Synaptic Energy Use and Supply
Authors: Julia J. Harris, Renaud Jolivet, David Attwell
Journal: Neuron (2012)

Neuronal computation is energetically expensive. Consequently, the brain's limited energy supply imposes constraints on its information processing capability. Most brain energy is used on synaptic transmission, making it important to understand how energy is provided to and used by synapses. We describe how information transmission through presynaptic terminals and postsynaptic spines is related to their energy consumption, assess which mechanisms normally ensure an adequate supply of ATP to these structures, consider the influence of synaptic plasticity and changing brain state on synaptic energy use, and explain how disruption of the energy supply to synapses leads to neuropathology. Neuronal computation is energetically expensive. Consequently, the brain's limited energy supply imposes constraints on its information processing capability. Most brain energy is used on synaptic transmission, making it important to understand how energy is provided to and used by synapses. We describe how information transmission through presynaptic terminals and postsynaptic spines is related to their energy consumption, assess which mechanisms normally ensure an adequate supply of ATP to these structures, consider the influence of synaptic plasticity and changing brain state on synaptic energy use, and explain how disruption of the energy supply to synapses leads to neuropathology. The nervous system consumes a disproportionate fraction of the resting body's energy production: in humans the brain is only 2% of the body's mass, yet it uses ∼20% of the O2 consumed by the resting body (Mink et al., 1981Mink J.W. Blumenschine R.J. Adams D.B. Ratio of central nervous system to body metabolism in vertebrates: its constancy and functional basis.Am. J. Physiol. 1981; 241: R203-R212PubMed Google Scholar), while the retina alone uses 10% of the fly's resting ATP consumption (Laughlin et al., 1998Laughlin S.B. de Ruyter van Steveninck R.R. Anderson J.C. The metabolic cost of neural information.Nat. Neurosci. 1998; 1: 36-41Crossref PubMed Google Scholar). The relative energy consumption of the brain has increased particularly during the evolution of humans from lower primates (Mink et al., 1981Mink J.W. Blumenschine R.J. Adams D.B. Ratio of central nervous system to body metabolism in vertebrates: its constancy and functional basis.Am. J. Physiol. 1981; 241: R203-R212PubMed Google Scholar; Aiello and Wheeler, 1995Aiello L.C. Wheeler P. The expensive tissue hypothesis: the brain and the digestive system in human and primate evolution.Curr. Anthropol. 1995; 36: 199-221Crossref Google Scholar), reflecting a 3-fold expansion in the size of the brain relative to the body and an increase in the number of synapses per cortical neuron (Abeles, 1991Abeles M. Corticonics: Neural Circuits of the Cerebral Cortex. CUP, Cambridge1991Crossref Google Scholar). This greater energy allocation to CNS tissue over millions of years underpins our brains' greater cognitive powers, and was made possible by an increased and higher-quality food intake, along with less energy expenditure on the gut and locomotion (Aiello and Wheeler, 1995Aiello L.C. Wheeler P. The expensive tissue hypothesis: the brain and the digestive system in human and primate evolution.Curr. Anthropol. 1995; 36: 199-221Crossref Google Scholar; Navarrete et al., 2011Navarrete A. van Schaik C.P. Isler K. Energetics and the evolution of human brain size.Nature. 