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Stochastic, adaptive sampling of information by microvilli in fly photoreceptors.
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PMID:  22704990     Owner:  NLM     Status:  MEDLINE    
BACKGROUND: In fly photoreceptors, light is focused onto a photosensitive waveguide, the rhabdomere, consisting of tens of thousands of microvilli. Each microvillus is capable of generating elementary responses, quantum bumps, in response to single photons using a stochastically operating phototransduction cascade. Whereas much is known about the cascade reactions, less is known about how the concerted action of the microvilli population encodes light changes into neural information and how the ultrastructure and biochemical machinery of photoreceptors of flies and other insects evolved in relation to the information sampling and processing they perform.
RESULTS: We generated biophysically realistic fly photoreceptor models, which accurately simulate the encoding of visual information. By comparing stochastic simulations with single cell recordings from Drosophila photoreceptors, we show how adaptive sampling by 30,000 microvilli captures the temporal structure of natural contrast changes. Following each bump, individual microvilli are rendered briefly (~100-200 ms) refractory, thereby reducing quantum efficiency with increasing intensity. The refractory period opposes saturation, dynamically and stochastically adjusting availability of microvilli (bump production rate: sample rate), whereas intracellular calcium and voltage adapt bump amplitude and waveform (sample size). These adapting sampling principles result in robust encoding of natural light changes, which both approximates perceptual contrast constancy and enhances novel events under different light conditions, and predict information processing across a range of species with different visual ecologies.
CONCLUSIONS: These results clarify why fly photoreceptors are structured the way they are and function as they do, linking sensory information to sensory evolution and revealing benefits of stochasticity for neural information processing.
Zhuoyi Song; Marten Postma; Stephen A Billings; Daniel Coca; Roger C Hardie; Mikko Juusola
Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2012-06-14
Journal Detail:
Title:  Current biology : CB     Volume:  22     ISSN:  1879-0445     ISO Abbreviation:  Curr. Biol.     Publication Date:  2012 Aug 
Date Detail:
Created Date:  2012-08-10     Completed Date:  2012-12-26     Revised Date:  2014-11-05    
Medline Journal Info:
Nlm Unique ID:  9107782     Medline TA:  Curr Biol     Country:  England    
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Languages:  eng     Pagination:  1371-80     Citation Subset:  IM    
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Copyright © 2012 Elsevier Ltd. All rights reserved.
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MeSH Terms
Adaptation, Physiological
Drosophila / physiology*,  ultrastructure
Feedback, Physiological
Microvilli / physiology*
Models, Biological
Photoreceptor Cells, Invertebrate / physiology*,  ultrastructure
Stochastic Processes
Grant Support
BB/D001900/1//Biotechnology and Biological Sciences Research Council; BB/D007585/1//Biotechnology and Biological Sciences Research Council; BB/F012071/1//Biotechnology and Biological Sciences Research Council; BB/G006865/1//Biotechnology and Biological Sciences Research Council; BB/H013849/1//Biotechnology and Biological Sciences Research Council; E19850//Biotechnology and Biological Sciences Research Council
Comment In:
Curr Biol. 2012 Aug 7;22(15):R595-7   [PMID:  22877777 ]

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

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Journal Information
Journal ID (nlm-ta): Curr Biol
Journal ID (iso-abbrev): Curr. Biol
ISSN: 0960-9822
ISSN: 1879-0445
Publisher: Cell Press
Article Information
© 2012 ELL & Excerpta Medica.
Received Day: 13 Month: 1 Year: 2012
Revision Received Day: 14 Month: 3 Year: 2012
Accepted Day: 25 Month: 5 Year: 2012
pmc-release publication date: Day: 07 Month: 8 Year: 2012
Print publication date: Day: 07 Month: 8 Year: 2012
Volume: 22 Issue: 15
First Page: 1371 Last Page: 1380
ID: 3420010
PubMed Id: 22704990
Publisher Id: CURBIO9633
DOI: 10.1016/j.cub.2012.05.047

Stochastic, Adaptive Sampling of Information by Microvilli in Fly Photoreceptors
Zhuoyi Song12
Marten Postma34
Stephen A. Billings2
Daniel Coca2 Email:
Roger C. Hardie3∗∗ Email:
Mikko Juusola15∗∗∗ Email:
1Department of Biomedical Science, University of Sheffield, Sheffield S10 2TN, UK
2Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UK
3Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge CB2 3DY, UK
4Swammerdam Institute for Life Sciences, University of Amsterdam, 1090 GE Amsterdam, The Netherlands
5State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China
Corresponding author
∗∗Corresponding author
∗∗∗Corresponding author


