A neuroanatomical minimal network circuit for salt klinotaxis in C. elegans.

The white circles represent chemosensory neurons, the gray circles represent interneurons, and the black circles denote motor neurons. The black and green connections between neurons represent the chemical synaptic connections and electrical gap junctions, respectively. The minimal circuit was derived from the C. elegans connectome, with two constraints applied as described in the text (Izquierdo and Beer, 2013).

The trajectories of the worm’s locomotion.

The highest-performing network models, with and without the AIY-AIZ connections constrained to be inhibitory, were placed at the initial position, 4.5 cm away from the salt gradient peak, at 10 different angles of worm orientation, and allowed to move freely for 250 sec. The salt concentrations were represented by a Gaussian distribution. The color of the trace represents the passage of time. (a) The highest-CI network model that evolved without any constraints. The CI is 0.855, with a standard deviation of 0.006. (b) The highest-CI network model that evolved with the constraint that the AIY-AIZ connection be inhibitory. The CI is 0.877, with a standard deviation of 0.002. The insets provide an enlarged view of the sinusoidal locomotion and turning processes.

The best evolved neural network circuits, with and without constraining the AIY-AIZ connections to be inhibitory, and the resulting network responses to step changes in salt concentration.

(a) and (b) The best evolved neural network circuits without (a) and with (b) the constraints. The blue arrow and the red blunt arrow indicate an excitatory and an inhibitory synaptic connection, respectively. The green connections represent electrical gap junctions. The color intensity of these connections indicates the strength of the synaptic connections. (c) The neurotransmitter release, zi, from each neuron in the best evolved network without the constraints is illustrated as a response to step changes in the salt concentration. The responses to positive and negative step changes I the salt concentration are represented by the colors blue and red, respectively. (d) The illustration is the same as (c), but the outcome was obtained from the best evolved network with the constraints. In both (c) and (d), the black horizontal line represents the level of the bias term, θi, in the interneurons and motor neurons. In both (c) and (d), the turning angle φ, as defined by Eq. A13a (see Fig. A2b), is illustrated in the second panel from the bottom. In order to identify the direction of the sweep of the head sensory neurons upon introducing step changes in salt concentration, it is necessary to confirm the ideal sinusoidal trajectory of the model worm in the absence of sensory input. This is illustrated in the lowest panel from the bottom in (c) and (d).

The analysis of klinotaxis in the best evolved model with the constraints.

(a) The curving rate as a function of the bearing. (b) The definitions of the curving rate and the normal direction of translational movement, which are utilized in the klinotaxix analysis, are illustrated. (c) The curving rate as a function of the normal gradient of salt concentration. (d) The positive (red) and negative (blue) components of the curving rate as a function of the translational gradient of salt concentration. The black dots represent the mean value of the two components. In the analysis, the salt concentration profile was modeled with a Gaussian distribution. All the error bars represent the standard deviation.

The reversal of salt concentration memory-dependent preference behavior in klinotaxis is attributed to the alteration from inhibitory to excitatory connections between ASER and AIY.

(a) and (b) In the best evolved neural circuit with the constraints, it was postulated that the synaptic connections between ASER and AIY would be altered from (a) inhibitory connections to (b) excitatory connections when the cultivated salt concentration was replaced from (a) a higher to (b) a lower concentration than the current environment. The figure shown in (a) is identical to Fig. 3b and #0 of Fig. S4. (c) The curving rates obtained from the networks illustrated in (a) and (b) (corresponding to #0 and #15 in Figs. S4 and S5, respectively), are presented as a function of the normal gradient of salt concentration. In addition, the curving rate obtained from the neural circuit with an intermediate connections between ASER and AIY (corresponding to #9 in Figs. S4 and S5) is also presented. (d) The curving rates as a function of the normal gradient of salt concentration, which were experimentally determined when the cultivated salt concentration was higher (black) and lower (red) than the current environment (Kunitomo et al., 2013). The case in which the cultivated salt concentration was close to the current environmental concentration (50 mM) is also shown in green. (e) The analysis presented here is identical to Fig. 3d, except that the ASER-AIY inhibitory connections in the best evolved model with the constraints have been replaced with excitatory connections as illustrated in Fig. 5b.

Inhibition of SMB activity suppresses the salt concentration memory-dependent preference behavior in klinotaxis, as observed experimentally.

(a) The curving rates as a function of the normal gradient of salt concentration that were experimentally observed in starved individuals cultivated at a salt concentration higher, comparable, and lower than the current environment (Kunitomo et al., 2013). (b) The curving rates as a function of the normal gradient of salt concentration that were obtained from the neural circuits that yielded the results in Fig. 5c, except that here the synaptic connections between AIZ and SMB and the self-connections of SMB were multiplied by 0.9 to inhibit the SMB activity. (c) The trajectories of the model worm obtained by inhibiting the SMB activity in the best evolved network, where the ASER-AIY connections remained inhibitory, as shown in Fig. 5a (or #0 of Fig. S4). (d) The trajectories of the model worm obtained by inhibiting the SMB activity in the best evolved network, where the ASER-AIY connections were altered to be excitatory, as shown in Fig. 5b (or #15 of Fig. S4).

Modeling of the synaptic transmission from the ASEL and ASER sensory neurons in response to changes in NaCl concentration.

Worm locomotion model.

(a) The body of the worm, consisting only of the idealized head and neck regions of C. elegans. The worm model was represented as a point (rx, ry), located at the center of the boundary between the head and neck regions of the model. The μ represents the angle between the velocity vector v and the positive x-axis. In this context, a counterclockwise angle is considered positive. The dorsal (gray) and ventral (black) motor neuron pairs receive an out-of-phase constitutive oscillatory input from the motor systems, respectively. (b) Changes in the direction of locomotion. In the interval between time steps i −1 and i, the orientation of the velocity vector undergoes a change of the turning angle φi. The gray arc represents the path of the worm.

Terminology used in the analysis of the worm’s locomotion.

Orientation vectors used in the analysis of sinusoidal locomotion. Undulations occur in the x-y plane. The white circles represent the start and end points of n-cycles of locomotion, where n was set to three throughout the analysis of the worm’s locomotion characteristics.

The parameters that were evolved by the genetic algorithm in the worm’s chemotaxis simulation.

The parameters used in the simulations of worm’s chemotaxis.

The parameters that control the evolutionary algorithm.

The parameters of the best evolved network model with the constraints, as obtained from the evolutionary algorithm with the assumption that the AIY-AIZ connections are inhibitory.