The Metabolic Cost of Information - a Fundamental Factor in Visual Ecology
177
This precise optimization of response strongly supports Barlow's proposal that
the goal of retinal processing is to maximize the information coded by neurons;
but is this goal relevant? Information theory treats all bits of information as units
of equal value. This disregard of context and meaning apparently contradicts the
purpose of sensory processing, namely the assignment of biological significance
to incoming data. However, one must use a context-independent measure, such as
the bit, when one is assessing the overall quality of a large data set from which
many different meanings will be extracted. The visual system interrogates the
retinal image to discern shape, depth, motion, color, and polarization, under a
variety of lighting conditions, and with objects at different angles and distances.
Note that efficient coding involves a careful match between sensitivity and
signal. Systems that code efficiently are adhering to one of the oldest principles in
sensory ecology: they place their receptors and neural machinery where they
expect the signals to be (Laughlin 1983). For example, bats and electric fish tune
their receptors to the signals that they use for communication and active sense.
Moreover, many sensory systems take account of redundant and predictable
components; e.g. efference copy exploits the predictable outcomes of releasing
energy into the environment (Bell et al. 1993). These examples reinforce the
proposition that, because the resources available for sensory processing are
limited, Natural Selection favours the individuals who use their resources efficiently so as to improve the ratio between benefit and cost. We can quantify one
cost-benefit relationship, the metabolic energy required to code information.
6 The Metabolic Cost of Neural Information
Measurements from the blowfly compound eye suggest fun~amental relationships
between energy and information, of the type seen in telecommunications and
computation, and first suggested by Szilard's analysis of Maxwell's demon
(Laughlin et al. 1998). The analogue electrical responses of photoreceptors and
LMCs are analyzed to determine the rates at which they transmit information
about the stimulus contrast at their pixel. From the biophysical properties of the
photoreceptor and LMC one calculates the current required to generate the
electrical responses (Fig. 3), and this gives the metabolic cost.
The information transmission rates were measured by driving photoreceptors
and LMCs with random stimuli of natural contrast and daylight intensity (de
Ruyter van Steveninck and Laughlin 1996). Signal and noise were extracted
from responses and converted into their respective power spectra, S(f} and N(f),
where f is frequency in Hz. Because signal and noise are Gaussian, the rate at
which information transmitted, /, in bits s· 1 , is given by
1= Jiog 2 [1+S(f)/ N(f)]df
0
177
This precise optimization of response strongly supports Barlow's proposal that
the goal of retinal processing is to maximize the information coded by neurons;
but is this goal relevant? Information theory treats all bits of information as units
of equal value. This disregard of context and meaning apparently contradicts the
purpose of sensory processing, namely the assignment of biological significance
to incoming data. However, one must use a context-independent measure, such as
the bit, when one is assessing the overall quality of a large data set from which
many different meanings will be extracted. The visual system interrogates the
retinal image to discern shape, depth, motion, color, and polarization, under a
variety of lighting conditions, and with objects at different angles and distances.
Note that efficient coding involves a careful match between sensitivity and
signal. Systems that code efficiently are adhering to one of the oldest principles in
sensory ecology: they place their receptors and neural machinery where they
expect the signals to be (Laughlin 1983). For example, bats and electric fish tune
their receptors to the signals that they use for communication and active sense.
Moreover, many sensory systems take account of redundant and predictable
components; e.g. efference copy exploits the predictable outcomes of releasing
energy into the environment (Bell et al. 1993). These examples reinforce the
proposition that, because the resources available for sensory processing are
limited, Natural Selection favours the individuals who use their resources efficiently so as to improve the ratio between benefit and cost. We can quantify one
cost-benefit relationship, the metabolic energy required to code information.
6 The Metabolic Cost of Neural Information
Measurements from the blowfly compound eye suggest fun~amental relationships
between energy and information, of the type seen in telecommunications and
computation, and first suggested by Szilard's analysis of Maxwell's demon
(Laughlin et al. 1998). The analogue electrical responses of photoreceptors and
LMCs are analyzed to determine the rates at which they transmit information
about the stimulus contrast at their pixel. From the biophysical properties of the
photoreceptor and LMC one calculates the current required to generate the
electrical responses (Fig. 3), and this gives the metabolic cost.
The information transmission rates were measured by driving photoreceptors
and LMCs with random stimuli of natural contrast and daylight intensity (de
Ruyter van Steveninck and Laughlin 1996). Signal and noise were extracted
from responses and converted into their respective power spectra, S(f} and N(f),
where f is frequency in Hz. Because signal and noise are Gaussian, the rate at
which information transmitted, /, in bits s· 1 , is given by
1= Jiog 2 [1+S(f)/ N(f)]df
0