Nature Neuroscience
1, 36 - 41 (1998)
doi:10.1038/236
The metabolic cost of neural informationSimon B. Laughlin1, Rob R. de Ruyter van Steveninck2
& John C. Anderson1, 31 Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, UK 2 NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540, USA 3 Sussex Centre for Neuroscience, University of Sussex, Brighton BN1 9QG, UK
Correspondence should be addressed to Simon B. Laughlin SL104@cam.ac.ukWe derive experimentally based estimates of the energy used by neural
mechanisms to code known quantities of information. Biophysical measurements
from cells in the blowfly retina yield estimates of the ATP required to generate
graded (analog) electrical signals that transmit known amounts of information.
Energy consumption is several orders of magnitude greater than the thermodynamic
minimum. It costs 104 ATP molecules to transmit a bit at a
chemical synapse, and 106 - 107 ATP for graded
signals in an interneuron or a photoreceptor, or for spike coding. Therefore,
in noise-limited signaling systems, a weak pathway of low capacity transmits
information more economically, which promotes the distribution of information
among multiple pathways.Neural processing is metabolically expensive. The human brain accounts
for 20% of resting oxygen consumption, and half of this energy drives the
pumps that exchange sodium and potassium ions across cell membranes1.
Because these pumps are maintaining the ionic concentration gradients that
power electrical signaling by neurons, 10% of a resting human's energy is
used to keep the brain's batteries charged. In the rabbit retina, second messenger
systems, synapses and ion pumps make large contributions to a high metabolic
rate2,
3. Therefore, when the basic cellular mechanisms for
signaling and information processing are concentrated in brains and sense
organs, the metabolic demands are considerable.
These metabolic demands could be large enough to influence the design,
function and evolution of brains and behavior. Comparative studies suggest
that the metabolic expense of maintaining the brain throughout life4,
or the demands made by the developing brain on the maternal energy budget5, have limited the sizes of primate brains. The human brain's susceptibility
to anoxia and its precise local regulation of cerebral blood flow also suggest
that the supply of energy limits neural function. If metabolic energy is limiting,
then neurons, neural codes and neural circuits will have evolved to reduce
metabolic demands. Two elegant theoretical analyses show that metabolic efficiency
can profoundly influence neural coding. The minimization of metabolic cost
promotes the distribution of signals over a population of weakly active cells6,
7.
Although metabolic energy is clearly important in determining neural function,
we lack basic data on the quantitative relationships between energy and information
in nervous systems. Precisely how much energy must a neuron consume to do
a given amount of useful work, transmitting and processing information? How
does energy consumption scale with the quantity of information that neurons
handle? We can now address these fundamental questions because we have recently
measured the quantities of information transmitted by photoreceptors and interneurons
of the intact blowfly retina8 and can use biophysical data to
estimate the amount of energy required to transmit these signals. We find
that information is expensive, and that, for a given communication channel,
the cost per bit increases with bit rate. Thus metabolic cost can have a profound
influence on the structure, function and evolution of cell signaling systems,
neurons, neural circuits and neural codes.
Results
The metabolic cost of information in a photoreceptor
Information transmission rate, measured in bits per second, is a useful
measure of the neural work done by photoreceptors and interneurons of the
fly compound eye, for the following reasons. Increasing the number of bits
transmitted per cell improves the retinal image by increasing the number of
gray levels coded per second per pixel. A number of studies conclusively demonstrate
that the large monopolar cell (LMC), the second-order retinal neuron, is optimized
to maximize bit rate9. We have recently measured the rates at
which retinal cells transmit information under daylight conditions8.
