3 Photoreceptors
In this chapter we will review how photoreceptors work. We will start from the highest level of abstraction, where photoreceptors can be seen as photon counting devices. The photon counting capability is fundamentally a result of the photoreceptors’ ability to absorb photons (selectively) over wavelengths. We will then lower the level of abstraction, reviewing in detail how a photon is absorbed in a photoreceptor, a.k.a., the phototransduction process and its recovery. Understanding photoreceptors at this low level, in turn, allows us to reason about key high-level behaviors of vision, such as sensitivity and saturation.
3.1 Counting Photons: Principle of Univariance
Anatomically, a photoreceptor has two parts: an inner segment and an outer segment. Photons enter from the inner segment, which for the most part can be thought of as a waveguide that funnels the photons to the outer segment. The outer segment contains the photon-absorbing pigments. This is illustrated in Figure 3.1.
Conceptually, we can think of each photoreceptor as a bucket that collects photons. There are millions of buckets sitting on the retina, taking a shower of photons. Many photons entering the eye will not hit any bucket: they are absorbed before they reach the bucket (e.g., by the lens). Any photon that does hit the bucket has a certain probability of being absorbed. The absorption probability varies with the photoreceptor type and the photon’s wavelength.
Fundamentally, a photoreceptor can absorb photons because it contains light-sensitive, photon-absorbing pigments, each of which is able to absorb one photon. Each rod photoreceptor has tens of millions of such pigments (Milo and Phillips 2015, p. 142–47; Nathans 1992). Why is a photon’s absorption probability not 100% once it enters a photoreceptor? For one, a photon might not meet a photopigment as it travels through the photoreceptor before the exit. Even if a photon hits a pigment, its absorption is still probabilistic, as absorption is dictated fundamentally by quantum mechanics.
Once a photon is absorbed, it has a certain probability of “exciting” or “isomerizing” the pigment. A pigment excitation or isomerization generates a certain level of electrical signal — in the form of a current or voltage change across the cell membrane of the photoreceptor. The excitation probability once a photon is absorbed is called the quantum efficiency of the pigment. Quantum efficiency is about two-thirds in the visible spectrum and is not wavelength sensitive (H. J. A. Dartnall 1972; Kropf 1982; Fu 2010). A pigment excitation is also called pigment bleach, since the pigment after excitation is no longer responsive to light as if it is bleached.
The process of initiating an electrical response upon a photon absorption is called phototransduction. We will study this process in detail shortly in Section 3.4. For now, it is important to know that for a given photoreceptor class, the electrical response caused by a photon absorption is constant regardless of the photon’s wavelength. This is called the Principle of Univariance (W. A. Rushton 1972; W. H. Rushton 1972; Naka and Rushton 1966): each photon that generates an electrical response has the same effect as any other photon that does so. In other words, the only effect that wavelength has is to impact the probability a photon gets absorbed; after absorption, the wavelength information is lost.
A crucial implication of this principle is that any two lights that are equally absorbed/excited will be seen as the same light by the human vision. For the purpose of comparing two lights, we can think of each bucket as having a counter; every time a photon is absorbed and excites a pigment, the counter gets incremented by 1. If two lights lead to the same counter value, they are perceptually the same. Crucially, if a bucket’s counter is, say, twice as high as another’s, it does not mean the electrical responses produced by the first photoreceptor are twice as high as that of the second. We will see why this is the case shortly.
3.2 Spectral Absorbance, Absorptance, and Sensitivity
To understand vision in everyday scenarios, what we care about is not the probability of how a single photon is absorbed and excites a pigment, but the collective behavior of a flux of photons that enter our eyes. Conveniently, when we have a large population of photons, the probability that an individual photon causes an excitation translates to the percentage of incident photons that are absorbed and/or cause excitations. In fact, the percentage of absorption is the quantity that we can directly measure.
There are in general two ways to estimate the absorption rate of a flux of photons. The direct way of measurement is using a technique called microspectrophotometry (MSP). The indirect method is to measure the electrical responses using, e.g., a suction electrode, and then estimate the absorption. The indirect method gives us only relative absorption across wavelengths, while the MSP approach gives us absolute absorption.
3.2.1 Absorbance Spectra from Microspectrophotometry
The idea of MSP is to shine a beam of light through a photoreceptor and then measure, at the other side, the percentage of photons that are transmitted, i.e., unabsorbed (J. Bowmaker 1984). Ignoring back-scattering 1, photon absorption by photopigments in a photoreceptor can be modeled using the Beer-Lambert law. The transmittance at wavelength \(\lambda\) is defined as the ratio between the amount of transmitted photons \(I_d(\lambda)\) and the amount of total incident photons \(I_0(\lambda)\):
\[\begin{align} T(\lambda) = \frac{I_d(\lambda)}{I_0(\lambda)} = e^{-\epsilon(\lambda) c l}, \end{align}\]
where \(\epsilon(\lambda)\) is called the absorption coefficient and is wavelength dependent, \(c\) is the concentration (the number of pigments per unit volume), and \(l\) is the optical length, the length through which a photon has to travel. Both \(c\) and \(l\) are inherent properties of a photoreceptor and are not dependent on photon wavelength.
