REVIEWS
NEUROENERGETICS AND THE KINETIC DESIGN OF EXCITATORY SYNAPSES David Attwell* and Alasdair Gibb‡ Abstract | Why is the characteristic timescale of neural information processing in the millisecond range, corresponding to a ‘clock speed’ of about 1 kHz, whereas the clock speed of modern computers is about 3 GHz? Here we investigate how the brain’s energy supply limits the maximum rate at which the brain can compute, and how the molecular components of excitatory synapses have evolved properties that are matched to the information processing they perform.
MEMBRANE TIME CONSTANT
The product of the capacitance and resistance of the cell membrane, which sets the timescale over which membrane currents change the voltage. A small time constant means that the membrane potential can change rapidly. MEMBRANE RESISTANCE
The ratio of the voltage change produced across the cell membrane to the size of current injected into the cell: the resistance is set by the number and conductance of the ion channels in the cell membrane. MEMBRANE CAPACITANCE
The cell membrane separates and stores electrical charge, thereby producing an electrical capacitance, which increases in proportion to membrane area.
Departments of *Physiology and ‡Pharmacology, University College London, Gower Street, London WC1E 6BT, UK. Correspondence to D.A. e-mail:
[email protected] doi:10.1038/nrn1784
For any computational device, the processing power is limited by the energy supply available1. The availability of metabolic energy has been suggested to limit the size of the brain2, and much of the brain’s energy use goes on reversing the ion fluxes that generate action potentials and synaptic currents3. This implies that there will be evolutionary pressure for metabolically efficient wiring patterns4,5 (in which action potentials do not have to travel so far) and neural codes6–8 (to limit the number of active synapses and neurons). A limited energy supply is also likely to limit the speed of information processing by individual neurons. Here we investigate the consequences of this constraint for the molecular components of glutamatergic signalling (FIG. 1). We show that the maximum information processing rate of the brain is limited to a millisecond timescale by the brain’s energy supply. This constraint determines the maximum useful speed of operation of AMPA (αamino-3-hydroxy-5-methyl-4-isoxazole propionic acid) receptors and their low affinity for glutamate, as well as the size of synapses and the rate of glutamate uptake. By contrast, the high affinity of NMDA (N-methyl-d-aspartate) receptors, and the ionic stoichiometry of glutamate transporters, are determined by the evolution of NMDA receptors to mediate coincidence detection. Energy supply limits computational speed
Rapid processing of information by the brain requires both the rapid processing of subthreshold synaptic
NATURE REVIEWS | NEUROSCIENCE
potentials in dendrites and the propagation of information by action potentials at high frequencies. Increasing the temporal rate of either of these operations carries a heavy metabolic price, which we explain below. The timescale of processing of subthreshold signals is limited, in part, by the MEMBRANE TIME CONSTANT, τm, which is the product of the cell MEMBRANE RESISTANCE, Rm, and MEMBRANE CAPACITANCE, Cm, and is ~1–20 ms. For a VOLTAGEUNIFORM CELL, the capacitance filters out synaptic current signal components above a frequency of 1/(2πτm), ~8–160 Hz, whereas for synaptic currents in neuronal dendrites the frequency of filtering is somewhat higher9 than 1/(2πτm). An upper frequency of ~200 Hz is matched fairly well to the maximum action potential firing rate of neurons in vivo, which is ~100–300 Hz (although the mean firing rate is much lower, ~4 Hz in rodents3). Therefore, the timescale of both (passive) dendritic and action potential information processing is in the millisecond range. To raise to higher frequencies the temporal range over which synaptic currents can convey information, it is necessary to decrease τm, and, therefore, to decrease either Cm or Rm. It might not be feasible to reduce Cm in all neurons BOX 1, but Rm could be decreased by inserting more ion channels into the membrane. This strategy is used, for example, to speed the photoreceptor responses of flies10. However, the resulting higher conductance and higher resting flux of Na+ and K+ across the membrane will increase the energy
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REVIEWS
Glutamate
NMDA receptor
mGluR
AMPA receptor
Kainate receptor
Glutamate transporter
Presynaptic neuron
3Na+
H+
Na+ Ca2+
Na+
Postsynaptic neuron
K+
Na+ Glial cell
Figure 1 | Schematic diagram of a glutamatergic synapse. Glutamate released from the presynaptic terminal acts on postsynaptic AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid), NMDA (N-methyl-D-aspartate), kainate and metabotropic (mGluR) receptors. The synaptic actions of glutamate are terminated when its concentration in the synaptic cleft is reduced by diffusion, and by uptake by glutamate transporters into surrounding glial cells and into the pre- and postsynaptic neurons.