Fly photoreceptors provide classical model systems for studying how sensory neurons sample and process information. By adapting dynamically to ambient illumination, their voltage responses can represent intensity fluctuations over a truly astronomical scale—from scattered photons of night sky to 108 times brighter daylight [1, 2]—and do so with the fastest temporal resolution known in the animal kingdom. Structural and functional adaptations of fly photoreceptors have been investigated extensively, and we have a wealth of knowledge about their ultrastructure, molecular constituents, and response dynamics [2]. However, we lack a deeper understanding of how these structures and reactions sample and process visual information under different light conditions (but see [3–6]).

To address this, we generated biophysically realistic photoreceptor models and compared their performance to real photoreceptors. In fly photoreceptors, single photon responses (quantum bumps), with variable waveforms and timing (latency distribution), are generated within single microvilli and sum to produce macroscopic voltage responses [7, 8]. By combining stochastic simulations with single cell recordings from Drosophila photoreceptors, we show how the number of light-activated microvilli (regarded as elementary sampling units), and the speed and refractoriness of the bumps they generate, dynamically adjust the pool of available microvilli according to the instantaneous photon arrival rate. By extracting the average bump waveforms and latency distributions from real recordings at different light levels and incorporating these into the stochastic models, we quantified how “unreliable” biochemical reactions and refractory sampling units generate reliable neural representations of natural light changes, how increasing the number of sampling units or their sampling speed improve vision, and how feedbacks and stochastic reactions assist encoding. Thus, sensory encoding of naturalistic stimuli can be understood through simple adaptive sampling principles, set by the dynamic availability and variable bump waveforms of the microvilli population. Finally, we demonstrate how these principles can successfully predict the ultrastructure and information transfer of other fly photoreceptors.


To better understand how light information is sampled and processed through the interplay between the phototransduction cascade and voltage-sensitive plasma membrane [8], we constructed a detailed biophysical model of a Drosophila outer photoreceptor (R1–R6), based on the dynamics of its molecular components. As in real photoreceptors, the model incorporates two parts (Figure 1A; see Figure S1A and Table S1 available online): a light-sensitive rhabdomere, made out of ∼30,000 microvilli, each of which operates independently as a phototransduction unit, housing an identical stochastic phototransduction cascade (Figures S1B and S1C) and a voltage-sensitive plasma membrane (Figure S1D), which translates the phototransduction current into a voltage response [2, 8].

Single Microvilli Generate only One Quantum Bump at a Time

We first modeled how a single microvillus (Figure 1B) detects single photons by tracking the numbers and dynamics of photons and cascade intermediates (Figure 1C). Following absorption of one photon by a single rhodopsin molecule, the G protein-based transduction cascade culminates in the opening of 5-15 TRP/TRPL channels within an individual microvillus [9]. The resulting influx of calcium, magnesium, and sodium ions generates a quantum bump [6, 10]. The model shows how dead-time [11, 12] and bump latency distribution [7, 8] arise from the stochasticity, finite speed, and success of these reactions [5, 6]. We see that not all absorbed photons cause bumps; in this particular simulation, six absorbed photons evoked three bumps. Very rarely the molecules downstream fail to activate their targets and the signal fades before the amplification takes off (marked ). In other cases, the reactions are blocked because the photons (marked ∗∗) arrived during the 100–200 ms “refractory period,” which follows each bump. Critically, calcium provides sequential positive and negative feedbacks (red) to multiple targets, greatly amplifying the signal and accelerating response speed [7, 10]. As soon as a bump is generated, the negative feedback holds the microvillus in a state of inhibition during which it cannot respond to light. This refractory period ends when the negative feedback relaxes and ultimately sets the maximum sample rate (bump production rate) of the microvillus (Figure S2A).

The model further highlights how the bumps adapt to the frequency of the past bumps. Although showing stochastic variation, the first bumps are typically the largest and later ones smaller. Overall, these simulated dynamics generate bumps (Figure 1D) with broadly distributed latencies (Figure 1E) that closely resemble real bumps to very dim illumination, sampled in whole cell patch-clamp recordings of dissociated photoreceptors.

