|Title:||Self-assembly at temperature 1|
Department of Computer Science, University of British Columbia
Self-assembly is the process by which simple parts autonomously assemble into larger, more complex objects. To study self-assembly, a large body of research has concentrated on the Tile Assembly Model proposed by Rothemund and Winfree (2000) which uses Wang square tiles with glues of different types on the sides. The popularity of this model comes from its simplicity on one hand, and yet possibility to "implement" it in the lab using DNA double-crossover molecules on the other hand.
In my talk I will consider two self-assembly models: the standard model, which starts from a seed tile and let the tiles attach one by one to a growing structure; and the step-wise assembly model, which allows the assembly process to be controlled by application of a sequence of tile sets on the growing structure. In both models, assembly process is controlled by temperature, i.e., a threshold of the total glue strength a tile needs to reach to attach to a growing complex. At temperature 1, matching glues on one side of a tile are enough for a tile to attach. Hence, at this temperature, there is no cooperativity of binding interactions. With cooperativity, for instance, at temperature 2, tile assembly model is powerful enough to simulate a computation of Turing machine, i.e., it's Turing universal. Without cooperativity, it is conjectured that the standard model is not Turing universal. In the first part of my talk, I will discuss some related results on this topic. In the second part, I will show that the extra control (a sequence of tile sets) provided in the step-wise assembly model allows us to assembly any shape scaled by factor 2 with only 14 tile types and other related results.
This is a joint work with Ladislav Stacho, Christine Stoll and Bahar Behsaz.