Cells were driven by randomly modulating the light intensity of an LED (Fig. 1), with a depth of modulation (contrast) that resembled
natural signals. Photoreceptors responded to this random test stimulus with
a graded modulation in membrane potential that encoded the fluctuations in
light level (Fig. 1). The photoreceptor signal
is contaminated by noise, both signal and noise have a Gaussian distribution,
and the system is approximately linear over this natural contrast range. Under
these conditions, we can determine the rate at which the photoreceptor transmits
information, I, from measurements of the power spectra of signal,
S(f) and noise, N(f), by applying Shannon's equation
 (1)
We estimated I = 1000 bits per
second for the fully light-adapted cell, but we expect lower rates under natural
conditions because natural signals contain correlations that are not present
in our random stimuli.
 | | |
We can now estimate the cost of a bit of information by determining the
metabolic energy required to code information under these fully light-adapted
conditions. We recorded from five photoreceptors that were stimulated at
the same daylight level, 106 effective photons per receptor
per second. These photoreceptors had an average membrane potential, E
m, of -33  6 mV. Injection of current yielded an average
input resistance of 7.1 1.8 M , giving a mean total conductance
for the single photoreceptor, gtotal, of 141 nS. We incorporate
these electrical data into a simple electrical model of the photoreceptor
membrane (Fig. 2), based on published biophysical
data. The model calculates the ionic currents that flow across the membrane
during signaling. These ion fluxes define the rate at which a vigorous Na/K
exchange pump10,
11,
12 must hydrolyze ATP to maintain the ionic
concentration gradients that are driving currents across the membrane. Dividing
this rate of ATP consumption, 7.5  109 ATP molecules
per second, by the information transmission rate, 1000 bits per second, gives
the metabolic cost for sensory information, 7 106
ATP molecules per bit.
| | Figure 2. The electrical models of photoreceptor and LMC membranes. | | |  | By estimating the currents required to generate electrical signals, the
models calculate the rates at which pumps (P) must hydrolyze ATP to sustain
electrical signalling. Symbols, Photoreceptor: gL,
light-gated conductance; iL, light gated current; g
K, voltage-gated potassium conductance; iK, potassium
current; P, Na/K exchange pump. LMC: gCl,
histamine-gated chloride conductance; iCl, histamine-gated
chloride current; g0, non-specific cation conductance
assumed to oppose chloride conductance; io, non-specific
cation current; P, chloride pump (see Methods).
 Full Figure and legend (8K) |
| |
Measurements of the oxygen consumed by isolated insect retinas confirm
that our estimate of ATP consumption, and hence bit cost, is of the right
order of magnitude. In the drone bee retina13 each photoreceptor
consumes 2 109 ATP molecules per second, compared with
our estimate in the blowfly of 7 109 ATP molecules
per second. In the blowfly there are approximately 35,000 photoreceptors per
retina14. Consequently, aerobic glycolysis must consume 6.5
10−5 mls O2 per minute to meet our
estimated consumption of ATP. The measured value is almost identical, 6
10−5 mls O2 per minute11.
Our value, 7 106 ATP molecules per bit, is a lower
bound because photoreceptors will transmit information at lower rates under
natural conditions. Moreover, by basing our cost on electrical current, we
exclude the intermediate steps in phototransduction. A second-messenger cascade
passes the signal from rhodopsin to ion channel, amplifies the signal, and
consumes energy in at least two processes, the phosphorylation of intermediates
and the transfer of a second messenger, calcium ions, between compartments15. However, the costs of the cascade, although appreciable, are unlikely
to inflate consumption by an order of magnitude for the following reason.
We find that a photoreceptor transducing 106 photons per second
consumes 7 109 ATP molecules per second. Consequently
the cascade would have to hydrolyze almost 104 ATP molecules
per transduced photon to equal the energy demands of the electrical current.
We conclude that our estimate of 7 106 ATP molecules
per bit is a conservative figure that is strongly supported by independent
experimental data.
Our costing of phototransduction suggests an important principle that can
simplify the calculation of neural energy budgets. Neural signaling and processing
can involve a cascade of amplification in which increasing numbers of molecules
are recruited at each successive step. The last stage, which often results
in the flow of ionic current across the cell membrane (synaptic transmission),
will consume the most energy. This could be why ion pumps are responsible
for over half of the human brain's energy consumption3. When
ion currents dominate energy requirements, then reasonable lower bounds for
metabolic costs can be calculated from conductance measurements, as demonstrated
here, without recourse to direct measurements of oxygen consumption. We will
use this principle again when we consider the chemical synapse.