Microvilli Availability Contributes to Fast Adaptation

An individual microvillus can only produce one bump at a time, and the photoreceptor sums many of them to generate a continuous response, as shown schematically for a dim 2 s step in Figure 2A. With simple summation, such macroscopic responses would be square-like but noisy due to the low bump production rate by microvilli. However, the real light-induced currents (LIC) to light steps, measured under voltage-clamp (Figures 2B and 2C) show additional adaptive trends as the intensity increases. The combined response of few activated microvilli to a dim stimulus is smaller, slower, and noisier (Figure 2B) than that of many activated microvilli (Figure 2C) to a bright stimulus, which reaches a transient peak that rapidly decays and rebounds, before gradually settling to a steady-state (plateau). Here, fast adaptation happens during the early transient response (Figure 2C), whereas slow adaptation establishes the slower trend toward the plateau (Figure 2B).

To elucidate the processes behind fast and slow adaptation, we fixed all free parameters in our model and simulated the output of 30,000 microvilli to dim (3,000 photons/s) and bright (3 × 105 photons/s) pulses. We first assume that each of the microvilli operates independently and the macroscopic LIC response is a summation of the bumps they produce [2, 7].

The results imply that fast adaptation, i.e., processes shaping the early transient response, depends directly on the number of microvilli that can participate in the response, determined jointly by the intensity and (stochastic) duration of the refractory period. During dim stimulation at low photon rates (Figure 2B), only a small fraction of the microvilli is activated (or refractory) at any one time (Figure 2D), leaving a large pool of unused microvilli to sample further incident photons. By contrast, at the onset of a bright stimulus (Figure 2C), a large fraction of the microvilli is activated simultaneously but then becomes refractory (Figure 2E). This leaves only a small fraction of the microvilli to respond to the next photons in the stimulus until more microvilli become available again (see also [13]). Therefore, the number of activated microvilli shows a large initial peak, followed by a rapid drop that then settles to a steady-state as photon arrivals and refractory periods become decorrelated. Thus, the early transient response (Figure 2C) is evoked largely by the initial bumps from a large pool of microvilli (Figure S2B) and its width is largely shaped by bump latencies (Figure S2C), which vary in dark and light adaptation and with temperature [7, 8, 14].

If all bumps were identical, then the macroscopic current would simply represent the number of activated microvilli at a given photon rate, with a flattened steady-state response (Figures 2D and 2E). However, compared to these microvilli counts, the measured light-induced currents to dim light show a slowly decaying trend (Figures 2B and 2D), whereas the plateau levels in response to bright light are much smaller (Figures 2C and 2E). This is because bumps adapt, becoming smaller and briefer with brighter backgrounds [8, 15, 16]. These effects have been modeled in the simulated light currents to dim and bright pulses by introducing a global negative feedback parameter, ns, which increases exponentially with time and accelerates with increasing intensity (Table S2). This global feedback presumably represents Ca2+-dependent inhibition or adaptation due to light-induced calcium spread between microvilli via the cell body [2]. This attenuates bump waveforms (Figures 2F and 2G) by progressively strengthening the negative feedback to multiple targets [2, 8, 15, 17]. Thus, reduction both in the number of activated microvilli [13, 18] and in their bump waveforms largely accounts for the transient dynamics of the LIC response to bright stimuli, whereas calcium-induced bump adaptation accounts for key aspects of slow adaptation including the reduced plateau response.

Whereas Ca2+-dependent light adaptation is well established [2, 17, 19], our analysis indicates for the first time how sampling by microvilli leads inevitably to adaptation by stochastic saturation of transduction units. To make this structural connection more obvious, we consider simulations, in which a dim light input (300 photons/s) is sampled either by 3,000 or 300 microvilli. For the given photon rate, 3,000 microvilli can generate a macroscopic response (Figure 2H) that is comparable to a real LIC (Figure 2B), but with only 300 microvilli, the summed response shows early saturation (Figure 2I). However, crucially, the responses always recover to a steady-state output level, as set by the dynamic ratio of used and available microvilli, but this output level is higher in a photoreceptor with more microvilli. Thus, although the simulations confirm two classic hypotheses: that the microvilli represent transduction units [20] and that the number of transduction units determines the maximum rate at which photons can be sampled [21], they also reveal new insight into light adaptation and the design of microvillar photoreceptors.

