Abstract: The methods and apparatus 100 disclosed herein concern DNA sequencing. In some embodiments of the invention, the methods comprise measuring the distance between labeled nucleotides 220, such as nucleotides labeled with bulky groups. The methods may further comprise placing identical template DNA 200 into four reaction chambers 110, 120, 130, 140, each containing a different labeled nucleotide precursor, synthesizing complementary strands 230, 240, 250 and detecting labeled nucleotides 220. The distances between labeled nucleotides 220 may be used to construct 450 distance maps 310, 320, 330, 340 for each type of labeled nucleotide 220. The distance maps 310, 320, 330, 340 may be aligned 520 to obtain a nucleic acid sequence 210. Overlapping data analysis and frequency analysis may be used to construct 450 the distance maps 310, 320, 330, 340 and non-overlapping data analysis may be used to align 520 the distance maps into a sequence 210.

Abstract: A catalytic system and method of catalyzing reactions that uses a novel toehold exchange mechanism that allows a specified input to catalyze the release of a specified output, which in turn can serve as a catalyst for other reactions is provided. This toehold exchange catalyst system, which can be driven forward by the configurational entropy of the released molecule, provides an amplifying circuit element that is simple, fast, modular, composable, and robust. Using this toehold exchange catalyst system it has been possible to construct and characterize several circuits that amplify nucleic acid signals, including a feed-forward cascade with quadratic kinetics and a positive feedback circuit with exponential growth kinetics.