The cost of information in a retinal neuron
Six photoreceptors carrying the same signal converge on a second order
neuron, the LMC. Each photoreceptor drives the LMC, with 220 identical parallel
synapses, giving 1320 synapses in all (Fig. 1)16. At each synapse a fast neurotransmitter, histamine, gates chloride
channels17 to generate a graded response in the LMC. This analog
signal is an inverted, amplified and high-pass-filtered version of the photoreceptor
input (Fig. 1). Using the random stimuli applied
to photoreceptors, we found that, as a result of convergence, the LMC is more
reliable than a single photoreceptor, and transmits information at a higher
rate, 1600 bits per second8.
Again, a simple electrical model (Fig. 2)
calculates the currents that flow during the LMC response, and hence the ATP
consumption by pumps. In the model, the postsynaptic chloride current is generated
by the histamine-gated chloride conductance gCl, with a
reversal potential ECl of -65 mV18. The counter-current
that holds the LMC membrane potential above ECl has not
been identified. We assume a nonspecific cation conductance, g0,
with a reversal potential E0 of 0 mV. If one assumes
that the chloride pump is not electrogenic, then the simple circuit model
for the postsynaptic LMC membrane (Fig. 2) is
equivalent to equations 2 ,3,5 and 6 in the receptor model (Methods).
Inserting published measurements of total membrane conductance and membrane
potential18,
19, the LMC model gives a postsynaptic chloride
current in bright light of 0.66 nA. A chloride pump maintains ECl20, but it has not been characterized. Known pumps transfer between
1 and 3 chloride ions per ATP hydrolyzed. Equating the synaptic influx of
chloride ions with pump efflux gives a threefold range of pump consumption,
1.4 109 to 4.1 109 ATP molecules
per LMC per second . Dividing by the measured bit rate gives a range of metabolic
costs for information, 9 105 to 3 10
6 ATP molecules per bit.
Note that the LMC codes at a lower cost per bit than the photoreceptor.
Although several assumptions had to be made to calculate ion fluxes and pump
rates in LMCs, this conclusion is likely to be correct. The LMC has a lower
membrane conductance18 and, through redundancy reduction and
signal convergence9, transmits information at a higher rate8. In addition, photoreceptors employ a large membrane area to capture
and transduce photons, and this increases their overall conductance.
The cost of information at a chemical synapse
Each of the 1320 photoreceptor synapses driving an LMC is a tetrad with
an average contact area 200 nm  500 nm and a prominent presynaptic
bar (Fig. 1). From the number of identical synapses16 and the information rates in a photoreceptor and an LMC, we have
previously calculated that each synapse transmits 55 bits per second8. Because identical synapses contribute equally to the total LMC
chloride conductance, gCl, the post-synaptic chloride current
at one synapse accounts for 1/1320 of the LMC ATP consumption, calculated
above. Dividing consumption by transmission rate gives a range of metabolic
costs for information at a single chemical synapse of 2 10
4 to 6 104 ATP molecules per bit.
This estimate of synaptic cost is based on postsynaptic current and ignores
all presynaptic mechanisms. On present evidence, this simplification will
not significantly change our conclusions. Using experimental data, we estimate
that the costs of neurotransmitter uptake and vesicle refilling total less
than 10% of the postsynaptic current (see Methods). Estimates of presynaptic
calcium flux vary from 200 to 1.3 104 ions per vesicle
discharged21. With 240 vesicles released per second (see Methods),
and 1 calcium ion pumped per ATP22, presynaptic calcium fluxes
would add from 2% to 60% to our synaptic costs. The energy used to recycle
vesicles is unknown but, given a vesicle discharge rate of 240 per second,
it would need to be 3 103 ATPs per vesicle to equal
the postsynaptic cost. We conclude that our lower bound for synaptic cost
is of the right order of magnitude and, on the present evidence, within a
factor of two of the real cost.