Global Feedbacks Affect All Microvilli

Thus far, we have considered only the light-sensitive conductance under voltage-clamp conditions. Next, we extended the modeling to the voltage domain by allowing interplay between light- and voltage-gated ion channels and compared our results with intracellular voltage recordings with sharp microelectrodes. We used a detailed Hodgkin-Huxley type model of a typical Drosophila photoreceptor's plasma-membrane, which incorporates a suite of voltage-sensitive K+-channels and accurately simulates voltage responses to current pulses [22, 23] (Figure 3A). Here, we further allow the voltage of the plasma membrane to feed back to the phototransduction cascade by regulating the electromotive force for the light-sensitive current across all microvilli (Figure 3B; Figure S3A), as must happen in vivo. As the photoreceptor depolarizes to a light stimulus, both the battery that drives calcium and sodium ions through TRP channels and the membrane resistance reduces throughout the cell, adapting (attenuating) bumps in every active microvillus, irrespective of their bump history. Thus, together intracellular voltage and calcium accumulation (Figures 2F and 2G) provide global feedbacks, which affect all microvilli, causing a divisive nonlinearity [24] that dynamically adapts their bump sizes to the ongoing photon rate, as supported by noise analysis [8, 14, 15, 25]. Consequently, the macroscopic voltage response becomes compressed (Figure 3C). Furthermore, the transition from prolonged dark adaptation to light adaptation [7, 8], which narrows the width of the early transient voltage responses, can be replicated by narrowing the bump latency distribution (Figures S2C–S2E) and understood as a memory of light exposure [26], presumably mediated by intracellular calcium accumulation affecting the microvilli globally.

Microvillar Bump Production Dynamics Set Information Rate

To examine how Drosophila photoreceptors sample and process visual information in different light-adapted states, we recorded voltage responses to repeated pseudorandom (white noise) and naturalistic (collected from natural environment [1]) contrast sequences at six different intensity levels in vivo at 25°C. By using established noise analysis techniques on the responses to the white noise sequence [8, 12, 14, 26], we extracted the average bump shapes and their latency distributions under different adaptational states (Figures 3D–3J). As previously reported, the average bumps were larger and slower at dim intensities and smaller and faster at brighter illumination (Figure 3I), whereas the bump latency distributions, in even a weakly light-adapted state (Figure 3J), were narrower than following prolonged dark adaptation (Figure 1E), but then changed little during adaptation to further increasing background intensity [8].

The estimated bump shape and latency distribution statistics at each light intensity level were incorporated into the full model by refixing two negative feedback parameters: ns and la (Figures S3B and S3F), which regulate the strength and speed of the Ca2+-dependent negative feedback in each simulated microvillus (Figures 4A and 4B). By simulating bump production over all 30,000 microvilli, the model was then used to predict microvilli availability and macroscopic voltage responses during repeated naturalistic stimulation (NS) at each light intensity level.

Because the model's bump statistics were now fixed to the steady-state adapted natural bump variations at any one background, the close correspondence of experiment and simulation indicated that voltage responses of fully light-adapted photoreceptors to naturalistic stimuli (Figures 4C and 4D) can be largely accounted for by the changing fraction of their activated microvilli (Figures 4E and 4F). With dim stimulation (low photon rate), this sampling utilized <2% of microvilli, allowing detection of essentially all absorbed photons. With bright stimulation, maximal microvillar usage approached 62% (mean usage: 48%). With increasing background intensities, the increased probability of photons arriving during a refractory period resulted in steep fall-off in quantum efficiency but with no loss of information transfer (Figure 4H). The encoding was logarithmic; larger bumps to dim NS generated macroscopic responses, which reached ∼1/3 of those to bright NS, although the dim and bright intensities differed by 100-fold. Such gain control is due to a combination of passive and active membrane and reduction in bump current, which is reduced to <1 pA during bright stimulation. Crucially, the responses predicted by the model, their signal-to-noise ratios (SNR; Figure 4G), and rate of information transfer (Figure 4H), as quantified from their capacity to distinguish different stimulus values [27], closely resembled those of actual recordings at each light level. Minor discrepancies between model and experiment can be readily accounted for by factors not included in the model. Thus, under bright stimulation, the simulations had higher information content due to their higher low-frequency SNR (Figure 4G, marked ). This difference is probably because the model lacks an intracellular pupil, which progressively filters out photons [21, 28], and additional slow adaptation mechanisms, such as translocation of components of the transduction cascade [29–32]. These processes, together with any damage, recording, or instrumental noise, increase variability in low frequency responses of real cells. The model also lacks regulation from synaptic feedbacks [33, 34], which spread extra information from other photoreceptors in the network, boosting high-frequency signals (SNR) [34–36] (Figure 4G, marked ∗∗). Nonetheless, these results indicate that the photoreceptor output mostly represents a complex function between the biophysical sampling rate (bump production rate) and sample size (bump waveform).