2011; 480: 91-93Crossref PubMed Scopus (90) Google Scholar). What is all this energy used for in the brain, how does it determine the brain's information processing power, and how does the brain's high energy use predispose it to problems when energy is not supplied at the necessary rate? We will review how most brain energy is used on synapses, investigate how pre- and postsynaptic terminals are optimized to maximize information transmission at minimum energy cost, and assess how ATP provision to synapses is regulated to satisfy their energetic needs. We then consider how synapse energy use changes with development and synaptic plasticity, and between wake and sleep states, before relating how defects in synaptic energy supply can lead to disease. The ATP consumption by the major subcellular processes underlying signaling in the brain (Figure 1) has been estimated for rat cerebral cortex (Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar) and for human cortex (Lennie, 2003Lennie P. The cost of cortical computation.Curr. Biol. 2003; 13: 493-497Abstract Full Text Full Text PDF PubMed Scopus (319) Google Scholar). Anatomical data on mean cell size, and the capacitance per area of membrane, were used to estimate the Na+ that enters to produce action potentials and thus needs to be pumped out again by the Na+/K+-ATPase, consuming ATP. Similarly, patch-clamp data provided quantification of the ions entering to generate typical synaptic currents, which also need to be pumped out (for simplicity all neurons, rather than ∼85% [Abeles, 1991Abeles M. Corticonics: Neural Circuits of the Cerebral Cortex. CUP, Cambridge1991Crossref Google Scholar], were assumed to be excitatory). The ATP used on ion pumping maintaining the resting potential, and on biochemical pathways underlying synaptic transmitter and vesicle recycling, were also calculated. This analysis of where ATP is used suggested that electrical signaling processes are the major consumer of energy in the brain. Furthermore, the largest component of the signaling energy use is on synaptic transmission. Figure 2A shows the predicted distribution of ATP use across the different signaling mechanisms in rat neocortex, updated from the earlier Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar calculations by taking into account the fact that action potentials in mammalian neurons use less energy than Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar assumed based on squid axon data (Alle et al., 2009Alle H. Roth A. Geiger J.R. Energy-efficient action potentials in hippocampal mossy fibres.Science. 2009; 325: 1405-1408Crossref PubMed Scopus (110) Google Scholar; Carter and Bean, 2009Carter B.C. Bean B.P. Sodium entry during action potentials of mammalian neurons: incomplete inactivation and reduced metabolic efficiency in fast-spiking neurons.Neuron. 2009; 64: 898-909Abstract Full Text Full Text PDF PubMed Scopus (56) Google Scholar; Sengupta et al., 2010Sengupta B. Stemmler M. Laughlin S.B. Niven J.E. Action potential energy efficiency varies among neuron types in vertebrates and invertebrates.PLoS Comput. Biol. 2010; 6: e1000840Crossref PubMed Scopus (6) Google Scholar; Harris and Attwell, 2012Harris J.J. Attwell D. The energetics of CNS white matter.J. Neurosci. 2012; 32: 356-371Crossref PubMed Scopus (39) Google Scholar). These calculations predict that the pre- and postsynaptic mechanisms mediating synaptic transmission (including glutamate accumulation in vesicles) consume 55% of the total ATP used on action potentials, synaptic transmission, and the resting potentials of neurons and glia. This is equivalent to 41% of the total ATP used in the cortex if housekeeping energy use, on tasks like synthesis of molecules and organelle trafficking, uses 25% of the total energy (Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar). The percentage of energy used on synapses may be even larger in the primate cortex, where the number of synapses per neuron is larger (Abeles, 1991Abeles M. Corticonics: Neural Circuits of the Cerebral Cortex. CUP, Cambridge1991Crossref Google Scholar). In contrast, the energy use of the white matter is 3-fold lower than the gray matter, mainly because it has an 80-fold lower density of synapses (Harris and Attwell, 2012Harris J.J. Attwell D. The energetics of CNS white matter.J. Neurosci. 2012; 32: 356-371Crossref PubMed Scopus (39) Google Scholar). The distribution of ATP consumption across the various mechanisms contributing to synaptic transmission (Figure 2B) shows that reversing the ion movements generating postsynaptic responses consumes the great majority of the energy used (at excitatory synapses: inhibitory synapses are predicted to use much less energy to reverse postsynaptic Cl− fluxes because the chloride reversal potential is close to the resting potential [Howarth et al., 2010Howarth C. Peppiatt-Wildman C.M. Attwell D. The energy use associated with neural computation in the cerebellum.J. Cereb. Blood Flow Metab. 