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MULTIDIMENSIONAL FUNCTION OPTIMIZATION BASED ON

DNA COMPUTING

Introduction

The main purpose of this paper is to analyze the main structure of DNA molecules to simulate

a molecular computer to facilitate the solution of complex large-scale problems such as NP-Complete

problems. In the late 1950s, the physicist Richard Feynman first proposed the idea of using living cells

and molecular complexes to construct sub-microscopic computers, thus founding the field of

nanotechnology. In 1994, Leonard Adleman of the University of Southern California was inspired to

use DNA by reading how the DNA polymerase enzyme reads and writes at the molecular level. [1]

DNA Molecule: Structure and Manipulation

DNA (deoxyribonucleic acid) encodes the genetic information of cellular organisms. It

consists of polymer chains, commonly referred to as DNA strands. Each strand may be viewed as a

chain of nucleotides, or bases, attached to a sugar-phosphate backbone. An n-letter sequence of

consecutive bases is known as an n-meror an oligonucleotideof length n.

The four DNA nucleotides are adenine, guanine, cytosine, and thymine, commonly abbreviated to A,

G, C, and T respectively. Each strand, according to chemical convention, has a 5 and a 3 end; thus,

any single strand has a natural orientation. This orientation is due to the fact that one end of the single

strand has a free 5 phosphate group, and the other end has a free 3 deoxyribose hydroxyl group. The

classical double helix of DNA (Fig 1.2) is formed when two separate strands bond. Bonding occurs by

the pairwise attraction of bases; A bonds with T and G bonds with C. The pairs (A, T) and (G, C) are

therefore known as complementary base pairs.

The two pairs of bases form hydrogen bonds between each other, two bonds between A and T and

three between G and C. We will adopt the following convention: if denotes an oligo, then denotes

the complement of. The bonding process is well known as annealing, a strand will only anneal to its


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complement if they have opposite polarities. Therefore, one strand of the double helix extends from 5

to 3 and the other from 3 to 5, as we can see in Fig. 1.2.

Genetic Informationon DNA

DNA produces RNA, which in turn produces proteins. The basic building blocks of genetic

information are known as genes. Each gene codes for one specific protein and may be turned on

(expressed) or off(repressed) when required.

One of the most important functions proteins carry out is to act as enzymes. Enzymes act as specific

catalysts; each type of enzyme catalyses a chemical reaction. The chain of amino acids folds into a

specific three-dimensional shape. The protein self-assembles into this conformation, using only the

information encoded in its sequence. Most enzymes assemble into a globular shape, with cavities on

their surface. The proteins substrate fit into these cavities like a key in a lock. These cavities enable

proteins to bring their substrates close together in order to facilitate chemical reactions between them.

Transcription andTranslation

In order for a DNA sequence to be converted into a protein molecule, it must be read

(transcribed) and the transcript converted (translated) into a protein. Transcription of a gene produces

a messenger RNA (mRNA) copy, which can then be translated into a protein.

Transcription proceeds as follows. The mRNA copy is synthesized by an enzyme known as RNA

polymerase. In order to do this, the RNA polymerase must be able to recognize the specific region to

be transcribed. This specificity requirement facilitates the regulation of genetic expression, thus

preventing the production of unwanted proteins. Transcription begins at specific sites within the DNA

sequence, know as promoters. These promoters may be thought of as markers or signs, in that they

are not transcribed into RNA. The regions that are transcribed into RNA are referred to as structural

genes. The RNA polymerase recognizes the promoter, and transcription begins. In order for the RNA

polymerase to begin transcription, the double helix must be opened so that the sequence of bases may

be read. This opening involves the breaking of the hydrogen bonds between bases.

The RNA polymerase then moves along the DNA template strand in the 3 5 directions. As it does so,

the polymerase creates an antiparallelmRNA chain.


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Operations on DNA

Synthesis.Oligonucleotides may be synthesized to order by a machine the size of a microwaveoven.

Denaturing, annealing and ligation. Double-stranded DNA may be dissolved into single

strands (denatured) by heating the solution to a temperature determined by the composition of the

strand. Heating breaks the hydrogen bonds between complementary strands; this is shown on Fig. 1.6.

Since a G-C pair is joined by three hydrogen bonds, the temperature required to break it is slightly

higher than that for an A-T pair, joined by only two hydrogen bonds. This factor must be taken into

account when designing sequences to represent computational elements.

Annealing is the reverse of melting, whereby a solution of single strands is cooled, allowing

complementary strands to bind together.

In double-stranded DNA, if one of the single strands contains a discontinuity, for example, if

one nucleotide is not bonded to its neighbor, then this may be repaired by DNA ligase. This allows us

to create a unified strand from several strands bound together by their respective complements.

Separationofstrands.Separation involves the extraction from a test tube of any single strands

containing a specific short sequence. If we want to extract single strands containing the sequence , wemay first create many copies of its complement. We attach to these oligos biotin molecules, which in

turn bind to a fixed matrix. (Page 22)


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Gelelectrophoresis.Is an important technique for sorting DNA strands by size. Is the movement of

charged molecules in an electric field. Since DNA molecules carry a negative charge, when placed in

an electric field they tend to migrate toward the positive pole. The rate of migration of a molecule in an

aqueous solution depends on its shape and electric charge. Since DNA molecules have the same charge

per unit length, they all migrate at the same speed in an aqueous solution. However, if electrophoresis

is carried out in a gel, the migration rate of a molecule is also affected by its size. This is due to the fact

that the gel is a dense network of pores through which the molecules travel. Smaller molecules

therefore migrate faster through the gel, thus sorting them according to size.

