Figure 4.

The energy cost of the propagation of action potentials in the dopamine neuron models. (A) Estimates of the energy cost of the propagation of action potentials throughout axonal arborizations of neurons with 1–14 levels of branching expressed as number of ATP molecules consumed. ATP molecules are consumed as a consequence of the movement of sodium ions (i.e., sodium current; red plot) and calcium ions (i.e., calcium current; blue plot). ATP demand increases exponentially with increasing levels of axonal branching for both ions (R²: Na⁺ = 0.9986; Ca⁺⁺ = 0.9999). (B) A log-log plot of the number of ATP molecules consumed by the sodium current during action potential propagation against the number of branch points and the surface area of neurons with increasing levels of branching. The linear relationship of the parameters indicates that the increase in the number of ATP molecules consumed is a power law function of the number of branch points (multiple R²: Na⁺ = 0.9997, degrees of freedom = 10, p-value <2.2e–16) and the surface area (multiple R²: Na⁺ = 0.9965, degrees of freedom = 10, p-value <5.3e–16) beyond the segment connecting axon initial segment with the striatum. The discontinuity is the point at which synaptic stimulation (arrows) was required for propagation of the action potential. (C) Similar plot to that in (B) but for the calcium current. This plot shows that the increase in the number of ATP molecules consumed as a consequence of the calcium current also follows a power law relative to the two variables (except in the case of 60% Ca⁺⁺; see Table 2). Reducing calcium conductance by 20% and 40% leads to the number of ATP molecules reducing by 10.5% and 26%, respectively (average values). The continuous lines in each plot are the regression fits for the data. (D) To examine how ATP is related to the reduction of the axonal network as occurs after blocking calcium channels, we plot the log of number of ATP molecules against the log of the product of number of branches and degree of calcium blockade. This reveals that the number of ATP molecules consumed is dependent on calcium and the size of the axon Blocking the calcium channels by 20% and 40% not only reduced the number of ATP molecules required for the propagation of an action potential (C). The number of ATP molecules required in 60% calcium conditions for neurons with less than 8191 branch points (black arrows) was the same as for neurons one level of branching less (i.e., 4095 branch points; red arrows) in normal calcium (inset).