2010; 30: 403-414Crossref PubMed Scopus (23) Google Scholar]). Figure 2C compares the predicted energy expenditure in the dendrites and soma, axons, and glia with the fraction of mitochondria observed in these locations by Wong-Riley, 1989Wong-Riley M.T.T. Cytochrome oxidase: an endogenous metabolic marker for neuronal activity.Trends Neurosci. 1989; 12: 94-101Abstract Full Text PDF PubMed Scopus (763) Google Scholar. The subcellular location of mitochondria reflects well the high predicted energy consumption of postsynaptic currents (Figure 2A). The fraction of energy expenditure predicted for axons and synaptic terminals is lower than the fraction of mitochondria observed in those areas, perhaps implying that there is some energy consuming presynaptic process that is unaccounted for (possibly vesicle trafficking: Verstreken et al., 2005Verstreken P. Ly C.V. Venken K.J. Koh T.W. Zhou Y. Bellen H.J. Synaptic mitochondria are critical for mobilization of reserve pool vesicles at Drosophila neuromuscular junctions.Neuron. 2005; 47: 365-378Abstract Full Text Full Text PDF PubMed Scopus (315) Google Scholar), while the predicted astrocyte energy use is substantially larger than the fraction of mitochondria observed in astrocytes, possibly because astrocytes are more glycolytic than neurons. Since synapses use such a large fraction of the brain's energy, we might expect evolution to have optimized their function to maximize the information they transmit while minimizing their energy use, in order to reduce the ATP consumption of neural circuits. Based on this idea, in the following sections we present some "energetic design principles" for presynaptic terminals and postsynaptic spines. First, we estimate how much ATP is needed to transmit information across a single synapse, as a prelude to explaining how the information transmitted can be maximized at minimum energy cost. The input to a synapse can be considered over a sequence of time intervals, Δt, in which an action potential either does or does not arrive along the axon, e.g., signifying the presence or absence of some stimulus (Figure 3A , Δt is the smallest interval over which the neuron can represent information, set by the refractory period of the action potential). If the mean spike firing rate is S, the probability of an action potential arriving in any given interval is s = SΔt (with 0 < s < 1), and we assume no correlation between the occurrence of different action potentials, the rate at which information arrives in the input train is (Shannon, 1948Shannon C.E. A mathematical theory of communication.Bell Syst. Tech. J. 1948; 27: 379-423Crossref Google Scholar; Dayan and Abbott, 2001Dayan P. Abbott L. Theoretical Neuroscience. MIT Press, Cambridge, MA2001Google Scholar, Equation 4.4; Levy and Baxter, 1996Levy W.B. Baxter R.A. Energy efficient neural codes.Neural Comput. 1996; 8: 531-543Crossref PubMed Google Scholar, Equation 2.1)Iinput(s)=−s⋅log2(s)–(1−s)⋅log2(1−s)(1) bits per Δt (Figure 3A). This is maximized with s = 0.5, or S = 1/(2Δt), i.e., with the neuron firing at half its maximum rate. This is ∼200 Hz for a refractory period of Δt = 2.5 ms, yet in practice the mean firing rate of neurons in vivo is much lower than this, around 4 Hz (Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar; Perge et al., 2009Perge J.A. Koch K. Miller R. Sterling P. Balasubramanian V. How the optic nerve allocates space, energy capacity, and information.J. Neurosci. 2009; 29: 7917-7928Crossref PubMed Scopus (39) Google Scholar). To explain this difference, Levy and Baxter, 1996Levy W.B. Baxter R.A. Energy efficient neural codes.Neural Comput. 