An Energy Budget for Signaling in the Grey Matter of the Brain

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An Energy Budget for Signaling in the Grey Matter of the Brain Journal of Cerebral Blood Flow and Metabolism 21:1133–1145 © 2001 The International Society for Cerebral Blood Flow and Metabolism Published by Lippincott Williams & Wilkins, Inc., Philadelphia Review Article An Energy Budget for Signaling in the Grey Matter of the Brain David Attwell and *Simon B. Laughlin Department of Physiology, University College London, London, and *Department of Zoology, University of Cambridge, Cambridge, U.K. Summary: Anatomic and physiologic data are used to analyze signaling is a large fraction of the total energy used by the the energy expenditure on different components of excitatory brain; this favors the use of energy efficient neural codes and signaling in the grey matter of rodent brain. Action potentials wiring patterns. Our estimates of energy usage predict the use and postsynaptic effects of glutamate are predicted to consume of distributed codes, with Յ15% of neurons simultaneously much of the energy (47% and 34%, respectively), with the active, to reduce energy consumption and allow greater com- resting potential consuming a smaller amount (13%), and glu- puting power from a fixed number of neurons. Functional mag- tamate recycling using only 3%. Energy usage depends netic resonance imaging signals are likely to be dominated by strongly on action potential rate—an increase in activity of 1 changes in energy usage associated with synaptic currents and action potential/cortical neuron/s will raise oxygen consump- action potential propagation. Key Words: Action potential— tion by 145 mL/100 g grey matter/h. The energy expended on Energy—fMRI—Resting potential—Signaling—Synapse. The neural processing of information is metabolically of functional imaging techniques. These techniques de- expensive. Although the human brain is 2% of the body’s tect the mismatch between energy use and blood supply weight, it accounts for 20% of its resting metabolism in small volumes of brain, and an increase in signal is (Kety, 1957; Sokoloff, 1960; Rolfe and Brown, 1997). taken to indicate heightened neural activity. However, This requirement for metabolic energy has important im- with the exception of retina (Ames, 1992; Ames and Li, plications for the brain’s evolution and function. The 1992; Ames et al. 1992; Laughlin et al., 1998), little is availability of energy could limit brain size, particularly understood regarding the metabolic demands made by in primates (Aiello and Wheeler, 1995), and could de- neural activity and the distribution of energy usage termine a brain’s circuitry and activity patterns by favor- among identified neural mechanisms. ing metabolically efficient wiring patterns (Mitchison, The restoration of the ion movements generated by 1992; Koulakov and Chklovskii, 2001) and neural codes postsynaptic currents, action potentials, and neurotrans- (Levy and Baxter, 1996; Baddeley et al., 1997; Balasu- mitter uptake contributes to the brain’s energy needs bramanian et al., 2001). The brain’s energy requirements (Siesjö, 1978; Ames, 1992, 2000; Erecin´ska and Silver, make it susceptible to damage during anoxia or ischemia, 1989; Sokoloff et al., 1996). Excitatory synapses domi- and understanding the demands made by different neural nate the brain’s grey matter (Abeles, 1991; Braitenberg mechanisms may help the design of treatments (Ames et and Schüz, 1998), and the distribution of mitochondria al., 1995). Interest in the relation between neural activity points to these glutamatergic synapses being major users and energy use has been heightened by the development of metabolic energy (Wong-Riley, 1989; Wong-Riley et al., 1998). Magnetic resonance studies (Sibson et al., 1998) find that glucose utilization is equal to the rate at Received May 1, 2001; final revision received July 17, 2001; ac- cepted July 18, 2001. which glutamate is converted to glutamine in the brain, Supported by the Wellcome Trust, the Rank Prize Fund, the BBSRC, which is a measure of synaptic glutamate release because and the Gatsby Foundation. the glia that take up glutamate convert some of it to Address correspondence and reprint requests to David Attwell, Dept. Physiology, University College London, Gower St., London, WC1E glutamine. If the activity evoked by glutamate release is 6BT, U.K. a major demand on brain energy supplies, then changes 1133 1134 D. ATTWELL AND S. B. LAUGHLIN in this glutamatergic activity may generate the imbalance centrations, involving extra energy consumption. Rewriting Eq. 1 in terms of changes (⌬) from the resting values, the change of between O2 supply and metabolism that is detected as “activation” in functional magnetic resonance imaging membrane potential is ⌬ =( ⌬ + ⌬ − ⌬ )ր( + )() experiments (Shulman and Rothman, 1998). However, V gNa VNa