Chapter nine
Rods and cones as wave detectors

It is easy to see why an analogy between this photomultiplier and a photoreceptor cell is so often drawn. But the analogy is a trap.The photomultiplier tube was invented in the summer of 1930 in the Soviet Union by L.A. Kubetsky. It is easy to see from the photo why an analogy between the photoreceptor cell and this splendid antique technology is so often drawn. However, the analogy is not very strong, and it tends to make the photoreceptor story seem shorter and more succinct than it is.

Particles, rays and waves
A quantum of blue-green (500 nm) light packs quite a lot of chemical energy — 46 kcal/mole. Incoming photons can thus be conceived as vigorous potential reactants with the pigments: chlorophyll, phytochrome, the flavins and retinal. This physical biochemical perspective — in which light is styled as an energetic particle that might or might not strike and react with a pigment molecule target — underlies the commonplace view of the photoreceptor as a photon detector.

There are two other ways biologists regard light: as rays and as waves. The ray approach is typical and serviceable, but the wave description of light is essential in understanding diffraction, double diffraction image formation, natural mirrors based on interference, and structural color.

In the specific study of photoreceptors, the light-as-a-wave approach has chiefly been taken by investigators of the waveguide (fiberoptic) properties of these cells, and by the standing wave theorists. Let’s consider here what it would take to make the photoreceptors operate as standing wave detectors.

Particle detector versus wave detector
In the conventional view the photoreceptor is a one-channel analog device. It is a particle detector — it triggers on photons.

Here is how, in the retinal rod, the particle detector is thought to work. In darkness, the plasma membrane sodium channels are open, the membrane is depolarized, and at the output synapse the cell drips neurotransmitter like a constantly dripping faucet. Now admit a little light. When photons hit the pigment in disks, a biochemical cascade ensues that ends by closing the photoreceptor cell membrane’s ion channels. (These ion channels are for the most part ligand activated, rather than voltage activated.)

Thus, in response to light, the plasma membrane hyperpolarizes, that is, the transmembrane potential increases. Typical membrane potentials recorded from photoreceptors in the dark are about -30 mV. In response to bright light the cell may hyperpolarize by 20 to 30 mV to about -60 mV. Note that this is a value close to the resting potential of most neurons.

The transmembrane voltage change at the outer segment is “felt” all the way out at the ribbon synapse at the end of the inner segment, and at this synapse the dripping neurotransmitter faucet is tightened up. In understanding the system it is helpful to regard the neurotranmitter as inhibitory: Reduced inhibition => stimulation. In fact it isn’t consistently inhibitory, but it helps to think of it that way in a first pass.

Note that this is an utterly analog system. There are analog degrees of membrane hyperpolarization, dialed up and down by the intensity of the impinging light. It follows that while the system is within its operating range, not all of the ion channels are closed. In light, the synaptic faucet continues to drip neurotransmitter (glutamate), but it drips much less than it did in darkness. As the light gradually strengthens, more channels close, the transmembrane potential rises, and the synaptic output of dispensed neurotransmitter gradually decreases. Where that neurotransmitter is inhibitory, downstream cells are un-inhibited –stimulated. More photons, fewer drips, less inhibition, more downstream stimulus.

How could we possibly detect waves with this thing?
As a first step, the system needs a mirror to reflect incoming light waves back on themselves, and thus create a measurable standing wave. Several candidate mirrors have been suggested in the literature. In cone cells a mirror effect can be physically demonstrated. It seems probable that a rod cell mirror exists as well. Types of biological mirrors will be discussed in subsequent paragraphs.

The second, more challenging problem is one of keeping individual disks’ output signals straight. The photoreceptor response is, in textbooks, completely melded and generalized – a whole-cell response to impinging photons. The response is amplified in rod cells by a biochemical multiplication effect somewhat analogous (I would say slightly analogous) to the electronic avalanche in a photomultiplier tube. The voltage change at the plasma membrane is felt at the synapse, but there is no way to dissect the summed voltage signal. By this I mean there is no way to parse and trace the source of a signal back to any single disk. The individual disks’ signals have been magnified and pooled, and so the signal source is essentially the whole outer segment.