1996; 8: 531-543Crossref PubMed Google Scholar suggested that, in fact, the nervous system maximizes the ratio of information transmitted to energy consumed (rather than maximizing coding capacity). They showed that, if the energy use of a neuron (and associated glia) is r-fold higher when producing a spike than when inactive, then the spike probability (s∗) that maximizes the information transmitted per energy consumed is much lower than that which would maximize information coding capacity. Their analysis implies that the factor, r, by which spiking increases energy use is related to s∗ via the equationr=log2(s∗)log2(1−s∗),(2) which we use below. Applying similar principles to the transmission of information through a synapse leads to the surprising conclusion that the energetic design of synapses is optimized if presynaptic release of transmitter fails often—just as is seen in most synapses. To understand this we need to consider information flow through synapses and the energy it consumes. For a synapse with a single release site (e.g., to the orange cell in Figure 3), if each time a presynaptic action potential arrives a vesicle is released with probability p, then for p < 1 information is lost during synaptic transmission. This is because, while the occurrence of a postsynaptic current tells the postsynaptic cell that there definitely was a presynaptic action potential (ignoring spontaneous vesicle release which will be considered below), if no current occurs that may be due either to no presynaptic action potential occurring or alternatively due to an action potential failing to evoke transmitter release. The amount of information passing through the synapse can be measured as the so-called mutual information, i.e., how much the sequence of postsynaptic currents (EPSCs) tells us about the input train of action potentials (APs), which is calculated (see Figure 3B legend) in bits per Δt asIm(EPSCs;APs)=Iinput(s)+(1−s)⋅log2((1−s)(1−p⋅s))+s⋅(1−p)⋅log2(s⋅(1−p)(1−p⋅s))(3) where s is again the probability of a spike arriving within Δt. The sum of the last two terms is negative and decreases the transmitted information below the input information defined in Equation 1. Equation 3 is plotted in Figure 3B for various values of s, normalized to the information in the incoming action potential stream in Equation 1 above, to show the fraction of incident information that is transmitted to the postsynaptic cell by the synapse. To assess the energetic efficiency of this information transfer (Laughlin et al., 1998Laughlin S.B. de Ruyter van Steveninck R.R. Anderson J.C. The metabolic cost of neural information.Nat. Neurosci. 1998; 1: 36-41Crossref PubMed Google Scholar; Balasubramanian et al., 2001Balasubramanian V. Kimber D. Berry 2nd, M.J. Metabolically efficient information processing.Neural Comput. 2001; 13: 799-815Crossref PubMed Scopus (49) Google Scholar), Figure 3C shows the ratio of the fraction of information emerging from the synapse to the energy consumed, which we take as being proportional to the rate of vesicle release, s·p (see figure legend). As an example of the energetic cost of information transmission through synapses, if we set typical physiological values of s = 0.01 (implying a firing rate of S = 4 Hz) and p = 0.25, Equation 3 states that, out of the 32 bits/s arriving at the synapse, 6.8 bits/s are transmitted, and from the estimate by Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar of the underlying synaptic energy cost (Evesicle = 1.64 × 105 ATP molecules per vesicle released), this is achieved at a cost of S·p·Evesicle = 1.64 × 105 ATP/s. Thus, information transmission typically costs ∼24,000 ATP per bit, similar to the estimate of Laughlin et al., 1998Laughlin S.B. de Ruyter van Steveninck R.R. Anderson J.C. The metabolic cost of neural information.Nat. Neurosci. 1998; 1: 36-41Crossref PubMed Google Scholar. Increasing the release probability to 1 leads to an information transmission rate of 32 bits/s, at a cost of 20,500 ATP/bit. Both the fraction of information transmitted and the information transmitted per energy used are maximized when the release probability is 1 (Figures 3B and 3C). Why then do CNS synapses typically have a release probability of 0.25–0.5 (Attwell and Laughlin, 2001Attwell D. Laughlin S.B. An energy budget for signaling in the grey matter of the brain.J. Cereb. Blood Flow Metab. 