The reasons why and how the optimal light intensity input (that drives a photoreceptor’s information transfer maximally) is different for bursts and Gaussian white-noise stimulation are
summarized inAppendix 2—figure 3. Here we assess both cases using data from the stochasticDrosophilaR1-R6 photoreceptor model simulations, starting with light bursts.
Bursts
(Appendix 2—figure 3A-–D). These light intensity time series characteristically contain periods of longer dark contrasts, intertwined with brief and bright contrast events, as shown for 100 Hz bandwidth stimulation (Appendix 2—figure 3A, dark-yellow trace). Based on our previous analyses (Song and Juusola, 2014), longer dark contrasts help to recover more refractory microvilli than equally-bright stimuli without these features, improving neural information capture. This makes it more difficult for bursty stimuli to saturate the photoreceptor output. By increasing the stimulus intensity 8-fold, here from 1105to 8105effective photons/s, simply evoked larger macroscopic responses. These, thus, integrated more samples (bumps); as indicated by the larger (black) and smaller (blue) trace, respectively.
Because noise changes little in light-adapted photoreceptor output (Juusola et al., 1994; Juusola and Hardie, 2001b, Juusola and Hardie, 2001aJuusola and Hardie, 2001a; Song et al., 2012;Song and Juusola, 2014) (Figure 2—figure supplement 2), the larger responses to brighter bursts have higher and broader signal-to-noise ratio,SNRoutput(f), (Appendix 2—figure 3B). This, in turn, results in higher information transfer rate estimates,
Routput(Appendix 2—figure 3C), following Shannon’s equation (Shannon, 1948): Routput¼
Z ¥
0
ðlog2½SNRoutputðfÞ þ1Þdf (A2.1)
Note that with 1 kHz sampling rate used in every experiment, this estimation did not integrate information rate for frequencies from 0 to infinite, but from 2 to 500 Hz instead. However, the limited bandwidth would not considerably affect estimation results because: (i) high-frequency components have SNR <<1 and therefore contain mostly noise. (ii) Whereas even a high
SNRoutput(f) contains little information in its low-frequency components, below 2 Hz. Note also that we have previously shown the generality of Shannon’s information theory for estimating information transfer rates of continuous (analogue) repetitive responses, irrespective of their statistical structure (Juusola and de Polavieja, 2003;Song and Juusola, 2014). That is, for sufficient amount of data, Shannon’s equation and triple extrapolation method, which is free of signal and noise additivity and Gaussian distribution assumptions, give comparable rate estimates. Thus, these estimates should evaluate the simulations’ relative information rate differences truthfully;i.e.consistently with only small errors.
Markedly, a photoreceptor’s performance is systematically better to the brighter bursts (black line) than to the less bright ones (blue line), irrespective of their bandwidth (Appendix 2— figure 3C). Thus, for the brighter bursts, more microvilli are dynamically activated, generating larger sample rate changes. These bumps sum up larger (and more accentuated – see [Song and Juusola, 2014]) macroscopic responses, packing in more information than the corresponding responses to the less bright bursts.
Appendix 2—figure 3.Estimating optimal light intensity for 100 Hz high-contrast bursts and Gaussian white-noise (GWN) stimuli for a R1-R6 photoreceptor’s maximal information transfer. We hypothesize that the role of photomechanical adaptations, which include the intracellular pupil and contracting rhabdomere (Appendix 7) of a photoreceptor, is to maximize
information capture of microvilli by dynamically adjusting the light input falling upon them. The left side of the figure shows how encoding of light bursts (A–D) depends upon light intensity; the right side shows the same for GWN (E–H). (A) Owing to sufficient dark periods, a photoreceptor’s sampling units (microvilli) have enough time to recover from their
refractoriness even after they have responded to very bright bursts. This enables a
photoreceptor to maintain a large pool of available microvilli to sum up high sample (bump) rate changes to any new incoming input, generating larger macroscopic responses to the brighter bursts (8105photons/s, black) than to the less bright bursts (105photons/s, blue).
(B) Macroscopic responses with larger sample rate changes (black trace, grey area) have higher and broader signal-to-noise ratios (Song and Juusola, 2014). (C) Correspondingly, as the sample sizes (bumps) are similar to both stimuli (cf.Figure 2—figure supplement 2B), the larger responses carry a higher information transfer rate (Song and Juusola, 2014),
irrespective of the tested stimulus bandwidth. (D) Therefore, a photoreceptor’s information transfer rate to bursty inputs increases with light intensity, until the sample rate changes eventually saturate at 8105photons/s; when most of 30,000 microvilli become refractory (i.
e.more microvilli are refractory than available to be light-activated). (E) A R1-R6 generates similar size responses to the brighter (8105photons/s, black) and the less bright (105 photons/s, blue) GWN inputs. But the response to the less bright input shows more high- frequency modulation. (F) Consequently, the response to the less bright input (blue area) has higher and broader signal-to-noise ratio than the response to the brighter input (grey area). (G) This is reflected also in the photoreceptor’s information transfer rate, regardless of the
GWN bandwidth. (H) Information transfer rate in macroscopic photoreceptor output to GWN
stimulation saturates at 8-times less bright intensity levels than to bursts (D), reaching its
maximum at 105photons/s.
DOI: https://doi.org/10.7554/eLife.26117.043
However, because aDrosophilaphotoreceptor has a finite amount of microvilli, each of which - once activated by a photon’s energy - stays briefly refractory, its sample rate changes and thus signaling performance first increases monotonically until about 6105photons/s, before
gradually saturating, and eventually decreasing, with increasing burst brightness
(Appendix 2—figure 3D). The photoreceptor model’s maximum information transfer rate estimate (Rmax= 631±31 bits/s; marked by a square) for 100 Hz bright bursts is reached at the optimal stimulus intensity of 8105effective photons/s. In other words, this is the amount
light the photomechanical adaptations, including the intracellular pupil mechanism and rhabdomere contractions (see Appendix 7), should let through (to be absorbed) in bright daylight for the fly to see bursty real-world events best. The corresponding performance estimate with the less bright bursts (105effective photons/s) is 493±12 bits/s (circle).