Absorptance \(a(\lambda)\), the percentage of absorption at \(\lambda\), is naturally \(1-T(\lambda)\). Absorbance \(A(\lambda)\) (also called the optical density), whose spelling is subtly and annoyingly different from that of absorptance, is defined as:
\[ A(\lambda) = -\ln(T(\lambda)) = \epsilon(\lambda) c l. \tag{3.1}\]
Therefore, absorptance \(a(\lambda)\) and absorbance \(A(\lambda)\) are related by:
\[ a(\lambda) = 1 - e^{-A(\lambda)}. \tag{3.2}\]
We would repeat this experiment over a frequency range and obtain the axial absorbance at each sampled frequency. The resulting plot is usually called the absorbance spectrum. One such example is shown in the right panel in Figure 3.2, measured by H. J. Dartnall, Bowmaker, and Mollon (1983) on humans. Much such data has been obtained in the literature, the earliest of which is perhaps by George Wald and his colleagues (Marks, Dobelle, and MacNichol Jr 1964; Brown and Wald 1964) who identified three distinct absorbance spectra in cone-mediated vision and, thus, provided direct physiological evidence for the existence of three classes of cones. The three cone types are generally referred to as the L, M, and S cones, since their absorbances peak at, relatively, long, medium, and short wavelengths.
Decades before the work by Wald et al., Ragnar Granit measured the spectral sensitivities of the retinal ganglion cells (Granit 1941, 1943, 1945b, 1945a) 2. Granit showed the existence of two classes of RGCs: 1) one that has a broader spectral sensitivity whose peak shifts to shorter wavelengths from photopic vision to scotopic vision, and 2) one whose spectral sensitivities are narrower and fall generally into three main groups. The former is the physiological version of the Purkinje shift that we will discuss in Section 4.3.2, and provides direct evidence for the convergence of the rod and the cone vision pathways (Section 2.4.1.4 and Figure 2.4). The latter is the first direct evidence of the existence of three dinstinct wavelength encoding mechanisms (albeit not at the photoreceptor level), essential for the trichromatic color vision.
Normalization
Quite often, the absorbance spectrum is normalized to peak at unity, as is the case in Figure 3.2 (right). According to Equation 10.9, normalizing absorbance across different wavelengths is equivalent to normalizing \(\epsilon\) across wavelengths, since \(c\) and \(l\) are not wavelength specific, whereas \(\epsilon\) is. \(c\) and \(l\) might vary across species and across individuals and might differ between different illumination methods (see below), but \(\epsilon\), which is fundamental to the photopigment, does not. Therefore, the normalized absorbance spectrum tells us something fundamental about the wavelength sensitivity of the photopigments.
Perhaps a subtlety but quite confusing when perusing the literature, the maximum absolute absorbance across all wavelengths (i.e., the peak of an absorbance spectrum) is usually simply called the optical density; “peak optical density” would have been more accurate, as optical density is wavelength specific. Using the peak optical density and the normalized absorbance spectrum, we can reconstruct the absolute absorbance spectrum; from there we can get the absolute absorptance spectrum.
While not shown here, the peak absorbance between rods and cones is not that different. The peak absorbance of rods is about 0.475, and the value is about 0.375 for foveal S cones and 0.525 for foveal L/M cones (J. Bowmaker et al. 1978; J. K. Bowmaker and Dartnall 1980). The large sensitivity difference between rod vision and cone vision is not primarily attributed to the difference in their ability to absorb photons.
Correcting for Transverse Illuminations
There is one more complication. With MSP, we illuminate a photoreceptor transversely, i.e., the light passes from one side of the photoreceptor to the other side. In reality, when a photon enters a photoreceptor, it travels axially from the inner segment through the outer segment. The main difference between these two scenarios is the optical length that a photon has to travel. A photoreceptor is tall and skinny, so its width is much smaller than its length, about 2.5 \(\mu\text{m}\) wide and 35 \(\mu\text{m}\) long for a fovea L/M cone (Polyak 1941).
Therefore, we need to first calculate the absorbance per unit length, called the specific absorbance, and then scale the specific absorbance by the axial length of the photoreceptor to obtain the axial absorbance, from which we can estimate the axial absorptance using Equation 10.9. This is shown below (omitting \(\lambda\) for simplicity):
\[ \begin{align} A_{\text{transverse}} &= -\ln(p_{\text{transverse}}) = \epsilon c l_{\text{transverse}} \\ A_{\text{specific}} &= \frac{A_{\text{transverse}}}{l_{\text{transverse}}} = \epsilon c \\ A_{\text{axial}} &= A_{\text{specific}} l_{\text{axial}} \\ T_{\text{axial}} &= e^{-A_{\text{axial}}} \end{align} \tag{3.3}\]
3.2.2 Relative Absorptance Spectra from Electrical Responses
Another method is by measuring the photoreceptor’s electrical responses across different wavelengths using techniques such as suction electrode, which records the electrical responses of an isolated photoreceptor sucked into a micropipette. Spectra so estimated are usually called the spectral sensitivity of the photoreceptors in the literature, but as we will see, they are equivalent to the normalized absorptance spectra.
Figure 3.3 illustrates the idea, where Baylor and Hodgkin (1973) measured the peak electrical response of a turtle cone (in photovoltage; \(y\)-axis) as a function of light intensity (\(x\)-axis) at two wavelengths: 644 \(\text{nm}\) and 539 \(\text{nm}\). We see that the curves are almost parallel to each other: we can laterally move the 644 \(\text{nm}\) curve to coincide with that of 539 \(\text{nm}\). In this case, we have to shift the former by 1.27 log units.
