Limits...
Fly photoreceptors demonstrate energy-information trade-offs in neural coding.

Niven JE, Anderson JC, Laughlin SB - PLoS Biol. (2007)

Bottom Line: Comparing species, the fixed cost, the total cost of signalling, and the unit cost (cost per bit) all increase with a photoreceptor's highest information rate to make information more expensive in higher performance cells.This law of diminishing returns promotes the evolution of economical structures by severely penalising overcapacity.Similar relationships could influence the function and design of many neurons because they are subject to similar biophysical constraints on information throughput.

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of Cambridge, Cambridge, United Kingdom.

ABSTRACT
Trade-offs between energy consumption and neuronal performance must shape the design and evolution of nervous systems, but we lack empirical data showing how neuronal energy costs vary according to performance. Using intracellular recordings from the intact retinas of four flies, Drosophila melanogaster, D. virilis, Calliphora vicina, and Sarcophaga carnaria, we measured the rates at which homologous R1-6 photoreceptors of these species transmit information from the same stimuli and estimated the energy they consumed. In all species, both information rate and energy consumption increase with light intensity. Energy consumption rises from a baseline, the energy required to maintain the dark resting potential. This substantial fixed cost, approximately 20% of a photoreceptor's maximum consumption, causes the unit cost of information (ATP molecules hydrolysed per bit) to fall as information rate increases. The highest information rates, achieved at bright daylight levels, differed according to species, from approximately 200 bits s(-1) in D. melanogaster to approximately 1,000 bits s(-1) in S. carnaria. Comparing species, the fixed cost, the total cost of signalling, and the unit cost (cost per bit) all increase with a photoreceptor's highest information rate to make information more expensive in higher performance cells. This law of diminishing returns promotes the evolution of economical structures by severely penalising overcapacity. Similar relationships could influence the function and design of many neurons because they are subject to similar biophysical constraints on information throughput.

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Intracellular Recordings of Voltage Responses and the Distribution of Information across Frequencies in R1–6 Photoreceptors of D. melanogaster and S. carnaria(A) Quantum bumps (*) recorded from D. melanogaster in response to continuous illumination by the white-noise stimulus (lower trace, grey), which was attenuated by 5.5 log units to give a mean effective photon rate of 9 s−1.(B) Average responses of a D. melanogaster R1–6 photoreceptor to 50 repetitions of a randomly modulated light of mean contrast 0.32.(C) The corresponding average response of an R1–6 photoreceptor from S. carnaria. Note that the responses in (B) and (C) have dissimilar waveforms because they were generated by different random sequences of intensity modulation, shown in grey beneath each voltage record. In both (B) and (C) the mean stimulus intensity was set to approximately 5 × 106 effective photons s−1. Note that S. carnaria R1–6 responses (C) vary more rapidly than D. melanogaster (B).(D) This faster response gave the S. carnaria R1–6 a wider bandwidth, as demonstrated in (D) by plotting the distribution of information across response frequency for the two cells.
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pbio-0050116-g001: Intracellular Recordings of Voltage Responses and the Distribution of Information across Frequencies in R1–6 Photoreceptors of D. melanogaster and S. carnaria(A) Quantum bumps (*) recorded from D. melanogaster in response to continuous illumination by the white-noise stimulus (lower trace, grey), which was attenuated by 5.5 log units to give a mean effective photon rate of 9 s−1.(B) Average responses of a D. melanogaster R1–6 photoreceptor to 50 repetitions of a randomly modulated light of mean contrast 0.32.(C) The corresponding average response of an R1–6 photoreceptor from S. carnaria. Note that the responses in (B) and (C) have dissimilar waveforms because they were generated by different random sequences of intensity modulation, shown in grey beneath each voltage record. In both (B) and (C) the mean stimulus intensity was set to approximately 5 × 106 effective photons s−1. Note that S. carnaria R1–6 responses (C) vary more rapidly than D. melanogaster (B).(D) This faster response gave the S. carnaria R1–6 a wider bandwidth, as demonstrated in (D) by plotting the distribution of information across response frequency for the two cells.

Mentions: We measured information rates from intracellular recordings of voltage responses to optical signals (Figure 1) [33]. The photoreceptor was first adapted to a background light whose effective intensity had been calibrated as an effective photon rate by counting that same photoreceptor's discrete responses to single photons (see Materials and Methods; Figure 1A). This calibration takes account of differences in acceptance angle and sensitivity and enables us to compare the performance of photoreceptors receiving the same number of photons. Once stably adapted, the photoreceptor was presented with multiple repeats of the same brief sequence of pseudorandom modulation of the light around the background intensity (Figure 1B and 1C). The mean contrast of this modulation (standard deviation/mean) was 0.32, a value close to that of natural scenes (see Materials and Methods). Photoreceptors encode the fluctuations in stimulus contrast as a graded (analogue) modulation of membrane potential that is contaminated by noise. We extracted the photoreceptor's voltage signal (Figure 1B and 1C) by averaging the responses (averaging eliminates noise) and then extracted the noise by subtracting our estimate of the signal from the response to each stimulus repeat. Our estimate of the signal was transformed into the signal power spectrum S(f). Each of the extracted noise traces was transformed, and the resulting ensemble of spectra was averaged to generate the noise power spectrum N(f). Both signal and noise were distributed normally, allowing the rate at which the photoreceptor transmits information I in bits s−1 to be determined by applying Shannon's formula [38] to the power spectra of the signal S(f) and noise N(f):The logarithmic term in this equation is the distribution of information across frequencies, as plotted in Figure 1D.


