Fig 1.
Tadpole, swimming and neuronal pathways.
a. Tadpole hanging from mucus (arrow) secreted by cement gland (cg). b. If touched (arrow), it flexes to one side and then swims off. c. Functional diagram of CNS model network with 12 neuron types forming 5 layers: 1) skin sensory; 2) sensory projection; 3) inhibitory reticulospinal; 4) sensory memory; 5) central pattern generator. The list shows colour coding and population of each neuron type on one side. The total number of neurons in CNS model is 2,308 (half on each side) including 788 sensory pathway and 1,520 CPG neurons. Connections shown by solid lines have been established by “developmental” modelling based on single cell recording and dye injections [19]; dash-dotted and dotted lines indicate connections prescribed by the “probabilistic” model (dashed line means that connections probabilities are based on some limited experimental evidence). Red are excitatory and blue are inhibitory connections; resistor sign shows electrical connections. Abbreviations not defined in text: Interneurons: aIN = ascending; cIN = commissural, tIN = trigeminal; dla = dorsolateral ascending; dlc = dorsolateral commissural; mn = motoneuron; dIN = descending interneurons. d-f. Diagrams of the brain and spinal cord illustrating the neuronal pathways from head (d) or trunk touch (f) to start and from head pressure (e) to stop swimming. Only selected neurons are shown to make the signal propagation pathways clear: coloured arrows show activity propagation pathways (red = excitation; blue = inhibition). The hindbrain extends from 0–500 microns and the spinal cord from 500–3500 microns.
Fig 2.
Overview of CNS model responses to a sequence of sensory signals.
a. The “Voltage” panels show membrane potentials of selected active neurons on the left and right sides respectively. The two central panels show spike times (coloured dots, zoomed views in b-d) of all active neurons, the vertical coordinate is the rostro-caudal (RC) position of the spiking neuron. All current pulse sensory stimuli are applied to the left side of the body as indicated by black arrows at the top. 1) Head skin touch initiates swimming from rest (stimulus of 0.3 nA for 5ms excites 13 tSts at time zero); 2) Head skin pressure stops swimming (stimulus 0.3nA for 30ms excites 10 tSps at time 1.3s; 3) Trunk skin touch initiates swimming (stimulus of 0.3nA, for 5ms excites 2 RBs at time 2s); 4) Trunk skin touch during swimming leads to acceleration (stimulus of 0.3nA, for 5ms excites 2 RBs at time 4s); 5) Swimming slows and stops spontaneously. b-d. Zoomed in view of spike times for neurons on the left side responding to each type of skin stimulation. Inserts show small diagrams of each sensory pathway (see Fig 1c).
Fig 3.
a. Visualisation of the adjacency matrix (connectome), where red are excitatory and blue are inhibitory connections. Rows and columns correspond to pre- and post-synaptic neurons, respectively. There are 12 types of neuronal populations in the CNS model and they are separated by solid grey lines. Dashed lines separate the matrix into symmetrical sub-blocks. Within each sub-block vertical and horizontal dotted lines separate the left body side (top rows and left columns) from the right body side (bottom rows and right columns). In each sub-block neurons are ordered according to increasing rostro-caudal position. The matrix describes 128,958 pair-wise connections in one CNS model (in 100 models, the mean of total connection number: 128,845.8; s. d. is 1,715.4). b-c. Examples of connection probabilities distributions (histograms) and zoomed extraction (lower panels) of excitatory (red) and inhibitory (blue) connections for tSt->tIN and MHR->dIN, respectively. (b) Probabilities pk, (k = 1,..,m) for tSt->tIN connections are in the range [0.06, 0.66]. Note: this sub-matrix has been extracted from the adjacency matrix A(i,j) and transposed: here columns and rows correspond to pre- and post-synaptic neurons, respectively. The number of connections m = 691 and the mean and standard deviation: s = 17.6 (the mean of non-zero probabilities
(s.d. is 0.08)—about half of possible connections. (c) For MHR->dIN connections the probabilities are in the range [0.001, 0.21]. The number of connections m = 338, the mean and standard deviation:
s = 16.9, the mean of non-zero probabilities
= 0.1 (s.d. is 0.07)–sparse connections.
