Figure 1.
Searching the connectome for the klinotaxis network.
A, Maximal network. All paths between chemosensory neurons (white disks) and neck motor neurons (black disks). Interneurons shown in gray. Chemical synapses shown as black lines. Directionality not shown. Gap junctions shown in red. Line thickness represents the relative number of chemical synapses or gap junctions between the two neurons. B, C, Number of neurons and number of chemical synapse and gap junctions in the network as a function of path length. Points represent the number of total neurons and contacts in the network. Dashed lines represent the total number of neurons and synapses and junctions in the connectome.
Figure 2.
Neuroanatomy of the minimal klinotaxis circuit.
White disks, chemosensory neurons; gray disks, interneurons; dark gray disks, motor neurons. Black connections represent chemical synapses. Red connections represent electrical gap junctions. The strength and polarity of the connections are still unknown. We show the strength and polarity from the best evolved network. Arrowheads, excitatory connections; filled circles, inhibitory connections. Line thickness shows relative connection strength. Color of the disk's border represents the sign of the bias term θ (black, positive; gray, negative). Thickness of the disk's border represents the magnitude of the bias. All parameters were symmetrical across the dorso-ventral midline.
Table 1.
Chemotaxis efficiency of the high-performance subpopulation in conical and Gaussian gradients.
Figure 3.
A representative model worm was placed at 10 random orientations 4.5 cm from the gradient peak and allowed to move for 300 sec. The gradient is Gaussian shaped. Trace color represents time. Inset: Enlargement of a gradual turn.
Figure 4.
A, Average turning bias vs. bearing. B, Average turning bias vs. the component of the gradient in the normal direction. C, Average turning bias vs. the component of the gradient in the translational direction. Black points represent all of the data averaged into bins according to the translational gradient. Gray points show the data separated between positive and negative turning bias. The two red points highlight the significance of the difference between the turning bias when moving down the gradient versus when moving up the gradient at the same angle. Error bars are standard error of the mean.
Figure 5.
Phase sensitivity of orientation responses.
A, Response to upsteps. B, Response to downsteps. Plots show turning bias vs. the phase of locomotion at which the concentration step occurred. Each point represents the average across all networks; error bars are standard error of the mean. Shades of gray indicate the magnitude of the concentration step (0.005 black, 0.00333 dark gray, and 0.00166 light gray). Positive and negative values of turning bias result, respectively, in counterclockwise and clockwise rotations of the translational vector. Abbreviations: VS, ventral head sweep; DS, dorsal head sweep (shaded region).
Figure 6.
Neuron output traces in response to step changes in concentration in the best evolved network.
A, Chemosensory neuron output, ASE. B, First layer interneuron output, AIY. C, Second layer interneuron output, AIZ. D and E, neck motor neuron output (D, SMBD; E, SMBV). Time is shown on the x-axis. Neuron output is shown on the y-axis. Each trace is color-coded according to the magnitude and sign of the step of the concentration step. The black trace represents the neuron output without input. The neuron output from left cells is shown on the left; the neuron output from right cells is shown on the right.
Figure 7.
Dynamics of the neck motor neurons.
Input-output diagrams for the left (A) and right (B) pair of dorsal and ventral motor neurons. Gray trace, steady-state input-output (SSIO) curve when the head sweep oscillation is absent. Red trace, instantaneous input-output relation when the head sweep oscillation is present. Arrows show the effects of output of the indicated chemosensory neuron on motor neuron input. Shaded areas show the range of oscillation. For each of the SSIO curves, there are dorsal and ventral motor neurons moving out of phase over the red trajectory due to the out of phase input from the oscillatory component. When the dorsal motor neuron is at point a in the curve, the ventral motor neuron is at point d, and vice versa. When the dorsal motor neuron is at point b in the curve, the ventral motor neuron is at point c, and vice versa. For the dorsal/ventral SMBL pair (A), an increase/decrease in chemical concentration would decrease/increase the output of the neuron in d, but not of the neuron in a; decreasing/increasing the difference between the two left neck motor neurons. For the dorsal/ventral SMBR pair (B), a and d represent the opposite regions: a neuron at a is more sensitive to changes in input than the other neuron at d; but the result is the same: an increase/decrease in chemical concentration decreases/increases the difference between the two neck right motor neurons. To different degrees, the same is the case for other points along the curve.
Figure 8.
Range of sensitivity to changes in concentration.