Think for a second what this means. When we increase the intensity at 644 \(\text{nm}\) by a factor of \(10^{1.27}\), the sheer number of photons absorbed at 644 nm is increased by a factor of \(10^{1.27}\), too. That means without scaling the number of incident photons at 644 \(\text{nm}\) is \(10^{-1.27}\) (about 5.4%) of that at 539 \(\text{nm}\). Even with just 5.4% of incident photons, 644 \(\text{nm}\) light is able to produce the same level of electrical response, i.e., cause the same amount of photon absorption (given the Principle of Univariance), as the light at 539 \(\text{nm}\). Therefore, we can say the absorption rate (absorptance) at 644 \(\text{nm}\) is \(10^{1.27}\) higher than of that at 539 \(\text{nm}\).
We repeat this experiment across other wavelengths and obtain the relative spectral sensitivity/absorptance spectra. The left panel in Figure 3.2 shows one such example obtained by Baylor, Nunn, and Schnapf (1987) on macaque cones. Critically, the absorptance so obtained is relative: we do not know the absolute absorptance at either wavelength. The \(y\)-axis is necessarily normalized to peak at unity. Similar data have been collected on humans as well (Schnapf, Kraft, and Baylor 1987; Kraft, Schneeweis, and Schnapf 1993).
Normalized Spectra From the Two Methods Match Well
It is worth noting that the suction electrode method also uses transversely illuminated lights. Since the absorptance obtained here is relative, we cannot easily use the method in to obtain the absorptance spectra for the axial illumination.
Here is the catch. Numerically, \(1 - e^{-A} \approx A\) when \(A\) is small. When we illuminate a photoreceptor transversely, the optical length \(l\) is the photoreceptor width, which is short, which means \(A\) is small (Wyszecki and Stiles 1982, p. 588, 594). Therefore, the transverse absorbance and transverse absorptance are approximately equal. So the normalized absorptance spectrum given by the suction electrode method is approximately the normalized absorbance spectrum, as is shown experimentally (Schnapf, Kraft, and Baylor 1987; Stockman and Sharpe 2000, fig. 11).
The normalized absorbance spectra are still not sufficient, since to use the method in Equation 3.3 we need to know the absolute absorbance spectra. People usually have to resort to another data source that provides absolute peak absorbance or fit the data against, e.g., psychophysical measurements that provide some form of absolute measures (Kraft, Schneeweis, and Schnapf 1993; Baylor, Nunn, and Schnapf 1984, 1987).
3.3 Cone Fundamentals: Cornea-Referred Spectral Sensitivities
Our discussions so far have focused on absorption by the photoreceptors, but for a flux of photons arriving at the cornea about to enter our eye, they are also absorbed even before reaching the photoreceptors. Accounting for these pre-receptoral filters is important to model human vision. Spectral sensitivities that account for these pre-receptoral filters are what we call the cornea-referred spectral sensitivities.
3.3.1 Cone Fundamentals From Physiology
There are two such pre-receptoral filters: the ocular media (Section 2.2.2) and the macular pigments, which are located at a small area in the fovea. Macular pigments absorb light presumably to counter some of the aberrations from the ocular media and to protect the retina from light damage (Snodderly et al. 1984). Both ocular media and macular pigments absorb light selectively over the spectrum, just like photoreceptors do.
We can model \(E(\lambda)\), the fraction of photons arriving at the cornea that are absorbed by the photoreceptors:
\[\begin{align} E(\lambda) = l(\lambda) m(\lambda) a(\lambda) \end{align}\]
where \(a(\lambda)\) represents the photoreceptor absorptance spectrum, \(l(\lambda)\) and \(m(\lambda)\) represent ocular and macular transmittance spectrum, respectively, i.e., the fraction of photons at \(\lambda\) unabsorbed by the ocular media (e.g., lens) (Boettner and Wolter 1962; Norren and Vos 1974) and the macular pigments. Figure 3.4 illustrates this process.
We call \(E(\lambda)\) the cornea-referred spectral sensitivity function, since it is calculated with respect to the incident lights at the cornea surface. When \(a(\lambda)\) is replaced by the absorptance spectra of the three classes of cones, the resulting sensitivity functions are more commonly referred to as the cone fundamentals.
We can make a few general observations about the cone fundamentals. First, the cone sensitivity drops to 0 beyond the 380 \(\text{nm}\) and 780 \(\text{nm}\) range, a range we usually call the visible spectrum, since there will be no pigment excitation beyond that range: lights beyond that range are invisible. Second, S cones are generally the least sensitive of the three cone types, but it is not because of the photoreceptors but because of the pre-receptoral filters, which absorb mostly low-wavelength lights. Finally, the sensitivity peaks of the L cones and M cones are very similar (off by about 20 \(\text{nm}\)), but both are rather far from the peak of the S cones. We have discussed the reason behind this when discussing Figure 2.8.
3.3.2 Cone Fundamentals From Psychophysics
The spectral sensitivities discussed above are measured physiologically. We can also measure such functions through psychophysics using the increment-threshold method. A typical set up is one where there is a uniform background illumination and a spot light superimposed at the center of the background. We ask a participant to adjust a knob to control the intensity of the spot light so that it is just noticeable from the background. The sensitivity is then defined as the reciprocal of the threshold intensity. We repeat this experiment for each sampled wavelength across the spectrum to obtain a sensitivity curve. This method is first used in the pioneering work done by W.S. Stiles (Stiles 1939, 1959, 1964), and is adopted in virtually all later work (Wald 1964; Smith and Pokorny 1975; Stockman, Sharpe, and Fach 1999; Stockman and Sharpe 2000).