Fig 4.
Activity of hexNs and neuronal mechanism of swimming initiation.
a-b. Six recordings of responses to head skin stimulation (black arrow) on the unstimulated side from the same hdIN (from Fig 6C and 6D in [24]). (a) Excitation ramps to threshold and firing leads to swimming (arrow shows first spike). (b) Excitation ramp does not reach threshold. c. Two recordings of a possible hindbrain sensory processing hexN neuron response to a trunk skin stimulation (at arrow; from Fig 3g in [9]). d. Recordings from model hexNs to a trunk stimulation (at arrow). e-f. The averaged ramp of 5 randomly selected model hdINs (e) and 5 experimentally (exp) recorded hdINs (f) (from Fig 6F in [24]) to a subthreshold trunk skin stimulation (at arrow). In the model, the ramp decays significantly by 1.5 s due to synaptic depression of hexNs interconnections. The strength of hexN->hdIN connection is selected to match the average hdIN potential. g-j. CNS model responses to trunk stimulation: swimming (g), no response (h); one sided activity (i); synchrony (j). Top and bottom subpanels show spike times of active neurons. The central panel shows the averaged voltage dynamics of hdINs on left (VL(t), blue) and right (VR(t), red) sides. Coloured dots indicate crossing the threshold (dotted line). In the case of swimming (g), the green area corresponds to swimming activity and the initiation time t* is the mean of hdIN spike times on right. NOTE: To make spikes of RB sensory neurons visible, we show them by black colour. k. Bar chart shows distribution of four responses for different connection probabilities between hexNs on opposite sides. For each probability we run 100 simulations with randomised connectivity and synaptic weights.
Fig 5.
Swimming initiation in response to trunk and head touch stimulation.
a-b. Neuronal activities on the left and right sides (2 upper and two lower panels, respectively). Central panels show spiking times where the vertical coordinate corresponds to the neuron rostro-caudal position. Other panels show the voltage traces of selected active neurons (one from sensory pathway and CPG populations plus three hexNs) and black arrows indicate the first dIN spike. (a) To mimic trunk touch 4 RBs are activated by a brief stimulation at time 0 (arrow, amplitude 0.3nA, duration 5ms). This starts swimming. (b) To mimic head touch, 4 sensory tSts fire one spike in response to stimulation at time 0 (arrow, amplitude 0.3nA, duration 5ms). c-d. Summary of statistics for simulated responses to high (low) trunk or head skin stimulation. (c) Simulation outputs are classified as swim, no swim, synchrony (sync) and one sided. Distribution of outputs is shown for each protocol as well as the percentages of swimming starting on the stimulated side. (d) Boxplots of swimming delays for each type of stimulation. Head skin touch (HT) is mimicked by stimulation of four sensory tSt neurons on the left side to fire once (Fig 5B). This excites tINs and rdlcs which fire once to excite hexNs on both sides and initiate reverberating firing. Short latency direct inputs from tINs and hexNs recruit left dINs which then excite left CPG neurons and initiate swimming.
Fig 6.
a-c. Neuronal activities on the left (top) and right (bottom) body side for one selected simulation of the CNS model near swimming termination. Central subpanels show neuron spike times vs their rostro-caudal position (vertical) and upper and lower subpanels display the voltage traces for different types of CPG neurons. (a) Swimming slows before spontaneous termination by synaptic depression at about 5.6 s after stimulation. In the left side dIN trace there is no rebound spike after the last reciprocal IPSP (red arrow). (b) To mimic the head skin pressure, 10 sensory tSp neurons on the left side are injected with a step current (duration 0.4 s, 0.2nA). Both tSp and MHR neurons fire rhythmically (the mean frequency 32.5Hz), inhibit CPG neurons on both sides and stop swimming. In this case some caudal dINs on the right fire after the start of the inhibition but there is no mn activity. (c) A single randomly selected MHR is injected with 5 equal DC current pulses starting at 2,500 ms (total duration 0.3 s, each pulse is 30 ms). The single MHR fires twice to each pulse, inhibits CPG neurons and this is sufficient to stop swimming. (d) Percentage of simulations where swimming was stopped by the activation of a single randomly selected MHR vs the onset time of the MHR’s current, green dot shows experimentally determined value of stoppings for 2.4 s onset.
