Point process analysis of noise in early invertebrate vision

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.

噪声广泛存在于众多生物学过程中，有时甚至会成为其主导性特征。尽管诸多自然系统已演化出衰减乃至有效整合噪声的能力，但噪声所引入的变异性，仍常常制约着生物学功能可实现的精准度。这一点在视觉光转导（visual phototransduction）中尤为突出——该过程负责将光子转化为可用电信号，其基本响应单元为量子 bumps（quantum bumps）。在此，光子输入的随机性（被视为外源性噪声（extrinsic noise））与转化过程的随机性（被视为内源性噪声（intrinsic noise）），被认为是影响视觉可靠性的两个独立且显著的限制因素。过往研究试图通过近似方法量化这两类噪声源的相对影响，但此类方法未能充分兼顾该问题的离散点过程及时序本质，致使不同研究方法得出的结论，对光转导噪声性能的阐释存在不一致之处。

本文针对无脊椎动物光转导过程中的内源性与外源性噪声相对影响，采用基于贝叶斯点过程（Bayesian point process）斯奈德滤波器（Snyder filters）的最小均方误差（minimum mean squared error）重建技术，展开了全新且完整的分析。本文开发了一种基于整合-发放（integrate-fire）的算法，可从量子 bumps 中可靠估算光子到达时间；随后利用斯奈德滤波器，对光转导级联（phototransduction cascade）的前端与后端的随机光强进行因果性估算。对这些估算结果的对比显示，随着光强升高，主导噪声源会从外源性噪声向内源性噪声转变。通过扩展滤波技术以纳入延迟因素的考量，研究进一步发现，在内源性噪声组分（包括 bumps 潜伏期（bump latency），即平均延迟与抖动，以及波形（振幅与宽度）方差）中，平均延迟对噪声性能起着决定性作用。由于视觉信息的时效性对实时行为至关重要，这类延迟可能会限制无脊椎动物对刺激作出响应的速度。因此，若要提升视觉保真度（visual fidelity），缩短光转化延迟（photoconversion lag）远比改善电信号的规整性更为重要。