Mathematical Considerations in the Design of Microreactor-Based DNA Computers

DNA-based computation in microreactors allows the use of smaller volumes and simplifies automation, reducing both cost and time commitments. We examine ways to construct and implement small microreactor systems implementing analogues of the Boolean functions AND and OR. Relative positions of microreactors (in series and in parallel) are considered, as are different methods of recovery of solution strands, i.e. either from the fraction specifically retained in the microreactor (positive selection) or allowed to pass through after non-solution strands are removed (negative selection). Primary consideration is given to the overall accuracy of the system implementing the functions, and a secondary concern for the OR function is a balanced representation of correct solution strands in the final pool. We conclude that positive selection should confer higher accuracy than negative selection and that both AND and OR functions are better implemented by microreactors arranged in series.