Dna Final Report

7/29/2019 Dna Final Report

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1. Introduction

Computer chip manufacturers are furiously racing to make the next

microprocessor that will topple speed records. Sooner or later, though, thiscompetition is bound to hit a wall. Microprocessors made of silicon will

eventually reach their limits of speed and miniaturization. Chip makers need

a new material to produce faster computing speeds.

Scientists have found the new material they need to build the next

generation of microprocessors. Millions of natural supercomputers exist

inside living organisms, including your body. DNA (deoxyribonucleic acid)molecules, the material our genes are made of, have the potential to perform

calculations many times faster than the world's most powerful human-built

computers. DNA might one day be integrated into a computer chip to create

a so-called biochip that will push computers even faster. DNA molecules

have already been harnessed to perform complex mathematical problems.

Despite their respective complexities, biological and mathematical

operations have some similarities:

The very complex structure of a living being

is the result of applying simple operations to initial

information encoded in a DNA sequence.

The very complex structure of a living being

is the result of applying simple operations toinitial information encoded in a DNA sequence

(genes).

All complex math problems can be reduced

to simple operations like addition and subtraction.


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For the same reasons that DNA was presumably selected for living

organisms as a genetic material, its stability and predictability in reactions,

DNA strings can also be used to encode information for mathematical

systems.

Human DNA

While still in their infancy, DNA computers will be capable of

storing billions of times more data than your personal computer. Scientists

are using genetic material to create nano-computers that might take the place

of silicon-based computers in the next decade.

Israeli scientists have built a DNA computer so tiny that a trillion of

them could fit in a test tube and perform a billion operations per second with

99.8 percent accuracy.

Instead of using figures and formulas to solve a problem, the

microscopic computer's input, output and software are made up of DNA


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molecules -- which store and process encoded information in living

organisms.

Scientists see such DNA computers as future competitors to for their

more conventional cousins because miniaturization is reaching its limits and

DNA has the potential to be much faster than conventional computers.

"We have built a nanoscale computer made of biomolecules that is so

small you cannot run them one at a time. When a trillion computers run

together they are capable of performing a billion operations," Professor

Ehud Shapiro of the Weizmann Institute in Israel told.

It is the first programmable autonomous computing machine in which

the input, output, software and hardware are all made of biomolecules.

Although too simple to have any immediate applications it could form

the basis of a DNA computer in the future that could potentially operate

within human cells and act as a monitoring device to detect potentially

disease-causing changes and synthesize drugs to fix them.

The model could also form the basis of computers that could be used

to screen DNA libraries in parallel without sequencing each molecule, which

could speed up the acquisition of knowledge about DNA.


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When it is all mixed together in the test tube, the software and

hardware operate on the input molecule to create the output.

The DNA computer also has very low energy consumption, so if it is

put inside the cell it would not require much energy to work.

DNA computing is a very young branch of science that started less

than a decade ago, when Leonard Adleman of the University of Southern

California pioneered the field by using DNA in a test tube to solve a

mathematical problem.

Scientists around the globe are now trying to marry computer

technology and biology by using nature's own design to process information.

DNA to Chip formation


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Scientific Idea Of DNA Computer

For biological systems, DNA is a master problem solver, storing and

manipulating prodigious amounts of information. Recently, researchers have

been investigating whether the problem-solving power of DNA can be used

to solve nonbiological problems, specifically, problems from computer

science that are out of the reach of traditional computers. Would a DNA

computer actually work? To answer this question, one must turn to

mathematics.

In a groundbreaking 1994 paper, Leonard Adleman described a

laboratory experiment involving DNA and a problem known as the Directed

Hamiltonian Path Problem. Because of their massive complexity, this problem and others like it have eluded solution by conventional computers;

no known algorithm can solve them in a reasonable amount of time. DNA

has the potential to solve these kinds of problems because of its capacity to

store a great deal of information compactly and to speedily perform


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Information Storage In DNA

For traditional computers, these two questions have been answered

affirmatively. And this is why traditional computers work: What they do can

be represented mathematically and proven to produce the right answers.

Fuses may blow, screens may freeze up, and the Pentium chip might be

faulty, but the underlying mathematics is flawless. What the DNA computer

needed was similar mathematical bedrock. Happily for the investment

capitalists, mathematicians have provided the proof.

These results lift the DNA computer out of the realm of science

fiction and put it on a firm mathematical foundation.


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First Invented DNA Chip

DNA computer components -- logic gates and biochips -- will take

years to develop into a practical, workable DNA computer. If such a

computer is ever built, scientists say that it will be more compact, accurateand efficient than conventional computers. In the next section, we'll look at

how DNA computers could surpass their silicon-based predecessors, and

what tasks these computers would perform.


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4. The Experiment

The Adleman experiment

Adleman is often called the inventor of DNA computers. His article in

a 1994 issue of the journal Science outlined how to use DNA to solve a

well-known mathematical problem, called the directed Hamilton Path

problem , also known as the "traveling salesman" problem. The goal of the

problem is to find the shortest route between a numbers of cities, going

through each city only once. As you add more cities to the problem, the

problem becomes more difficult. Adleman chose to find the shortest route between seven cities.

