How robust is a neural circuit?

Parallel Computations in Insect and Mammalian Visual Motion Processing

Sensory systems use receptors to extract information from the environment and neural circuits to perform subsequent computations. These computations may be described as algorithms composed of sequential mathematical operations. Comparing these operations across taxa reveals how different neural circuits have evolved to solve the same problem, even when using different mechanisms to implement the underlying math. In this review, we compare how insect and mammalian neural circuits have solved the problem of motion estimation, focusing on the fruit fly Drosophila and the mouse retina. Although the two systems implement computations with grossly different anatomy and molecular mechanisms, the underlying circuits transform light into motion signals with strikingly similar processing steps. These similarities run from photoreceptor gain control and spatiotemporal tuning to ON and OFF pathway structures, motion detection, and computed motion signals. The parallels between the two systems suggest that a limited set of algorithms for estimating motion satisfies both the needs of sighted creatures and the constraints imposed on them by metabolism, anatomy, and the structure and regularities of the visual world.

Why do axons differ in caliber?

CNS axons differ in diameter (d) by nearly 100-fold (∼0.1-10 μm); therefore, they differ in cross-sectional area (d(2)) and volume by nearly 10,000-fold. If, as found for optic nerve, mitochondrial volume fraction is constant with axon diameter, energy capacity would rise with axon volume, also as d(2). We asked, given constraints on space and energy, what functional requirements set an axon's diameter? Surveying 16 fiber groups spanning nearly the full range of diameters in five species (guinea pig, rat, monkey, locust, octopus), we found the following: (1) thin axons are most numerous; (2) mean firing frequencies, estimated for nine of the identified axon classes, are low for thin fibers and high for thick ones, ranging from ∼1 to >100 Hz; (3) a tract's distribution of fiber diameters, whether narrow or broad, and whether symmetric or skewed, reflects heterogeneity of information rates conveyed by its individual fibers; and (4) mitochondrial volume/axon length rises ≥d(2). To explain the pressure toward thin diameters, we note an established law of diminishing returns: an axon, to double its information rate, must more than double its firing rate. Since diameter is apparently linear with firing rate, doubling information rate would more than quadruple an axon's volume and energy use. Thicker axons may be needed to encode features that cannot be efficiently decoded if their information is spread over several low-rate channels. Thus, information rate may be the main variable that sets axon caliber, with axons constrained to deliver information at the lowest acceptable rate.

Ectopic synaptic ribbons in dendrites of mouse retinal ON- and OFF-bipolar cells

The ectopic distribution of synaptic ribbons in dendrites of mouse retinal bipolar cells was examined by using genetic ablation of metabotropic glutamate receptor subtype 6 (mGluR6), electron microscopy, and immunocytochemistry. Ectopic ribbons were observed in dendrites of rod and ON-cone bipolar cells in the mGluR6-deficient mouse but not in those of wild-type mice. The number of rod spherules facing the ectopic ribbons in mGluR6-deficient rod bipolar dendrites increased gradually during early growth and reached a plateau level of about 20% at 12 weeks. These ectopic ribbons were immunopositive for RIBEYE, a ribbon-specific protein, but the associated vesicles were immunonegative for synaptophysin, a synaptic-vesicle-specific protein. The presence of ectopic ribbons was correlated with an increase in the roundness of the invaginating dendrites of the rod bipolar cells. We further confirmed ectopic ribbons in dendrites of OFF-cone bipolar cells in wild-type retinas. Of the four types of OFF-cone bipolar cells (T1-T4), only the T2-type, which had a greater number of synaptic ribbons at the axon terminal and a thicker axon cylinder than the other types, had ectopic ribbons. Light-adapted experiments revealed that, in wild-type mice under enhanced-light adaptation (considered similar to the mGluR6-deficient state), the roundness in the invaginating dendrites and axon terminals of rod bipolar cells increased, but no ectopic ribbons were detected. Based on these findings and known mechanisms for neurotransmitter release and protein trafficking, the possible mechanisms underlying the ectopic ribbons are discussed on the basis of intracellular transport for the replenishment of synaptic proteins.

