Matthew R. Lakin

Design and analysis of DNA strand displacement devices using probabilistic model checking

Designing correct, robust DNA devices is difficult because of the many possibilities for unwanted interference between molecules in the system. DNA strand displacement has been proposed as a design paradigm for DNA devices, and the DNA strand displacement (DSD) programming language has been developed as a means of formally programming and analysing these devices to check for unwanted interference. We demonstrate, for the first time, the use of probabilistic verification techniques to analyse the correctness, reliability and performance of DNA devices during the design phase. We use the probabilistic model checker prism, in combination with the DSD language, to design and debug DNA strand displacement components and to investigate their kinetics. We show how our techniques can be used to identify design flaws and to evaluate the merits of contrasting design decisions, even on devices comprising relatively few inputs. We then demonstrate the use of these components to construct a DNA strand displacement device for approximate majority voting. Finally, we discuss some of the challenges and possible directions for applying these methods to more complex designs.

Abstractions for DNA circuit design

DNA strand displacement techniques have been used to implement a broad range of information processing devices, from logic gates, to chemical reaction networks, to architectures for universal computation. Strand displacement techniques enable computational devices to be implemented in DNA without the need for additional components, allowing computation to be programmed solely in terms of nucleotide sequences. A major challenge in the design of strand displacement devices has been to enable rapid analysis of high-level designs while also supporting detailed simulations that include known forms of interference. Another challenge has been to design devices capable of sustaining precise reaction kinetics over long periods, without relying on complex experimental equipment to continually replenish depleted species over time. In this paper, we present a programming language for designing DNA strand displacement devices, which supports progressively increasing levels of molecular detail. The language allows device designs to be programmed using a common syntax and then analysed at varying levels of detail, with or without interference, without needing to modify the program. This allows a trade-off to be made between the level of molecular detail and the computational cost of analysis. We use the language to design a buffered architecture for DNA devices, capable of maintaining precise reaction kinetics for a potentially unbounded period. We test the effectiveness of buffered gates to support long-running computation by designing a DNA strand displacement system capable of sustained oscillations.

Signal Propagation in Multi-Layer DNAzyme Cascades Using Structured Chimeric Substrates**

Signal propagation through enzyme cascades is a critical component of information processing in cellular systems. Although such systems have potential as biomolecular computing tools, rational design of synthetic protein networks remains infeasible. DNA strands with catalytic activity (DNAzymes) are an attractive alternative, enabling rational cascade design through predictable base-pair hybridization principles. Multi-layered DNAzyme signaling and logic cascades are now reported. Signaling between DNAzymes was achieved using a structured chimeric substrate (SCS) that releases a downstream activator after cleavage by an upstream DNAzyme. The SCS can be activated by various upstream DNAzymes, can be coupled to DNA strand-displacement devices, and is highly resistant to interference from background DNA. This work enables the rational design of synthetic DNAzyme regulatory networks, with potential applications in biomolecular computing, biodetection, and autonomous theranostics.

Catalytic molecular logic devices by DNAzyme displacement.

Chemical reactions catalyzed by DNAzymes offer a route to programmable modification of biomolecules for therapeutic purposes. To this end, we have developed a new type of catalytic DNA‐based logic gates in which DNAzyme catalysis is controlled via toehold‐mediated strand displacement reactions. We refer to these as DNAzyme displacement gates. The use of toeholds to guide input binding provides a favorable pathway for input recognition, and the innate catalytic activity of DNAzymes allows amplification of nanomolar input concentrations. We demonstrate detection of arbitrary input sequences by rational introduction of mismatched bases into inhibitor strands. Furthermore, we illustrate the applicability of DNAzyme displacement to compute logic functions involving multiple logic gates. This work will enable sophisticated logical control of a range of biochemical modifications, with applications in pathogen detection and autonomous theranostics.

Modelling, simulating and verifying turing-powerful strand displacement systems

We demonstrate how the DSD programming language can be used to design a DNA stack machine and to analyse its behaviour. Stack machines are of interest because they can efficiently simulate a Turing machine. We extend the semantics of the DSD language to support operations on DNA polymers and use our stack machine design to implement a non-trivial example: a ripple carry adder which can sum two binary numbers of arbitrary size. We use model checking to verify that the ripple carry adder executes correctly on a range of inputs. This provides the first opportunity to assess the correctness and kinetic properties of DNA strand displacement systems performing Turing-powerful symbolic computation.

