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What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpolehindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.
Fig 1. The hatchling tadpoleCNS with a population of electrically-coupled dIN neurons.(A) Top view diagram of tadpole showing skin (blue), swimming muscles (pink), and CNS with hindbrain and spinal cord. The CNS region able to generate swimming rhythm when isolated (grey) contains a population of ∼30 dINs (brown) on each side. (B) On each side of the nervous system, the electrically-coupled population of ~30 dINs in the isolated region make excitatory feedback NMDAR synapses onto each other.
Fig 2. A simple generative model of spike times for a single tIN.(A) The probability distribution of a single tIN firing different numbers of spikes at levels of head-skin stimulation. (B) The times of the spikes measured experimentally are shown as coloured crosses and the means and standard deviations (μk and Ïk) used to generate the spike times of a model tIN. Means are shown as coloured circles, standard deviations are shown as horizontal error bars.
Fig 3. Perfusing NMDA onto the dIN population model.(A) The population of electrically-coupled dINs, onto which NMDA was perfused. (B) In life, perfusion of NMDA onto a dIN causes depolarisation and repetitive firing (black traces from Fig 2 in Li et al., 2010 [19]) where hatched bar denotes NMDA perfusion. Red box shows region expanded below. (C) Similar firing is seen in a model dIN (blue trace) where green line shows the NMDA activation reaching a maximum conductance of 1 nS. (D) Current-voltage curve of a single model dIN NMDA synapse, with (yellow) and without (pink) voltage dependence. (E) The steady state membrane potentials of dINs as a function of NMDAR conductance (with sodium channel conductance set to zero to prevent firing) with and without voltage dependency of the NMDAR as in D. (F—H) The response of the network of 30 dINs to NMDA perfusion with (F) and without (G) voltage dependency. Top: somatic membrane voltages (all dINs overlapped), middle: somatic membrane voltage of dIN number 15, bottom: conductance of NMDAR synaptic channels. (H) Plots of dIN firing frequency vs NMDAR conductance with (yellow) and without (pink) voltage dependence. Grey bar shows synaptic strength used in plots F and G (7.5nS). Blue bar shows estimated total synaptic conductance to a neuron during swimming, based on voltage clamp recordings (0.6–1.5nS). Green area shows the range of swimming frequencies observed in the tadpole.
Fig 4. Summed conductance of feedback NMDAR synapses as a function of frequency.(A) Spike trains of different frequencies were delivered to a model NMDAR synapse with a closing time of 80 ms, and the maximum conductance recorded experimentally. (B) Faster spike trains produced a larger maximum conductance. At the frequencies of tadpole swimming, the conductances did not rise above ~3 times the conductance of a single NMDAR synaptic event (yellow trace).
Fig 5. The response of a dIN network with feedback glutamate excitation to brief sensory excitation.(A) The network of 30 electrically-coupled dINs excited by sensory pathway tINs and with feedback glutamatergic synapses. (B) The conductance time-courses of the feedback dIN excitation with faster AMPAR (magenta) and slower NMDAR (green) components. (C) The resulting combined dIN to dIN EPSP. (D—F) Response to sensory input from tINs at 100 ms. (D) The conductance of sensory synapses onto one dIN (magenta: AMPAR, green: NMDAR) and summed NMDAR conductance from dIN feedback (blue). (E) After firing once to sensory input from the tINs, the dIN network shows rhythmic activity within the tadpole frequency range driven by feedback NMDAR excitation (0.11nS/synapse). (F) A single dIN voltage trace from E. (G) The effect of dIN to dIN NMDA feedback conductance on dIN firing frequency (conductance values are for a single dIN to dIN synapse). Rhythmic firing at physiologically observed frequencies is observed (green area). At low levels of synaptic strength, swimming is not reliable (red area, I). (H) At higher levels of feedback synaptic strength (0.15 nS/synapse) firing is outside normal tadpole range. (I) At lower feedback strengths (0.07nS/synapse) rhythmic firing cannot self-sustain and activity ceases after a few cycles.
Fig 6. Switching off the swimming network using synaptic inhibition.(A) The dIN network with MHRs to inhibit all dINs synchronously. (B) The model GABA-A IPSP in a dIN (light grey, offset by 10 mV) matches the time-course of recorded MHR IPSP in a spinal neuron (black; Perrins et al. (2002) [29]). (C) Sensory activated rhythm generation in the dIN network (lower voltages traces), is turned off at 700 ms by five IPSPs from the MHR pathway (red conductance trace) in each dIN. (D, E). A single inhibitory synaptic event delivered to all the dINs simultaneously could delay (D) or terminate firing (E). Lower red traces show the inhibitory conductances onto a single dIN. (F) Stopping became more reliable as inhibition was made longer.
Fig 7. Generalising the feedback excitation activity generation mechanism.(A) The network with HH neurons replacing dINs (on/off; 100 ms/300 ms, 600 ms/1400 ms). (B) The effect of synaptic feedback strength on neuron firing (green shows regions of unstable firing). (CâF) Network activity can be switched on and off by brief synaptic input. (C) Shows the excitatory (green: NMDA, magenta: AMPA) and inhibitory (red) input to the network. (D) Voltage trace of activity in one neuron. (EâF) Shows a raster plot of action potential times for every 5th neuron in the network. (GâH) Raster plots of 10 neurons in a network with excitation at 100ms and without inhibition. (G) When feedback conductance was too low (gpeak = 0.15 nS); the network was unable to sustain rhythm. (left, green region of B). (G) When NMDA feedback strength was too high (gpeak = 2 nS), firing became unreliable.
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