In this variably hyperpolarized system, how could we arrange to “wire” each disk in order to detect localized light intensities, e.g., standing wave peaks?

And how could we signal the detected result to the ribbon synapse? Where can we run the necessary cable?

There are two conduits available to send discrete biochemical signals from the disks toward the ribbon synapse: internal and external. The internal pathways could run through aligned incisures in the disks. I would be inclined to reserve these for communication or processing within the outer segment, but this is mainly because I lean toward the solution offered by the external pathways.

The external pathways are, theoretically, longitudinal channels in the plasma membrane, those of a multichannel neuron based on linked transmembrane sodium channels, and they are essentially what this blog is about.

In this micrograph, the “pm” signifies the plasma membrane.
To localize the response to each disk, it will be necessary as a first step to draw a line linking each disk to a corresponding point on the plasma membrane. In the cone there is no problem. Disk and wall are continuous. In the rod, given the proximity of the rim of each disk and the plasma membrane, some link or localized biochemical bridge is a realistic first assumption.

But how can we get a signal from a local point on the plasma membrane, opposite a disk, all the way out to the synapse?

Suppose we stick very closely to the linked sodium channel hypothesis described in Chapter 2, the Corduroy Neuron. Recall that in the model of the multichannel axon, the sodium channels are re-conceived as 300 or 400 linked continuous, longitudinal channels. The linked sodium channels were conceived as a model device to convey, and impart meaning to, action potentials. In the context of an analog photoreceptor neuron, about all we can say is that the hypothetical linkage of sodium channels provides a way to draw a continuous line, or channel, from a point on the plasma membrane opposite the rim of a disk — to a point as distant as the ribbon synapse.

Action potentials in rods and cones. But why?
Drawing a line isn’t enough. The channels must operate. The simplest and most typical operation would produce an action potential. There is another way to make the system work, discussed below, but let’s think about action potentials for a moment.

There is actually a nice body of literature on the subject of action potentials detected with patch clamps in vertebrate photoreceptors. It is thought that in lower vertebrates these action potentials depend upon calcium channels, but it was discovered in 2001 that in the human retinal rod, action potentials can arise quite conventionally from the operation of voltage-gated sodium channels. (In light of this discovery it was wondered whether in lower vertebrates the involvement of Na channels, as opposed to Ca channels, in the production of action potentials might have been missed.)

In humans, the voltage-gated Na channels and action potentials have now been demonstrated in both rods and cones.

Amacrine cells have also been shown to fire action potentials.

In other words, superimposed on the neat textbook story about the photoreceptor cell as an analog transduction system and photomultiplier, there is this other, isn’t-it-curious sidebar story, in which action potentials might figure in some obscure way in the operation of photoreceptor cells.

Night and day
Possibly what we are looking at here is a day/night divide. The rod photoreceptor could be like a computer with two different operating systems. Or like a photosynthetic organism, equipped with both a day biochemistry and night biochemistry. There would be many pathways in common, useful in either mode, but let’s guess it would take a major biochemical switch to get from day mode to night mode. A light switch.

The textbook, analog photoreceptor story is essentially a description of, and extrapolation from, the nocturnal rod’s operation as a photon detector and photomultiplier. This is an excellent system in dim light. None of the standing wave receptor theories is going to work in the dead of night. In darkness, a depolarized rod membrane could not possibly support an action potential.

At the other extreme, in broad daylight you would expect photomultipliers to saturate and ultimately shut down, and standing wave sensors to wake up and come into their own. Along with a daytime detection system, you might expect to see a distinct daytime rod biochemistry. Photoreceptor membranes would be hyperpolarized to the level of typical neurons’ resting potentials. And action potentials could thus become the favored mode of communication.

On a multichannel photoreceptor, the action potentials would rarely need to appear. Maybe once every time the eye shakes. But they would give us a way to get standing wave information out of the photoreceptor disks. Assuming some internal pre-processing of the photoreceptor (e.g., peak picking) it should be possible to communicate intensity and wavelength with just two or three spikes. A photoreceptor of this type is modeled in Chapter 12, in the discussion of the role of photoreceptors in memory.

