 # Book of Abstracts: Albany 2005 Volume 22
No. 6
June 2005

# Multiplication Using DNA

A functional machine is not only an assembly of parts, but also an assembly of processes. The processing of each part must obey laws that respect to the property of this part. For example, computation in an electronic computer is an assembly of voltage switching processes in its components. The binary-phase of voltage is the property of the computational unit. The circuit defines the law of switching with respect to this property. Thus, building any kind of computer entails selecting appropriate components and assembling their properties to function in computation.

Here, we describe computation using a DNA strand as the basic unit and we have used this unit to achieve the function of multiplication. We took the advantage of the property of DNA duplex, in which each strand can represent two individual units that can hybridize to form a single unit. We represent the numbers we multiply in binary, with different lengths representing each digit present in the number. This is shown in the figure, where all binary representations up to 512 are shown. If a particular binary digit is missing in the representation of the number, it is omitted. Each strand has a constant length region and the constant length regions (yellow in the figure) on the two numbers to be multiplied are complementary. Thus, the green digits and the tan digits will pair with each other when the strands are mixed. In principle, all combinations of the numbers will be present in solution. Following hybridization, there is present a collection of duplex molecules that are tailed by single-stranded ends (the green and tan portions of the strands). To read out the result, these intermediates are converted to complete duplex molecules by filling in the ends with DNA polymerase. The lengths that are present represent the digits that are present, and they may be separated by denaturing PAGE. The bands in each length position tell us what the digit in the resulting number is. The increments on one of the multiplicands are designed to be slightly different from those on the other one so as to avoid overlap on the gel. The results give a series of bands for each power of two. The number of bands in the size domain for a particular power of two is converted to binary and the sum of all present bands is then added together. The result of this process is always the correct answer.

Acknowledgement

This research supported by NIGMS, ONR, NSF and Nanoscience Technologies, Inc.

Gang Wu