A curious question is how we can separate the sensitivity of different photoreceptor types, given that the spectral sensitivities of the four photoreceptor types overlap. There are two methods to isolate rods from cones. We can either use very dim lights, to which cone responses are too small to contribute to vision (Crawford 1949), or we could measure from people with rod monochromacy — individuals who have only rods. When measuring cone sensitivities, we will use intense lights that almost completely saturate rods.
Isolating the three cone types from each other is generally challenging with individuals with normal vision. W.S. Stiles’ initial work (Stiles 1939, 1959) designed special conditions of background illumination to suppress the sensitivity of two unwanted cone types while sparing the one under study. Modern studies usually turn to color-deficient individuals who lack one or two cone types. Isolating S cones is done by measuring from S-cone monochromats (Stockman, Sharpe, and Fach 1999). Isolating L and M cones is challenging because individuals with only L or M cones are very rare and the spectral sensitivities of the L and M cones overlap substantially. Instead, a common approach is to resort to Protanopes and Deuteranopes; the former has only M and S cones, and the latter has only L and S cones. To isolate M (L) cones from the S cones, we measure from Protanopes (Deuteranopes) using lights that have high spatial and/or temporal frequencies, to which S cones are known to be insensitive (Stockman and Sharpe 2000; Smith and Pokorny 1975).
3.3.3 Physiological and Psychophysical Sensitivities Match Well
We can then compare the spectral sensitivity data from physiology and from psychophysics. This is shown in Figure 3.5. See the figure caption for details. Overall it is fair to say that the two sets of data match well.
Think about what this comparison means. What we measure in psychophysics is the threshold intensity (at each wavelength) needed to evoke a criterion level of human behavioral response (i.e., just noticeability). The threshold intensity in the physiological measurement represents how much light is needed (at each wavelength) to cause the same amount of pigment absorption and, by the Principle of Univariance, the amount of electrical responses. The fact that the two sets of data match suggests that the amount of electrical response we need to evoke a just-noticeable level of perception is a constant regardless of wavelength, a perhaps unsurprising inference.
Interestingly, the physiological data in Figure 3.5 is obtained from macaques, and the psychophysical data is from humans. The fact that they match well suggests the similarities of the visual system among primates — we have come a long way since the monkey days, but our photoreceptors have not changed much. Other studies obtaining the physiological sensitivity data from humans show similarly good matches with human psychophysical data (Crescitelli and Dartnall 1953; Kraft, Schneeweis, and Schnapf 1993; J. K. Bowmaker and Dartnall 1980; Mollon 1982).
3.4 Beyond Counting Photons: Phototransduction and Recovery
The discussion so far about (spectral) sensitivity has focused on the ability of different types of photoreceptors to absorb (“count”) photons at different wavelengths, and by that measure, rods and cones are not that different: their peak absorbances differ by less than 10% (Section 3.2.1). So then why do we say rod vision is more sensitive than cone vision? What we have ignored is the absolute strength of the electrical response once photons are absorbed. To understand the absolute response strength, we need to understand the cellular and molecular processes underlying how electrical responses are actually produced from pigment excitations. These processes constitute the so-called phototransduction cascade and are the focus of this section. George Wald is largely credited for elucidating these processes (Wald 1933, 1968).
3.4.1 Phototransduction Cascade
The phototransduction cascades in rods and (different types of) cones are exactly the same. The differences appear to be quantitative rather than qualitative and are dictated by the genes expressing the isoforms of the molecules participating in phototransduction (Ingram, Sampath, and Fain 2016; Yau 1994). We will mainly use rods as an example to drive the discussion here.
Photoreceptor Has a Stable Transmembrane Current in Dark
A visual pigment in a rod is a special molecule called a rhodopsin, which has two parts: a long strand of protein called opsin (which is insensitive to light) and the light-sensitive 11-cis retinal, a form of Vitamin A as discovered by Wald (1933), that is attached to the opsin and acts as a chromophore. Hofmann and Lamb (2023) presents a comprehensive survey of what is known about rhodopsin to date.
In the dark, there is a stable current of -34 pA that flows into the outer segment called the dark current. By convention, inward current is defined as negative. This is illustrated in Figure 3.6. The dark current is a result of a particular kind of cation-selective ion channel that is permeable to both Na+ and Ca2+ flowing into the outer segment. Critically, these channels are ligand-gated channel — gated by cyclic guanosine monophosphate (cGMP) molecules (Fesenko, Kolesnikov, and Lyubarsky 1985; Yau and Baylor 1989). Think of cGMPs as the guards of the channels; on average, each channel needs three cGMPs to remain open (Rodieck 1998, p. 169). In a rod outer segment in the dark, there is an ample amount (3-4 micromoles) of cGMPs, which bind to a large amount of channels and keep them open.
As a result of the dark current, the membrane potential of a photoreceptor in the dark is about -35 mV. If you are familiar with basic neuroscience, you would notice that the photoreceptor in the dark is depolarized, since the membrane potential is higher than that of the resting potential of a typical neuron. The depolarization is exactly caused by the inward flow of cations through the cGMP-gated channels.
Closing Ion Channels Produces Electrical Responses
Once a photon is absorbed and, with a two-thirds chance, excites a pigment (dictated by quantum efficiency, as discussed in Section 3.1), the 11-cis retinal of the pigment changes to its isomer called all-trans retinal (which will later be separated from the pigment). This is why a pigment excitation is often called a photoisomerization. This all takes place remarkably fast: the absorption takes about 3 fs and the photoisomerization takes about 200 fs (Gruhl et al. 2023; Rodieck 1998, p. 162).
