Changes in action potential shape do not explain the decrease in Na⁺ entry and Na⁺/K⁺ current overlap with increases in temperature.

<p>A. Action potential waveform occurring in the model axon at 18°C. B. Currents obtained from the model when the action potential in (A) was injected into the model, using ionic current kinetics obtained at 18°C. This result is the same as <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002456#pcbi-1002456-g001" target="_blank">Figure 1B</a>, 18°C. C–D. Running the model through the action potential waveform of (A), but with the channel kinetics of 27°C (C) or 37°C (D) results in a large decrease in Na⁺/K⁺ channel overlap (cf. B). E. Action potential waveform occurring in the model axon at 37°C. F. Injecting the action potential waveform in (E) into the model with Na⁺/K⁺ kinetics appropriate for 18°C results in a large inward Na⁺ current during the falling phase of the action potential, which overlaps extensively with the outward K⁺ current. G–H. Increasing the kinetics to those appropriate for 27°C (G) and 37°C (H) results in a large decrease in the overlap of Na⁺/K⁺ currents and the near disappearance of the Na⁺ current occurring during the falling phase of the spike (H). Dashed lines are aligned to the peak of the injected spike. See also supplemental <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002456#pcbi.1002456.s001" target="_blank">figure S1</a>.</p

Contribution of changes in Na⁺ and K⁺ channel time constants on the effects of temperature on spike efficiency and duration.

<p>A. The maximum of Na⁺ inactivation time constant τ_h decreases as temperature increases for the normal model (control; black). For the test group, the maximum of Na⁺ inactivation time constant τ_h is invariant with temperature change (red). B. The Na⁺ entry ratio decreases as a function of temperature for control (black), while the Na⁺ entry ratio increases as a function of temperature when the inactivation time constant of I_Na (τ_h) is fixed. Keeping I_Na activation time constant (τ_m) invariant or I_K activation time constant (τ_n) invariant with temperature reveals effects of temperature on Na⁺ excess entry similar to that in control. C. The half-height spike duration decreases as a function of temperature for the control group (black), while it becomes relatively independent to temperature change when I_Na inactivation time constant, τ_h, is invariant. The test group with invariant τ_m, or τ_n, has similar behavior as that in control group. D. Example membrane potential and I_Na, I_K for 11, 23, and 37°C when the time constant of I_Na inactivation (τ_h) is kept constant. Note that the overlap of Na⁺ and K⁺ currents becomes larger with temperature, which is opposite to the normal situation (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002456#pcbi-1002456-g001" target="_blank">Figure 1B</a>).</p

Increasing temperature decreases oxygen concentration and decreasing oxygen content decreases neuronal excitability.

<p>A. Oxygen levels (mm Hg), as measured at the upper surface of the slice, at different temperatures. Increasing temperature can dramatically decrease oxygen levels. B. Response of layer 2/3 pyramidal cells (n = 5) to the intracellular injection of a depolarizing current pulse (200 pA, 500 ms) at different temperatures (same experiments as in A). C. Plot of response of individual cells to the current pulse at different temperatures. D–F. Decreasing oxygen levels (mm Hg) at a constant temperature of 30°C does not have a significant effect on the duration of action potentials (D), but does decrease average firing rate (E), as seen in individual recordings (F; n = 8 cells).</p

The kinetics of Na⁺ and K⁺ channels are heavily dependent on temperature change in the model neuron.

<p>A–C. The maximal value of Na⁺ activation time constant τ_m (A) and Na⁺ inactivation time constant τ_h (B), and K⁺ activation time constant τ_n (C) as a function of temperature. Inset: Time constants of the variables as a function of membrane potential for temperature T = 18°C, 36°C and 42°C, respectively. D–F. Phase plots of membrane potential V vs. Na⁺ activation variable m (D), Na⁺ inactivation variable h (E) and K⁺ activation variable n (F) for temperature T = 18°C, and 36°C, respectively. Note that at 36°C, the peak inactivation of the Na⁺ current is considerably more complete (e.g. attains a lower value) (E) and the K⁺ activation during the rising phase of the action potential is significantly less (F) than at 18°C.</p

Increases in temperature increase the intrinsic excitability and change spike shape in pyramidal neurons as predicted by the HH model.

