Ferrario A , Merrison-Hort R , Soffe SR , Li WC , Borisyuk R .

BB/L002353/1 Biotechnology and Biological Sciences Research Council (GB), BB/L000814/1 Biotechnology and Biological Sciences Research Council , BB/L00111X/1 Biotechnology and Biological Sciences Research Council

	Fig. 1. Scheme of neurons and connections in the reduced model. Currents \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I_{1} (t)$\end{document}I1(t) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I_{2} (t)$\end{document}I2(t) represent external depolarizing step currents injected to the two dINs to mimic sensory input. Both currents have the same duration d and amplitude A. The current pulses for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I_{1} (t)$\end{document}I1(t) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I_{2} (t)$\end{document}I2(t) are initialised at time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t_{1}$\end{document}t1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t_{2}$\end{document}t2, respectively (see Sect. 3.1 for details)
	Fig. 2. Property of PIR in the dIN model. (A) Voltage dynamics in one dIN (black line) during the injection of the current function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I ( t )$\end{document}I(t) (blue line). (B) and (C) show the dynamics of the dIN’s gating variables and ionic currents during the same current injection of part (A), respectively
	Fig. 3. Voltage traces of dINs in the reduced model during swimming and synchrony. The left panel shows experimental pairwise recordings from one left-centre dIN and one right-centre dIN during swimming and synchrony. The right panel shows the voltage variable of the two dINs of the reduced model during swimming and synchrony. We show three cycles of swimming (3T) and two cycles of synchrony (2T) to highlight the characteristic shapes of the membrane potential during these two regimes and to compare experiments and model simulations. Arrows indicate the firing of cINs and mark the inhibition preceding PIR spikes in dINs. Model parameters used to obtain swimming are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${w}_{\mathrm{inh}} =23$\end{document}winh=23 nS, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${w}_{\mathrm{ampa}} =12$\end{document}wampa=12 nS and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${w}_{\mathrm{nmda}} =10$\end{document}wnmda=10 nS, with initiation parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta=140$\end{document}Δ=140 ms and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${d}=6$\end{document}d=6 ms. Model parameters used to obtain synchrony are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${w}_{\mathrm{inh}} =55$\end{document}winh=55 nS, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${w}_{\mathrm{ampa}} =12$\end{document}wampa=12 nS and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${w}_{\mathrm{nmda}} =10$\end{document}wnmda=10 nS, and initiation parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta=0$\end{document}Δ=0 ms and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{d}=6$\end{document}d=6 ms. The experimental recordings have been obtained using the same experimental protocols and conditions described in [12]
	Fig. 4. One-dimensional bifurcation diagram for the swimming (black) and synchrony (red) limit cycles at varying inhibitory strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ihn}}$\end{document}wihn. Blue and purple lines show two unstable limit cycles appearing at bifurcation points \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{3}$\end{document}w3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{4}$\end{document}w4, respectively. The y-axis shows the maximum of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K_{f}$\end{document}Kf-gating variable f of the left cIN for each limit cycle. Stable and unstable limit cycles are shown by continuous and dashed lines, respectively. The superscript − refers to subcritical bifurcations. Bifurcation parameter values (in nS) are the following: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{1} =8.57$\end{document}w1=8.57, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{2} =2.86$\end{document}w2=2.86, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{3} =15.74$\end{document}w3=15.74, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{4} =27.6$\end{document}w4=27.6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{5} =11.23$\end{document}w5=11.23 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{6} =11.21$\end{document}w6=11.21