How the optic nerve allocates space, energy capacity, and information

Fiber tracts should use space and energy efficiently, because both resources constrain neural computation. We found for a myelinated tract (optic nerve) that astrocytes use nearly 30% of the space and >70% of the mitochondria, establishing the significance of astrocytes for the brain's space and energy budgets. Axons are mostly thin with a skewed distribution peaking at 0.7 microm, near the lower limit set by channel noise. This distribution is matched closely by the distribution of mean firing rates measured under naturalistic conditions, suggesting that firing rate increases proportionally with axon diameter. In axons thicker than 0.7 microm, mitochondria occupy a constant fraction of axonal volume--thus, mitochondrial volumes rise as the diameter squared. These results imply a law of diminishing returns: twice the information rate requires more than twice the space and energy capacity. We conclude that the optic nerve conserves space and energy by sending most information at low rates over fine axons with small terminal arbors and sending some information at higher rates over thicker axons with larger terminal arbors but only where more bits per second are needed for a specific purpose. Thicker axons seem to be needed, not for their greater conduction velocity (nor other intrinsic electrophysiological purpose), but instead to support larger terminal arbors and more active zones that transfer information synaptically at higher rates.

Ideal observer analysis of signal quality in retinal circuits

The function of the retina is crucial, for it must encode visual signals so the brain can detect objects in the visual world. However, the biological mechanisms of the retina add noise to the visual signal and therefore reduce its quality and capacity to inform about the world. Because an organism's survival depends on its ability to unambiguously detect visual stimuli in the presence of noise, its retinal circuits must have evolved to maximize signal quality, suggesting that each retinal circuit has a specific functional role. Here we explain how an ideal observer can measure signal quality to determine the functional roles of retinal circuits. In a visual discrimination task the ideal observer can measure from a neural response the increment threshold, the number of distinguishable response levels, and the neural code, which are fundamental measures of signal quality relevant to behavior. It can compare the signal quality in stimulus and response to determine the optimal stimulus, and can measure the specific loss of signal quality by a neuron's receptive field for non-optimal stimuli. Taking into account noise correlations, the ideal observer can track the signal-to-noise ratio available from one stage to the next, allowing one to determine each stage's role in preserving signal quality. A comparison between the ideal performance of the photon flux absorbed from the stimulus and actual performance of a retinal ganglion cell shows that in daylight a ganglion cell and its presynaptic circuit loses a factor of approximately 10-fold in contrast sensitivity, suggesting specific signal-processing roles for synaptic connections and other neural circuit elements. The ideal observer is a powerful tool for characterizing signal processing in single neurons and arrays along a neural pathway.

Loss of sensitivity in an analog neural circuit

A low-contrast spot that activates just one ganglion cell in the retina is detected in the spike train of the cell with about the same sensitivity as it is detected behaviorally. This is consistent with Barlow's proposal that the ganglion cell and later stages of spiking neurons transfer information essentially without loss. Yet, when losses of sensitivity by all preneural factors are accounted for, predicted sensitivity near threshold is considerably greater than behavioral sensitivity, implying that somewhere in the brain information is lost. We hypothesized that the losses occur mainly in the retina, where graded signals are processed by analog circuits that transfer information at high rates and low metabolic cost. To test this, we constructed a model that included all preneural losses for an in vitro mammalian retina, and evaluated the model to predict sensitivity at the cone output. Recording graded responses postsynaptic to the cones (from the type A horizontal cell) and comparing to predicted preneural sensitivity, we found substantial loss of sensitivity (4.2-fold) across the first visual synapse. Recording spike responses from brisk-transient ganglion cells stimulated with the same spot, we found a similar loss (3.5-fold) across the second synapse. The total retinal loss approximated the known overall loss, supporting the hypothesis that from stimulus to perception, most loss near threshold is retinal.

Role of the synaptic ribbon in transmitting the cone light response

Cone photoreceptors distinguish small changes in light intensity while operating over a wide dynamic range. The cone synapse encodes intensity by modulating tonic neurotransmitter release, but precise encoding is limited by the quantal nature of synaptic vesicle exocytosis. Cones possess synaptic ribbons, structures that are thought to accelerate the delivery of vesicles for tonic release. Here we show that the synaptic ribbon actually constrains vesicle delivery, resulting in a maintained state of synaptic depression in darkness. Electron microscopy of cones from the lizard Anolis segrei revealed that depression is caused by the depletion of vesicles on the ribbon, indicating that resupply, not fusion, is the rate-limiting step that controls release. Responses from postsynaptic retinal neurons from the salamander Ambystoma tigrinum showed that the ribbon behaves like a capacitor, charging with vesicles in light and discharging in a phasic burst at light offset. Phasic release extends the operating range of the cone synapse to more accurately encode changes in light intensity, accentuating features that are salient to photopic vision.