How to do without with action potentials

The model requires some means to convey signals, via multiple channels, from each disk in the outer segment. The outer segment of a photoreceptor is analogous to the dendrites of a less exotic neuron. If action potentials are to appear here, they would have to be called dendritic spikes. It would seem more realistic to postpone the appearance of action potentials to a downstream site, the photoreceptor’s nominal axon. Is there a way, then, to launch a signal from a single photorecptor disk without using action potentials?


Na+ channels as a row of dominos.

In Chapter 3, in the discussion of myelinated nerves, we introduced the concept of a signal that moves along a neuron simply through the successive displacement of Na+ channel voltage sensors. The signal can be characterized as a wavefront of conformational change.

In the myelinated internode the sodium channels are inaccessible to sodium ions, and so the signal is perforce unaccompanied by action potentials. This type of signal might be detectable in principle, but in 2017 it could not be detected with any common instrument.

The signal is initially enabled by a sharp positive shift in the normally negative interior of the axon. The voltage sensors of the sodium channels, which are positively charged protein, are impelled outward (normal to the axolemma) by this enabling positive charge.

In the model, the voltage sensors are restrained from moving in unison by latches. The latch of each voltage sensor can only be released by the movement of the preceding voltage sensor. Accordingly, once a signal has been launched, the displacement of voltage sensors proceeds from the first unit Na+ channel in line to the next. The wavefront proceeds down the line of voltage sensors as though they were a row of falling dominos or, perhaps more aptly, popping corks.

In myelinated nerves, the initializing positive voltage shift is provided by the firing of action potentials at the nodes of Ranvier. Suppose we were to try to overlay this process on the outer segment of a photoreceptor.

What could provide the essential enabling positive charge? Possibly the disks.
These Na pumps are, in effect, flipped over as the cell membrane is transformed into disk membranes.
Disks form at the base of the outer segment by an outpouching of the cell membrane, as shown at a, b and c in the drawing. (Adopted from Steinberg et al, 1980). The green lines indicate the future interior of the disks. Suppose there were sodium pumps in the cell membrane. As the cell membrane is transformed into disk membrane, the sodium pumps are, in effect, flipped. In other words, they will actively pump any available Na+ into the disk instead of out of the cell. The rims of each disk could, by this means, be given a strong positive charge, positioned directly underneath the Na+ channel voltage sensors.

This is electronically similar to the enabling positive voltage found in the internode of a myelinated nerve, but there is an important difference.

In the internode, the voltage declines in a gradient as we move futher and further along the axon from its source: the positive ion current injection accompanying action potentials at the node.

In the photoreceptor, the positive charge is produced in each disk at the expense of ATP and it is solidly positive all along the length of the disk stack in the outer segment.

Here is a means to silently transmit a signal from each disk. The signal is “silent” in the sense that it does not create action potentials. In Chapter 3, we characterized this signal as a stealth impulse. The signal would be carried and energized, as in an internode, by a wave of successively ejecting voltage sensors. To avoid producing an action potential, which seems like a waste of time and energy in this context, the sodium channels would have to be inactivated in some way, since these cells, unlike myelinated internodes, do have access to extracellular sodium ions.

So there‘s a sketch of the basic idea: A line of successively unlatching voltage sensors carries the signal without inducing action potentials.

There are lots of questions here, including how (in detail) to launch a signal from a specific disk. Note too that the positive charges are close to the voltage sensors. If these charges are unrelenting, then how do the sensors recover after a channel is fired? The sensors must re-latch to recover. This suggests a periodic wave of negativity may pass down the outer segment to re-cock the sensors en masse.

Beyond the disk stack, the stealth impulse could no longer borrow its power from the positively charged disks. To create the necessary internal positive charge in the neuron, it would be necessary to proceed in the familiar way, that is, open the sodium channels and fire an action potential.

 
The ribbon synapse
At the output end of the photoreceptor is a ribbon synapse. This special type of synapse is found rods, cones, and bipolar cells. It is also found in the ear, in the cochlear hair cells and in the vestibular organ receptors. (The ear is more recently evolved than the eye. The resemblance of the two sensory systems, eye and ear, has often encouraged brain theorists to guess that the auditory system evolved following a pattern already established with the eye — and that whatever it is that the eye does, the ear probably does it too.)