	Fig. 5. Codimension-two bifurcation diagrams showing the stability regions for the swimming (light grey and red) and synchrony (light red) limit cycles under variation of (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}}$\end{document}winh, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}}$\end{document}wampa) in (A) and (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}}$\end{document}winh, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{nmda}}$\end{document}wnmda) in (B). Superscripts − and + refer to subcritical and supercritical bifurcations, respectively. To clarify the stability of the limit cycles for low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}}$\end{document}wampa, we computed the codimension-one bifurcation diagram at fixed value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}} =10$\end{document}wampa=10 nS shown in Fig. 6 (orange dotted line). Bifurcation points B and D switch the criticality of the PD bifurcation (subcritical to supercritical). The LPD point is a fold-flip bifurcation point. At this point, a pitchfork bifurcation curve (PFK, blue line) interacts with a PD line and both exchange criticality
	Fig. 6. (A) One-dimensional bifurcation diagram for the synchrony (red), swimming (black) and double-synchrony (purple) limit cycles at varying inhibitory strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ihn}}$\end{document}wihn and fixed parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}} =10$\end{document}wampa=10 nS and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{nmda}} =10$\end{document}wnmda=10 nS. The y-axis shows the maximum of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K_{f}$\end{document}Kf-gating variable f of the left cIN for each limit cycle. Blue and green lines show unstable limit cycles appearing at bifurcation points \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_{5}$\end{document}u5 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_{4}$\end{document}u4, respectively. Stable and unstable limit cycles are shown by continuous and dashed lines, respectively. The superscript − refers to subcritical bifurcations. (B) Zoom of selected regions of Fig. 6(A)
	Fig. 7. (A) Time evolution of the voltage of dINs (brown lines) and cINs (blue lines) during one period of synchrony (SyC), double-synchrony (2-SyC) and swimming (SwC). The three limit cycles are detected by AUTO in Fig. 6. Synaptic strength parameters used to generate each panel SyC, 2-SyC and SwC, respectively, are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =30$\end{document}winh=30 nS, 45 nS and 40 nS. (B) Time difference between left dIN and left cIN spikes during one cycle of the SwC at varying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}}$\end{document}wampa. The remaining vector of parameters used to obtain this figure are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =60$\end{document}winh=60 nS, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{nmda}} =10$\end{document}wnmda=10 nS, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta=50$\end{document}Δ=50 ms and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d=6$\end{document}d=6 ms
	Fig. 8. Stable attractors of the reduced model at varying initiation parameters (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta,d$\end{document}Δ,d) with fixed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}} =10$\end{document}wampa=10 nS and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ndma}} =10$\end{document}wndma=10 nS. We show three different values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =28,\ 42 $\end{document}winh=28,42 and 60 nS (title of each subplot). These values correspond to all the possible combinations of stable attractors of the system shown in Fig. 6. Each coloured region identifies the initialisation parameters (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta,d$\end{document}Δ,d) that converge to a stable limit cycle, or convergence to the resting state (black regions, fixed point). In the case of convergence to a limit cycle, the colour represents the period of the attractor. The orange region in the case \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =28$\end{document}winh=28 nS identifies the initial conditions where the system converges to stable synchrony, the yellow region in the case \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =42$\end{document}winh=42 nS corresponds to convergence to the stable 2-synchrony, while the white regions correspond to convergence to stable swimming
