Figure 1.
A network of six statocyst receptors (SRC1-6) used in our experiments to model a single statocyst. Each SRC is connected to the next two adjacent cells. The sensory network controlling routine swimming (left panel) and hunting (right panel) is the same. During routine swimming, the only source of excitation for the SRCs is the statolith, whereas during hunting the interneuron H adds significant excitation to all sensory neurons. Dark blue indicates the SRCs receiving excitatory inputs in each case.
Figure 2.
A representative recording of SRC firing activity in the biological system.
Spikes times of four SRC units during fictive hunting search behavior evoked by physostigmine in vitro. The activity was recorded extracellularly and the spikes were sorted as explained in [16]. Note the irregular sequential alternation in firing between different SRCs during hunting. During these experiments there is no motion and thus the WLC activity arises from the excitation of the hunting neuron to the SRCs. Grayed areas illustrate specific sequential activations among active SRCs.
Figure 3.
The behavior of the model network.
Left panels: Routine swimming activity pattern, in the absence of the hunting neuron excitation (c.f. Figure 1, left panel). Right panels: Search hunting behavior activity pattern when the hunting neuron is activated (c.f. Figure 1, right panel). (A) Behavior of the SRC model network. During routine swimming the model statocyst network shows a winner take-all dynamics. Only the SRC pressed by the statolith fires (and thus inhibits other SRCs connected to it). In the first part of the time series, the active neuron in the statocyst network is SRC01. A simulation of body orientation change by exciting SRC06 (denoted by the arrow) makes the new pressed SRC fire immediately while SRC01 becomes silent like the rest of the SRCs. The winnerless competition dynamics (WLC) appears in the statocyst model when the hunting neuron is activated. The irregular sequential activations of the WLC activity displayed by the model are very similar to the one observed in the biological circuit (see Figure 2). (B) Behavior of the CG network located between the statocyst and the wing CPG. During routine swimming either CG1 or CG2 is active, depending on which of the SRCs receives the excitation from the statolith. The CG3 cell integrates and sends this information to the CPG. When a deviation from the preferred position occurs, the identity of the active SRC pressed by the statolith changes and the cerebral interneurons interpret this change (see panel C). During hunting, both CG1 and CG2 cells are active. (C) Behavior of the wing CPG model responsible for generating the periodic wing beating rhythm. As in the biological circuit (Figure 6) the activity of the wing CPG model is affected by the statocyst dynamics which is evoked by the behavioral context. During routine swimming, the model CPG generates a regular rhythm. During the hunting behavior the pattern is faster and highly irregular. Note that during routine swimming, when a change of posture is simulated, the sensory information received in the wing CPG immediately generates a corrective activity. Here, for example, the change from SCR01 to SCR06 produces a short change in the frequency and shape of the rhythm. Afterward, the typical repetitive rhythm is restored.
Figure 4.
Lyapunov exponents calculated from WLC behavior.
Evolution in the calculation of the two positive Lyapunov exponents in the statocyst model under the action of the hunting neuron. The existence of two positive Lyapunov exponents means that the activity in the network is chaotic during hunting behavior.
Figure 5.
Statocyst model connected to a wing CPG model.
Statocyst dynamics drive the motoneurons that control the movement of the wings. Here we have modeled the wing CPG circuit by building a network with six neurons: 7, 8, 1A, 2A, 3 and 4. This network replicates the known wing CPG connectivity 20,42. Each single neuron represents the equivalent electrically coupled groups of cells in the biological circuit. We have chosen neurons 1A (for the dorsal group) and 2A (for the ventral) as representative cells of the CPG behavior. The statocyst is connected to this CPG through a simple model of cerebral cells that consists of three cerebro-pedal interneurons (CG1-3). Note that we omitted the hunting neuron in the statocyst circuit diagram to simplify the graphical representation.
Figure 6.
The behavior of the biological wing CPG.
The wing CPG generates the rhythm that controls the wing movements. Each panel of the figure displays intracellular recordings of the 1A neuron (blue traces) and the extracellular activity of the wing nerve (black traces) during the two behavioral contexts: routing swimming (top panel) and search hunting (bottom panel). The arrows in the extracellular traces point out the activity associated with the firing of the 1A and the 2A cells. 1A and 2A neurons have been reported to fire doublets as well as single spikes depending on the strength of the swimming.
Table 1.
Mean frequency of the CPG rhythm during routine swimming.
Figure 7.
Principal component analysis of the sensory-motor transformation.
We have selected three different types (A–C) of hunting episodes according to the duration of specific patterns of sequential activations among the SRCs. A total of six hunting episodes are shown in this figure, two examples for each kind. The top panels display the time intervals in which each neuron exceeds a threshold of . Different colors are used to indicate each neuron. The episodes labeled as type A correspond to long activations of neurons 1 and 4 (red and magenta, respectively). The episodes labeled as type B correspond to sequential activations of similar length in all neurons, while type C episodes correspond to long activations of SRCs 2, 3 and 5 (green, blue and cyan). The bottom panels display the first three principal components for the activity of the six receptor cells (left plot) and the four motoneurons in the wing CPG (right plot). The PCA shows that a similar sequential activity in the sensory network during hunting (different hunting episodes of the same type) evokes similar rhythmic activity in the motor system.
Figure 8.
Specific sensory network activation phase locks correspond to a unique motor activity during hunting behavior.
The figure illustrates two representative examples of activation phase-locks among activated SRCs in a given time window (dashed rectangles) and its corresponding motor output (arrows) during different hunting episodes. (A–B) Top panels: Statocyst sequential activation patterns. The color codes for the neurons are the same as in Figure 7. Bottom panels: Motor response to the sensory activity. Blue and red traces correspond, respectively, to the firing of 1A and 2A motoneuron. The analysis reported in the text refers to 120 s simulations but here, for representation purposes, we show a fragment of 12 s. The dashed rectangles point out the specific activation phase locks as statistically selected (see Methods) for time windows in which four specific neurons are active. Panel A displays activation phase locks for SRCs 1, 2, 4 and 5 during a hunting episode characterized by long activations for neurons 1 and 3. These specific activation phase locks result in similar responses in the motor network –see also panel C– in most cases (6 out of 7 in the example shown here). In the hunting episode of panel B the activations have a similar duration in all neurons. The sequences pointed out here involve SRCs 2, 3, 5 and 6. In this case, the sensory activation phase lock always induces the same response in the wing CPG –see also panel D–. (C) PSTHs of the 1A and 2A cells characterizing the motor response during the activation phase lock illustrated in panel A. (D) PSTHs of the same cells during the phase lock illustrated in panel B. PSTHs are calculated for the entire simulations (120 s). Spikes are aligned to the beginning of the activation sequence. The activation phase lock of panel A induces in most cases the firing of motoneuron 1A, which is not accompanied by activity in 2A. On the other hand, phase locks in panel B induce the firing of 1A followed by the activation of 2A in a similar interval.
Table 2.
Maximal conductances of the ionic channels.
Table 3.
Maximal conductances of chemical synapses.