A generic abstract machine for stochastic process calculi

This paper presents a generic abstract machine for simulating a broad range of process calculi with an arbitrary reaction-based simulation algorithm. The abstract machine is instantiated to a particular calculus by defining two functions: one for transforming a process of the calculus to a set of species, and another for computing the set of possible reactions between species. Unlike existing simulation algorithms for chemical reactions, the abstract machine can simulate process calculi that generate potentially unbounded numbers of species and reactions. This is achieved by means of a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. As a proof of concept, the generic abstract machine is instantiated for the stochastic pi-calculus, and the instantiation is implemented as part of the SPiM stochastic simulator. The structure of the abstract machine facilitates a significant optimisation by allowing channel restrictions to be stored as species complexes. We also present a novel algorithm for simulating chemical reactions with general distributions, based on the Next Reaction Method of Gibson and Bruck. We use our generic framework to simulate a stochastic pi-calculus model of plasmid co-transfection, where plasmids can form aggregates of arbitrary size and where rates of mRNA degradation are non-exponential. The example illustrates the flexibility of our framework, which allows an appropriate high-level language to be paired with the required simulation algorithm, based on the biological system under consideration.

Abstract Modelling of Tethered DNA Circuits

Sequence-specific DNA interactions are a powerful means of programming nanoscale locomotion. These systems typically use a DNA track that is tethered to a surface, and molecular interactions enable a signal or cargo to traverse this track. Such low copy number systems are highly amenable to mechanized analyses such as probabilistic model checking, which requires a formal encoding. In this paper we present the first general encoding of tethered DNA species into a formal language, which allows the interactions between tethered species to be derived automatically using standard reaction rules. We apply this encoding to a previously published tethered DNA circuit architecture based on hairpin assembly reactions. This work enables automated analysis of large-scale tethered DNA circuits and, potentially, synthesis of optimized track layouts to implement specific logic functions.

Supervised Learning in Adaptive DNA Strand Displacement Networks.

The development of engineered biochemical circuits that exhibit adaptive behavior is a key goal of synthetic biology and molecular computing. Such circuits could be used for long-term monitoring and control of biochemical systems, for instance, to prevent disease or to enable the development of artificial life. In this article, we present a framework for developing adaptive molecular circuits using buffered DNA strand displacement networks, which extend existing DNA strand displacement circuit architectures to enable straightforward storage and modification of behavioral parameters. As a proof of concept, we use this framework to design and simulate a DNA circuit for supervised learning of a class of linear functions by stochastic gradient descent. This work highlights the potential of buffered DNA strand displacement as a powerful circuit architecture for implementing adaptive molecular systems.

Online learning in a chemical perceptron

Autonomous learning implemented purely by means of a synthetic chemical system has not been previously realized. Learning promotes reusability and minimizes the system design to simple input-output specification. In this article we introduce a chemical perceptron, the first full-featured implementation of a perceptron in an artificial (simulated) chemistry. A perceptron is the simplest system capable of learning, inspired by the functioning of a biological neuron. Our artificial chemistry is deterministic and discrete-time, and follows Michaelis-Menten kinetics. We present two models, the weight-loop perceptron and the weight-race perceptron, which represent two possible strategies for a chemical implementation of linear integration and threshold. Both chemical perceptrons can successfully identify all 14 linearly separable two-input logic functions and maintain high robustness against rate-constant perturbations. We suggest that DNA strand displacement could, in principle, provide an implementation substrate for our model, allowing the chemical perceptron to perform reusable, programmable, and adaptable wet biochemical computing.

Modular Verification of DNA Strand Displacement Networks via Serializability Analysis

DNA strand displacement gates can be used to emulate arbitrary chemical reactions, and a number of different schemes have been proposed to achieve this. Here we develop modular correctness proofs for strand displacement encodings of chemical reaction networks and show how they may be applied to two-domain strand displacement systems. Our notion of correctness is serializability of interleaved reaction encodings, and we infer this global property from the properties of the gates that encode the individual chemical reactions. This allows correctness to be inferred for arbitrary systems constructed using these components, and we illustrate this by applying our results to a two-domain implementation of a well-known approximate majority voting system.