Abstract
Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na+ and K+ currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism.
Highlights
Neurons, as the basic information-processing unit of the nervous system, can accurately represent and transmit various spatiotemporal patterns of sensory input in the form of sequences of output spikes (Koch, 1999; Dayan and Abbott, 2005; Klausberger and Somogyi, 2008)
When spike threshold is sensitive to dV/dt, the neuron is unable to maintain repetitive spike at low rates and produces a discontinuous f − Iin curve in the cases of no or low noise levels (Figure 1C). This discontinuous f − Iin curve could be switched to continuous by high level of noise. Since noise is another ubiquitous feature of the nervous system with myriad effects on neural coding (Tuckwell, 1989; Gerstner and Kistler, 2002; Tuckwell et al, 2009; Tuckwell and Jost, 2010), we further investigate how noise modulates spike trains of the neuron with different spike threshold dynamics, as shown in Figures 2, 3
Biophysical Basis of the Spike Initiation Associated with Different Threshold Dynamics By varying parameter βn, we have identified the input-output property associated with each spike threshold dynamic
Summary
As the basic information-processing unit of the nervous system, can accurately represent and transmit various spatiotemporal patterns of sensory input in the form of sequences of output spikes (Koch, 1999; Dayan and Abbott, 2005; Klausberger and Somogyi, 2008). The spike threshold is dynamic, and varies with input properties as well as spiking history It is inversely correlated with the preceding rate of membrane depolarization (i.e., dV/dt) prior to spike initiation (Azouz and Gray, 2000, 2003; Henze and Buzsáki, 2001; Ferragamo and Oertel, 2002; Escabí et al, 2005; Wilent and Contreras, 2005; Kuba et al, 2006; Goldberg et al, 2008; Priebe and Ferster, 2008; Cardin et al, 2010; Higgs and Spain, 2011; Platkiewicz and Brette, 2011; Wester and Contreras, 2013; Fontaine et al, 2014). The dynamic threshold could effectively enhance feature selectivity (Azouz and Gray, 2003; Escabí et al, 2005; Wilent and Contreras, 2005; Priebe and Ferster, 2008), contribute to coincidence detection and gain modulation (Azouz and Gray, 2000, 2003; Platkiewicz and Brette, 2011), as well as facilitate precise temporal coding (Kuba et al, 2006; Higgs and Spain, 2011)
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