Photoreceptor cells equipped with ribbon synapses release transmitter constantly, and alter the rate of release in response to small graded changes in potential, rather than in response to action potentials. There could be a rather more complicated story here, as noted above, but this is our present understanding of this complex device.

A ribbon synapse, after Dieck and Brandstätter. Ribbon synapses have different exocytotic machinery from that of conventional synapses. The synapse exhibits a dense bar or “ribbon” which is anchored like a balloon on a string to the presynaptic membrane. The bar is associated with synaptic vesicles as shown.

It has been proposed that the ribbon synapse operates in such a way as to shuttle synaptic vesicles to exocytotic sites. Here is another helpful review of ribbon synapse research.


The ribbon synapse is the logical centerpiece of the whole problem of the retina. To make sense of the ribbon synapse in terms of a multichannel nervous system, one would as a first step interpret the ribbon synapse as a cable connector.

Where we are.
We don’t really have a model for a wave detector photoreceptor here. We have enough components of a model to make it seem wave detection in photoreceptors is a possible mode of operation.

An easy tranche would be to declare the cones are wave detectors while the rods are particle detectors. Maybe a little too easy. The particle detector is a specialized adaptation to a nocturnal life style — nature’s gift to bush babies. The photon detector probably evolved as an extreme specialization of a wave detector. In other words, it appears the wave detector came first, and that its machinery is inherent in both rods and cones. Hence the notion of a day/night mode switch.

What has changed, conceptually? We know rods work in daylight. Our periferal vision depends on them. We have proposed here a particular daytime mode of operation, as a wave detector, to the rod cells. We are regarding cone cells as wave detectors rather than particle detectors. The cones are still restricted, as in the conventional view, to daylight operation. And the rods, working as particle detectors, can still count solitary photons on a moonless night.

We are also suggesting a day/night knife switch or biochemical shunt. It could alter the operation of a rod, or it could imply the existence of day-rods and night-rods. The day rod would be a wave detector. The night-rod would be a particle detector.

We have arrived at the day/night dichotomy in a roundabout way, tinkering with this and that — but it is a standalone idea, and depends on none of these theories. We have the commonplace example of plant photochemistry, which is radically different in the dark and in the light. In this scheme of things, it might turn out that some of our interpretations of ganglion spikes could reflect the experimenters’ unintended manipulation of day/night switches.

I am grateful to Gerald Huth for emphasizing and drawing my attention, on his site, to the distinctions between particle detectors and wave detectors in photoreceptors. Dr. Huth invented the silicon avalanche detector, a solid state technology that has supplanted the photomultiplier tube in many applications.

The essential mirror
From the abundance and variety of standing wave photoreceptor hypotheses, it seems clear that we might indeed be looking at the parts and pieces of a standing wave measuring system, an electronic wavelength or perhaps even phase detector. But one must begin at the beginning, and the gate question immediately arises — are standing waves even possible in this system?
To create a standing wave inside a photoreceptor the incoming wave must be reflected back on its path, and this requires a biological mirror. Fortunately mirrors are ubiquitous in nature, and they are especially common in eyes. Examples of natural mirrors include the mirrored flanks of fish, cats eyes in the headlights, and the iridescent wings of butterflies, moths, peacocks, and birds of paradise.

Eyes that form images using mirrors instead of lenses also exist, for example in the scallop. Just as we might elect to make a telescope from a mirror rather than a lens, so too can nature choose to build an eye using reflecting, rather than refracting optics.

Some observers think our own eye probably evolved from a more primitive eye that used a mirror, rather than a lens, to form images.

A striking example of a natural mirror is the pupa of the butterfly Euploea core. It is impressive to us because its appearance is so like that of a man-made mirror. The surface seems metallic, like a gold or silvered glass Christmas ornament. In forest light the pupa so faithfully mirrors the leaf from which it depends and the surrounding foliage that it essentially disappears. The mechanism of this mirror was studied by R. A. Steinbrecht, W. Mohren, H. K. Pulker, D. Schneider and reported in a classic paper in Proceedings of the Royal Society of London.