Benefits of Stochasticity and Microvillar Feedbacks

If microvilli generated identical bumps with everything else being equal, then for the same slowly changing light input, two macroscopic outputs, one integrated from small and the other from large bumps, have the same rate of information transfer (simulated LICs: Figures S4A–S4D). This is because bump shape affects signal and noise equally and can be deconvolved, as a known filter, from the outputs, revealing their identical inputs (data processing theorem [27, 37]). A photoreceptor's rate of information transfer, therefore, depends fundamentally on changes in its bump production rate. However, when real photoreceptors adapt to a certain light level, the feedback mechanisms within microvilli make encoding more than just a summation of similar or independent bumps. Bumps generated in individual microvilli have adapted (albeit stochastic) bump waveform and refractory periods that reflect their specific absorption histories and which affect information in the macroscopic responses.

Interestingly, simulations indicate that bumps with such adaptive correlations generate less low-frequency noise during response summation than a mock series of bumps with the same distributions but lacking such correlations (Figure 5A). In addition, a stochastic refractory period distribution suppresses oscillations in macroscopic responses (Figure 5B) and opposes saturation by using microvilli and photoreceptor output range more evenly (Figure 5C). But most importantly, although the equilibrium between the used and available microvilli ultimately limits the bump production rate at very bright stimulation of high SNR [38] (Figure 5D), failures in bump production, whether stochastic or due to refractory period, promote output constancy. As long as the photoreceptor maintains its maximal bump production rate, its output will have the same rate of information transfer, irrespective of whether its microvilli were bombarded by 105 or 106 photons/s [8, 34, 39]. Furthermore, because microvilli will stochastically flip between processing states, even in very intense light, some will always return to the active “available pool,” making it difficult to inactivate all of them at once. Thus, the models show how microvillar feedbacks and stochasticity of sampling resist saturation and enable more invariable neural information capture.

Information Transfer in Different Fly Photoreceptors Is Also Predictable

Lastly, we extended this framework to sensory evolution by building stochastic models of R1–R6 photoreceptors in three different fly species (Figure 6): Drosophila, blowfly (Calliphora vicina), and killer fly (Coenosia attenuata), based on intracellular recordings at 19°C. Each of these flies has a different lifestyle (predatory or herbivorous) living in specific habitats, from shady forests to sunny shores [39]. Presumably to accommodate such differing visual demands, their rhabdomeres have evolved appropriately, hosting different numbers of microvilli with different reaction speeds [39]. Again, through noise and signal analysis (cf. Figure 3D), we extracted the average bump waveforms and latency distributions from their voltage responses to a pseudorandom contrast stimulus in vivo, and these statistics were incorporated accordingly in each model (Figures 6A–6C). Moreover, the properties of their voltage-sensitive membranes were approximated with Hodgkin-Huxley type membrane models, with parameters adjusted to simulate in vivo recordings to current injections (Figure S5).

In each case, simulated responses (red) closely resembled the real recordings (black) to the repeated naturalistic stimulus. Here, slow-flying Drosophila has the fewest microvilli (Figure 6A), with the slowest phototransduction reactions (see [39]), generating the widest latency distribution, slowest bumps, and longest refractory periods. Such low-passing sampling limits the SNR of responses at high frequencies, communicating 350 bits/s at daylight intensities, >105 photon/s (Figure 6D). Interestingly, this information transfer rate approximates that for the same stimulus at a higher temperature of 25°C (Figure 4F), suggesting that insect photoreceptors may have evolved to provide consistent representations of naturalistic image statistics in varying environmental conditions, in agreement with earlier suggestions [26]. In contrast, the fast-flying scavenger, Calliphora, has three times more microvilli (Figure 6B), which operate three times faster, extending the range of reliable signaling to three times higher frequencies and so doubling the rate of information transfer (Figure 6E). The small Coenosia has a similar number of microvilli to Drosophila (Figure 6C), but its phototransduction is by far the fastest of these species, enabling the largest sample rate changes. Its fast bumps, brief latencies, and short refractory periods generate the highest high-frequency SNR and rate of information transfer (Figure 6F), as required by its demanding predatory lifestyle of fast aerobatic hunting [39].

At high stimulus frequencies, the SNR of the Calliphora and Coenosia recordings exceeds that of the simulations (Figures 6E and 6F). Because later transformations by membrane filtering cannot improve their encoding performance, affecting signal and noise equally [27, 37], this improvement probably comes through functional contacts, which channel in new information from other photoreceptors [34] and stored information from the network [36, 40] in activity-dependent manner.


