Abstract Reaction systems are rooted in processes inspired by the functioning of the living cell. The key idea behind the resulting formal model is that such processes are determined by the interactions of biochemical reactions. Moreover, such interactions are based on the fundamental mechanisms of facilitation and inhibition. Since their inception, reaction systems have developed into an extensively investigated model of computation with unique characteristics and a wide range of potential applications. The semantical model of reaction systems is based on the concept of system states consisting of sets of entities, and state transformations enacted by sets of reactions. Another important behavioural property is the non-permanency of the entities, and so data persistence has to be consciously implemented. Issues like this need to be taken into account in all simulations of reaction systems by means of other existing models and tools, such as Petri nets. In this paper, we provide four different Petri net encodings of basic reaction systems operating without interacting with external environment. We start from a naive encoding that is based on the behaviour of a reaction system $$\mathscr {R}$$ only, transforming the transition system of $$\mathscr {R}$$ into a Petri net in the form of a marked graph. Such a solution introduces exponentially many places and transitions. In the subsequent encodings, we cope with this exponentiality ending up with a solution that is polynomial in the size of the original reaction system. We then show how this polynomial encoding can be adapted to provide a polynomial encoding for reaction systems operating with contexts provided by context automata. The encoding method proposed in this paper is modular and can provide a basis for compositional construction of reaction systems.

Abstract The abstract Tile Assembly Model (aTAM) provides an excellent foundation for the mathematical study of DNA-tile-based self-assembling systems, especially those wherein logic is embedded within the designs of the tiles so that they follow prescribed algorithms. While such algorithmic self-assembling systems are theoretically powerful, being computationally universal and capable of building complex shapes using information-theoretically optimal numbers of tiles, physical DNA-based implementations of these systems still encounter formidable error rates and undesired nucleation that hinder this theoretical potential. Slat-based self-assembly is a recent development wherein DNA forms long slats that combine together in 2 layers, rather than square tiles in a plane. In this approach, the length of the slats is key; while tiles typically only bind to 2 neighboring tiles at a time, slats may bind to dozens of other slats. This increased coordination between slats means that several mismatched slats must coincidentally meet in just the right way for errors to persist, unlike tiles where only a few are required. Consequently, while still a novel technology, large slat-based DNA constructions have been successfully implemented in the lab with resilience to many tile-based construction problems. These improved error characteristics come at a cost however, as slat-based systems are often more difficult to design and simulate than tile-based ones. Moreover, it has not been clear whether slats, with their larger sizes and different geometries, have the same theoretical capabilities as tiles. In this paper, we show that slats are capable of doing anything that tiles can, at least at scale. We demonstrate that any aTAM system may be converted to and simulated by an effectively equivalent system of slats. Furthermore, we show that these simulating slat systems can be made more efficiently, using shorter slats and a smaller scale factor, if the simulated tile system avoids certain uncommon growth patterns. Specifically, we consider 5 classes of aTAM systems with increasing complexity, from zig-zag systems which grow in a rigid pattern to the full class of all aTAM systems, and show how they may be converted to equivalent slat systems. We show that the simplest class may be simulated by slats at only a $$2c \times 2c$$ scale, where c is the freely chosen coordination number of the slats, and further show that the full class of aTAM systems can be simulated at only a $$5c \times 5c$$ scale. These results prove that slats have the full theoretical power of aTAM tiles while also providing constructions that are compact enough for potential DNA-based implementations of slat systems that are both capable of powerful algorithmic self-assembly and possessing of the strong error resilience of slats. This paper is an extended version of a version that appeared in the proceedings of the 30th International Conference on DNA Computing and Molecular Programming (DNA 30).

Abstract The q –gram distance between two strings $$s,s^\prime$$ , introduced by Ukkonen in 1992, is an alignment-free string similarity measure which can be computed in linear time, as opposed to the quadratic time necessary for alignment/edit distance. It is based on the $$L_1$$ -distance, or Manhattan-distance, between the multiplicity vectors of fixed-length substrings (so-called q-grams or k-mers ), and has been successfully applied in diverse bioinformatics settings. In this paper, we introduce the threshold q-gram distance (T q D), a new distance measure which is similar to the q -gram distance but uses reduced information on the multiplicities of the q -grams. The new measure retains the linear time computation of the q -gram distance but requires significantly less space. Storage space and accuracy of the measure can be controlled via a user-defined threshold t , which sets a limit on the maximum value of the integers in the multiplicity vectors. In particular, for $$t=1$$ , the comparison is made only on the basis of the sets of uniquely occurring q -grams on the one hand, and of repeated q -grams, on the other. We tested the new distance measure, using the benchmarking tool AFproject of Zielezinski et al. [Genome Biology, 2019], on several real-life data sets for phylogenetic reconstruction and compared the results with those of other k -mer based distance measures. Our experiments show that the new measure T q D compares well to other non-alignment based measures regarding accuracy, while requiring substantially less memory than the classic q -gram distance.