The Metabolic Cost of Information - a Fundamental Factor in Visual Ecology
179
This classic formula (Shannon 1949) shows how the information transmission
rate increases in proportion to bandwidth b, (the frequency range from zero to the
highest frequency transmitted, b) and as the log of the frequency dependent SNR,
S(f)/N(f). (For a clear introduction to information theory, in the context of neural
coding, consult Rieke et a!. 1997). Applying this formula to signal and noise
power spectra, a photoreceptor transmits I 000 bits s· 1 and the postsynaptic LMC
I600 bits s· 1 • The LMC transmits at a higher rate because the convergence of
signals from six photoreceptors has increased the SNR. Serial EM reconstruction
shows that each photoreceptor drives an LMC through 220 identical chemical
synapses (Nicol and Meinertzhagen I982). Transmission across this massive
parallel array of synapses improves the SNR because the synaptic noise (noise
generated independently in each synapse) is reduced by averaging over many
synapses. From the bit rates in pre- and postsynaptic cells, and the numbers of
synapses involved, each synapse transmits 55 bits s· 1 •
The metabolic cost of the information transmitted by photoreceptors, LMCs and
synapses is calculated from the electrical current used to produce voltage
responses (Laughlin et a!. I998). To estimate currents one constructs membrane
models from biophysical data. These electrical circuits (Fig. 3) incorporate the
ionic batteries that drive current, the conductances through which ionic currents
flow, and the pumps that keep the batteries charged by maintaining the ionic
concentration gradients. The circuits (Fig. 3) are solved, using appropriate
measurements of total membrane conductance and membrane potential to give
the flux of ions across the membrane and the rates at which pumps must
hydrolyze ATP to restore these ions and maintain the concentration gradients that
drive current.
Dividing the A TP hydrolysis rate by the bit rate gives a cost of 7 x I 0 6 A TP
molecules per bit in a photoreceptor and approximately 2 x I 0 6 A TP/bit in an
LMC. The LMC value is lower because efficient coding cuts costs. Redundant
components are removed when the signal is transferred from photoreceptor to
LMC. These components cost A TP to generate, but carry no information. It costs
50 times less, about 4 x 10 4 A TP molecules, to transmit a bit across a single
photoreceptor-LMC synapse. The reasons for this lower cost are instructive.
Because it is generated by 1320 identical synapses (220 from each of six
photoreceptors), the cost of the LMC signal is 1320 times the cost at a single
synapse. However, the rate at which information is transmitted by the LMC is
only 29 times the rate at a single synapse. The massive shortfall in LMC bit rate
results from massive redundancy - each of the 1320 synapses is carrying the
same signal. This redundancy is the inevitable consequence of using parallel
synapses to reduce the effects of synaptic noise. Each syn~pse severely
contaminates the signal with noise, hence its low rate of 55 bits s· 1 (de Ruyter van
Steveninck and Laughlin 1996). To rid the system of this synaptic noise, the
signal is transmitted through parallel synapses. This improves the SNR by -./1320,
and raises the information transmission rate to 1600 bits s· 1 • Essentially, the total
cost of transmission is increasing in proportion to the number of synapses, but the
179
This classic formula (Shannon 1949) shows how the information transmission
rate increases in proportion to bandwidth b, (the frequency range from zero to the
highest frequency transmitted, b) and as the log of the frequency dependent SNR,
S(f)/N(f). (For a clear introduction to information theory, in the context of neural
coding, consult Rieke et a!. 1997). Applying this formula to signal and noise
power spectra, a photoreceptor transmits I 000 bits s· 1 and the postsynaptic LMC
I600 bits s· 1 • The LMC transmits at a higher rate because the convergence of
signals from six photoreceptors has increased the SNR. Serial EM reconstruction
shows that each photoreceptor drives an LMC through 220 identical chemical
synapses (Nicol and Meinertzhagen I982). Transmission across this massive
parallel array of synapses improves the SNR because the synaptic noise (noise
generated independently in each synapse) is reduced by averaging over many
synapses. From the bit rates in pre- and postsynaptic cells, and the numbers of
synapses involved, each synapse transmits 55 bits s· 1 •
The metabolic cost of the information transmitted by photoreceptors, LMCs and
synapses is calculated from the electrical current used to produce voltage
responses (Laughlin et a!. I998). To estimate currents one constructs membrane
models from biophysical data. These electrical circuits (Fig. 3) incorporate the
ionic batteries that drive current, the conductances through which ionic currents
flow, and the pumps that keep the batteries charged by maintaining the ionic
concentration gradients. The circuits (Fig. 3) are solved, using appropriate
measurements of total membrane conductance and membrane potential to give
the flux of ions across the membrane and the rates at which pumps must
hydrolyze ATP to restore these ions and maintain the concentration gradients that
drive current.
Dividing the A TP hydrolysis rate by the bit rate gives a cost of 7 x I 0 6 A TP
molecules per bit in a photoreceptor and approximately 2 x I 0 6 A TP/bit in an
LMC. The LMC value is lower because efficient coding cuts costs. Redundant
components are removed when the signal is transferred from photoreceptor to
LMC. These components cost A TP to generate, but carry no information. It costs
50 times less, about 4 x 10 4 A TP molecules, to transmit a bit across a single
photoreceptor-LMC synapse. The reasons for this lower cost are instructive.
Because it is generated by 1320 identical synapses (220 from each of six
photoreceptors), the cost of the LMC signal is 1320 times the cost at a single
synapse. However, the rate at which information is transmitted by the LMC is
only 29 times the rate at a single synapse. The massive shortfall in LMC bit rate
results from massive redundancy - each of the 1320 synapses is carrying the
same signal. This redundancy is the inevitable consequence of using parallel
synapses to reduce the effects of synaptic noise. Each syn~pse severely
contaminates the signal with noise, hence its low rate of 55 bits s· 1 (de Ruyter van
Steveninck and Laughlin 1996). To rid the system of this synaptic noise, the
signal is transmitted through parallel synapses. This improves the SNR by -./1320,
and raises the information transmission rate to 1600 bits s· 1 • Essentially, the total
cost of transmission is increasing in proportion to the number of synapses, but the