptic connections (left panel) and gap junction connections (right panel) are proportional to the thickness of the arrows. Dashed lines for synaptic connections correspond to synaptic strength (average number of contacts) smaller or equal to 0.75.
Fig 2.
Synaptic connectivity matrix with polarity signs in the pre-motor network.
Synaptic strengths between neurons are shown as appropriate matrix elements (columns: presynaptic neurons; rows: postsynaptic neurons). The centered values correspond to mean number of synaptic contacts between neurons, upper values to means decreased by standard deviations, and lower values correspond to means increased by standard deviations. We highlighted in color those synapses whose signs were established by the optimization (the weakest synapses below 0.75 were not optimized). Blue color denotes inhibitory synapses, and red corresponds to excitatory. Note that all optimized connections are inhibitory. The only excitatory connection (Eb ↦ PVC) is fixed and set by hand, since A and B motor neurons are known to be excitatory [21, 57].
Table 1.
Results for synaptic “reshuffled weights” case.
Table 2.
Optimal values of neurophysiological parameters for “mean weights” case.
Fig 3.
Comparison of computational and experimental ratios of times for moving forward and backward across ablation types.
Computational forward vs. backward timings, i.e. Tf/(Tf + Tb), (red points) correspond to the model with optimized parameters and synaptic polarities. Note that most of the computational points lie within standard deviations of the experimental points (blue).
Table 3.
Optimal input pattern to pre-motor interneurons (σi) for “mean weights” case.
Fig 4.
Influence of input pattern on the goal function SED.
For the optimal synaptic configuration (all interneuron connections inhibitory) we varied the upstream input pattern (horizontal axis—bottom) and observed the change in SED value. Input to a given interneuron can be either excitatory (in red) or inhibitory (in blue), which gives 64 possible input patterns. The minimal SED is obtained when all interneurons except AVA get excitation.
Fig 5.
Sensitivity of SED on the synaptic cut-off weight.
Each point corresponds to the mean SED for an ensemble of wild type circuits with the following property: all connections whose strengths are above a given cut-off (horizontal axis) are set as inhibitory, while the polarities of the remaining connections are randomly chosen (100 versions). Lowering the synaptic cut-off generally decreases mean SED and its variability. Note that for the cut-off weights ≤ 0.75 the value of SED does not change much.
Fig 6.
Effect of single synaptic polarity switch on SED.
Switching the polarity of a single connection above a baseline with all inhibitory connections can have diverse impact on SED, from vary weak to very strong. The switched connections are labeled in the top and their corresponding strengths are shown in the bottom. The first point on the right corresponds to the configuration with all excitatory synapses. For all points, the inputs to the interneurons are fixed and optimal.
Fig 7.
SED as a function of input strength.
All other circuit parameters are kept fixed as optimal.
Fig 8.
SED as a function of synaptic and gap junction conductances.
All other circuit parameters are kept fixed as optimal.
Fig 9.
SED as a function of calcium related ionic conductances.
Similar as in Fig 8. (A) Global view and (B) more local view.
Fig 10.
Stationary membrane potential of each interneuron depends on ablation type.
Values of membrane potentials are computed for optimal parameters, synaptic polarities, and inputs. The lack of mark for a given ablation denotes the lack of neuron in the reduced circuit.
Fig 11.
Stationary calcium concentration of each interneuron depends on ablation type.
This is analogous to Fig 9.
Fig 12.
Stationary distributions of currents in neurons across ablations.
In a stationary state, all currents passing through a neuron’s membrane must sum up to zero, therefore each bar in the graph has equal positive and negative parts. The currents corresponding to different mechanisms are marked by different colors. Note a different y-axis scale in the subgraphs related to ablations involving ASH neuron.
Fig 13.
Examples of gap junction currents for wild type and ablated circuits.
Arrow width corresponds to the current magnitude. Ablated neurons are colored in black.
Fig 14.
Examples of synaptic currents for wild type and an ablated circuit.
For two selected ablation types we show synaptic weights (left column) and synaptic currents (right column) as arrows with widths proportional to their strengths. Weak synaptic connections (below 1.0) and weak synaptic currents (below 0.01 μA/cm2) are shown as dashed lines.
Table 4.
Description of optimized parameters.