Cloning.Defined as the production of multiple identical copies of a single gene, cell, virus or

organism. In the context of molecular computation, cloning therefore allows us to obtain multiple

copies of specific strands of DNA. This is achieved as follows:

The specific sequence is inserted in a circular DNA molecule, known as a vector, producing

recombinant DNA molecule. This is performed by cleaving both the double-stranded vector DNA and

the target strand with the same restriction enzyme. Since the vector is double stranded, restriction with

suitable enzymes produces two short single-stranded regions at either end of the molecule. The vector

acts as a vehicle, transporting the sequence into a host cell.


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Models of Molecular Computation

The Hamiltonian Path Problem

The objective is to find a path from start to end going through all the points only once. This problem is

difficult for conventional computers to solve because it is a "non-deterministic polynomial time

problem" (NP). NP problems are intractable with deterministic (conventional/serial) computers, but

can be solved using non-deterministic (massively parallel) computers. A DNA computer is a type of

non-deterministic computer. The Hamiltonian Path problem was chosen because it is known as "NP-

complete"; every NP problem can be reduced to a Hamiltonian Path problem.


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The following algorithm solves the Hamiltonian Path problem:

1. Generate random paths through the graph.2. Keep only those paths that begin with the start city (A) and conclude with the end city (G).3. If the graph has n cities, keep only those paths with n cities. (n=7)4. Keep only those paths that enter all cities at least once.5. Any remaining paths are solutions.[1]

The key to solving the problem was using DNA to perform the five steps in the above algorithm. The

following operations can be performed with DNA:

o Synthesis of a desired strando Separation of strands by lengtho Merging: pour two test tubes into one to perform uniono Extraction: extract those strands containing a given patterno Melting/Annealing: break/bond two ssDNA molecules with complementary sequenceso Amplification: use PCR to make copies of DNA strandso C

utti

ng: cut DNA with restriction enzymeso Ligation: Ligate DNA strands with complementary sticky ends using ligaseo Detection: Confirm presence/absence of DNA in a given test tube[4]

The above operations can be used to "program" a DNA computer.

To implement step 1 of the algorithm, Adleman created a 20-mer sequence of DNA for each city A

through G. For each path i>j, an oligonucleotide was created that was the 3' 10-mer of i and 5' 10-mer

of j (see figure 2). A>B contained all of A and the 5' 10-mer of B, and E G contained the 3' 10-mer of

E and all of G to eliminate any possible sticky ends. For each city i, a Watson-Crick complementary

oligonucleotide was synthesized and designated ~i.

Step 2 was implemented by using A and ~G as primers for PCR to amplify all "paths" from starting

with A and ending with G.

For step 3, the product of step 2 was run on an agarose gel, and the 140 bp band (corresponding to adsDNA path entering exactly seven cities) was excised and soaked in double-distilled H2O to extract

the DNA. This product was then PCR amplified and gel-purified several times to enhance its purity.

In order to complete step 4, the product of step 3 was affinity-purified with a biotin-avidin magnetic

beads system. The dsDNA from step 3 was melted and the ssDNA product was incubated with ~A

conjugated to magnetic beads. Only those ssDNA molecules that entered city A at least once were


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annealed to the bound ~B and retained. The process was successively repeated with ~C, ~D, ~E, and

~F.

Step 5 was performed by amplifying the product of step 4 with PCR and running it on a gel. Figure 3

shows the results of these procedures. In figure 3A, lane 1 is the result of the ligation reaction in step 1.

The smear is consistent with the construction of molecules encoding random paths through the graph.Lanes 2-5 show the results of the PCR reaction in step 2. The densest bands correspond to the

amplification of molecules encoding paths that began at A and ended at F.

Figure 3B shows graduated PCR of the final product of the computer. Graduated PCR allows one to

"print" the results of a computation, using A as the right primer and ~B through ~G as the left primer

lanes 1-7, respectively. The graduation shows the progression from A>B>C>D>E>F>G.

Advantages and Disadvantages

The advantages presented by a DNA computer are amazing. Their capacity for memory storage is

tremendous. Also, they are inexpensive to build, being made of common biological materials. Many of

the DNA molecules could be reused with a little splicing, so the whole computer is really

materialistically very efficient. Then, their computational power is incomparable to anything in

existence. First and foremost, DNA computing is useful because it has a capacity lacked by all current

electronics-based computers: its massively parallel nature. What does this mean, you ask? Well,

essentially while DNA can only carry out computations slowly, DNA computers can perform a

staggering number of calculations simultaneously; specifically, on the order of 10^9 calculations per

mL of DNA per second! This capability of multiple cotemporal calculations immediately lends itself to

several classes of problems which a modern electronic computer could never even approach solving.

To give you an idea of the difference in time, a calculation that would take 10^22 modern computers

working in parallel to complete in the span of one human's life would take one DNA computer only 1

year to polish off!

However, DNA computers do have their disadvantages. Although Adleman's first application of the

computer took only milliseconds to produce a solution, it took about a week to fish the solution

molecules out from the rest of the possible path molecules that had formed. To make these computers

more realistically viable, the DNA splicing and selection equipment needs to be refined for this

purpose and better methods for fishing developed. There is also no guarantee that the solution

produced will necessarily be the absolute best solution, though it will certainly be a very good one,

arrived at in a much shorter time than with a conventional computer. DNA computers could not (at this

point) replace traditional computers. They are not programmable and the average dunce can not sit


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down at a familiar keyboard and get to work. Some think that in the future, computers will be a

combination of the current models and DNA, using the most attractive features of both to create a

vastly improved total product. However, research is ongoing in doing Boolean logic with DNA and

designing universal (programmable) DNA computers.

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