Stable Leader Election in Population Protocols Requires Linear Time

Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka-Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior.

Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or fabrication methods based on self-organization. To achieve this, molecular control circuits need to be engineered to perform integrated sensing, computation and actuation. Here we report a DNA-based technology for implementing the computational core of such controllers. We use the formalism of chemical reaction networks as a 'programming language' and our DNA architecture can, in principle, implement any behaviour that can be mathematically expressed as such. Unlike logic circuits, our formulation naturally allows complex signal processing of intrinsically analogue biological and chemical inputs. Controller components can be derived from biologically synthesized (plasmid) DNA, which reduces errors associated with chemically synthesized DNA. We implement several building-block reaction types and then combine them into a network that realizes, at the molecular level, an algorithm used in distributed control systems for achieving consensus between multiple agents.