Borisyuk R et al. (2017), To swim or not to swim: A population-level mode...

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Biosystems 2017 Nov 01;161:3-14. doi: 10.1016/j.biosystems.2017.07.004.

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To swim or not to swim: A population-level model of Xenopus tadpole decision making and locomotor behaviour.

Borisyuk R , Merrison-Hort R , Soffe SR , Koutsikou S , Li WC .

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We present a detailed computational model of interacting neuronal populations that mimic the hatchling Xenopus tadpole nervous system. The model includes four sensory pathways, integrators of sensory information, and a central pattern generator (CPG) network. Sensory pathways of different modalities receive inputs from an "environment"; these inputs are then processed and integrated to select the most appropriate locomotor action. The CPG populations execute the selected action, generating output in motor neuron populations. Thus, the model describes a detailed and biologically plausible chain of information processing from external signals to sensors, sensory pathways, integration and decision-making, action selection and execution and finally, generation of appropriate motor activity and behaviour. We show how the model produces appropriate behaviours in response to a selected scenario, which consists of a sequence of "environmental" signals. These behaviours might be relatively complex due to noisy sensory pathways and the possibility of spontaneous actions.

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	Fig. 1. Schematic representation of the sensory pathways. Arrows represent excitatory synaptic connections, circles represent inhibitory connections.
	Fig. 2. Schematic representation of CPG populations. The upper rectangular area (light blue dashed border) shows populations which are mostly active during swimming. The lower rectangular area (red dashed border) shows populations which are mostly active during struggling. Motor neurons are shown by green circles attached to both rectangular areas because the motor neurons receive connections from both swimming and struggling populations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 3. Superposition of 3 two-parametric bifurcation diagrams under variation of a third parameter (θ). The horizontal and vertical axes show parameter values of P and a (Eq. (3)). The rightmost curve shows the bifurcation diagram when θ = 5. Blue lines limiting the area filled by the horizontal line pattern correspond to saddle-node bifurcations (intersection of the line means that the saddle and the node fixed points merge and disappear). There are 3 fixed points in the patterned area (one saddle and two stable nodes) and outside of this area there is one stable node only. A similar explanation applies to the middle curve (this bifurcation diagram relates to θ = 4 and to the leftmost curve (θ = 3). Parameter b = 1.3 is fixed for all bifurcation diagrams. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 4. Noisy activity of sensory population vs time. There are multiple activity transitions between a low level (near zero) and a high level (near 0.5) Parameter values: a = 6, P = 1.2, σ = 0.2, b = 2, θ = 3.
	Fig. 5. Swimming. Activities of dIN, aIN and cIN populations (from bottom to top) vs time during swimming. The lower three traces are from the left and upper three are from the right.
	Fig. 6. Swimming. Activity of motor neurons on the left (red) and right (blues) sides vs time. Red and blue short bars correspond to times of external input application to the left and right sides respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 7. Swimming. Lower curve: Projection of the swimming limit cycle to the phase plane showing left and right cIN population activities. Upper curve: Projection of the limit cycle to the phase plane showing left and right dIN population activities. The shape of these curves is typical for anti-phase oscillations.
	Fig. 8. Swimming activities of dIN and aIN populations on the left side. A. Projection of the limit cycle to dIN (horizontal) and aIN (vertical) axes. B. Oscillatory activity of aIN (red) and dIN (blue) populations vs time. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 9. Struggling regime: Initiation of struggling from the rest position. Stimulation of dINr on both sides from 1000 to 2000 ms (1030–2000 for the right side). Motor neuron activity on the left (red) and right (blue) sides are shown vs time (blue curve was shifted up by 0.02 to avoid an overlap of graphs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 10. Struggling: Activities of dINr populations on left (red) and right (blue) body side vs time. Oscillations are shown with a vertical shift to avoid overlap. This figure demonstrates anti-phase oscillations at low frequency. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 11. Struggling behaviour initiated from swimming. Stimulation was applied from 1000 to 2000 ms to excite dIN populations (red and blue bars) and dINr populations (green bar). Motor neuron population activity on the left and right sides is shown by red and blue lines, respectively. After the end of stimulation the CPG network returns to swimming. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
	Fig. 12. Activity of motor neuron populations on the left (red) and right (blue) body sides. These activities show a sequence of behaviours arising according the scenario events. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

References [+] :

Borisyuk, Dynamics and bifurcations of two coupled neural oscillators with different connection types. 1995, Pubmed