DNA walker circuits: computational potential, design, and verification

Dannenberg, Frits; Kwiatkowska, Marta; Thachuk, Chris; Turberfield, Andrew J.

doi:10.1007/s11047-014-9426-9

Cited by 37 publications

(39 citation statements)

References 25 publications

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“…[48] experimentally demonstrated that a walker can be directed to any leaf in a complete two-level binary tree by selectively unblocking the anchorages. In [16,15], we have studied the expressive power of DNA walker circuits implemented by this technology and showed that the circuits can compute any Boolean function through reduction to 3-CNF. Compared to DNA strand displacement systems in solution, an advantage of this technology is its spatial locality, but we have found that the undirected nature of the tracks imposes limitations on the use of parallelism.…”

Section: Background On Molecular Walkersmentioning

confidence: 99%

“…The behaviour of molecular walkers is inherently probabilistic and we have studied their performance and reliability in [15,14,16]. In [38], we have developed techniques to automatically synthesise rates so that a given quantitative requirement is guaranteed to be satisfied.…”

Section: Introductionmentioning

confidence: 99%

“…We demonstrate how DNA walker circuits can be modelled using stochastic Petri nets, matching the layout of the original circuit designs, and analyse the reliability and performance characteristics of the designs. In view of state-space explosion observed in the original study [15,16], we focus on evaluating the potential of statistical model checking using the tool Cosmos. We develop a family of models, some designed by biochemist and some artificial schemes aimed to exhibit design challenges, and a range of quantitative requirements.…”

Section: Introductionmentioning

confidence: 99%

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On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets

Barbot¹,

Kwiatkowska²

2015

Application and Theory of Petri Nets and Concurrency

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Abstract. Molecular programming is an emerging field concerned with building synthetic biomolecular computing devices at the nanoscale, for example from DNA or RNA molecules. Many promising applications have been proposed, ranging from diagnostic biosensors and nanorobots to synthetic biology, but prohibitive complexity and imprecision of experimental observations makes reliability of molecular programs difficult to achieve. This paper advocates the development of design automation methodologies for molecular programming, highlighting the role of quantitative verification in this context. We focus on DNA 'walker' circuits, in which molecules can be programmed to traverse tracks placed on a DNA origami tile, taking appropriate decisions at junctions and reporting the outcome when reaching the end of the track. The behaviour of molecular walkers is inherently probabilistic and thus probabilistic model checking methods are needed for their analysis. We demonstrate how DNA walkers can be modelled using stochastic Petri nets, and apply statistical model checking using the tool Cosmos to analyse the reliability and performance characteristics of the designs. The results are compared and contrasted with those obtained for the PRISM model checker. The paper ends by summarising future research challenges in the field.

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Section: Background On Molecular Walkersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets

Barbot¹,

Kwiatkowska²

2015

Application and Theory of Petri Nets and Concurrency

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“…PRISM has been used previously to model a variety of biological case studies, including DNA circuits and DNA nanorobotic walkers [11,27]. PRISM also is used widely to model probabilistic protocols, e.g., in distributed sensor networks, and stochastic multi-player games [26].…”

Section: Related Workmentioning

confidence: 99%

Automated requirements analysis for a molecular watchdog timer

Ellis

Henderson

Klinge

et al. 2014

Proceedings of the 29th ACM/IEEE International Conference on Automated Software Engineering

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Dynamic systems in DNA nanotechnology are often programmed using a chemical reaction network (CRN) model as an intermediate level of abstraction. In this paper, we design and analyze a CRN model of a watchdog timer, a device commonly used to monitor the health of a safety critical system. Our process uses incremental design practices with goal-oriented requirements engineering, software verification tools, and custom software to help automate the software engineering process. The watchdog timer is comprised of three components: an absence detector, a threshold filter, and a signal amplifier. These components are separately designed and verified, and only then composed to create the molecular watchdog timer. During the requirements-design iterations, simulation, model checking, and analysis are used to verify the system. Using this methodology several incomplete requirements and design flaws were found, and the final verified model helped determine specific parameters for biological experiments.

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“…Depending on prior input, certain anchorages can be blocked, which in turn directs the walker at each junction. A Markov chain model of the walker was developed [5] previously, and in this paper we apply model checking with FAU, using the parameter set ε = 10 −6 and δ = 10 −8 . We analyse three XOR-circuits, from Fig.…”

Section: Dna Strand Displacementmentioning

confidence: 99%

Computing Cumulative Rewards Using Fast Adaptive Uniformisation

Dannenberg¹,

Hahn²,

Kwiatkowska³

2013

Computational Methods in Systems Biology

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Abstract. The computation of transient probabilities for continuous-time Markov chains often employs uniformisation, also known as the Jensen's method. The fast adaptive uniformisation method introduced by Mateescu approximates the probability by neglecting insignificant states, and has proven to be effective for quantitative analysis of stochastic models arising in chemical and biological applications. However, this method has only been formulated for the analysis of properties at a given point of time t. In this paper, we extend fast adaptive uniformisation to handle expected reward properties which reason about the model behaviour until time t, for example, the expected number of chemical reactions that have occurred until t. To show the feasibility of the approach, we integrate the method into the probabilistic model checker PRISM and apply it to a range of biological models, demonstrating superior performance compared to existing techniques.

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DNA walker circuits: computational potential, design, and verification

Cited by 37 publications

References 25 publications

On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets

On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets

Automated requirements analysis for a molecular watchdog timer

Computing Cumulative Rewards Using Fast Adaptive Uniformisation

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