Genetic designs for stochastic and probabilistic biocomputing.

The programming of computations in living cells is achieved by manipulating information flows within genetic networks. Typically, gene expression is discretized into high and low levels, representing 0 and 1 logic values to encode a single bit of information. However, molecular signaling and computation in living systems operate dynamically, stochastically, and continuously, challenging this binary paradigm. While stochastic and probabilistic models of computation address these complexities, there is a lack of work unifying these concepts to implement computations tailored to these features of living matter. Here we design genetic networks for stochastic and probabilistic computing, developing the underlying theory. Moving beyond the digital framework, we propose random pulses and probabilistic-bits (p-bits) as better candidates for encoding and processing information genetic networks. Encoding information through the frequency of expression burst frequency offers robustness to noise, while p-bits enable unique circuit designs with features like invertibility. We illustrate these advantages by designing circuits and providing mathematical models and simulations to demonstrate their functionality. Our approach to stochastic and probabilistic computing not only advances our understanding of information processing in biological systems but also opens new possibilities for designing genetic circuits with enhanced capabilities.