2001; 21: 1133-1145Crossref PubMed Google Scholar)? In this section we show that a low release probability can maximize the ratio of information transmitted to ATP used. It has been suggested that a low release probability allows synapses to have a wide dynamic range, increases information transmission from correlated inputs, or maximizes information storage (Zador, 1998Zador A. Impact of synaptic unreliability on the information transmitted by spiking neurons.J. Neurophysiol. 1998; 79: 1219-1229PubMed Google Scholar; Goldman, 2004Goldman M.S. Enhancement of information transmission efficiency by synaptic failures.Neural Comput. 2004; 16: 1137-1162Crossref PubMed Scopus (22) Google Scholar; Varshney et al., 2006Varshney L.R. Sjöström P.J. Chklovskii D.B. Optimal information storage in noisy synapses under resource constraints.Neuron. 2006; 52: 409-423Abstract Full Text Full Text PDF PubMed Scopus (27) Google Scholar). However, two energetic aspects of synaptic function also benefit from a low release probability. First, considering the influence of a single axon on a postsynaptic neuron, the existence of multiple synaptic release sites (usually onto different spines), at each of which a vesicle is released with probability p onto the postsynaptic cell (as for the brown cell in Figure 3), results in the ratio of information transmitted to energy used being larger if the release probability is low (see below). Second, if the rate at which information arrives in all the synapses impinging on the dendritic tree is matched to the rate at which the output axon of the cell can convey information, this also implies that synaptic failures should occur (Levy and Baxter, 2002Levy W.B. Baxter R.A. Energy-efficient neuronal computation via quantal synaptic failures.J. Neurosci. 2002; 22: 4746-4755PubMed Google Scholar). Taking first the issue of several (N) synaptic release sites from one axon onto a postsynaptic cell, we define a response in the postsynaptic cell as occurring whenever it receives at least one synaptic current. (Because we are only considering information transfer across the synapse, i.e., determining how much the arrival of EPSCs in the postsynaptic cell tells that cell about the presynaptic input spike train, the amplitude of the EPSC in the postsynaptic cell is immaterial [although its size may determine how it affects the firing of the postsynaptic cell].) If we ignore postsynaptic noise and variability in the currents evoked by different vesicles, then the information received by the postsynaptic cell (i.e., the mutual information between the occurrence of responses in the postsynaptic cell and the action potentials arriving with probability s in each interval Δt, see Figure 3B legend) is given byIm=Iinput(s)+(1−s)⋅log2((1−s)[1−s+s⋅(1−p)N])+s⋅(1−p)N⋅log2(s⋅(1−p)N[1−s+s⋅(1−p)N])(4) bits per Δt. The number of release sites, N, varies (Zador, 2001Zador A.M. Synaptic connectivity and computation.Nat. Neurosci. 2001; 4: 1157-1158Crossref PubMed Scopus (4) Google Scholar), but is often greater than 1, e.g., more than 6 for cortical pyramidal to interneuron synapses (Deuchars and Thomson, 1995Deuchars J. Thomson A.M. Innervation of burst firing spiny interneurons by pyramidal cells in deep layers of rat somatomotor cortex: paired intracellular recordings with biocytin filling.Neuroscience. 1995; 69: 739-755Crossref PubMed Scopus (47) Google Scholar), 4–6 for spiny stellate and pyramidal cell to pyramidal cell synapses in cortex (Markram et al., 1997Markram H. Lübke J. Frotscher M. Roth A. Sakmann B. Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex.J. Physiol. 1997; 500: 409-440Crossref PubMed Google Scholar; Silver et al., 2003Silver R.A. Lübke J. Sakmann B. Feldmeyer D. High-probability uniquantal transmission at excitatory synapses in barrel cortex.Science. 2003; 302: 1981-1984Crossref PubMed Scopus (108) Google Scholar), and ∼6 for excitatory synapses onto pyramidal cells in hippocampal area CA1 (Larkman et al., 1997Larkman A.U. Jack J.J. Stratford K.J. Quantal analysis of excitatory synapses in rat hippocampal CA1 in vitro during low-frequency depression.J. Physiol. 