The isomerization changes the conformation of a rhodopsin pigment, which becomes “activated”: it diffuses randomly and activates a transducin (a form of G protein) whenever they meet. This is illustrated by step ① in Figure 3.7. On average, an activated pigment activates about 700-800 transducins (Purves et al. 2017, p. 243; Rodieck 1998, p. 170). Each activated G protein then meets and binds to a molecule called “cGMP-specific phosphodiesterase” (PDE), activating the PDE. This is step ② in Figure 3.7. Each activated PDE has the ability to catalyze the hydrolysis of several dozen cGMPs~, reducing the cGMP concentrations. This is step ③ in Figure 3.7.
We know that the ion channels that induce dark current are gated by cGMPs. A reduction in cGMP concentration will close some of these channels, reducing the dark current and increasing the membrane potential (i.e., the photoreceptor hyperpolarizes). This membrane current/potential change is the electrical response of photon absorptions and is the signal that will be delivered to the rest of the visual system to eventually give rise to vision.
At the peak of this transduction process, a single activated rhodopsin in a rod can reduce the number of cGMPs by about 1,400, which translates to about 2% closure of the cGMP-gated channels (Rodieck 1998, p. 170). Since each cGMP-gated channel carries the same amount of current, this means the total membrane current is reduced by about 2%. This is step ④ in Figure 3.7. In the literature, the change of membrane current and voltage potential is usually termed photocurrent and photovoltage, respectively. Since the change in the membrane current is positive and the change in the membrane voltage is negative, the photocurrent is positive and the photovoltage is negative. The actual transmembrane current and voltage are always negative. Some electrophysiological techniques measure the total membrane current/voltage, while others measure the photocurrent/photovoltage. Be careful of what quantity is being reported when perusing the literature.
3.4.2 Deactivation of Phototransduction and Pigment Regeneration
If phototransduction continues without any hindrance, eventually 1) all pigments will be bleached (isomerized), and 2) all the ion channels will be open. If so, the photoreceptor and, ultimately, our visual system will not be able to respond to further lights: additional photons cannot be absorbed, and even if they are absorbed and excite pigments, there are no ion channels to close, and so no electrical response will be produced; at that point, our visual system saturates.
In order for our visual system to continue to respond to lights, two things must take place. First, there must be mechanisms to terminate the phototransduction and re-open the ion channels (Burns and Arshavsky 2005; Burns and Baylor 2001). Second, new pigments must be continuously regenerated. This is the job of the retinoid cycle or the visual cycle.
Phototransductions are Continuously Being Deactivated
There are activities constantly at work attempting to terminate the phototransduction. This can be seen by observing the response kinetics of a photoreceptor to light. The left panel in Figure 3.8 shows the photocurrent kinetics of macaque rods in response to a flash light (Baylor, Nunn, and Schnapf 1984); the right panel shows the photocurrent kinetics of macaque M cones when presented with a step light, i.e., a constant background illumination (Schnapf et al. 1990). Without the deactivation activities, the responses to the flash light would not have been eliminated after the flash light was removed, and the responses to the step light would not have reached an equilibrium.
For the phototransduction cascade to terminate, there are mechanisms to deactivate every step in the transduction: activated rhodopsins must be deactivated so that they cannot activate more G proteins, activated G proteins must come off the PDE so that the PDE cannot hydrolyze more cGMPs, the cGMPs must be replenished, and the cGMP-gated ion channels must reopen. Every step must be deactivated; for instance, it is not sufficient to just deactivate the pigments: that just means the inactivated pigments will not activate more G proteins, but existing G proteins that are still activated will continue activating PDEs and the rest of the phototransduction.
The deactivation also involves a set of biochemical reactions that we will not detail here, but just to give you a flavor, here is how the pigments are deactivated, and the process is illustrated in Figure 3.9. An enzyme, rhodopsin kinase (RK), binds to and phosphorylates an activated pigment. Another protein called arrestin (A) then binds to phosphorylated pigment, which inhibits the pigment’s ability to activate G proteins, essentially deactivating the pigment.
Deactivation is Accelerated by Negative Feedbacks
Interestingly, some of the deactivation steps are accelerated by negative feedback mechanisms mediated by Ca2+ concentration. One such mechanism is shown in Figure 3.10. Let’s briefly take a look at this, not only because it is a classical example of the dynamics common in visual neuroscience (and many dynamical systems) but also because we will come back to this negative feedback when we discuss light adaptation later in the class.
The closing of cGMP-gated channels from phototransduction reduces the inward flows of Ca2+ and Na+ to the outer segment. Importantly, Ca2+ inhibits guanylate cyclase (GC), which inherently re-synthesizes cGMPs. As the Ca2+ level reduces, the cGMP re-synthesis rate increases, which replenishes cGMPs and re-opens ion channels. That is, phototransduction initially reduces the cGMP concentration, and the very reduction of concentration serves to replenish the cGMPs — the feedback is negative. Without this negative feedback, the response still would have stabilized. For instance, soon after we move the flash light the cGMP concentration will stop falling while the GC-induced resynthesis is steadily going on. Eventually, the cGMP concentration will be restored to the original level 3. The negative feedback simply accelerates this process.
The strength of the negative feedback is much stronger in cones than in rods (Yau and Hardie 2009; Burns and Baylor 2001). The stronger negative feedback is the reason why cone responses recover much faster than do rods: compare the kinetics of macaque rods under flash lights of varying intensities in Figure 3.8 (left) and the macaque L cone kinetics under the same set of lights in Figure 3.10 (right), and pay attention to the timescale on the \(x\)-axis. In cones, the negative feedback is so strong that there is actually a temporary over-provision of cGMPs during the deactivation phase, leading to an undershoot in the current (right panel in Figure 3.10).
