Metabolic cost as a unifying principle governing neuronal biophysics - PubMed (original) (raw)
Metabolic cost as a unifying principle governing neuronal biophysics
Andrea Hasenstaub et al. Proc Natl Acad Sci U S A. 2010.
Abstract
The brain contains an astonishing diversity of neurons, each expressing only one set of ion channels out of the billions of potential channel combinations. Simple organizing principles are required for us to make sense of this abundance of possibilities and wealth of related data. We suggest that energy minimization subject to functional constraints may be one such unifying principle. We compared the energy needed to produce action potentials singly and in trains for a wide range of channel densities and kinetic parameters and examined which combinations of parameters maximized spiking function while minimizing energetic cost. We confirmed these results for sodium channels using a dynamic current clamp in neocortical fast spiking interneurons. We find further evidence supporting this hypothesis in a wide range of other neurons from several species and conclude that the ion channels in these neurons minimize energy expenditure in their normal range of spiking.
Conflict of interest statement
The authors declare no conflict of interest.
Figures
Fig. 1.
(A) At rest, both sodium channels (light red) and K+ channels (light blue) are closed, Na+ ions (red ovals) are concentrated extracellularly, and K+ ions (blue diamonds) are concentrated intracellularly. (B) Depolarization causes Na+ channels to open, permitting Na+ ions to flow down their concentration gradients into the cell. This influx of positive charge depolarizes the neuron. (C) This depolarization causes K+ channels to open, letting K+ leave the cell, hyperpolarizing the membrane potential; at the same time, depolarization causes Na+ channel inactivation gates (dark red ball and chain) to close, limiting Na+ influx. Eventually the hyperpolarization is sufficient to close and deinactivate the Na+ channels and close the K+ channels, restoring the channel states to baseline. (D) The Na+ influx and K+ efflux are reversed by the Na+,K+ ATPase.
Fig. 2.
(A and E) Voltage waveforms. (B and F) Gate states. Light red, “m” (Na+ channel activation) gate; dark red, “h” (Na+ channel inactivation) gate; blue, “n” (K+ channel activation) gate. 1 = fully open, 0 = fully closed or inactivated. (C and G) Na+ (red) and K+ (blue) conductances. (D and H) (Upper) Na+ (red) and K+ (blue) currents; (Lower) cumulative Na+ current influx. (Right) The traces from the broad action potential in A_–_D are overlaid on the corresponding traces from a narrower action potential, generated by tripling the rate of K+ channel activation/deactivation.
Fig. 3.
(A_–_C) (Top) Time constants as a function of membrane potential. Gate kinetics were systematically speeded or slowed by multiplying the time constants at all voltages by the same constant speed factor. (Middle) Maximum spike rate as a function of speed factor. (Bottom) Cost (in ATP) for a single action potential (solid line) or for an action potential in a 50-Hz train (dashed line) as a function of speed factor. (D) Maximum number of spikes per 107 ATP (z axis) as a function of n-gate speed factor (x axis) and h-gate speed factor (y axis and surface color). (E) Na+ channel inactivation speed factor that maximizes the spikes/cost, for spikes generated as efficiently as possible (black) and for spikes generated in 25-, 50-, and 75-Hz trains (red, green, blue).
Fig. 4.
The default membrane Na+ and K+ channel densities (A) can be changed by adding or removing K+ channels (B Top), or by adding or removing Na+ channels (C Top). (B and C) (Middle) Maximum spike rate as a function of channel density. (B and C) (Bottom) Cost (in ATP) for a single action potential (solid line), or for an action potential in a 50-Hz train (dashed line), as a function of speed factor.
Fig. 5.
(A) Dynamic clamp schematic: A computer (left), simulating a voltage-gated sodium conductance is reciprocally connected to a neuron (right). The cell's voltage determines the driving force on the simulated conductance and thus the current command sent to the amplifier; at each time step, the dynamic clamp computer uses the cell's voltage to update the state of its sodium conductance model. (B) Intracellular recording of a fast-spiking interneuron showing its ability to generate fast, nonadapting trains of action potentials. TTX application (Middle) blocks action potential generation. Dynamic clamp restoration of sodium conductance (Right; command current in red) permits the neuron to generate fast, nonadapting trains of action potential-like waveforms. (C) Maximum spike rate (Upper) and spike cost (Lower) as a function of Na+ channel activation rate (i), inactivation rate (ii), and channel density (iii). Black traces, average of normalized values for all cells; gray traces, normalized values for each cell.
Fig. 6.
(A) Action potential rate (Left) and shape (Right) in a thin-spiking interneuron (black) and a regular-spiking neuron (gray) during up and down states in vivo. (B, i) Percentage of pyramidal neurons and PV+ interneurons identified as KCNC1-positive through single-cell PCR. (B, ii) Microarray measurements of KCNC1 RNA levels in pyramidal neurons and PV+ interneurons. (C) Maximum action potential upstroke velocity in regular spiking (RS) and fast spiking (FS) cortical neurons. (D, i) electric organ discharge (EOD) frequency in the electric organ of n = 28 different fish, vs. K+ current activation time constant in EOD cells of the same fish (measured at 25 mV above threshold). (D, ii) Na+ current inactivation time constant vs. K+ activation time constant in n = 17 fish. (A) Adapted from ref. . (B, i) Adapted from ref. . (B, ii) Adapted from ref. . (C) Adapted from ref. . (D) [Reproduced with permission from McAnnelly and Zakon (39) (Copyright 2000, Society for Neuroscience).]
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