	Fig. 9. Transition from synchrony to swimming. Plot of dINs’ voltage recordings at varying time shows synchronous activity before the dynamics are locked into synchronous (A) and double-synchronous regimes (B) before then converging to the swimming mode. In both (A) and (B) initiation parameters are set to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta=0$\end{document}Δ=0, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d=6$\end{document}d=6 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A=0.04$\end{document}A=0.04. At time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t^{*} =0.3$\end{document}t∗=0.3 s the system is integrated starting from a perturbed initial point. This point is obtained by adding a normally distributed vector of numbers with equal variance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma=10^{-3}$\end{document}σ=10−3 to each variable at time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t^{*}$\end{document}t∗. Values of synaptic strengths are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}} =10$\end{document}wampa=10, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{nmda}} =10$\end{document}wnmda=10, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =22.2$\end{document}winh=22.2 in case (A) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}} =60$\end{document}winh=60 in case (B)
	Fig. 10. Distribution of times spent in the synchrony (double-synchrony) transition in the system with noise. (A) and (B) show the histogram of times spent in synchronous state before switching to swimming. The selected parameter values of (A) and (B) are the same as the ones used in Fig. 7(A) and (B), respectively
	Fig. 11. Plot of dIN voltage dynamics showing transitions from swimming to synchrony (A) or double-synchrony (B), and back to swimming. In both (A) and (B) a brief step current (0.45 nA, 5 ms) is manually injected to the left dIN at the time of right dIN firing (black arrows). Parameter values used to obtain (A) and (B) are the same as the ones used in Fig. 9(A) and (B), respectively, except that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta=50$\end{document}Δ=50
	Fig. 12. Stability of the attractors of after symmetry breaking (A) Projection of the three stable limit cycles (SwC̅, SyC̅ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\overline{2-\mathrm{SyC}}$\end{document}2−SyC‾) to the phase plane of dINs voltages and zoom of selected regions (black boxes). The green diagonal line shows the loss of mid-line symmetry of the stable limit cycles. The vector of parameters (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}}, w_{\mathrm{ampa}}, w_{\mathrm{nmda}},\Delta,d$\end{document}winh,wampa,wnmda,Δ,d) used for the SwC̅ case are (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$60,10,10,100,6$\end{document}60,10,10,100,6), for the SyC̅ case are (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$25,12,10,10^{-4},6$\end{document}25,12,10,10−4,6), and for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\overline{2-\mathrm{SyC}}$\end{document}2−SyC‾ case are (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$40,10,10,10^{-4},6$\end{document}40,10,10,10−4,6) (B) Period of the attracting limit cycle found by numerical simulation at varying (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}}, w_{\mathrm{ampa}}$\end{document}winh,wampa) and fixed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{nmda}} =10$\end{document}wnmda=10 nS in cases (i)–(ii) and at varying (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{inh}}, w_{\mathrm{nmda}} $\end{document}winh,wnmda) and fixed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w_{\mathrm{ampa}} =12$\end{document}wampa=12 nS in cases (iii), (iv). Initiation parameters for cases (i)–(iii) are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta=50 $\end{document}Δ=50 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d=6$\end{document}d=6, while for cases (ii)–(iv) are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta= 10^{-4}$\end{document}Δ=10−4 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d=6$\end{document}d=6

Angstadt, Mechanisms of postinhibitory rebound and its modulation by serotonin in excitatory swim motor neurons of the medicinal leech. 2005, Pubmed

Angstadt, Mechanisms of postinhibitory rebound and its modulation by serotonin in excitatory swim motor neurons of the medicinal leech. 2005, Pubmed
Arshavsky YuI, Neuronal control of swimming locomotion: analysis of the pteropod mollusc Clione and embryos of the amphibian Xenopus. 1993, Pubmed , Xenbase
Ashwin, Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. 2016, Pubmed
Borisyuk, A developmental approach to predicting neuronal connectivity from small biological datasets: a gradient-based neuron growth model. 2014, Pubmed , Xenbase
Briggman, Imaging dedicated and multifunctional neural circuits generating distinct behaviors. 2006, Pubmed
Briggman, Multifunctional pattern-generating circuits. 2008, Pubmed
Buhl, The role of a trigeminal sensory nucleus in the initiation of locomotion. 2012, Pubmed , Xenbase