Using experiments and modeling, we have shown how stochastic adapting sampling principles, which can be directly derived from biochemical and biophysical reactions occurring within a finite population of microvilli, govern information processing in fly photoreceptors.

Adaptive Sampling Promotes Contrast Constancy while Enhancing Novel Events

Our results suggest that by compartmentalizing its inherently stochastic biochemical reactions into semiautonomous transduction units (microvilli), phototransduction in flies evolved to generate reliable neural representations of their visual environment. Adaptive sampling by microvilli relies upon local stochastic reactions and global nonlinear interactions (calcium and voltage feedbacks) to encode natural contrast changes. By adjusting the microvilli availability and the speed and the size of their individual bumps, local stochasticity and global feedbacks promote matching of the information transfer rate of the macroscopic voltage responses with the ecological demands of each fly species, approximating contrast constancy under varying conditions.

In dim conditions, every photon counts, and the quantum efficiency of Drosophila photoreceptors is probably close to 100%. The resulting bumps are at their slowest and largest (Figure 7A) [8] and are integrated to generate consistent voltage responses to slow contrast changes, which dominate in the 1/f statistics of the natural scenes. In bright conditions, however, many microvilli are refractory (not available), reducing quantum efficiency. This desensitization stabilizes the bump production rate below saturation (Figure 7B) and, with the help of the global feedbacks, tends to equalize the allocation of visual information within the photoreceptor's limited signaling range (Figures 3C and 5D). Individual photons carry now less value (Figure 7C), and the resulting bumps are small and fast [8], integrating to generate robust macroscopic voltage responses; but again the responses dominantly represent slower contrast changes, attributable to the 1/f statistics. Importantly, the adaptive stochastic bump shape and refractory period distributions smoothen integrated responses (improving low-frequency SNR; Figure 5A) and resist oscillations to sudden, large light changes (Figure 5C). For these reasons, the macroscopic (normalized) voltage responses to light contrasts are highly similar at different illuminations (Figure 7D) [see also: 26], capturing the temporal pattern in the image sequences, as projected by the lens system of a fly in motion [1].

Adaptive sampling also provides an intrinsic capacity to enhance novel events. Although after phototransduction subsequent adaptation cannot increase the photoreceptor's rate of information transfer [27], during sampling it can if it produces a differential change of signal relative to noise between successive responses to the same stimulus. Simulations indicated that the first “towering” response to a bright step contains more samples, and thus has a higher signal-to-noise ratio than subsequent responses, for which less microvilli are activated. Similarly, the first, negative voltage response to a dim step will be enhanced because more microvilli will be in an inactive state than in subsequent responses, because initially many are still refractory [41]. Accordingly, photoreceptors' information transfer is higher at large dim-to-bright or bright-to-dim stimulus transitions and decreases afterwards in correlation with the adaptation to the stimulus [27, 34, 36]. Thus, not only does adaptive sampling lead to robust encoding of natural light changes over the full dynamic range of environmental light intensities, it also enhances novel or surprising stimuli, which generate the largest sample rate changes (increments or decrements) in respect to the ongoing average.

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Supplemental Information

Document S1. Figures S1–S5, Tables S1 and S2, and Supplemental Experimental Procedures


We thank Gonzalo de Polavieja for discussions and Paloma Gonzalez-Bellido and Trevor Wardill for supplying Coenosia. This work was supported by the BBSRC grants BB/F012071/1 and BB/D001900/1 (M.J.), BB/G006865/1 and BB/D007585/1 (R.C.H.), and BB/H013849/1 (D.C., M.J., and S.A.B.); the open research fund of the State Key Laboratory of Cognitive Neuroscience and Learning (M.J.); EPSRC grant EP/H00453X/1 (S.A.B. and D.C.); and ERC Advanced Investigator Grant 226037 NSYS (S.A.B.). M.J., R.C.H., M.P., D.C., S.A.B., and Z.S. initiated the study, and M.J. and Z.S. designed it. M.J. and Z.S. formalized the ideas and analyzed the data. M.J. and R.C.H. designed and performed experiments. Z.S. developed the model, wrote the code, and ran the simulations under the supervision of D.C., M.J., and S.A.B. M.P. developed an alternative modeling approach, which helped to refine the used parameter range. M.J. developed the analytical tools. M.J. and R.C.H. wrote the main paper, while Z.S. did its illustrations. Z.S. and M.J. wrote the supplement. All authors discussed the results and commented on the manuscript at different stages.

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