Two-Domain DNA Strand Displacement

We investigate the computing power of a restricted class of DNA strand displacement structures: those that are made of double strands with nicks (interruptions) in the top strand. To preserve this structural invariant, we impose restrictions on the single strands they interact with: we consider only two-domain single strands consisting of one toehold domain and one recognition domain. We study fork and join signal-processing gates based on these structures, and we show that these systems are amenable to formalization and to mechanical verification

DNA as a universal substrate for chemical kinetics

Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka–Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior

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, representing 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 playing with 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 relative proportion represents the application of Bayes? Law: the conditional probability of the disease given the signal. The models presented in this paper can empower the application of probabilistic reasoning in genetic diagnosis in vitro

Leaderless deterministic chemical reaction networks

This paper answers an open question of Chen, Doty, and Soloveichik [1], who showed that a function f:N^k --> N^l is deterministically computable by a stochastic chemical reaction network (CRN) if and only if the graph of f is a semilinear subset of N^{k+l}. That construction crucially used "leaders": the ability to start in an initial configuration with constant but non-zero counts of species other than the k species X_1,...,X_k representing the input to the function f. The authors asked whether deterministic CRNs without a leader retain the same power. We answer this question affirmatively, showing that every semilinear function is deterministically computable by a CRN whose initial configuration contains only the input species X_1,...,X_k, and zero counts of every other species. We show that this CRN completes in expected time O(n), where n is the total number of input molecules. This time bound is slower than the O(log^5 n) achieved in [1], but faster than the O(n log n) achieved by the direct construction of [1] (Theorem 4.1 in the latest online version of [1]), since the fast construction of that paper (Theorem 4.4) relied heavily on the use of a fast, error-prone CRN that computes arbitrary computable functions, and which crucially uses a leader.Comment: arXiv admin note: substantial text overlap with arXiv:1204.417