The negative feedback through Ca2+ concentration also accelerates other steps in deactivation, including accelerating pigment deactivation (although with a much less potent effect than that on the GC (Nikonov, Lamb, and Pugh Jr 2000; Pugh Jr, Nikonov, and Lamb 1999)) and increasing the sensitivity of cGMP-gated channels to cGMPs (so that the channels can be open even at lower cGMP levels) (Hsu and Molday 1993).
Pigments are Continuously Being Regenerated
Deactivating phototransduction is not enough; it reopens ion channels and replenishes all the materials involved in phototransduction — except the pigments themselves. Pigments must somehow be restored so that they are available for phototransduction again, and this is the job of the retinoid cycle. An activated pigment roams about randomly and gets deactivated when it meets rhodopsin kinase and arrestin. When an activated pigment is deactivated, the all-trans retinal falls off the pigment. This is shown in the top panel in Figure 3.9. The all-trans retinals then leave the photoreceptor and are transported to the Retinal Pigment Epithelium (RPE), which is a layer of special skin cells just outside the retina and is where all-trans retinals are converted back to 11-cis retinals, which are then transported back to the outer segment, recombining with the opsin portion of the pigment, at which point the pigment is reconstituted to its original form and is sensitive to photons again. This is shown in the bottom panel in Figure 3.9.
Rushton used retinal densitometry to measure the pigment regeneration of both cones and rods in the living eye. The kinetics of the rod and cone pigment regenerations are shown in Figure 3.11. The half-life of of cone pigments regeneration is about 3 times shorter than that of rod pigments (W. A. H. Rushton 1961, 1963, 1965). The fast regeneration of cone pigments means it is unlikely that the steady-state cone pigment bleaching level exceeds about 90% under the normal range of illumination levels throughout a day (Burns and Lamb 2014, p. 15). In contrast, under normal daylight, rod pigments are almost all bleached.
Compared to the speed of pigment generation, the deactivation of phototransduction takes place much more rapidly. On average, a cone pigment is regenerated in about 2 minutes (Rodieck 1998, p. 184–85), and phototransduction deactivation (and activation for that matter) happens in millisecond scale. Imagine in your visual field there is a brief flash. You see the flash as a flash because the phototransduction initiated by the flash quickly goes away almost immediately as the flash is removed.
Steady Vision Means Equilibrium
Both pigment regeneration and phototransduction deactivation are constantly at work, countering the effect of the phototransduction in light. The more pigments are excited and the more ion channels are open, the stronger the deactivation and pigment regeneration processes are.
Under a modest background illumination, the opposing forces reach an equilibrium where the rate of closing cGMP-gated ion channels matches that of re-opening them. So dynamically a fixed number, not all, of the ion channels are open. If after light exposure we move to a dark room, there are no photons coming in, so there is no phototransduction. The countering forces completely dominate, and eventually all the materials involved in phototransduction are replenished and all the ion channels are open — another equilibrium. If we flash a light on top of the background, some cGMP channels open for a short period of time and then close as the flash goes away; our vision goes back to the steady state.
If we increase the intensity of the steady background a little, again some cGMP channels will open, and simultaneously the countering forces are at work trying to close them. Eventually a new equilibrium is reached where more channels are steadily open than before. What if we keep increasing the background light’s intensity? Every time we intensify the background light a little, we reach a new equilibrium with fewer channels steadily open. This is readily seen in the right panel in Figure 3.8, where the steady-state response increases (i.e., fewer channels are open) as the background light intensity increases. Eventually all the channels will close, and our vision is said to be saturated. This is what we will study next.
3.5 Absolute Sensitivity and Saturation in Rods vs. Cones
Now that we understand phototransduction and its recovery, we can appreciate some fundamental differences between rods and cones in their absolute sensitivity and saturation levels, which shape our daily visual experience.
3.5.1 Rods Have a Much Higher Signal-to-Noise Ratio Than Cones
Psychophysical experiments show that humans can reliably detect a flash when only about 5 to 7 pigments are excited in a field of about 500 rods; in contrast, it takes about 5 pigment excitations per cone in a pool of about 10 cones for humans to signal a flash (Hecht, Shlaer, and Pirenne 1942; Barlow 1956; Donner 1992; Angueyra-Aristizábal 2014). Assuming the visual system requires the same level of electrical response to see a flash, the difference suggests that rods are able to produce the same amount of electrical response using fewer pigment excitations than cones.
Part of this can be explained by the different levels of neural convergence in the rod and cone pathway, which we have discussed before. But the difference in sensitivity between the photoreceptors themselves also plays a significant role: rod photoreceptors have a higher electrical response and a lower noise floor than cones. This contributes to the lower detection threshold in rod vision. Let’s examine the signal and the noise separately.
Single Photon Response is Much Larger in Rods than in Cones
The photocurrent, i.e., the signal part of the SNR, from a single rod pigment excitation is about 20 times higher than that from a cone pigment excitation (34 pA vs. 0.7 pA) (Baylor, Lamb, and Yau 1979b; Baylor, Nunn, and Schnapf 1984; Baylor 1987; Schnapf et al. 1990; Ingram, Sampath, and Fain 2016; Angueyra-Aristizábal 2014). A single rod pigment excitation already closes about 2% of the ion channels in a rod, and about 30 pigment excitations would close half of the ion channels in a rod in the dark. In contrast, it requires about 650 pigment excitations in a cone photoreceptor to provide a half-maximal response in dark (Baylor, Nunn, and Schnapf 1984; Schnapf et al. 1990).
