Photoentrainment as Bayesian Inference: How the central circadian clock may weight and integrate the intensity and wavelength of natural light to estimate astronomical time

Synchronising with the Earth's 24-hour rotation using natural light as a timing cue presents a problem for the mammalian brain's central circadian clock. Natural light is highly variable and can take a range of values at any given time of day. For example, it fluctuates due to differences in weather conditions and across seasons. Therefore, an absolute value of light provides an uncertain indication of the time of day. Despite this uncertainty, the central clock maintains close alignment with astronomical time, and here we describe how this may be achieved computationally. We present a Bayesian model in which the clock's endogenous oscillation is used to predict the probability of observing features of light, including intensity and spectral composition, and their co-occurrence given the time of day. These predictions are drawn from a distribution of values typically experienced. When observed light falls outside the predicted range, a prediction error provides evidence that the clock may be misaligned with astronomical time. How much the clock adjusts its phase depends on the relative uncertainty associated with its internal prediction and observed light. These are combined as a weighted average according to their relative reliability, drawing the clock's updated phase towards whichever provides the more reliable estimate of astronomical time. Using natural light measurements collected over one week from 59 human observers and 100 days of environmental spectral measurements, we characterize how the variability of natural light systematically changes across the day and show how the clock may exploit this structure for circadian timekeeping. The model explains how the canonical shape of the phase response curve emerges from the relationship between light distributions and time of day, and how properties of light, including intensity and spectral composition, can be integrated according to their reliability. The central clock's synchrony to light may represent a specific instance of a general computational strategy employed by the mammalian nervous system, whereby sensory information is interpreted relative to an internally generated prediction.