Point process analysis of noise in early invertebrate vision

Abstract

Noise is a prevalent and sometimes even dominant aspect of many biological processes. While many natural systems have adapted to attenuate or even usefully integrate noise, the variability it introduces often still delimits the achievable precision across biological functions. This is particularly so for visual phototransduction, the process responsible for converting photons of light into usable electrical signals (quantum bumps). Here, randomness of both the photon inputs (regarded as extrinsic noise) and the conversion process (intrinsic noise) are seen as two distinct, independent and significant limitations on visual reliability. Past research has attempted to quantify the relative effects of these noise sources by using approximate methods that do not fully account for the discrete, point process and time ordered nature of the problem. As a result the conclusions drawn from these different approaches have led to inconsistent expositions of phototransduction noise performance. This paper provides a fresh and complete analysis of the relative impact of intrinsic and extrinsic noise in invertebrate phototransduction using minimum mean squared error reconstruction techniques based on Bayesian point process (Snyder) filters. An integrate-fire based algorithm is developed to reliably estimate photon times from quantum bumps and Snyder filters are then used to causally estimate random light intensities both at the front and back end of the phototransduction cascade. Comparison of these estimates reveals that the dominant noise source transitions from extrinsic to intrinsic as light intensity increases. By extending the filtering techniques to account for delays, it is further found that among the intrinsic noise components, which include bump latency (mean delay and jitter) and shape (amplitude and width) variance, it is the mean delay that is critical to noise performance. As the timeliness of visual information is important for real-time action, this delay could potentially limit the speed at which invertebrates can respond to stimuli. Consequently, if one wants to increase visual fidelity, reducing the photoconversion lag is much more important than improving the regularity of the electrical signal. The invertebrate phototransduction system captures and converts environmental light inputs into electrical signals for use in later visual processing. Consequently, one would expect it to be optimised in some way to ensure that only a minimal amount of environmental information is lost during conversion. Confirming this requires an understanding and quantification of the performance limiting noise sources. Photons, which are inherently random and discrete, introduce extrinsic noise. The phototransduction cascade, which converts photons into electrical bumps possessing non-deterministic shapes and latencies, contributes intrinsic noise. Previous work on characterising the relative impact of all these sources did not account for the discrete, causal, point process nature of the problem and thus results were often inconclusive. Here we use non-linear Poisson process filtering to show that photon noise is dominant at low light intensity and cascade noise limiting at high intensity. Further, our analysis reveals that mean bump delay is the most deleterious aspect of the intrinsic noise. Our work emphasises a new approach to assessing sensory noise and provides the first complete description and evaluation of the relative impact of noise in phototransduction that does not rely on continuity, linearity or Gaussian approximations.