Part of the reason why rods have larger responses than cones is because the phototransduction cascade in rods is much more rapid (Ingram, Sampath, and Fain 2016): the rate of PDE activation is higher, the rate of cGMP concentration reduction is higher, etc. As a result, a lot of cGMP-gated ion channels already close before much of the “countering forces” (that are simultaneously trying to deactivate phototransductions) kick in, resulting in higher peak responses in rods than in cones.
Cones are Much Noisier than Rods
Not only do rods produce a higher response per pigment excitation, but the inherent noise in a rod is much lower than that in a cone. Photocurrents exist even in the dark due to noise, which comes from two main sources (Baylor, Matthews, and Yau 1980; Fred Rieke and Baylor 2000): 1) the spontaneous, thermal-induced activations of pigments, which show up as discrete spikes in photocurrents, and 2) the spontaneous activation of PDEs, which causes the cGMP concentration to fluctuate and shows up as the continuous rumbling of the photocurrent (F. Rieke and Baylor 1996). Photocurrent in the dark has the equivalent effect of a background illumination in the dark, so it is also termed dark noise, dark light, or “eigengrau” (German: one’s own light). As we can imagine, dark noise interferes with light detection when the signal is weak, i.e., illumination is dim (Barlow 1957), where behaviorally we cannot tell for certain if we are seeing actual light or dark light.
Dark noise is much higher in cones than in rods (Angueyra-Aristizábal 2014; Donner 1992). For instance, the dark light in rods is equivalent to about one pigment excitation every 90 seconds (Baylor, Nunn, and Schnapf 1984) and about 500 – 1,000 times per second in cones (Schnapf et al. 1990; Schneeweis and Schnapf 1999; Fred Rieke and Baylor 2000; Burns and Lamb 2014; Foster Rieke and Baylor 1998). The dark light in cones is high enough to allow a rod to reach its half-maximum response (Tamura, Nakatani, and Yau 1991; Nakatani and Yau 1988; Matthews et al. 1988)! As a result, the SNR in cones is much lower than that in rods.
3.5.2 Rods Saturate Much More Easily Than Cones
We know the rod-mediated vision saturates under much lower light levels than does the cone-mediated vision. Because of this, rods are not useful in mediating vision in typical daylight illuminations. Cones are much harder to saturate, if ever, under normal daylight (Burns and Lamb 2014; Barlow 1972; Shevell 1977), so they are primarily responsible for daylight vision. But why do the rod-mediated vision saturate more easily, other than the higher degree of neural convergence? Again, the difference in the photoreceptors themselves plays a role.
First, the photocurrent generated by a pigment excitation is much higher in rods than in cones, as discussed before. Second, the phototransduction kinetics is faster in cones than in rods. As we have seen in Figure 3.8, the electrical response of a pigment excitation is an event that does not finish instantaneously: it takes time for the photocurrent to rise, reach its peak, and then decay. The rising phase, as discussed in Section 3.5.1, is briefer in rods than in cones, but the decay phase is much longer in rods than in cones (Ingram, Sampath, and Fain 2016). The faster decay is due to the stronger phototransduction deactivation in cones than in rods (Yau and Hardie 2009; Burns and Baylor 2001) (which is attributed to the stronger negative feedbacks as discussed in Section 3.4.2), which means ion channels are more rapidly restored. Overall, the duration of a cone phototransduction is about four times shorter than that for a rod (100 ms vs. 400 ms) (Baylor 1987; Angueyra-Aristizábal 2014; Nakatani and Yau 1988; Rodieck 1998, p. 185).
Why does the time duration matter? It is because a longer duration integrates responses of more incoming photons. Consider an example where two excitations are taking place, say, 200 ms apart in a photoreceptor. In a rod, the time durations of these two excitations overlap, so the total electrical response the photoreceptor generates is greater than that if only one excitation takes place. In a cone, however, these two events do not overlap, and so their effects do not add up.
As a side, the slow kinetics of rods is the reason we cannot sense object movement very well in low light conditions. If you have ever played basketball at night, you would know that even though you can tell where the ball is when it is still, but you cannot track the movement of the ball well.
It is worth noting that even though cone pigments regenerate much faster than rods (Section 3.4.2), the slower pigment regeneration rate unlikely affects the saturation in rods. There are tens of millions of pigments in a mammalian rod cell (Nathans 1992; Milo and Phillips 2015, p. 142–47) but a rod is almost saturated by only several hundreds of pigment excitations, so when a rod is saturated, the vast majority of pigments are still available (Lamb 1980). It is the fact that almost all cGMP-gated ion channels are closed, rather than all pigments are bleached, that prevents rods from responding further to lights. The slow regeneration rate in rods does affect dark adaptation time, which we will discuss later in the class.
3.6 Response vs. Light Intensity
The Principle of Univariance tells us that the electrical response from a photon absorption is constant without regard to the photon wavelength, but it does not tell us how the magnitude of the electrical response varies with the number of photons absorbed. With the basic understanding of phototransduction, we can now turn to this question. You might be tempted to think that the relationship is linear, and you would be wrong!
3.6.1 Peak Response is Not Linearly Proportional to Light Intensity
Figure 3.12 (left) shows the response (photocurrents) kinetics of macaque rods under flash lights of different intensities. The right plot shows the peak response (normalized to the maximum response) as a function of flash intensity.