Bit rate versus cost in noise-limited systems
The low capacity (55 bits per second) synapse transmits at a much lower
cost per bit than the high capacity (1600 bits per second) interneuron, the
LMC (Fig. 3). Thus, as in many communication
systems, a lower transmission rate is cheaper. This trade-off between cost
and capacity is enforced by the stochastic nature of cell signaling. Cost
is proportional to N, the number of elementary stochastic events that
produce signals, such as photon absorptions, channel openings, synaptic vesicle
releases, receptor or G-protein activation. The signal-to-noise power ratio
also increases as N, and information as log2(N) (see
Methods), to produce a savage law of diminishing returns. We illustrate this
relationship (Fig. 4) by modeling the array of
parallel synapses that connects a photoreceptor to an LMC (see Methods). To
increase the rate at which information is transmitted between this pair of
cells, the number of synapses must be increased (see Methods, eqn. 7), and this increases the cost of transmitting a bit Fig. 4. It would be more economical to transmit the extra
information through a second pair of cells. Thus, in the face of fundamental
noise limitations, energy efficiency promotes the division of information
among parallel pathways, each of low capacity, so favoring the use of parallel
messenger systems within cells, and sparse coding in neural networks6. A similar conclusion has been reached independently by extrapolating
from an energy-efficient electronic cochlea to neural mechanisms7.
| | |
The cost of transmitting information by spikes
The photoreceptors and interneurons of the fly retina use graded (analog)
responses because they carry information at high rates. Perhaps spike coding
is more economical. We investigated this possibility by estimating the cost
for spike transmission down an LMC and comparing it to our estimate of the
analog cost (derived above). The LMC's graded synaptic signal is conducted
along its axon to output synapses, approximately 425  m away. Transmission
is passive19; consequently its cost is included in generation
of postsynaptic LMC response and therefore is 9 105
to 3 106 ATP molecules per bit. Were a spike to carry
information over this same distance, it would transiently depolarize the entire
length of the axon by 100 mV. The known axon capacitance19 defines
the minimum sodium ion influx needed to propagate the spike and hence a pump
consumption of 9 106 ATP molecules per spike. A sensory
spike carries between 1 and 10 bits of information23, giving
a range of costs, 9 105 to 9 106
ATP molecules per bit. This cost per bit brackets the analog costs (Fig. 3), leading us to conclude that action
potentials do not greatly enhance metabolic efficiency over short distances,
at least in this unmyelinated insect axon. A primary function of spikes could
be to reduce the effects of synaptic noise7 by tightly coupling
vesicle release to presynaptic action potentials.
Discussion
Is information costly?
Metabolic efficiency will only be an important determinant of the evolution
and design of signaling systems when metabolic costs impose a significant
penalty on the parent organism. Our estimate of photoreceptor ATP consumption
in bright light is equivalent to 8% of the total consumption by the resting
fly24 and, if we add to this the consumption by LMCs, this figure
approaches 10%. This consumption compares with a figure for the human brain
of 20%, which is widely considered to be significant1,
3 and
could have shaped its evolution25. The significance of retinal
ATP consumption is reinforced by comparative studies. Blowfly photoreceptors
consume more energy, gram for gram, than active mammalian muscle, metabolic
investment in vision varies widely between insect species, in accordance with
lifestyle and habitat (Laughlin and D.C. O'Carroll, unpublished results),
and the visual systems of burrowing and cave-dwelling species are greatly
reduced26.
Why is neural information costly?
