Efficient in-message computation of prevalent mathematical operations in DNA-based nanonetworks

One of the most important research issues in the field of nanonetworks is the problem of constructing real networks in practice. To build such networks, one needs to create the nano-devices themselves as well as a computing and a communication mechanism. We already have developed such a concept based on DNA building blocks (so called DNA tiles), which is able to generate all three mechanisms by self-construction, basically by providing a sufficiently large number of specific DNA building blocks. Such networks are Turing complete; however, as we demonstrate in this paper, the number of required building blocks to execute computations by simulating Turing machines is large. We will show in this paper that the number can be reduced by using specific, more efficient sets of building blocks for problems that can be modeled as boolean formulas. For specific mathematical operations like AND or ADD, even smaller solutions/message molecules can be created. This paper presents small message molecules for frequently requested mathematical problems. We present nanonetworks for the THRES and ADD operations. THRES operations can be used to register if critical concentrations of disease markers have been reached. ADD forms the basis for many advanced communication protocols. Furthermore, message molecules for MULT, XOR and INC are conceptualized. The presented message molecules are smaller and less error prone compared to the tilesets that result from more generic approaches. It is therefore more likely that they can be employed in groundbreaking wet-lab experiments in the near future.