Molecular Machines from Topological Linkages

Life is built upon amazingly sophisticated molecular machines whose behavior combines mechanical and chemical action. Engineering of similarly complex nanoscale devices from first principles remains an as yet unrealized goal of bioengineering. In this paper we formalize a simple model of mechanical motion (mechanical linkages) combined with chemical bonding. The model has a natural implementation using DNA with double-stranded rigid links, and single-stranded flexible joints and binding sites. Surprisingly, we show that much of the complex behavior is preserved in an idealized topological model which considers solely the graph connectivity of the linkages. We show a number of artifacts including Boolean logic, catalysts, a fueled motor, and chemo-mechanical coupling, all of which can be understood and reasoned about in the topological model. The variety of achieved behaviors supports the use of topological chemical linkages in understanding and engineering complex molecular behaviors. 2012 ACM Subject Classification Theory of computation → Models of computation; Theory of computation → Computational geometry