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Probabilistic reasoning with a Bayesian DNA device based on strand displacement


We present a computing model based on the DNA strand displacement technique, which performs Bayesian inference. The model will take single-stranded DNA as input data, that represents the presence or absence of a specific molecular signal (evidence). The program logic encodes the prior probability of a disease and the conditional probability of a signal given the disease affecting a set of different DNA complexes and their ratios. When the input and program molecules interact, they release a different pair of single-stranded DNA species whose ratio represents the application of Bayes’ law: the conditional probability of the disease given the signal. The models presented in this paper can have the potential to enable the application of probabilistic reasoning in genetic diagnosis in vitro.

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  1. 1.

    Note the copy numbers assigned below and in Fig. 5 are only intended to illustrate the inference flow. For the model to converge to realistic Bayesian probability estimations, it needs higher copy numbers as in the Sect. 5.

  2. 2.

    Equation notations: “\(\cdot\)” molecule bonds; “*” complementary domains; “\(\mathop{\longrightarrow}\limits^{k}\)” irreversible reaction with rate k; “\(\mathop{\rightleftharpoons}\limits_{k_{-1}}^{k_1}\)” reversible reaction with forward rate k 1 and reverse rate k −1.


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This research was partially supported by the BACTOCOM Project funded by a European Commission 7th Framework Programme Grant (FET Proactive area) and by the Spanish Ministry of Finance Project TIN2012-36992.

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Correspondence to Iñaki Sainz de Murieta.

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Sainz de Murieta, I., Rodríguez-Patón, A. Probabilistic reasoning with a Bayesian DNA device based on strand displacement. Nat Comput 13, 549–557 (2014).

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  • Bayesian inference
  • DNA computing
  • Genetic diagnosis