1997; 505: 457-471Crossref PubMed Scopus (38) Google Scholar). This multiplicity of synaptic release sites in parallel, usually onto different spines, may exist to ensure stable information processing in the face of spine turnover (Xu et al., 2007Xu H.-T. Pan F. Yang G. Gan W.-B. Choice of cranial window type for in vivo imaging affects dendritic spine turnover in the cortex.Nat. Neurosci. 2007; 10: 549-551Crossref PubMed Scopus (149) Google Scholar). Figure 3D (black lines) shows the fraction of the axonal input information that is transmitted to the postsynaptic cell, for various numbers of release sites (with the same release probability p), and for s set to 0.01 implying a firing rate of ∼4 Hz for Δt = 2.5 ms (higher values of firing rate give curves that are similar in shape). Having several synaptic release sites (N > 1) from the axon to the receiving neuron increases the reliability of transmission, so that a larger fraction of the input information is received postsynaptically (de Ruyter van Steveninck and Laughlin, 1996de Ruyter van Steveninck R.R. Laughlin S.B. The rate of information transfer at graded-potential synapses.Nature. 1996; 379: 642-645Crossref Scopus (116) Google Scholar; Manwani and Koch, 2001Manwani A. Koch C. Detecting and estimating signals over noisy and unreliable synapses: information-theoretic analysis.Neural Comput. 2001; 13: 1-33Crossref PubMed Scopus (27) Google Scholar; Zador, 2001Zador A.M. Synaptic connectivity and computation.Nat. Neurosci. 2001; 4: 1157-1158Crossref PubMed Scopus (4) Google Scholar). However, as shown from the black lines in Figure 3E, for N > 1 it is no longer the case that the information transmitted per energy used is maximal with a release probability of 1; indeed, the highest ratio of information transmission to energy used is with p very low. For example, Figure 3D shows that for N = 4 synaptic release sites from each axon onto the postsynaptic cell, a release probability of p = 0.25 transmits over 60% of the information that would occur with p = 1, yet it uses only 25% of the energy to do so (since only 1/4 the number of vesicles are released). Surprisingly, the preceding analysis predicts the greatest energy efficiency (information transmitted/energy used) for convergent synapses if they have zero release probability (Figure 3E). A more realistic result is obtained if it is recognized that the postsynaptic neuron will also experience a low rate of spontaneous vesicle release from all its input synapses (i.e., miniature synaptic currents at a total rate of m per Δt), each of which produces a postsynaptic effect indistinguishable from the action potential evoked release of one vesicle. In this case Equation 4 becomesIm=Iinput(s)+(1−m)⋅{(1−s)⋅log2((1−s)[1−s+s⋅(1−p)N])+s⋅(1−p)N⋅log2(s⋅(1−p)N[1−s+s⋅(1−p)N])}+(1−s)⋅m⋅log2{(1−s)⋅m[m+s⋅(1−m)⋅(1−(1−p)N)]}+s⋅[1−(1−p)N⋅(1−m)]⋅log2{s⋅[1−(1−p)N⋅(1−m)][m+s⋅(1−m)⋅(1−(1−p)N)]}(5) The presence of spontaneous release decreases the maximum information transmittable (red curves in Figure 3D) because some postsynaptic currents are not driven by presynaptic action potentials, and the information transmitted per energy used drops off at low p values (red curves in Figure 3E), because the frequency of evoked release becomes comparable with that of spontaneous release. For a physiological spike rate (s = 0.01 per 2.5 ms interval, implying 4 Hz firing), and a total spontaneous release rate onto the cell of 1.2 Hz as measured in cortical pyramidal cells (Dani et al., 2005Dani V.S. Chang Q. Maffei A. Turrigiano G.G. Jaenisch R. Nelson S.B. Reduced cortical activity due to a shift in the balance between excitation and inhibition in a mouse model of Rett syndrome.Proc. Natl. Acad. Sci. USA. 2005; 102: 12560-12565Crossref PubMed Scopus (265) Google Scholar) so that m = 0.003 for a 2.5 ms interval, this creates an optimal release probability in the range 0.05–0.25, depending on the number of synapses converging onto the postsynaptic cell. Figure 3E (red lines) predicts that the optimal release probability is lower the more synapses that a single axon makes onto the same postsynaptic neuron. Strikingly, just such a relationship between release probability and number of release sites has been reported by Hardingham et al., 2010Hardingham N.R. Read J.C.A. Trevelyan A.J. Nelson J.C. Jack J.J.B. Bannister N.J. Quantal analysis reveals a functional correlation between presynaptic and postsynaptic efficacy in excitatory connections from rat neocortex.J. Neurosci. 