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.

中文翻译：

---

计算核酸装置中反应计数的几何框架。

DNA 链置换反应的级联使得能够设计具有复杂行为的潜在大型电路。此类系统的计算建模有助于实现快速设计和分析。在之前的工作中，图论的表达能力被用来枚举在各种复杂结构中实现链位移的反应。然而，处理丰富多样的可能的基于图的结构需要具有复杂附加条件的枚举规则。本文提出了一种替代方法，通过与几何约束求解算法集成来解决涉及复杂结构的领域级别的枚举反应问题。通过对枚举算法生成的结构的几何合理性进行一般检查来替换附带条件，从而简化了先前工作的规则集。这产生了用于反应计数的高度通用的几何框架。在这里，我们实例化这个框架，通过结构采样方法来解决几何约束，在该方法中，我们随机生成坐标集并检查它们是否满足所有约束。我们通过将其应用于分子几何学发挥重要作用的文献中的示例来演示该系统，包括 DNA 发夹和远程立足点反应。因此，这项工作能够整合反应枚举和结构建模。