Fly photoreceptors demonstrate energy-information trade-offs in neural coding.

Niven JE, Anderson JC, Laughlin SB - PLoS Biol. (2007)

Intracellular Recordings of Voltage Responses and the Distribution of Information across Frequencies in R1–6 Photoreceptors of D. melanogaster and S. carnaria(A) Quantum bumps (*) recorded from D. melanogaster in response to continuous illumination by the white-noise stimulus (lower trace, grey), which was attenuated by 5.5 log units to give a mean effective photon rate of 9 s−1.(B) Average responses of a D. melanogaster R1–6 photoreceptor to 50 repetitions of a randomly modulated light of mean contrast 0.32.(C) The corresponding average response of an R1–6 photoreceptor from S. carnaria. Note that the responses in (B) and (C) have dissimilar waveforms because they were generated by different random sequences of intensity modulation, shown in grey beneath each voltage record. In both (B) and (C) the mean stimulus intensity was set to approximately 5 × 106 effective photons s−1. Note that S. carnaria R1–6 responses (C) vary more rapidly than D. melanogaster (B).(D) This faster response gave the S. carnaria R1–6 a wider bandwidth, as demonstrated in (D) by plotting the distribution of information across response frequency for the two cells.
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pbio-0050116-g001: Intracellular Recordings of Voltage Responses and the Distribution of Information across Frequencies in R1–6 Photoreceptors of D. melanogaster and S. carnaria(A) Quantum bumps (*) recorded from D. melanogaster in response to continuous illumination by the white-noise stimulus (lower trace, grey), which was attenuated by 5.5 log units to give a mean effective photon rate of 9 s−1.(B) Average responses of a D. melanogaster R1–6 photoreceptor to 50 repetitions of a randomly modulated light of mean contrast 0.32.(C) The corresponding average response of an R1–6 photoreceptor from S. carnaria. Note that the responses in (B) and (C) have dissimilar waveforms because they were generated by different random sequences of intensity modulation, shown in grey beneath each voltage record. In both (B) and (C) the mean stimulus intensity was set to approximately 5 × 106 effective photons s−1. Note that S. carnaria R1–6 responses (C) vary more rapidly than D. melanogaster (B).(D) This faster response gave the S. carnaria R1–6 a wider bandwidth, as demonstrated in (D) by plotting the distribution of information across response frequency for the two cells.
Mentions: We measured information rates from intracellular recordings of voltage responses to optical signals (Figure 1) [33]. The photoreceptor was first adapted to a background light whose effective intensity had been calibrated as an effective photon rate by counting that same photoreceptor's discrete responses to single photons (see Materials and Methods; Figure 1A). This calibration takes account of differences in acceptance angle and sensitivity and enables us to compare the performance of photoreceptors receiving the same number of photons. Once stably adapted, the photoreceptor was presented with multiple repeats of the same brief sequence of pseudorandom modulation of the light around the background intensity (Figure 1B and 1C). The mean contrast of this modulation (standard deviation/mean) was 0.32, a value close to that of natural scenes (see Materials and Methods). Photoreceptors encode the fluctuations in stimulus contrast as a graded (analogue) modulation of membrane potential that is contaminated by noise. We extracted the photoreceptor's voltage signal (Figure 1B and 1C) by averaging the responses (averaging eliminates noise) and then extracted the noise by subtracting our estimate of the signal from the response to each stimulus repeat. Our estimate of the signal was transformed into the signal power spectrum S(f). Each of the extracted noise traces was transformed, and the resulting ensemble of spectra was averaged to generate the noise power spectrum N(f). Both signal and noise were distributed normally, allowing the rate at which the photoreceptor transmits information I in bits s−1 to be determined by applying Shannon's formula [38] to the power spectra of the signal S(f) and noise N(f):The logarithmic term in this equation is the distribution of information across frequencies, as plotted in Figure 1D.

Bottom Line: Comparing species, the fixed cost, the total cost of signalling, and the unit cost (cost per bit) all increase with a photoreceptor's highest information rate to make information more expensive in higher performance cells.This law of diminishing returns promotes the evolution of economical structures by severely penalising overcapacity.Similar relationships could influence the function and design of many neurons because they are subject to similar biophysical constraints on information throughput.

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of Cambridge, Cambridge, United Kingdom.

ABSTRACT
Trade-offs between energy consumption and neuronal performance must shape the design and evolution of nervous systems, but we lack empirical data showing how neuronal energy costs vary according to performance. Using intracellular recordings from the intact retinas of four flies, Drosophila melanogaster, D. virilis, Calliphora vicina, and Sarcophaga carnaria, we measured the rates at which homologous R1-6 photoreceptors of these species transmit information from the same stimuli and estimated the energy they consumed. In all species, both information rate and energy consumption increase with light intensity. Energy consumption rises from a baseline, the energy required to maintain the dark resting potential. This substantial fixed cost, approximately 20% of a photoreceptor's maximum consumption, causes the unit cost of information (ATP molecules hydrolysed per bit) to fall as information rate increases. The highest information rates, achieved at bright daylight levels, differed according to species, from approximately 200 bits s(-1) in D. melanogaster to approximately 1,000 bits s(-1) in S. carnaria. Comparing species, the fixed cost, the total cost of signalling, and the unit cost (cost per bit) all increase with a photoreceptor's highest information rate to make information more expensive in higher performance cells. This law of diminishing returns promotes the evolution of economical structures by severely penalising overcapacity. Similar relationships could influence the function and design of many neurons because they are subject to similar biophysical constraints on information throughput.

Show MeSH