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Computing cumulative rewards using fast adaptive uniformisation
- In CMSB, volume 8130 of LNCS
, 2013
"... 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 proba-bility by neglecting insignificant states, and has proven to be ..."
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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 proba-bility by neglecting insignificant states, and has proven to be effective for quanti-tative 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. 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
Probabilistic Model Checking for Biology
"... Probabilistic model checking is an automated method for verifying the correctness and performance of probabilistic models. Property specifications are expressed in probabilistic temporal logic, denoting, for example, the probability of a given event, the probability of its occurrence within a given ..."
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Probabilistic model checking is an automated method for verifying the correctness and performance of probabilistic models. Property specifications are expressed in probabilistic temporal logic, denoting, for example, the probability of a given event, the probability of its occurrence within a given time interval, or expected number of times it has occurred in a time period. This chapter fo-cuses on the application of probabilistic model checking to biological systems modelled as continuous-time Markov chains, illustrating the usefulness of these techniques through relevant case studies performed with the probabilistic model checker PRISM. We begin with an introduction to discrete-time Markov chains and the corresponding model checking algorithms. Then continuous-time Markov chain models are defined, together with the logic CSL (Continuous Stochastic Logic), and an overview of model checking for CSL is given, which proceeds mainly by reduc-tion to discrete-time Markov chains. The techniques are illustrated with examples of biochemical reaction networks, which are verified against quantitative tempo-ral properties. Next a biological case study analysing the Fibroblast Growth Factor (FGF) molecular signalling pathway is summarised, highlighting how probabilistic model checking can assist in scientific discovery. Finally, we consider DNA compu-tation, and specifically the DSD formalism (DNA Strand Displacement), and show how errors can be detected in DNA gate designs, analogous to model checking for digital circuits.
Abstract modelling of tethered DNA circuits
"... Abstract. Sequence-specific DNA interactions are a powerful means of pro-gramming 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 ..."
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Abstract. Sequence-specific DNA interactions are a powerful means of pro-gramming 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 mech-anized 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. 1
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
The Formal Language and Design Principles of Autonomous DNA Walker Circuits
"... Simple computation can be performed using the interactions between single-stranded molecules of DNA. These interactions are typically toehold-mediated strand displacement reactions in a well-mixed solution. We demonstrate that a DNA circuit with tethered reactants is a distributed system and show ho ..."
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Simple computation can be performed using the interactions between single-stranded molecules of DNA. These interactions are typically toehold-mediated strand displacement reactions in a well-mixed solution. We demonstrate that a DNA circuit with tethered reactants is a distributed system and show how it can be described as a stochastic Petri net. The system can be verified by mapping the Petri net onto a continuous-time Markov chain, which can also be used to find an optimal design for the circuit. This theoretical machinery can be applied to create software that automatically designs a DNA circuit, linking an abstract propositional formula to a physical DNA computation system that is capable of evaluating it. We conclude by introducing example mechanisms that can implement such circuits experimentally and discuss their individual strengths and weaknesses.
Automated Design and Verification of Localized DNA Computation Circuits
"... Simple computations can be performed using the interactions between single-stranded molecules of DNA. These interactions are typically toehold-mediated strand displacement reactions in a well-mixed solution. We demonstrate that a DNA circuit with tethered reactants is a distributed system and show ..."
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Simple computations can be performed using the interactions between single-stranded molecules of DNA. These interactions are typically toehold-mediated strand displacement reactions in a well-mixed solution. We demonstrate that a DNA circuit with tethered reactants is a distributed system and show how it can be described as a stochastic Petri net. The system can be verified by mapping the Petri net onto a continuous time Markov chain, which can also be used to find an optimal design for the circuit. This theoretical machinery can be applied to create software that automatically designs a DNA circuit, linking an abstract propositional formula to a physical DNA computation system that is capable of evaluating it.
Automated Requirements Analysis for a Molecular Watchdog Timer
"... Dynamic systems in DNA nanotechnology are often pro-grammed 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 de-vice commonly used to monitor the health of a safety critical system. Our proc ..."
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Dynamic systems in DNA nanotechnology are often pro-grammed 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 de-vice 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 de-signed 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 incom-plete requirements and design flaws were found, and the fi-nal verified model helped determine specific parameters for biological experiments. Keywords probabilistic model checking; requirements engineering; molec-ular programming; chemical reaction networks 1.
Robust Biomolecular Finite Automata∗
"... In this paper we present a uniform method for translating an arbitrary nondeterministic finite automaton (NFA) into a deterministic mass action bio-chemical reaction network (BRN) that simulates it. The BRN receives its input as a continuous time signal consisting of concentrations of chemical speci ..."
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In this paper we present a uniform method for translating an arbitrary nondeterministic finite automaton (NFA) into a deterministic mass action bio-chemical reaction network (BRN) that simulates it. The BRN receives its input as a continuous time signal consisting of concentrations of chemical species that vary to represent the NFA’s input string in a natural way. The BRN exploits the inherent parallelism of chemical kinetics to simulate the NFA in real time with a number of chemical species that is linear in the number of states of the NFA. We prove that the simulation is correct and that it is robust with respect to perturbations of the input signal, the initial concentrations of species, the output (decision), and the rate constants of the reactions of the BRN. 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
