Adaptive trust in internal models alleviates trade-offs in biophysical inference of the environment

Living organisms often make unreliable measurements of their external environment while also making unreliable internal predictions of what their environment should be. The theory of Kalman filtering (or recursive Bayesian estimation) suggests that these two data should be combined using a time-dependent `trust’ factor that accounts for the relative unreliability of these two data. Using recent quantitative experimental measurements of circadian clocks in Synechococcus elongatus, we show that the coupling between the circadian clock and metabolism can naturally provide such an adaptive trust mechanism. Such adaptive trust allows the circadian clock to break sensitivity-robustness trade-offs on average, ignoring intensity fluctuations in natural light and yet responding quickly to phase changes.