Photo by Viren Vaz.
The pupa of the danaid butterfly Euploea core.

The most strongly reflective natural mirrors work according to the principle of thin film interference, and are made up of multiple fine layers spaced at precisely specified intervals. However, some natural reflectors are just polished optical surfaces, offering simple specular reflection, like Bruch’s membrane or the surfaces of the lens or the cornea. We know that a reflection can occur at the interface between two materials with different refractive indices. For example, a reflection can occur at the interface between a photoreceptor cell and its extracellular surround. Similarly, a reflection can occur within the photoreceptor cell – that is, reflection can occur at the interfaces between the disks and the intracellular fluid.

As we begin to itemize reflective surfaces within the eye and, perhaps especially, within the individual photoreceptors, things start to get overcomplicated. To order the problem, let’s sort the mirrors by the two major planes in which they can reverse light. We will begin with the longitudinal mirrors and then consider transverse mirrors.

In the hall of mirrors…
In the various standing wave color vision hypotheses reviewed and discussed above, the effect of their essential orthogonal mirror would be to reflect (reverse) light waves arriving along the longitudinal or optical axis of the photoreceptor.

In their 1992 book, “Standing Wave Analysis: A new vision of color,” Jörg Krumeich and Alfred Knülle-Wenzel review the historical literature of standing wave color hypotheses, critique trichromacy, and present their own concept of color perception based on standing wave analysis. I am indebted to these authors for their deep and extensive literature search. Their hypothesis is also published in a 2002 paper, in Optica Applicata.

Drs. Krumeich and Knülle include a discussion of potential longitudinal mirrors in the eye. To their list I have added a mirror or two suggested in a different body of literature. Investigators of the Stiles Crawford effect have remarked that cone cells bounce back some of the light that enters. This implies the existence of a mirror, and so these researchers have also been interested in identifying candidate reflectors in the eye.

There appear to be at least six candidate mirrors.

    1. Bruch’s membrane
    2. the tapetum lucidum (although not in primates)
    3. disks or ensembles of disks within the photoreceptors
    4. lamellar inclusions clustered beneath the cones in the pigment epithelium. (in primates)
    5. The interface between the inner and outer segments
    6. The end of the outer segment

In the eye, the anatomically most evident reflective surfaces like the tapetum or Bruch’s membrane are positioned as planes orthogonal to, and skewered by, the optical or z-axis of the eye.

A less obvious mirror in this same plane, orthogonal to the optical axis of the eye, is formed by the photoreceptors’ disks, which can be conceived as reflectors working in concert. This concept was detailed by van Der Kratz in the 1996.

In a standing wave system it is also possible the disks may consititute internal mirrors positioned at wavelength intervals along the optical axis, since the disks’ “bleaching” necessarily alters their properies of transmittance and reflectance. The basic idea that the disks might form a mirror is a very old one. Krumeich and Knülle point out that Zenker, in the mid-1800s, seized upon this idea as soon as the disks were discovered. Zenker incorporated the disks as reflectors in his original hypothesis of standing wave color detection.

Krumeich and Knülle make a convincing case for Bruch’s membrane as the essential mirror. I will quote one of their points here: “Retinal detachments from Bruch’s membrane ceases immediately any function of the retina in this area. Traditionallly this blindness is put down to the interruption of nutrition to the cones, which should follow from the choroid. It is unknown why this blindness occurs immediately together with the detachment and why the reattachment of the retina onto Bruch’s membrane leads to an instant restoration of sight.” [italics added].

Upon detachment of the photoreceptors from the mirror one would surmise the standing wave would cease to exist. Upon reattachment, the standing wave would be instantly restored.

Krumeich and Knülle offer another fascinating conjecture: If Bruch’s membrane is the mirror for a standing wave, then the backwall of the eye is, in effect, the origin of the standing wave signal we would wish to detect. This offers, at long last, a physiological reason for inverted structure of the retina, in which the photoreceptors are mounted against, can be said to “look backwards” toward — the mirror.