<p>A. Increasing temperature from 21°C to 36°C and 41°C results in shorter duration action potentials that are also decreased in amplitude in layer 5 pyramidal cells in vitro. Spikes were initiated with the intrasomatic injection of a depolarizing current pulse (100 pA, 500 msec duration). B. The spike duration, measure at half peak amplitude, decreases gradually as a function of temperature for pyramidal neurons (n = 6; black). The action potentials of the simulated neuron results show a similar property (red). C. Action potential amplitude decreases with increases in temperature for both pyramidal neurons in vitro (black) and for the model neuron (red). D. For a fixed current pulse amplitude, the average firing rate of pyramidal cells in vitro (n = 6) increases gradually as a function of temperature. Notice that for temperatures >36°C, the firing rate increases more rapidly. The model neuron (red) also exhibits a non-linear increase in firing rate to a current pulse with increases in temperature. Differences between the real neuron and model results presumably arise from the complex morphology and properties of ionic channels not included in the simple HH model. E. Same data set as B, the average value of dv/dt ratio (minimum dV/dt divided by maximum dV/dt during the spike) increases gradually as a function of temperature for the recorded pyramidal cells in vitro (n = 6) (black). The model neuron exhibits a similar relationship (red).</p

The ratio of absolute minimal dV/dt to maximal dV/dt is affected by the overlap level of Na⁺ and K⁺ currents.

<p>A. For a given action potential at 18°C, the Na⁺ and K⁺ currents have a large overlap, resulting in a cancelled effect in the total membrane charge current C*dV/dt and the ratio of absolute minimal dV/dt to maximal dV/dt ratio is small, approximately 0.06. For a given action potential at 37°C, the Na⁺ and K⁺ currents exhibit significantly less overlap, leading to a relatively large minimal dV/dt peak (similar in amplitude-time course as I_K), while the maximal dV/dt peak resembles the amplitude-time course of I_Na. The absolute minimal dV/dt to maximal dV/dt is increased to 0.14. B. The ratio γ (defined as the ratio of absolute minimal dV/dt to maximal dV/dt) increases as a function of temperature for both classical HH neuron and cortical neuronal models, owing largely to the decrease in overlap of Na⁺ and K⁺ currents with increases in temperature. C. The excess Na⁺ entry ratio decreases as a function of γ for both HH and cortical neuronal models.</p

Increases in temperature result in a decrease in AHP duration.

<p>A. The action potential demonstrates a large and prolonged afterhyperpolarization (AHP) for low temperature (e.g., T = 18°C), and a smaller and shorter duration AHP for higher temperatures (e.g., T = 36, and 42°C, respectively). B. During an action potential, the ratio of potassium current I_K over I_Na as a function of time shows that there is a large amount of I_K available after the peak of action potential for low temperature (e.g., T = 18°C) in comparison with that at high temperatures (e.g., T = 36, and 42°C, respectively). C. Plot of the amplitude of I_K during action potential generation at different temperatures reveals that increasing temperature results in a marked reduction in the amplitude of I_K, especially 20–60 msec after the spike, but also during the repolarizing phase of the action potential. D. Action potential AHP duration decreases slowly with increases in temperature for temperatures below approximately 37°C, while decreases rapidly for temperatures greater than approximately 37°C. Keeping the time constant of I_K activation (τ_n) invariant abolishes this effect, while keeping the time constants of I_Na activation (τ_m) or inactivation (τ_h) invariant does not, although they do alter the magnitude and temperature range of the effect.</p

The energy efficiency of action potential generation increases as temperature increases.