Combes, Developmental segregation of spinal networks driving axial- and hindlimb-based locomotion in metamorphosing Xenopus laevis. 2004, Pubmed , Xenbase
Cymbalyuk, Bursting in leech heart interneurons: cell-autonomous and network-based mechanisms. 2002, Pubmed
Dale, Experimentally derived model for the locomotor pattern generator in the Xenopus embryo. 1995, Pubmed , Xenbase
Danner, Central control of interlimb coordination and speed-dependent gait expression in quadrupeds. 2016, Pubmed
Davis, Studying the role of axon fasciculation during development in a computational model of the Xenopus tadpole spinal cord. 2017, Pubmed , Xenbase
Destexhe, Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. 1994, Pubmed
Dickinson, Neuropeptide fusion of two motor-pattern generator circuits. 1990, Pubmed
Dimitrijevic, Evidence for a spinal central pattern generator in humans. 1998, Pubmed
Eisenhart, A central pattern generator underlies crawling in the medicinal leech. 2000, Pubmed
Ferrario, Structural and functional properties of a probabilistic model of neuronal connectivity in a simple locomotor network. 2018, Pubmed , Xenbase
Golubitsky, Symmetry in locomotor central pattern generators and animal gaits. 1999, Pubmed
Govaerts, Computation of the phase response curve: a direct numerical approach. 2006, Pubmed
Grillner, Neural bases of goal-directed locomotion in vertebrates--an overview. 2008, Pubmed
Grillner, Biological pattern generation: the cellular and computational logic of networks in motion. 2006, Pubmed
Hull, Modelling the Effects of Electrical Coupling between Unmyelinated Axons of Brainstem Neurons Controlling Rhythmic Activity. 2015, Pubmed , Xenbase
Ijspeert, Central pattern generators for locomotion control in animals and robots: a review. 2008, Pubmed
Kahn, Experiments on the central pattern generator for swimming in amphibian embryos. 1982, Pubmed , Xenbase
Kahn, The central nervous origin of the swimming motor pattern in embryos of Xenopus laevis. 1982, Pubmed , Xenbase
Kepler, Reduction of conductance-based neuron models. 1992, Pubmed
Laing, A spiking neuron model for binocular rivalry. 2002, Pubmed
Li, The control of locomotor frequency by excitation and inhibition. 2012, Pubmed , Xenbase
Li, The generation of antiphase oscillations and synchrony by a rebound-based vertebrate central pattern generator. 2014, Pubmed , Xenbase
Li, Specific brainstem neurons switch each other into pacemaker mode to drive movement by activating NMDA receptors. 2010, Pubmed , Xenbase
Li, Persistent responses to brief stimuli: feedback excitation among brainstem neurons. 2006, Pubmed , Xenbase
Li, Axon and dendrite geography predict the specificity of synaptic connections in a functioning spinal cord network. 2007, Pubmed , Xenbase
Marder, Principles of rhythmic motor pattern generation. 1996, Pubmed
Marder, Central pattern generators and the control of rhythmic movements. 2001, Pubmed
Molkov, Mechanisms of left-right coordination in mammalian locomotor pattern generation circuits: a mathematical modeling view. 2015, Pubmed
Roberts, Origin of excitatory drive to a spinal locomotor network. 2008, Pubmed , Xenbase
Roberts, Mutual Re-excitation with Post-Inhibitory Rebound: A Simulation Study on the Mechanisms for Locomotor Rhythm Generation in the Spinal Cord of Xenopus Embryos. 1990, Pubmed , Xenbase
Roberts, Central circuits controlling locomotion in young frog tadpoles. 1998, Pubmed , Xenbase
Roberts, How neurons generate behavior in a hatchling amphibian tadpole: an outline. 2010, Pubmed , Xenbase
Roberts, Can simple rules control development of a pioneer vertebrate neuronal network generating behavior? 2014, Pubmed , Xenbase
Roberts, Neural control of swimming in a vertebrate. 1981, Pubmed , Xenbase
Rubin, Multiple rhythmic states in a model of the respiratory central pattern generator. 2009, Pubmed
Sautois, Role of type-specific neuron properties in a spinal cord motor network. 2007, Pubmed
Soffe, Activity of myotomal motoneurons during fictive swimming in frog embryos. 1982, Pubmed , Xenbase
Soffe, Activity of commissural interneurons in spinal cord of Xenopus embryos. 1984, Pubmed , Xenbase
Soffe, Defining the excitatory neurons that drive the locomotor rhythm in a simple vertebrate: insights into the origin of reticulospinal control. 2009, Pubmed , Xenbase
Winlove, The firing patterns of spinal neurons: in situ patch-clamp recordings reveal a key role for potassium currents. 2012, Pubmed , Xenbase
Wojcik, Key bifurcations of bursting polyrhythms in 3-cell central pattern generators. 2014, Pubmed
Wolf, Longitudinal neuronal organization and coordination in a simple vertebrate: a continuous, semi-quantitative computer model of the central pattern generator for swimming in young frog tadpoles. 2009, Pubmed