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Abstract Molecular circuits implemented using molecular components tethered to a DNA tile nanostructure have certain advantages over solution-phase circuits. Tethering components in close proximity increases the speed of reactions by reducing diffusion and improves scalability by enabling reuse of identical DNA sequences at different locations in the circuit. These systems show great potential for practical applications including delivery of diagnostic and therapeutic molecular circuits to cells. When modeling such systems, molecular geometry plays an important role in determining whether the two species interact and at what rate. In this paper, we present an automated method for estimating reaction rates in tethered molecular circuits that takes the geometry of the tethered species into account. We probabilistically generate samples of structure distributions based on simple biophysical models and use these to estimate important parameters for kinetic models. This work provides a basis for subsequent enhanced modeling and design tools for localized molecular circuits. 

Localized molecular devices are a powerful tool for engineering complex information-processing circuits and molecular robots. Their practical advantages include speed and scalability of interactions between components tethered near to each other on an underlying nanostructure, and the ability to restrict interactions between more distant components. The latter is a critical feature that must be factored into computational tools for the design and simulation of localized molecular devices: unlike in solution-phase systems, the geometries of molecular interactions must be accounted for when attempting to determine the network of possible reactions in a tethered molecular system. This work aims to address that challenge by integrating, for the first time, automated approaches to analysis of molecular geometry with reaction enumeration algorithms for DNA strand displacement reaction networks that can be applied to tethered molecular systems. By adapting a simple approach to solving the biophysical constraints inherent in molecular interactions to be applicable to tethered systems, we produce a localized reaction enumeration system that enhances previous approaches to reaction enumeration in tethered system by not requiring users to explicitly specify the subsets of components that are capable of interacting. This greatly simplifies the user’s task and could also be used as the basis of future systems for automated placement or routing of signal-transmission and logical processing in molecular devices. We apply this system to several published example systems from the literature, including both tethered molecular logic systems and molecular robots. 

Cascades of DNA strand displacement reactions enable the design of potentially large circuits with complex behaviour. Computational modelling of such systems is desirable to enable rapid design and analysis. In previous work, the expressive power of graph theory was used to enumerate reactions implementing strand displacement across a wide range of complex structures. However, coping with the rich variety of possible graph-based structures required enumeration rules with complicated side-conditions. This paper presents an alternative approach to tackle the problem of enumerating reactions at domain level involving complex structures by integrating with a geometric constraint solving algorithm. The rule sets from previous work are simplified by replacing side-conditions with a general check on the geometric plausibility of structures generated by the enumeration algorithm. This produces a highly general geometric framework for reaction enumeration. Here, we instantiate this framework to solve geometric constraints by a structure sampling approach in which we randomly generate sets of coordinates and check whether they satisfy all the constraints. We demonstrate this system by applying it to examples from the literature where molecular geometry plays an important role, including DNA hairpin and remote toehold reactions. This work therefore enables integration of reaction enumeration and structural modelling.