DNA-based Parallel Computation of Simple Arithmetic Hubert Hug and Rainer Schuler Preliminary Proceedings of the 7th International Meeting on DNA Based Computers (DNA7) pp. 159-166 Cho, Dong-Yeon

(C) 2001 SNU CSE Biointelligence Lab Introduction The addition of binary numbers with DNA The procedure is sequential and does not use the power of DNA-computing for parallelization. Other approaches are based on selecting the correct result from a set of all possible values. Representing and manipulating binary numbers on a DNA chip Each of the operations can be performed in parallel (for each bit) with a constant number of steps Store a number on the chip Read the number on the chip Add a (second) number to the number on the chip (C) 2001 SNU CSE Biointelligence Lab

(C) 2001 SNU CSE Biointelligence Lab Model Representing numbers Each bit is represented by specific DNA-sequences which are attached at a particular position on the chip via its 3’ end. pi: the position i and is specific for each i A: the recognition site of a restriction enzyme RA ti: sequence for 0 or 1 (the same sequences are used for all bits) (C) 2001 SNU CSE Biointelligence Lab

(C) 2001 SNU CSE Biointelligence Lab Basic operations Read 0 with red (e.g. Cy3) 1 with green (e.g. Cy5) Addition of two numbers a and b Number a is stored on the chip. Bitwise addition modulo 2 of ai and bi is computed on the chip. The carry bit c are added to the number on the chip. (C) 2001 SNU CSE Biointelligence Lab

(C) 2001 SNU CSE Biointelligence Lab Writing number on the chip (C) 2001 SNU CSE Biointelligence Lab

(C) 2001 SNU CSE Biointelligence Lab Bitwise addition modulo 2 For all i such that the i-th bit of b is equal 1, the values of ti have to be flipped. (C) 2001 SNU CSE Biointelligence Lab

Computing the Carry Bits Adleman’s method Preparation ai = 1: ai = 0: bi = 1: 0qi and 1i1 (3’-0qi-5’ and 3’-1i1-5’) bi = 0: 0i1 and 1iqi (3’-0i1-5’ and 3’-1iqi-5’) qipi (edges) and (the 5’ end is biotinylated.) Node sequences ai = bi = 1 ai = bi = 0 ai = 1 and bi = 0 ai = 0 and bi = 1 5’ ends of the oligonucleotides are biotinylated. (C) 2001 SNU CSE Biointelligence Lab

(C) 2001 SNU CSE Biointelligence Lab The resulting DNA molecules contain sequences Starting with at the 5’ end, and ending with a 0 or 1 at the 3’ end If the carry bit ci+1=1, then the sequences end with a 1. If the carry bit ci+1=0, then the sequences end with a 0. Dextran matrix, to which the oligonucleotides 0 are attached This selects two sets of DNA. Adding to each set the oligonucleotide A, hybridzed and cut with restriction enzyme RA Block: (C) 2001 SNU CSE Biointelligence Lab