Gene regulatory networks as Boolean networks

Herrera-Delgado and colleagues (2018) describe a GRN as modular DNA sequences that bind activators and repressors, some of which control genes that are themselves regulators². They say this recursive set of links forms a transcriptional network, and its dynamics produce the spatial and temporal patterns of gene expression². Grodstein, McMillen and Levin (2023) describe the same thing from the cell's side. Promoters sense messenger signals, switch genes on or off, and so create new messengers⁸. Kouvaris and colleagues (2017) cite Leclerc's argument that sparser GRNs are more robust, and report that sparsity also favoured evolvability¹.

Newman (2019) notes speculations based on the multistability of GRNs, citing Kauffman (1969) and Furusawa and Kaneko (2002)³. He argues that the full range of cell types in a genome does not appear to be the global state-space attractors of any unitary physical system³. He does not reject attractor dynamics as an account of steps along developmental lineages, and cites Huang and colleagues (2007)³. Acharya and colleagues (2026) adopt the attractor view. They say GRN dynamics channel cells toward a limited set of stable configurations⁹. They read cancer as a deformation of this landscape⁹.

Hoel and Levin (2020) take the Boolean network and expand it to its full state space⁴. The result is a network of possible state transitions. Transition probabilities from a state match those of a random walker, so uncertainty at a node equals the noise in the probability of change in gene expression⁴. For their example GRN they report 2.78 bits of EI at the micro-scale⁵. They then search for macro-nodes with clustering or partitioning algorithms, and say the choice of algorithm may vary with the architecture of the system⁴.

Biswas, Clawson and Levin (2022) say dynamical approaches have explained how these systems settle on stable states, but designing interventions has lagged⁶. Levin (2022) argues that GRNs may sit at a different place on the continuum of agency than is usually assumed. He proposes training them with combinations of stimuli⁷. He cites recent analyses of GRN models that show associative learning, pattern completion and generalization⁷.