1. 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
Cho, Dong-Yeon

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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
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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)
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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.
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Writing number on the chip
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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.
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7. 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.
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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:
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