gK VK Ipump gNa gK 5 glutamate release stimulates a number of mechanisms The rates of change of [Na+] and [K+] in a cell of volume (for example, postsynaptic currents, action potentials, i i U are transmitter recycling) whose energy usage has not been systematically estimated. [ +] ր = (⌬ − ⌬ )− ⌬ ( ) UF d Na i dt gNa VNa V 3 Ipump 6 This article uses anatomic and physiologic data from [ +] ր = (⌬ − ⌬ )+ ⌬ ( ) rodents (primates are discussed at the end of the article) UF d K i dt gK VK V 2 Ipump 7 + ס + -to construct an energy budget for mammalian grey mat From Eq. 5 − Eq. 7, d[Na ]i/dt −d[K ]i/dt, and initially + ⌬ ס + ⌬ ter, specifying the metabolic cost of the mechanisms that [Na ]i − [K ]i (when the membrane potential has returned generate and transmit neural signals. Taking advantage essentially to its resting value, after an action potential or ex- of biophysical data gathered in recent years, we derive citatory input, when the Na+ entry has been balanced by K+ + ⌬ ס + ⌬ the first reasonable estimates of the amounts of energy exit). Thus, [Na ]i − [K ]i at all times. Equation 6 is solved by assuming that the pump rate varies linearly with consumed by the major processes underlying neuronal small changes of [Na+] around the resting value so that signaling. These values specify the distribution of energy i ⌬ = ␭⌬[ +] ( ) consumption between glia and neurons and between the Ipump Na i 8 neural mechanisms found in synapses, dendrites, and axons. The budget identifies major metabolic constraints and using (for small concentration changes) to cortical function and, by specifying the dependence of ⌬ =−( ր ) ([ +] ր[ +] ) VNa RT F ln Na i,new Na i,old energy usage on action potential frequency and synaptic ∼−( ր )(⌬[ +] ր ) RT F Na i Nai ; transmission, will help to define the ability of functional ⌬ ∼−( ր )(⌬[ +] ր ) VK RT F K i Ki imaging to detect changes in neural activity. where Nai and Ki are resting values. This gives (at time t) MATERIALS AND METHODS ⌬[ +] ( )=⌬[ +] ( = ) −tր␶ Na i t Na i t 0 e , Here, we present detailed calculations of energy expenditure where on different cellular mechanisms in the brain. Readers who are interested in the conclusions of the analysis, but do not wish to ր␶ =[{ ր( + )}{ ր }{( ր )+( ր )} + ␭( 1 gNagK gNa gK RT F 1 Nai 1 Ki 2gNa go through the calculations in detail, can read the Results sec- + 3g )ր(g + g )]րUF tion with no loss of continuity. Limitations on the accuracy of K Na K the calculations are considered in the Discussion. The extra ATP consumed is + Energy needed for Na extrusion ϱ + + + For a cell membrane with Na and K conductances (gNa and ⌬ ր = ␭␶ ⌬[ ] ( = )ր ∫ Ipump Fdt Na i t 0 F, gK, with reversal potentials VNa and VK), and a pump that extrudes 3 Na+ and imports 2 K+ per adenosine triphosphate O (ATP) consumed, on a time scale much slower than the mem- which is brane time constant, there is no net membrane current and ( ⌬[ +] ( = ))ր[{ ր( + )}{ ր }{( ր ) ( − )+ ( − )= ( ) U Na i t 0 gNagK gNa gK RT F 1 Nai gNa VNa V gK VK V Ipump 1 +( ր )}ր␭ +( + )ր( + )] ( ) 1 Ki 2gNa 3gK gNa gK 9 where V is membrane potential, and the pump current, Ipump,is + 1/3 of the Na+ extrusion rate. Adenosine triphosphate is con- If gNa<<gK, and the sensitivity of the pump to [Na ]i changes (␭) is large, this is ∼(Na+ load)/3, the approximation that is used sumed at a rate Ipump/F (F is the Faraday). At the resting po- in the rest of this article. In general, the ATP used differs from ס + ס + tential when d[Na ]i/dt d[K ]i/dt 0, ␭ this value by an amount that depends on gNa/gK and . For the ס + ס + I = g (V − V)ր3 (2) values of gNa/gK used below, [Na ]i 20 mmol/L, [K ]i pump Na Na + 140 mmol/L, and a pump rate that depends on [Na ]i according + From Eqs. 1 and 2, the current produced by Na influx at the to a Hill equation with a Hill coefficient of 3 and an EC50 of 20 resting potential, Vrp,is mmol/L, Eqs. 9, 8, and 2 show that for neurons and glia, re- spectively, the ATP used is 3% and 6% less than the value of ( − )= ( − )( − )ր{ ( + gNa VNa Vrp 3 VNa Vrp Vrp VK Rin Vrp 2VNa (Na+ load)/3. (The ATP usage can differ from (Na+ load)/3 − )} ( ) 3VK 3 because we are calculating the change in usage from its resting value, and the increase in [Na+] , decrease in [K+] , and altered where the input resistance, R , is 1/(g +g ) and the rate of i i in Na K potential change the passive Na+ influx, and hence the ATP ATP consumption is + needed to pump it out.) Other plausible [Na ]i dependencies for ( − )( − )ր{ ( + − )} ( ) the pump give similar small deviations from an ATP usage of VNa Vrp Vrp VK FRin Vrp 2VNa 3VK 4 (Na+ load/3)—for example, 9% and 11% less, for neurons and + When an action potential or synaptic current increases [Na ]i glia, for a Hill coefficient of 2, or for a pump rate proportional + + and decreases [K ]i, the sodium pump will restore these con- to [Na ]i.
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