Abstract
Finite-state automata (FSA) are simple computational devices that can nevertheless illustrate interesting behaviours. We propose that FSA can be employed as control circuits for engineered stochastic biological and biomolecular systems. We present an implementation of FSA using counts of chemical species in the range of hundreds to thousands, which is relevant for the counts of many key molecules such as mRNAs in prokaryotic cells. The challenge here is to ensure a robust representation of the current state in the face of stochastic noise. We achieve this by using a multistable approximate majority algorithm to stabilize and store the current state of the system. Arbitrary finite state machines can thus be compiled into robust stochastic chemical automata. We present two variants: one that consumes its input signals to initiate state transitions and one that does not. We characterize the state change dynamics of these systems and demonstrate their application to solve the four-bit binary square root problem. Our work lays the foundation for the use of chemical automata as control circuits in bioengineered systems and biorobotics.
Highlights
A key goal in the field of molecular programming is to program bioinspired behaviours in engineered biomolecular systems
Chemical reaction networks can be viewed as distributed computing systems, as each individual molecule acts independently according to the reactions in which it can participate
Biomolecular devices live in the nanoscale realm of stochastic interactions, and as such they require careful engineering to ensure predictable behaviour that is robust to stochastic fluctuations. We have tackled this challenge in the context of deterministic Finite-state automata (FSA) to define a class of stochastic chemical reaction networks (CRNs) implementations that can robustly store state information and transition between states in the face of stochastic noise
Summary
A key goal in the field of molecular programming is to program bioinspired behaviours in engineered biomolecular systems. FSA are abstract computational systems that move between states drawn from a finite set, with transitions chosen based on the current state and an observed input signal We conjecture that these are sufficient to implement interesting behaviours in molecular systems, even though they are strictly weaker computationally than Turing machines. Our designs use a multistable extension of the well-known approximate majority switch [10], which has previously been implemented in DNA [11], to store the current state in a robust manner In conjunction with this memory mechanism, we use a simple ‘flipping’ scheme and a finite control program to trigger state transitions as a function of the current state and the observed sequence of inputs provided to the system, thereby mimicking the behaviour of a particular theoretical finite state automaton. Our CRN implementation of deterministic finite automata could be a powerful tool for molecular programmers to build complex sensing and decision-making programs
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