Fig 7.
VT model: 3D body reconstruction and swimming in “water”.
a–c. Reconstruction of the 3D tadpole body from experimental images and body sections of the real tadpole (using the Blender software). Some body sections at different RC positions from head to tail are shown in (a). d. Scale diagram of a real tadpole (top) with the notochord (green) and muscle segments (yellow and orange) with a schematic representation of muscle segments 11 and 12) in Sibernetic (bottom-right). This simplified 3D construction includes particles (blue balls) connected by ordinary springs (green) and “elementary muscle fibers” (red) which can contract in response to motoneuron spiking. Bottom-left: Reconstructed 3D tadpole body (VT model) in the Sibernetic system. The 3D shape of the tadpole body (с) was loaded and visualized by Sibernetic to assist in building the VT model. The density of the VT model belly is higher (1060 kg/m3) than other tissues (1035 kg/m3). To simulate swimming the VT model is placed into a tank (18.4×3.7×3.7 mm) filled with “water” represented by ≈ 2 million liquid particles with density and dynamical viscosity (measured in the simulation using Stokes’ law) equal to those of water at 20°С. The swimming speed of the VT model ≈ 19.3 mm/s (tadpole length is 5 mm and period of muscle contraction on one body side is 100 ms), whereas the typical preferred speed of a real tadpole is ≈ 21 mm/s. The difference might be due to the skin cilia activity driving surface mucus caudally over the body which is not included to the model [20].
Fig 8.
VT-model: Motoneuron spiking, muscle contraction, swimming and stopping.
a. CNS model motoneuron spiking times (green dots) and corresponding body positions of VT model tadpole during swimming. Horizontal and vertical axes show motoneuron spike time and RC position. Spike related body shapes from video of VT model viewed from above are in the middle, and the grey strips show correspondence between spiking and VT model swimming (each body shape relates to the middle time point of grey strip). The first frame shows active rostral muscles (red) for the first right flexion. The next two frames show right and left flexions and the last frame corresponds to stopping. Body-water interaction is visualised by the speed of water particle movement (blue-yellow-red corresponds to slow-medium-fast movement). b–d. Video frames from the VT-model with views from above and one side. b. Swimming. Stimulation on the left side at 50 ms is followed by flexion on the right and swimming. Frames are from S1 Video. c. Stopping. Sequence of frames from S1 Video show body movements as the tadpole reaches the end of the tank and swimming stopping: the top frame shows the tadpole head approaching the wall; the next frame corresponds to wall contact and cement gland adhesion; last two frames show the attached head and tail moving by inertia. d. Effect of gravity. Frames from S2 Video show body rotation under influence of gravity during swimming. In the initial (left) frame the tadpole lies at the bottom on its right body side and the left side is stimulated. The next frame shows the first right side flexion and swimming starts. As it continues, the body rotates and the last two frames show tadpole swimming in a dorsal-up position in the middle of the tank.
Fig 9.
A simplified view of the particles and springs structure of the VT body cross-section (corresponding to the dotted line).
Four different types of particles are shown in different colours and the springs are shown by connections between particles. Thickness of connecting lines reflects rigidity of springs.
Fig 10.
Basic properties of the muscle model.
Left frame: contraction velocity vs force (load). Right frame: muscle tension vs initial muscle length, L0 is the resting (relaxed) muscle length.