A, Interneuron class AIY. B, Interneuron class AIZ. Left neuron shown in blue; right neurons shown in red. Flat regions of the curve correspond to areas of no-sensitivity to input over that region. The slope of the curve denotes the degree of sensitivity to changes around that region of the input. For example, AIYR is sensitive to large positive changes in concentration only, whereas AIYL is sensitive to changes in concentration around the midline. Dashed lines show the sensitivity when the gap junction between those two neurons is blocked. In AIY, blocking the gap junction does not affect the sensitivity of its left and right neurons. In AIZ, blocking the gap junction results in substantial differences in the range of sensitivity. C, D, Sensitivity in the left and right pair of motor neurons as a function of the phase of locomotion, respectively. The dorsal motor neuron is shown in blue-green-yellow shades; the ventral motor neuron is shown in gray scale. Similar to the interneurons, the motor neurons have a selective range of sensory input over which they are sensitive. Unlike the interneurons, their sensitivity changes as a function of the worm's sinusoidal movement. Because of the out of phase oscillation between dorsal and ventral motor neurons, which neuron is more sensitive to a certain input swaps back and forth between them.
Figure 9.
Orientation responses elicited by stepwise changes in concentration.
A, Response to upsteps. B, Response to downsteps. 1, Behavioral traces for four points in the locomotion phase. The black trace shows the trajectory in the absence of a concentration step. The colored traces show the trajectories obtained in response to concentration steps placed at the locations indicated by dots of matching color. The four locations chosen cover a complete cycle of locomotion (dashed box). Vectors indicating the direction of translation (dashed lines) are shown for no concentration step (u), and steps at locations a and c (ua, and uc). Abbreviations: DS, dorsal head sweep; VS, ventral head sweep (shaded region). 2, Generalization of the turning bias as a function of the timing within the locomotion phase where the step is introduced. The example traces from A1 and B1 are represented by labeled disks in A2 and B2, respectively.
Figure 10.
Interneuron types based on their response to step changes in concentration.
Type A: insensitive. Type B: sensitive only to either upsteps or downsteps. Type C: ambiguously sensitive to both upsteps and downsteps. Type D: unambiguously sensitive to upsteps and downsteps. Figures in column 1 show neuron output trace over time, colored according to the different steps in concentration received. The sign and magnitude of the step in concentration is given by the color bar. The black trace represents the output of the neuron without any input. Column 2 shows their corresponding sensitivity plot. Average output of the neuron (relative to the average output of the neuron in the absence of any input) as a function of step changes in concentration of different sign and magnitude over the range of sensory stimuli. Flat regions of the curve correspond to areas of no-sensitivity to input over that region. The slope of the curve denotes the degree of sensitivity to changes around that region of the input.
Figure 11.
Effects of simulated neuron ablations on klinotaxis performance.
Neuron activation set to resting potential (such that neuron output is 0) during assay. The middle bar inside the box is the statistical median. The outer edges of the box represent the 0.25 and 0.75 quantiles. The lines that extend out of the box span the full dataset.
Figure 12.
A, Unique information about the sensory input in the interneurons. The coverage of a cell measures the range of the sensory stimuli over which it is sensitive to changes. When the left and right cells specialize over a different range of possible sensory stimuli, their combined coverage can be greater than their average independent coverage. The x-axis represents the gain in coverage when the left and right AIY cells are considered jointly from when each cells is considered independently. The y-axis represents the same information for the AIZ pair. B, Role of gap junctions in the interneurons. Effects of simulated blocked gap junction on coverage of the interneurons over the range of step changes in concentration for AIY and AIZ cells. The x-axis represents the loss in coverage when the AIY gap junction is blocked, compared to when it is functioning normally. The y-axis represents the same information for the AIZ pair. Each point represents a network from the successful population.
Figure 13.
Neuroanatomical network connecting ASE to SMB, constrained to paths of length 3, but without a contact threshold.
White disks, chemosensory neurons; gray disks, interneurons; dark gray disks, motor neurons. (Note: ADFR is a chemosensory neuron, but it is not shown in white because it is not in the original target set. Similarly, RMGL is a motor neuron, but it is not shown in black because it is not in the motor target set). Black connections represent chemical synapses; red connections represent electrical gap junctions.
Figure 14.
A, Idealized body. The model worm was represented as a point (x, y) located at the center of the border between idealized head and neck regions of the model. The quantity μ is the angle between the instantaneous velocity vector v and the positive x axis. The dorsal (gray) and ventral (black) motor neuron pairs receive out of phase oscillatory input from the body. B, Changes in orientation. Between time steps i−1 and i, the orientation of the velocity vector changes by the turning angle φ. The gray arc is the model worm's path. C, Terminology. Orientation vectors used in the analysis of sinusoidal locomotion. Undulations occur in the x–y plane. The white circles represent the start and end of one locomotion cycle. Solid section of the trajectory represents ventral head sweeps. Dashed section of the trajectory represents dorsal head sweeps.