Genetic designs for stochastic and probabilistic biocomputing

Abstract

The programming of computations in living cells can be done by manipulating information flows within genetic networks. Typically, a single bit of information is encoded by a single genes steady state expression. Expression is discretized into high and low levels that correspond to 0 and 1 logic values, analogous to the high and low voltages in electronic logic circuits. However, the processes of molecular signaling and computation in living systems challenge this computational paradigm with their dynamic, stochastic and continuous operation. Although there is a good understanding of these phenomena in genetic networks, and there are already stochastic and probabilistic models of computation which can take on these challenges, there is currently a lack of work which puts both together to implement computations tailored to these features of living matter. Here, we design genetic networks for stochastic and probabilistic computing paradigms and develop the theory behind their operation. Moving beyond the digital abstraction, we explore the concepts of bit-streams (sequences of pulses acting as time-based signals) and probabilistic-bits or p-bits (values that can be either 1 or 0 with an assigned probability), as more suitable candidates for the encoding and processing of information in genetic networks. Specifically, the conceptualization of signals as stochastic bit-streams allows for encoding information in the frequency of random expression pulses, offering advantages such as robustness to noise. Additionally, the notion of p-bit enables the design of genetic circuits with capabilities surpassing those of current genetic logic gates, including invertibility. We design several circuits to illustrate these advantages and provide mathematical models and computational simulations that demonstrate their functionality. Our approach to stochastic and probabilistic computing in living cells not only enhances and reflects understanding of information processing in biological systems but also presents promising avenues for designing genetic circuits with advanced functionalities.