In 1974, Niels Bülow reported his discovery in a monkey eye of strongly reflective inclusions clustered beneath the cone cells where the outer segments are seated in the pigment epithelium. These inclusions were not found, however, beneath rod cells. He remarked that “…the rods were inserted deeper into the pigment epithelium than the cones and passsed by the cluster of melanin granules at the end of the cones.” He reported five types of inclusions. The most interesting of these were lamellar, showing the characteristic structure of a multilayer natural mirror. Bülow first discovered the inclusions using light microscopy, and then went back after them with an EM.

Neils Bülow is the author of the standing wave color detection hypotheses in which the cone photoreceptors are seen as tuned cavity resonators. He has published two papers detailing his view of this possibility. Of the inclusions he remarks: “As regards the physical effect, it has been suggested that light scattered by the melanin granules (Bülow, 1968) may pass backward through the outer segments of the photoreceptors, where standing light waves may be produced under certain circumstances (Bülow, 1968). The present observation, that melanin granules are situated at the end of the cones but not at the end of the rods, suggests that passage of light from the melanin granules, backwards through the outersegments of the photoreceptors is possible only in the cones, not in the rods.”

The state of play:
All of the orthogonal mirrors remarked here have been incorporated in standing wave models or hypotheses. In addition, mathematical models of standing waves in photoreceptors have been created choosing as reflectors (essentially by executive fiat) the interface between the inner and outer segment at the ellipsoid, and the “end” or closure of the photoreceptor cell where the outer segment abuts the pigment epithelium.
The basic idea that standing waves should be found within cone cells is not widely celebrated — nor is it strongly contested or resisted in the literature. From my reading my impression is, it sort of gets a nod. The six or seven standing wave color detection theories are largely forgotten or discounted or still unheard of, so let’s guess the existence of a standing wave in a photoreceptor is not viewed by many people as a dangerous, insidious threat to Fort Trichromacy. It might in fact represent a challenge to trichromacy, or it might alter in some way our understanding of trichromacy, but this is not an issue many people are aware of or hurrying to controvert. This is because almost no one with an orthodox view of how the eye works — imagines that standing waves in photoreceptors could be detected.

We do know that cones cells are directional waveguides. When light is aimed straight into the cones – some of it comes straight back out again. This is not hypothetical — it can be demonstrated physically. It appears that along the axis of a cone cell light is being reflected back on upon itself by some mirror or some system of virtual or pseudo or quasi mirrors – wherever and whatever they are. For this reason a longitudinal standing wave inside the photoreceptor seems likely and reasonable — in cones at least.

A pivotal paper
Rods are far less directional than cones in their response to incoming light, so one cannot remark that light goes straight in and comes straight back out again, as we could for a cone. Accordingly, in rods one should probably remain agnostic about longitudinal standing waves. However, there is a well known and well regarded computer simulation of standing waves set up within the outer segment of a rod cell. This work was a technological tour de force, and you will find it cited again and again: M. Piket-May, A. Taflove, J. Troy, “Electrodynamics of visible light interactions with the vertebrate retinal rod”, Optics Letters, vol. 18, pp. 568-570, 1993.

The basic idea is that the bulk structure of the photoreceptor has the physics of a waveguide, and that the internal disk stack adds to the system the physics of an optical interferometer. The authors conclude: “These effects combine to generate a complex optical standing wave within the rod, thereby creating a pattern of local intensifications of the optical field.”
The splendid centerpiece picture in this paper’s Figure 1 shows the standing wave pattern computed at three different wavelengths: blue, green and red. To compute just one of these three standing waves required 1.6 hours of grinding away by a Cray Y-MP supercomputer. The paper demonstrates the power of a computational technique called FDTD, for finite difference time-domain. It is a way to find numerical solutions to the Maxwell equations. Taflove, an electrical engineer at Northwestern with a renaissance range of interests, coined the term FDTD. He has developed and applied the FDTD technique to problems ranging from geophysics to oncology to neuroscience. Piket-May, who is now at Colorado, is also a high profile scientist both within and beyond the field of electrical engineering. Troy is a neuroscientist at Northwestern whose laboratory studies the activity patterns of the retina’s ganglion cells.

The photoreceptor electrodynamics paper was published in 1993, but it apparently relied upon some dimensional data from the biological literature of a decade or two earlier: Specifically, the interdisk interval used in the calculations is different from the width accorded the disk. Today these two dimensions would be probably be set up as identical, with each disk 15 nanometers wide and the space separating the disks also 15 nm.

