Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input

Abstract

Neurons rely on action potentials, or spikes, to encode information. But spikes can encode different stimulus features in different neurons. We show here through simulations and experiments how neurons encode the integral or derivative of their input based on the distinct tuning properties conferred upon them by subthreshold currents. Slow-activating subthreshold inward (depolarizing) current mediates positive feedback control of subthreshold voltage, sustaining depolarization and allowing the neuron to spike on the basis of its integrated stimulus waveform. Slow-activating subthreshold outward (hyperpolarizing) current mediates negative feedback control of subthreshold voltage, truncating depolarization and forcing the neuron to spike on the basis of its differentiated stimulus waveform. Depending on its direction, slow-activating subthreshold current cooperates or competes with fast-activating inward current during spike initiation. This explanation predicts that sensitivity to the rate of change of stimulus intensity differs qualitatively between integrators and differentiators. This was confirmed experimentally in spinal sensory neurons that naturally behave as specialized integrators or differentiators. Predicted sensitivity to different stimulus features was confirmed by covariance analysis. Integration and differentiation, which are themselves inverse operations, are thus shown to be implemented by the slow feedback mediated by oppositely directed subthreshold currents expressed in different neurons.

Combined Changes in Chloride Regulation and Neuronal Excitability Enable Primary Afferent Depolarization to Elicit Spiking without Compromising its Inhibitory Effects

“…Among transient spiking cells, the slow waveform required higher ḡ GABA than the fast waveform to elicit transient spiking (0.46 ± 0.09 nS/pF vs 0.27 ± 0.09 nS/pF) which, although not a statistically significant difference ( p = 0.25; paired t -test), is consistent with a spike initiation mechanism sensitive to the rate of depolarization. By comparison, the two repetitive spiking cells required exactly the same minimum ḡ GABA for the fast and slow waveforms, consistent with a spike initiation mechanism sensitive only to the amplitude of depolarization [40]. Comparing the responses to g GABA steps and ramps illustrates that the latter are far less effective in eliciting transient spiking ( Fig 2E ).…”

“…By comparison, an isolated change in β w could not enable PAD-induced spiking. As illustrated in panel c of Fig 1B, slow-onset GABA A R input required stronger input to elicit spiking because transient spiking involves a spike initiation mechanism that is sensitive to the rate of depolarization [40]. …”

“…Even if sustained, PAD is likely to produce only one spike at its onset (if it produces any spikes at all) and will likely not produce any spikes unless its onset is abrupt. This is because transient spiking involves a spike initiation mechanism that is sensitive to the rate of depolarization [40]. Sensitivity to g GABA onset kinetics would be inconsequential if presynaptic inhibition was phasic, which is to say that the GABA A Rs are clustered within the synaptic cleft and therefore receive an abrupt pulse of GABA upon its vesicular release [62], but evidence points toward a more tonic mode of action (unlike the phasic inhibition studied in the crayfish neuromuscular junction [63]) as outlined below.…”

Convergence, Divergence, and Reconvergence in a Feedforward Network Improves Neural Speed and Accuracy

“…Conversely, a differentiator is a neuron whose firing rate depends mainly on the variance of the input current. There is a continuous spectrum of behaviors from differentiation to integration (Ratte et al, 2013; Ratte et al, 2015). Our results extend this literature by showing how the intrinsic properties of a neuron—whether integrator or differentiator—may be usefully matched to population spiking statistics of its inputs.…”

Ion channel degeneracy enables robust and tunable neuronal firing rates

“…Previous work relies on planar reductions of conductance-based models to analyze dynamics in a phase plane (4,5,8,24,25,28,(38)(39)(40)(41). Our approach here is quite different and, we hope, more intuitive to physiologists who think about neuronal dynamics in terms of contributions of voltagedependent ionic currents at different timescales.…”