Probabilistic inference by biochemical circuits

Calvo and Baluška (2015) took as a working hypothesis that adaptive plant behaviour can only occur through a mechanism that predicts sensory states.¹ They noted that anticipation comes in a variety of forms. On weaker readings the system models environmental sources of stimulation internally. Stronger forms that explain away internal modelling, they wrote, cannot be discarded beforehand, and they cited Stepp and Turvey on this point.¹ They treated predictive coding and strong anticipation as working hypotheses open to empirical scrutiny.¹ Under predictive coding, as they cite Friston, a process of probabilistic inference lets animals scan their surroundings.¹

Katz and Springer (2016) took the posterior predictive distribution of the next environment, given its history, as the main quantity of interest.² They noted that this distribution can be calculated recursively in dynamic probabilistic models, which allowed a real-time estimation procedure using particle filtering.² They then constructed a transition counter for an environment with glucose and galactose. The circuit has sensors activated by sugars, activators produced downstream of them, and proteins that count glucose-to-galactose and galactose-to-glucose transitions and act as memory molecules.³

Kirchhoff and colleagues (2018) described belief in terms of a variational density, with the KL divergence measuring its discrepancy from the true posterior distribution.⁴ When free energy is minimized, they wrote, the variational density is approximately equal to the posterior.⁴ In their reading this is the same quantity that Bayesian inference seeks to optimize.⁴ The held passage states this at the level of the formalism. It does not describe a particular molecular circuit, which is the concern of the Katz papers.

Katz and Fontana (2022) built on the same idea with polymers. Their algorithm updates transition counts as the environment changes, then anticipates the next state by normalizing the row of counts for the current state and sampling from it.⁵ They sought biochemical realizations of two operations, directional counting and normalization-sampling.⁶ Directional counting used polymer assembly, relying on polymer polarity.⁶ Normalization-sampling used two proteins that bind a third integrator protein in mutually exclusive fashion.⁷ Levin (2023) lists protein interaction and gene-regulatory pathways among subcellular components shown to underlie anticipation and probabilistic inference.⁸