If the relationship between the response magnitude and the light intensity were linear, the curve would be a straight line. But in reality, we can see that the response grows quickly initially, but the growth slows down soon. What does the actual relationship tell us about photoreceptors? Let’s define the photoreceptor’s sensitivity, or its response rate, to flash lights as the additional response per unit increment in light intensity.
The sensitivity/response rate is given by the derivative of the curve, i.e., the slope at every point on the curve. Evidently, the response rate slows down as light becomes more intense; in other words, the photoreceptor becomes less sensitive as light becomes more intense. While the discussions here focus on photoreceptor responses to flash lights, the conclusion holds for responses to steady background lights as well.
This non-linear relationship can be used to explain our brightness perception. Our perceived brightness is not linear with respect to the light intensity. Imagine you walk into a dark room and turn one light on; the perceived brightness changes a lot (literally from 0 to 1); then you turn another light on and another light on; every time you turn on an additional light, your perceived brightness increases, but not as much as before. As you continue, the additional brightness you feel from turning one additional light on becomes smaller: you probably would not notice it if someone turned on one more light when there are 1,000 lights on already.
This non-linear relationship between perceived brightness and absolute light power is important when deciding how to effectively allocate digital bits when encoding pixel values. A classic example is the gamma encoding/compression in the popular sRGB color space, a topic we will turn to in Section 5.3.2.
3.6.2 Why and How Do Photoreceptors Desensitize?
The reduction of sensitivity under stronger lights is called desensitization, and is stereotypical of photoreceptor light adaptation. A curious question is, does desensitization provide us any benefits? Do we not want our photoreceptors to be more sensitive to light? Without desensitization, i.e., if the initial response rate was maintained, the rod would saturate at about 47 pigment excitations, as shown in Figure 3.12. The desensitization allows the photoreceptors to extend their operating range, which, in turn, allows our vision to operate at higher light levels.
What mechanisms cause photoreceptor desensitization? We will leave a thorough discussion for later in the class when we actually discuss adaptation, but briefly, there are two reasons.
The first reason is the natural exponential decay you would observe in pretty much any dynamical system. Recall that the reason a photoreceptor can produce electrical responses is because of the sequence of biochemical reactions, which require a bunch of materials, like the cGMPs, PDEs, etc., to bump into each other. Under stronger lights, the concentration of these materials is lower, which means they are less likely to meet each other. That in turn means the rate of cGMP concentration reduction becomes even slower, and the ion channels close even less frequently.
The second reason, first experimentally shown by Matthews et al. (1988) and Nakatani and Yau (1988), has to do with negative feedbacks regulated by Ca2+ ions. Interestingly, these negative feedback mechanisms are exactly the same as those that accelerate phototransduction deactivation, as discussed in Section 3.4.2. As we will discuss more quantitatively in the adaptation chapter (Section 7.1), this is not a coincidence: desensitization and faster recovery kinetics are two hallmarks of photoreceptor light adaptation.
3.6.3 Linear Range
If you observe Figure 3.12 (right) closely, you will see that the response vs. flash intensity is linear when the lights are dim. This linear relationship is used to estimate the single photon response: we cannot easily measure the response of a single photon as it is difficult to precisely deliver just one single photon, but this linear relationship in the dim range allows us to estimate such a response by scaling the response of a dim light by its intensity.
Mathematically, the response vs. intensity relationship is modeled in literature either by a negative exponential function (when negative feedbacks are weak) (Baylor, Nunn, and Schnapf 1984; Lamb, McNaughton, and Yau 1981; Kraft, Schneeweis, and Schnapf 1993) or by the Michaelis equation (when negative feedbacks are not negligible) (Baylor and Fuortes 1970; Baylor, Hodgkin, and Lamb 1974; Baylor, Lamb, and Yau 1979a; Normann and Perlman 1979; Fain 1976; Schneeweis and Schnapf 1995; Ingram, Sampath, and Fain 2016). The negative exponential model would look something like \(r/r_{max} = 1 - e^{-ki}\), where \(r\), \(r_{max}\), and \(i\) denote the response, maximum response, and flash light intensity, respectively; \(k\) is a constant fit to data. The Michaelis equation, which is also called the Naka–Rushton equation (presumably because Naka and Rushton (1966) was the first to use it), looks like \(r/r_{max} = \frac{i}{i+\sigma}\), where \(\sigma\) is a constant fit to data. Sometimes it would fit the data better to use the generalized Michaelis equation, which takes the form \(r/r_{max} = \frac{i^n}{i^n+\sigma^n}\), where \(n\) is the additional parameter that can fit to data. Both models can be approximated by a linear function when \(i\) is small. This linear region perhaps also explains why the sRGB encoding is a piece-wise function where the encoding is linear when light levels are low (Section 5.3.2).
Without back-scattering, we can assume any unabsorbed photons will be transmitted through, and measured at the other side of, the photoreceptor. In reality, a very small amount of some photons might be scattered backward toward where they come from and will not be measured either, but the effect is small.↩︎
Granit shared the Nobel Prize in 1967 with George Wald and Haldan Keffer Hartlin largely due to this work.↩︎
You might be wondering: if the GC-induced re-synthesis is always going on, wouldn’t the outer segment of a photoreceptor be packed with cGMP molecules? It turns out that in the dark even unactivated PDEs can hydrolyze cGMPs — at a much lower rate than activated PDEs do. These two forces counter each other and maintain a steady cGMP level in dark (Rodieck 1998, p. 373).↩︎