<p>A. Na⁺ entry ratio (defined as a ratio of the total actual sodium entry to the minimal amount needed to generate an action potential, i.e., ∫I_Na(t)dt/(C_mΔV), where I_Na(t) is the sodium current, C_m is membrane capacitance, ΔV is the change in voltage during the action potential) as a function of temperature. For both the HH simulation of the squid giant axon (DC injection 20×10⁻² pA/µm²), and for a model of cortical pyramidal cell axons (DC injection 0.5×10⁻² pA/µm²), increasing temperature strongly decreases the excess Na⁺ entry during action potential generation. At 18°C, this entry ratio is approximately 4 (dashed line), while at 37°C, this excess entry reaches 1.89 (HH, extrapolated) and 1.41 (cortical axon), which is close to the theoretical minimum. B. Top panel: the action potential of the cortical model neuron generated at 18, 27 and 37°C, respectively; Bottom panel: the corresponding Na⁺ and K⁺ currents during action potential generation for temperature at 18, 27 and 37°C, respectively. Note that there is substantial overlap of Na⁺ and K⁺ currents during action potential generation for 18°C, reduced overlap at 27°C and much less overlap at 37°C. The largely non-overlapping nature of the ionic currents at high temperature results in considerably lower excess Na⁺ entry ratio. Dashed lines indicate the peak of each action potential for reference. C. Top panel: the action potential of classical HH model neuron generated at 6, 18, and 27°C, respectively; Bottom panel: the corresponding Na⁺ and K⁺ currents during action potential generation for temperature at 6, 18, and 27°C, respectively. Notice that the overlap of Na⁺ and K⁺ currents during action potential generation is also reduced when temperature increases. D. The half-height spike duration decreases as a function of temperature increase for both classical HH neuronal model (black) and cortical neuronal model (green). Inset: The correlation between excess Na⁺ entry ratio and spike duration for both models. The large spike duration corresponds to a large Na⁺ entry ratio, indicating reduced energy efficiency.</p

Effect of temperature on firing rate and total energy usage for the cortical model neuron in response to different intensities of DC input.

<p>A. The firing rate of the model neuron increases as a function of temperature for DC = 0.5, 1, 1.5 and 2×10⁻² pA/µm² (500 ms duration) respectively. B. The total sodium charge entering during one action potential decreases exponentially as a function of temperature for DC = 0.5, 1, 1.5 and 2×10⁻² pA/µm², respectively. C. For the conditions in the above four DC inputs, the total sodium charge (sodium charge per spike times the firing rate) for a given DC signal as a function of temperature. Note that the total Na⁺ entry reaches a minimum at a temperature of between 37–42°C. D. The firing rate increases as a function of temperature for the normal situation (black), and when τ_m (green), τ_h (red) and τ_n(blue) are kept invariant. Notice that the I_K activation time constant τ_n is the key factor controlling the firing rate change as a function of temperature. E. For the above four situations, the total Na⁺ charge per single spike as a function of temperature. Notice that I_Na inactivation time constant τ_h is the key factor controlling the total Na⁺ charge per spike as a function of temperature. F. For the above four situations, the total Na⁺ charge per DC input (nC/cm²) as a function of temperature. Note that the total Na⁺ entry does not go through a global minimum for both test groups with temperature-independent τ_h and τ_n.</p

Increasing temperature increases neuronal responsiveness in layer 2/3 entorhinal cortical pyramidal cells.

<p>Intracellular recordings from a layer 2/3 pyramidal neuron to a DC input (150 pA, 500 ms duration) at a temperature of 24, 36, and 42°C respectively (A–C). Note that the neuron not only increases its firing rate, but also decrease its spike duration, to the current pulse with an increase in temperature. The dV/dt of action potentials shows a gradual increase of the peak rate of rise and fall with increases in temperature. D–G. Bar graphs illustrating that increasing temperature results in a depolarization of the membrane potential (cyan bars), an increase in spike rate, a decrease in single spike duration, an increase in the ratio of the absolute minimal dV/dt to maximal dV/dt, respectively. Similar effects were obtained when the depolarization of the membrane potential that was particularly prominent at 42°C was kept relatively negated by adjusting the holding current (orange bars). As a comparison, the cortical model results for a DC input (1×10⁻² pA/µm², 500 ms duration) are represented by the red line.</p