tenfold increase in energy expended on the neuronal resting potential would consume all the energy available for signalling; consequently there would be no energy left to power action potentials and synaptic currents, and the overall information processing rate of the brain would fall dramatically. Conversely, if the action potential rate were increased to increase the temporal resolution of information transmission by action potentials, only a 15% increase in the average firing rate (100%/87%, as 87% of the energy use is proportional to action potential frequency) would use all the energy available for signalling, so that no energy would be left to maintain the resting potential. We conclude that it is not possible to increase tenfold the energy expended on the resting potential, or on action potentials, to increase tenfold the upper frequency limit for information processing with synaptic or action potentials. Diversion of energy to increase the information processing rate for synaptic potentials in dendrites would decrease the rate for action potentials in axons, and vice versa. Therefore, the energy available to the brain for signalling limits its timescale of operation to the millisecond range. Possible approaches for circumventing this limitation are considered in BOX 1. AMPA receptor affinity
VOLTAGEUNIFORM CELL
A spatially compact cell with no voltage gradients along its cytoplasm, so that the voltage across the cell membrane is the same everywhere (by contrast, cells with long dendrites are often not voltage-uniform). CELL RESTING POTENTIAL
The membrane potential at which there is no net flow of current across the cell membrane. NERNST POTENTIAL
The potential at which there is no net movement of an ionic species across the cell membrane, because the free energy decrease resulting from the ion moving down its concentration gradient is balanced by the free energy increase needed to move the ionic charge through the membrane’s electric field. DISSOCIATION CONSTANT
The ratio of the unbinding rate constant (koff ) to the binding rate constant (kon) when transmitter binds to a receptor.
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expended on maintaining the CELL RESTING POTENTIAL, which is given in terms of the rate of ATP consumption by3: (VNa–Vrp)(Vrp–VK)/{FRm(Vrp+2VNa–3VK)} where VNa and VK are the NERNST POTENTIALS for Na+ and K+, Vrp is the resting potential and F is the Faraday constant. From this equation, if we decrease τm by decreasing Rm tenfold (maintaining the ratio of the Na+ and K+ conductances to keep Vrp constant) in order to allow a tenfold increase in the frequencies of synaptic current being processed, this will increase tenfold the energy expended on the neuronal resting potential. It will also increase the ion flux (and associated energy expenditure on ion pumping) needed to depolarize the cell during synaptic and action potentials. To assess whether this is possible, we need to consider the energy resources available to the brain. Calculations for rodent grey matter indicate that ~75% of the brain’s total measured energy usage (75% of 40 micromoles ATP per g per min) is expended on signalling-related processes3, whereas the remaining 25% is required for basal ‘housekeeping’ tasks and will not be considered further here. Of the energy available for signalling, 10% is estimated to sustain the resting potential of neurons, 3% sustains the resting potential of glia, and the remaining 87% scales approximately with the average action potential firing rate because it powers action potentials and the resulting pre- and postsynaptic ion fluxes and transmitter recycling (FIG. 2; for an extension of this analysis to the primate cortex, see REF. 11). This distribution of energy use allows information processing and transmission to occur in milliseconds in both dendrites and axons. However, if the neuronal Rm were decreased tenfold, the resulting
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If brain information processing can occur on a millisecond timescale, then the receptors that mediate rapid information transfer between neurons should have kinetics matched to this timescale: that is, activation by glutamate, and deactivation once glutamate is removed, should both occur in milliseconds. If the glutamate-evoked current does not subside rapidly (in milliseconds) when glutamate is removed, then transmission of information through the synapse on a millisecond timescale will not be possible. Therefore, the AMPA receptor must have fast glutamate unbinding and a low glutamate affinity to allow fast information processing. FIGURE 3a shows a simple kinetic scheme that is commonly used to describe the behaviour of AMPA receptors12–14 . Two glutamate molecules (G) bind sequentially to the receptor (R), which can then open, and the receptor can also enter desensitized states (D). The rate constants for glutamate binding, k1 and k2, are 4 × 106 M–1 s–1. So, for a glutamate concentration in the synaptic cleft15 of ~10–3 M, the rate becomes 4,000 s–1 and a significant fraction of channels will open during a glutamate transient that lasts
