Computational modelling of the kinetic Tile Assembly Model using a rule-based approach

The Tile Assembly Model (TAM), is a mathematical paradigm for the study and algorithmic design of DNA self-assembly systems. It employs the use of so-called DNA-tiles, which are abstractions of experimentally achievable complexes with similar inter-matching behaviour. To this day, there are more than 5 different experimental implementations of DNA tiles and their sub-sequent algorithmic assembly into larger complexes. In order to provide further insight into the assembly process, the abstract model has been extended to a kinetic counterpart (kTAM). Although there is a wide abundance of different variants of the abstract model, e.g., stage, step, hierarchical, temperature-k, signal-passing, etc., numerical simulations of the kinetic counterpart have been performed only for a few types of systems. This might be due to the fact that the numerical models and simulations of kTAM were almost exclusively implemented using classical stochastic simulation algorithms frameworks. In this paper we introduce an agentand rule-based modeling approach for the kTAM. We show not only how the modelling of kTAM can be implemented, but we also explore the advantages of this modelling framework for kinetic simulations of kTAM and the easy way such models can be updated and modified. We present numerical comparisons both with classical numerical simulations of kTAM, as well as comparison in between four different kinetic variant of the TAM model, all implemented within stand-alone rule-based models.