Natural perception relies inherently on inferring causal structure in the environment. However, the neural mechanisms and functional circuits that are essential for representing and updating the hidden causal structure during multisensory processing are unknown. To address this, monkeys were trained to infer the probability of a potential common source from visual and proprioceptive signals on the basis of their spatial disparity in a virtual reality system. The proprioceptive drift reported by monkeys demonstrated that they combined historical information and current multisensory signals to estimate the hidden common source and subsequently updated both the causal structure and sensory representation. Single-unit recordings in premotor and parietal cortices revealed that neural activity in premotor cortex represents the core computation of causal inference, characterizing the estimation and update of the likelihood of integrating multiple sensory inputs at a trial-by-trial level. In response to signals from premotor cortex, neural activity in parietal cortex also represents the causal structure and further dynamically updates the sensory representation to maintain consistency with the causal inference structure. Thus, our results indicate how premotor cortex integrates historical information and sensory inputs to infer hidden variables and selectively updates sensory representations in parietal cortex to support behavior. This dynamic loop of frontal-parietal interactions in the causal inference framework may provide the neural mechanism to answer long-standing questions regarding how neural circuits represent hidden structures for body-awareness and agency.

Single-cell measurements of mRNA copy numbers inform our understanding of stochastic gene expression, but these measurements coarse-grain over the individual copies of the gene, where transcription and its regulation take place stochastically. We recently combined single-molecule quantification of mRNA and gene loci to measure the transcriptional activity of an endogenous gene in individual Escherichia coli bacteria. When interpreted using a theoretical model for mRNA dynamics, the single-cell data allowed us to obtain the probabilistic rates of promoter switching, transcription initiation and elongation, mRNA release and degradation. Unexpectedly, we found that gene activity can be strongly coupled to the transcriptional state of another copy of the same gene present in the cell, and to the event of gene replication during the bacterial cell cycle. These gene-copy and cell-cycle correlations demonstrate the limits of mapping whole-cell mRNA numbers to the underlying stochastic gene activity and highlight the contribution of previously hidden variables to the observed population heterogeneity.