Figure 5.

Matched Na⁺ and K⁺ Channel Gating Maximizes Energy Efficiency in PV⁺-BC Axons

(A and B) Computational analysis of AP half-duration (A) and Na⁺ entry ratio (B) in a single-compartment model as a function of scaling factors for Na⁺ channel inactivation rates (ordinate) and maximal K⁺ conductance (abscissa). Scaling factors of 1 correspond to the experimentally determined default values. Short APs can be generated with a wide range of Na⁺ entry ratios. For model parameters, see Tables S5 and S6.

(C and D) Analysis of Na⁺ entry ratio (ER) with altered K⁺ channel gating. K⁺ channel activation curves were shifted by 20 mV in the hyperpolarizing (C, top) or depolarizing (C, bottom) direction, and delayed rectifier properties were altered by reducing (from 4 to 2; D, top) or increasing (from 4 to 8; D, bottom) the exponent of K⁺ channel activation. Note that both shift of the K⁺ channel activation curve in the hyperpolarizing direction and reduction of the exponent of K⁺ channel activation increased the Na⁺ entry ratio, i.e., decreased the energy efficiency. Numbers near contour lines indicate half-duration values in ms (A) or Na⁺ entry ratio values (B–D).

(E) Analysis of AP energetics in a detailed cable model of a dentate gyrus basket cell (BC2 from Nörenberg et al., 2010). Color code indicates Na⁺ entry ratio; scale bar shown as inset. For model parameters, see Table S7. Note that the entry ratio is lower in the axon than in the dendrites, whereas the subcellular distribution of the total Na⁺ charge is opposite, suggesting that subcellular structures with high Na⁺ load show better optimized entry ratio. Ax, axon; Ap, apical dendrite; Ba, basal dendrite; So, soma.

(F) Box chart of entry ratio (top) and total Na⁺ entry (bottom) in different subcellular compartments. Box charts indicate median and distribution of data points.

(G) Single-cell energy budget of PV⁺-BCs (number of ATP per AP).

Whiskers in box charts indicate the 5^th and 95^th percentile of data points, and the box itself indicates median, first quartile, and third quartile of the data points.