2010; 30: 1441-1451Crossref PubMed Scopus (17) Google Scholar (their Figure 7C) for cortical synapses and Branco et al., 2008Branco T. Staras K. Darcy K.J. Goda Y. Local dendritic activity sets release probability at hippocampal synapses.Neuron. 2008; 59: 475-485Abstract Full Text Full Text PDF PubMed Scopus (91) Google Scholar (their Figure 2D) for hippocampal synapses, with a mean release probability of ∼0.7 at connections with a single release site declining to ∼0.25–0.4 for connections with 4 release sites and to ∼0.1 at connections with ∼10 release sites. While there are some quantitative differences between their measurements and our Figure 3E (in particular their release probability being less than one for single release sites), this provides an important experimental confirmation of the unexpected inverse relationship between p and N that the analysis above predicts. Thus, if axons make multiple synapses onto each postsynaptic cell (as is found experimentally)—perhaps in order to provide stable information processing in the face of spine turnover (Xu et al., 2007Xu H.-T. Pan F. Yang G. Gan W.-B. Choice of cranial window type for in vivo imaging affects dendritic spine turnover in the cortex.Nat. Neurosci. 2007; 10: 549-551Crossref PubMed Scopus (149) Google Scholar)—more information is transmitted per energy used by having a low release probability. (This conclusion, and all of the analysis in this section, is independent of the amount of ion entry generating a postsynaptic EPSC [provided this quantity is the same for all release sites] and so does not depend on exactly which receptor subunits are expressed at the synapses.) Consequently, although synaptic failures appear intuitively to be wasteful, they allow the energy use per bit of information transmitted to be minimized. Another argument for having a low release probability to reduce energy use depends on the fact that a cortical neuron typically receives about 8,000 synapses on its dendritic tree (Braitenberg and Schüz, 1998Braitenberg V. Schüz A. Cortex: Statistics and Geometry of Neuronal Connectivity.Second Edition. Springer, Berlin1998Crossref Google Scholar). Levy and Baxter, 2002Levy W.B. Baxter R.A. Energy-efficient neuronal computation via quantal synaptic failures.J. Neurosci. 2002; 22: 4746-4755PubMed Google Scholar pointed out that the rate at which information arrives at all these synapses is greater than the rate at which the output axon of the cell can convey information, implying that energy is wasted on transmitting information that cannot possibly be passed on by the postsynaptic cell. They suggested that failures of synaptic transmission would reduce this energy waste. With the assumptions that all input synapses are independent and that their axons fire at the same energy-limited optimal rate (Equation 2) as does the postsynaptic cell's output axon, Levy and Baxter, 2002Levy W.B. Baxter R.A. Energy-efficient neuronal computation via quantal synaptic failures.J. Neurosci. 2002; 22: 4746-4755PubMed Google Scholar showed that the firing rate of the axons defines an optimal failure rate for synaptic transmission given by1−p=(14)Iinput(s∗)(6) where p is the synaptic release probability, Iinput is defined by Equation 1, and s∗ is the spike probability defined by Equation 2. Surprisingly, this ideal failure rate does not depend on the number of synaptic inputs to the cell (if there are more than a few hundred synapses). Figure 3F shows how Equation 6 predicts that the release probability should vary with the factor, r, by which energy consumption is increased during spiking. For the energy budget in Figure 2, r = 150 (see Figure 3F legend) and the predicted optimal release probability is approximately 0.2. The Levy and Baxter, 2002Levy W.B. Baxter R.A. Energy-efficient neuronal computation via quantal synaptic failures.J. Neuro