Synapses and cells are using 105 to 108 times
more energy than the thermodynamic minimum. Thermal noise sets a lower limit
of k T Joules for observing a bit of information (
k, Boltzmann's constant; T, absolute temperature, 290°K)27,
28 and the hydrolysis of one ATP molecule to ADP releases about
25 kT 29. It is beyond the scope of this paper to analyze
the factors that increase the cost of information by five to eight orders
of magnitude relative to the thermodynamic minimum, but elementary observations
are instructive. At the heart of most cell signaling systems are protein molecules
that code information by changing conformation. We can regard such a signaling
molecule as a switch that codes a binary digit, a single bit, by flipping
from one conformation to another. How fast can this molecule switch, and how
much energy is needed? The motor protein kinesin cycles conformation approximately
100 times per second, hydrolyzing 1 ATP per cycle30,
31 and
does considerable mechanical work. Freed from heavy mechanical work, ion channels
change conformation in roughly 100  s32. In principle, therefore,
a single protein molecule, switching at the rate of an ion channel with the
stoichiometry of kinesin, could code at least 103 bit per second
at a cost of 1 ATP per bit. We find that a molecular system, the chemical
synapse, transmits at only 5% of the rate of the single molecule but at 10
4 times the cost per bit. Highly specialized cells, the photoreceptor
and the LMC interneuron, achieve the same bit rate as the molecular switch,
but at 106 times the cost per bit. These elementary comparisons
suggest that costs soar when molecules are organized into cellular systems.
At least two biophysical constraints will contribute to these systems' costs.
First, there is the uncertainty associated with molecular interactions. The
stochastic nature of receptor activation (photon absorption), of molecular
collision, of diffusion, and of vesicle release, degrades information by introducing
noise (eqns.1 and 7), thereby substantially
increasing costs. Secondly, energy is required to distribute signals over
relatively large distances. We suggest, therefore, that the high metabolic
cost of information in systems is dictated by basic molecular and cellular
constraints to cell signaling, as independently proposed by Sarpeshkar7 (see also Sarpeshkar, R; Ph.D. dissertation, California Institute
of Technology, 1997). Because these systems' costs are substantial, further
investigation of the metabolic efficiency of cell signaling has the potential
to provide insights into the function, design and evolution of molecular signaling
complexes, second messenger systems33, sensory receptors, neurons,
neural networks and neural codes.
Methods
Measuring photoreceptor membrane potential and conductance.
Established techniques8,
34,
35 were used to record intracellular
responses from photoreceptors R1-6 in the intact retina of the blowfly (
Calliphora vicina) to calibrate the effective intensity of illumination
of each cell by counting quantum bumps and to measure membrane resistance
by injecting randomly modulated current via a single electrode-switched clamp.
Calculating photoreceptor atp consumption
Our circuit model of the photoreceptor membrane (Fig.
2) is based on biophysical measurements34,
36. The
light-gated conductance, gL, admits a current, i
L, with a reversal potential, EL = 5 mV, given
by
 (2)
A voltage-gated, delayed-rectifier conductance,
gK, provides a counter-balancing current of potassium ions,
iK, reversal potential EK = -85 mV, given
by
 (3)
The vigorous electrogenic pump10,
11,
12
extrudes three sodium ions and takes up two potassium ions for every ATP molecule
hydrolyzed. The pump maintains the internal potassium concentration by accumulating
potassium ions at a rate equal to the outward potassium current, i
K, and this specifies a net pump current,
 (4)
Equating all currents across the model membrane
 (5)
and specifying
that total membrane conductance
 (6)
gives five equations (2, 3, 4, 5
, 6) that specify the flow of ions in this circuit.
Inserting our measurements of Em and gtotal,
and published values of EL, & EK,34,
36, we solve to obtain the currents flowing across
the membrane of a single photoreceptor in daylight:
Note that the
ratio between currents, iL:iK, equals the Na
+:K+ ratio in the pump, and the system maintains both
sodium and potassium concentrations. Inserting the value for iK
in equation gives the pump current, and hence the rate of ATP hydrolysis
in a single photoreceptor as 7.5 109 ATP molecules
per second.
The presynaptic costs of neurotransmitter release and uptake.