In strong multilayer natural mirrors, identical layer thicknesses and intervals are a trademark structural feature. The strongest natural mirrors exhibit this morphology. Whether newer, more fashionable rod cell dimensions, showing the periodicity of the disk stack, would alter the ultimate results and conclusions, if the computations were to be repeated today, is difficult to guess. There is a more recent (2005) paper by A.M. Pozo et al in which FDTD was used to model the cone (rather than the rod) photoreceptor.

We are by now familiar with the idea of longitudinal standing waves in photoreceptors. But note that the long-pondering Cray supercomputer’s three standing waves, which look like Navajo carpets in Piket-May’s wonderful Figure 1, are not simply depictions of longitudinal standing waves: rather, they show more complex waveguided structures, also incorporating transverse standing waves.

Adding a transverse dimension
The inside of a rod or cone cell has a higher refractive index than the surround: The interface, or wall, is therefore a transverse reflector. The reflective cylindrical walls of the photoreceptors figure prominently in contemporary models of the photoreceptor as a waveguide. According to these models, the rods and cones resemble fiberoptic transmission lines — made more complicated of course by their internal disks and external anatomical shapes, which tend to flare or taper.

Waveguiding adds another dimension to the story — a transverse dimension which cannot be neglected. In the real world a mirror set up at a right angle to the optical axis of the photoreceptor can produce a longitudinal standing wave — but we must also consider as reflective/refractive surfaces the tubular walls of the photoreceptors. We must also consider the tiny diameter of the photoreceptor, which can only accomodate a few wavelengths of light. The diameter of frog rod photoreceptor, which is regarded as oversized, is still only 6 microns, or about 10 wavelengths of red light, wall to wall.

So, to the simple and familiar musical instrument models reviewed above, in which the standing waves are treated as longitudinal only, we must add transverse standing waves bookended by the walls of the waveguide.

We are still talking about standing waves in a biological organelle. However, light is an electromagnetic wave and per Maxwell this is how EM waves act. They propagate straight ahead, with transverse electric and magnetic field components positioned at right angles to each other and to the axis of propagation. Confined inside a photoreceptor by end and sidewall mirrors, this wave will produce a three-dimensional standing wave pattern. If the photoreceptor cylinder is cut, so that the 3D distribution of light can be viewed in section, certain characteristic 2-dimensional light patterns will appear.

These visible waveguide effects, first observed under a microscope in the early 19th century, are both intricate and spectacular.

Waveguide modes in the rod cells of a frog's retina, hand drawn by A. Hannover in 1843.

This is a frog retina. The curious, detailed kaliedoscopic patterns seen in the rod cell sections were drawn by hand (A. Hannover, Vid. Sel Naturv. Og Math. Sk. X, 1843). They look like targets, benzene rings, starbursts, dots and circles. They are also uncannily reminiscent of Venetian glass millefiori patterns. In the 1840s, as he sketched, Hannover thought these patterns must represent anatomical structures. Today, in an era of fiberoptics, we recognize the designs as typical, changeable light patterns called waveguide modes.

Here is a sampling of twelve different waveguide modes produced in modern fiberoptic waveguides.

In the photoreceptors of humans and monkeys, at least 10 waveguide modes can be readily observed. Waveguide modes change rather abruptly, shifting from mode to mode with changes in wavelength.

Amphibian rod photoreceptor disks are cut through by radial incisures into as many as 18 distinct lobes.What interests us here is detection. Within the photoreceptors, there exist resonant patterns of light intensity, waveguide modes, that are known to change decisively as a function of light wavelength. For a multichannel neuron, perhaps detection or recognition of these modal patterns is possible. Note that the amphibian rod photoreceptor “disks” are not really disks. They are cut through by radial incisures into as many as 18 distinct lobes — pieces of pie. The disks’ incisures are aligned. As you climb the ladder from amphibians, in higher vertebrates the disks have fewer lobes, anatomically. But at the level of biochemical domains cordoned off within the disks, who knows? In short, yes, it is possible that the waveguide modes, and therefore a staircase of about 10 distinct wavelengths, could be recognized and detected. In a multichannel photoreceptor, it could be accomplished by wiring and deploying, as sensors, sections of disks rather than whole disks. One might also look for sensor domains arrayed in concentric rings or bands on the surface of each disk.

