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DNA walker circuits: computational potential, design, and verification
"... Abstract. Unlike their traditional, silicon counterparts, DNA computers have natural interfaces with both chemical and biological systems. These can be used for a number of applications, including the precise arrangement of matter at the nanoscale and the creation of smart biosensors. Like silicon c ..."
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Abstract. Unlike their traditional, silicon counterparts, DNA computers have natural interfaces with both chemical and biological systems. These can be used for a number of applications, including the precise arrangement of matter at the nanoscale and the creation of smart biosensors. Like silicon circuits, DNA strand displacement systems (DSD) can evaluate non-trivial functions. However, these systems can be slow and are susceptible to errors. It has been suggested that localised hybridization reactions could overcome some of these challenges. Localised reactions occur in DNA ‘walker ’ systems which were recently shown to be capable of navigating a programmable track tethered to an origami tile. We investigate the computational potential of these systems for evaluating Boolean functions. DNA walkers, like DSDs, are also susceptible to errors. We develop a discrete stochastic model of DNA walker ‘circuits ’ based on experimental data, and demonstrate the merit of using probabilistic model checking techniques to analyse their reliability, performance and correctness. 1
Precise Parameter Synthesis for Stochastic Biochemical Systems
"... Abstract. We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given CSL time-bounded prop-erty is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised/minimised. We de-velop algorithm ..."
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Abstract. We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given CSL time-bounded prop-erty is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised/minimised. We de-velop algorithms based on the computation of lower and upper bounds of the probability, in conjunction with refinement and sampling, which yield answers that are precise to within an arbitrarily small tolerance value. Our methods are efficient and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for two biologically mo-tivated case studies, including the reliability analysis of a DNA walker. 1
Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation
"... Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equa-tion (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both appr ..."
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Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equa-tion (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is com-plex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approx-imate model checking algorithm based on the Linear Noise Approxima-tion (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order poly-nomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deter-ministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.
Challenges in automated verification and synthesis for molecular programming
"... Molecular programming is concerned with building synthetic nanoscale devices from molecules, which can be programmed to autonomously per-form a specific task. Several artifacts have been demonstrated experi-mentally, including DNA circuits that can compute a logic formula and molecular robots that c ..."
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Molecular programming is concerned with building synthetic nanoscale devices from molecules, which can be programmed to autonomously per-form a specific task. Several artifacts have been demonstrated experi-mentally, including DNA circuits that can compute a logic formula and molecular robots that can transport cargo. In view of their natural inter-face to biological components, many potential applications are envisaged, e.g. point-of-care diagnostics and targeted delivery of drugs. However, the inherent complexity of the resulting biochemical systems makes the manual process of designing such devices error-prone, requiring automated design support methodologies, analogous to design automation tools for digital systems. This paper gives an overview of the role that probabilis-tic modelling and verification techniques can play in designing, analysing, debugging and synthesising programmable molecular devices, and outlines the challenges in achieving automated verification and synthesis software technologies in this setting. 1
On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets
"... 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 p ..."
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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 ex-perimental 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 quan-titative 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 check-ing methods are needed for their analysis. We demonstrate how DNA walkers can be modelled using stochastic Petri nets, and apply statisti-cal 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. 1