Transmitter circulates by being released from vesicles into the synaptic
cleft, taken up from the cleft into the presynaptic terminal, and then pumped
back into vesicles. The costs of release (presynaptic calcium fluxes, vesicle
docking and release) are likely to be comparatively small because a large
number of transmitter molecules are released with each vesicle. Work on the
output synapses of barnacle photoreceptors37 suggests that histamine
is removed from the cleft by a sodium-dependent monoamine transporter in the
presynaptic terminal that cotransports three sodium ions per amine molecule38. Restoration of these three sodium ions by the exchange pump requires
one ATP molecule. We assume that synaptic vesicles are loaded by a monoamine/proton
exchange pump39 that exchanges two protons, and hence hydrolyzes
0.67 ATP molecules, for every histamine translocated. Combining these two
mechanisms, the rate of ATP hydrolysis is 1.67 times the circulating flux
of histamine.
Three methods are used to estimate the histamine flux. The first is from
the vesicle release rate. Analysis of synaptic noise40 indicates
that, at any one time, an LMC is being driven by at most 160 noise events,
each with a time constant of 0.5 ms. If a noise event is a vesicle discharge,
every synapse is discharging 240 vesicles per second. The average vesicle
outer diameter is 35 nm and the membrane thickness 4 nm41. With
a 0.1 M transmitter concentration22, each vesicle contains 600
histamine molecules. Multiplying vesicle content by release rate gives a histamine
flux of 1.4105 molecules per synapse per second. The
second calculation is from the affinity of the histamine-gated chloride channels
for histamine and the dimensions of the synaptic cleft. The synapses are tonically
active in the midpoint of their operating range. At the very most, approximately
half of the chloride channels are being gated at any one time. This requires
a minimum average histamine concentration in the cleft of 40 M42. The area of synaptic contact measures 500 nm x 200 nm, and the
cleft is 20 nm across, giving 50 histamine molecules per cleft. The brevity
of the synaptic impulse40 response suggests that histamine is
cleared from the cleft in approximately 1 ms, giving a histamine flux of 5
104 molecules per synaptic cleft per second. The third
calculation is from the histamine-gated chloride conductance, gCl,
which is 13 nS from our biophysical model based on measurements of LMC input
resistance. A single histamine-gated chloride channel has a conductance of
50 pS and binds three histamine molecules to open for 0.5 ms42.
Consequently an LMC's chloride conductance binds 1.6106
histamine molecules per second, corresponding to 1.2103
histamine molecules per synapse per second. An LMC is one of four postsynaptic
elements, and if each histamine released presynaptically is bound once by
a chloride channel before being taken up, the necessary histamine flux is
5 103 histamine molecules per synapse per second.
Note that the second and third calculations ignore the losses of histamine
by diffusion and by uptake from the cleft prior to channel activation.
To avoid underestimating synaptic costs, we take the highest (first) estimate
of histamine flux, which gives an ATP consumption of 1.67 1.4
105 or roughly 2 105 ATP molecules
per synapse per second.
Bit cost versus rate for an array of photoreceptor-to-lmc synapses.
We consider a signal carried from photoreceptor to LMC by a parallel array
of identical synapses. The power density spectrum for the optimal signal,
S(f), and for noise, N(f), at a single synapse has been estimated
experimentally8, using a signal of rms contrast 0.316. An array
of ns synapses transmits information at a rate, I,
of
 (7)
The rate of
ATP consumption by the array is ns times the consumption
by a single synapse, which we calculate from the postsynaptic chloride flux
derived in the main body of the text to be 4 106 ATP
molecules per second.
Received 19 February 1998; Accepted 18 March 1998
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Acknowledgments
We would like to thank W. Bialek, D. Bray, R. Carpenter, R.C. Hardie, J.H.
van Hateren and D.C. O'Carroll for their comments and suggestions, and A.
Ames for his encouragement and an excellent introduction to the energetics
of neural function.
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