There is an extensive literature developed over several decades on photoreceptors as waveguides, much of it focused on the two Stiles-Crawford effects. An accessible resource and a good place to begin is the Optical Society of America’s thick Handbook of Optics, available in many libraries. Part 2 of the Handbook is devoted to Vision Optics, and was edited by Jay M. Enoch, who pioneered the study of photoreceptors as waveguides. With lead author Vasudevan Lakshminarayanan he is also the co-author of the Handbook’s Chapter 9, “Biological Waveguides.” The wonderful 1843 Hannover drawing was perhaps unearthed by Lakshminarayanan and is reproduced in this chapter. He also includes fascinating photos of waveguide modes in human and monkey photoreceptors.

It would be nice if the waveguide modes simply clicked between higher and lower orders according to some well behaved and well understood clockwork, changing uniformly and predictably as a pure function of input power, wavelength and dimensions. But they do not. Along the light path within the photoreceptor energy is being bunched, reflected out, refracted out – lost and absorbed. There are often observable colors associated with certain modes, and the colors may be seen to change along with wavelength along the photoreceptor. Importantly, signals in one waveguide may influence the signals in adjacent photoreceptors, an intriguing phenomenon perhaps if you are looking for effects that might be helpful in phase or edge detection.

For experimentalists, the photoreceptors are difficult to study intact. If the cells are sectioned, as in the Hannover slice, the act of sectioning will change the optical dimensions of the structure under study and may, as Krumeich and Knülle point out, amputate an essential mirror.

For modelers and theoreticians, however, the field is rich. Do a quick scan for papers that cite Snyder and Pask (Snyder, A. W., and Pask, C.: The Stiles-Crawford effect—explanation and consequences, Vision Res. 13: 1115, 1973.). This paper was among the first theoretical characterizations of the cone as a waveguide. There are by now many waveguide theories (and alternative-to-waveguide theories), but at this point none is regarded as definitive.

Conclusion
The photoreceptor is an interface where input signals that move at the speed of light are transduced into output signals that move at the speeds of trucks and trains. The colossal signal speed transition in photoreceptors is rarely remarked, but it is the basic reason standing wave theories are so attractive. As a first step, standing waves in photoreceptors freeze incoming light signals and thus shift them into a physical regime that can be effectively measured and reported by biological sensors connected to slow neurons.

All of the information borne by incoming light waves could be conserved and captured by detectors sensitive to standing waves in photoreceptors: color, brightness, spatial phase and polarization.

The central idea we are playing with here is that the retina could read signals sampled by the disks at points throughout its depth. As many as 1500 distinct sensors – the disks — are arrayed in a row along the optical axis of each photoreceptor cell. If each disk is separately wired, then the retina can be conceived as a 3-dimensional sensor, a sensitive solid, rather than a flat 2-dimensional sensor like photographic film. In order to work, this “sensitive solid” or 3D sensor array depends upon a multichannel neuron and, thus, a multichannel photoreceptor.

From a sensor array of disks aligned along the longitudinal axes of the photoreceptor cells, one can spin theoretical models in several different ways. Many of them involve or require the detection of standing wave patterns.

 The sensor array can be used to detect chromatic aberration, and thus used as the basis for a corrector or even as a color separator.

 The array can be used to separately detect the image plane and the Fourier plane of the eye’s converging lens.

 It can be used to detect and measure basic properties exhibited by longitudinal standing waves — wavelength and intensity.

 By segmenting the sensors at each disk, and with a little further elaboration, the multichannel photoreceptor can be used to detect different waveguide modes and polarization.

 By integrating or simply memorizing signals from multichannel photoreceptors one can create a retina that detects and conserves spatial phase.

Standing waves in photoreceptors probably exist. This is not a very controversial proposition. The question is — could the brain detect them? Given a 1-channel photoreceptor, no. Given a multichannel photoreceptor, yes, there would be several different ways to make it work.

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