Sensitivity analysis of the backpropagation threshold to the right-shift of Na_V1.2 gating properties.

Along each curve, the gating properties named in the legend have their right-shift changed from V_RS to (V_RS + ΔV_RS), and all the others are left unchanged (full definition and notation in Section F.2 in S1 Text). When ΔV_RS = 0, the right-shift is the reference value (or ‘nominal value’) of used for Na_V1.2 in our simulations—see Section F.2 in S1 Text, V_RS indicated by small “→” in Fig P in S1 Text—around which we are performing this sensitivity analysis. The reference curve (legended ) shows the net effect of right-shifting all Na_V1.2 properties on I_BP, via its slope. (It may be useful to imagine points on the reference curve as being pulled toward all the other curves that only change one property. The reference curve would then be the result of the combined pulls of those curves.) For each mode of stimulation, we identify the key gating properties through which right-shift controls backpropagation, by comparing the single property curves (, , etc.) to the reference curve (). (A) Somatic stimulation: The reference curve has a positive slope (right-shift raises I_BP), and it follows curves legended with near the nominal point (i.e. near ΔV_RS = 0). Hence, I_BP is governed by Na_V steady-state activation and is insensitive to the right-shift of all Na_V time constants. (B) Axonal stimulation: The reference curve has a negative slope (right-shift lowers I_BP, i.e. promotes backpropagation), and it follows curves legended with or . I_BP is then governed by proximal Na_V availability, owing to the right-shift of Na_V1.2. Notably, with axonal stimulation, I_BP is also sensitive to the right-shift of , the—voltage-sensitive—availability time constant. Results are summarized in Table 1. The lines have been drawn to guide the eye. In both plots, x = 1.0. On the left κ = 0.7(to increase the slope, see Fig 2), and on the right, κ = 0.5.