Directed Hamilton Path problem

You could probably draw this problem out on paper and come to a

solution faster than Adleman did using his DNA test-tube computer. Here

are the steps taken in the Adleman DNA computer experiment:


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1. Strands of DNA represent the seven cities. In genes,

genetic coding is represented by the letters A, T, C and

G. Some sequence of these four letters represented each

city and possible flight path.2. These molecules are then mixed in a test tube, with some

of these DNA strands sticking together. A chain of these

strands represents a possible answer.

3. Within a few seconds, all of the possible combinations of

DNA strands, which represent answers, are created in the

test tube.

4. Adleman eliminates the wrong molecules through

chemical reactions, which leaves behind only the flight

paths that connect all seven cities.

There is no better way to understand how something works than by

going through an example step by step. So lets solve our own directed

Hamiltonian Path problem, using the DNA methods demonstrated by

Adleman. The concepts are the same but the example has been simplified to

make it easier to follow and present.

Suppose that I need to visit four cities: Houston, Chicago, Miami, and

NY, with NY being my final destination. The airline Im taking has aspecific set of connecting flights that restrict which routes I can take (i.e.

there is a flight from L.A. to Chicago, but no flight from Miami to Chicago).

What should my itinerary be if I want to visit each city only once?


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It should take you only a moment to see that there is only one route.

Starting from L.A. you need to fly to Chicago, Dallas, Miami and then to

N.Y. Any other choice of cities will force you to miss a destination, visit a

city twice, or not make it to N.Y. For this example you obviously dont need

the help of a computer to find a solution. For six, seven, or even eight cities,

the problem is still manageable. However, as the number of cities increases,

the problem quickly gets out of hand. Assuming a random distribution of

connecting routes, the number of itineraries you need to check increases

exponentially. Pretty soon you will run out of pen and paper listing all the

possible routes, and it becomes a problem for a computer......or perhaps

DNA. The method Adleman used to solve this problem is basically the

shotgun approach mentioned previously. He first generated all the possible

itineraries and then selected the correct itinerary. This is the advantage of

DNA. Its small and there are combinatorial techniques that can quickly

generate many different data strings. Since the enzymes work on many DNAmolecules at once, the selection process is massively parallel.

When the number of cities gets to around one hundred it could take

hundreds of years of conventional computer time to solve the problem, even

with the most advanced parallel processing available.

Adleman developed a method of manipulating DNA which, in effect,

conducts trillions of computations in parallel. Essentially he coded each city

and each possible flight as a sequence of 4 components. For example he

coded one city as GCAG and another as TCGG.


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Giving cities codes

Specifically, the method based on Adlemans experiment would be as

follows:

1. Generate all possible routes.2. Select itineraries that start with the proper city and end

with the final city.

3. Select itineraries with the correct number of cities.

4. Select itineraries that contain each city only once.

Part I: Generate all possible routes

Strategy : Encode city names in short DNA sequences. Encode

itineraries by connecting the city sequences for which routes exist.


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DNA can simply be treated as a string of data. For example, each city

can be represented by a "word" of six bases:

1. Los Angeles GCTACG

2. Chicago CTAGTA

3. Dallas TCGTAC

4. Miami CTACGG

5. New York ATGCCG

The entire itinerary can be encoded by simply stringing together these

DNA sequences that represent specific cities. For example, the route from

L.A -> Chicago -> Dallas -> Miami -> New York would simply be

GCTACGCTAGTATCGTACCTACGGATGCCG, or equivalently it could

be represented in double stranded form with its complement sequence.

So how do we generate this? Synthesizing short single stranded DNA

is now a routine process, so encoding the city names is straightforward. The

molecules can be made by a machine called a DNA synthesizer or even

custom ordered from a third party. Itineraries can then be produced from the

city encodings by linking them together in proper order. To accomplish this

you can take advantage of the fact that DNA hybridizes with its

complimentary sequence. For example, you can encode the routes between

cities by encoding the compliment of the second half (last three letters) of

the departure city and the first half (first three letters) of the arrival city. For

example the route between Miami (CTACGG) and NY (ATGCCG) can be

made by taking the second half of the coding for Miami (CGG) and the first

half of the coding for NY (ATG). This gives CGGATG. By taking the

complement of this you get, GCCTAC, which not only uniquely represents


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the route from Miami to NY, but will connect the DNA representing Miami

and NY by hybridizing itself to the second half of the code representing

Miami (...CGG) and the first half of the code representing NY (ATG...). For

example:

Random itineraries can be made by mixing city encodings with the

route encodings. Finally, the DNA strands can be connected together by an

enzyme called ligase . What we are left with are strands of DNA representing

itineraries with a random number of cities and random set of routes. For

example:

We can be confident that we have all possible combinations including

the correct one by using an excess of DNA encodings, say 10^13 copies of

each city and each route between cities. Remember DNA is a highly

compact data format, so numbers are on our side.

Part II: Select itineraries that start and end with the correct cities

Strategy : Selectively copy and amplify only the section of the DNA

that starts with LA and ends with NY by using the Polymerase Chain

Reaction .

After Part I , we now have a test tube full of various lengths of DNA

that encode possible routes between cities. What we want are routes that

start with LA and end with NY. To accomplish this we can use a techniquecalled Polymerase Chain Reaction (PCR), which allows you to produce

many copies of a specific sequence of DNA. PCR is an iterative process that

cycles through a series of copying events using an enzyme called

polymerase . Polymerase will copy a section of single stranded DNA


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starting at the position of a primer , a short piece of DNA complimentary to

one end of a section of the DNA that you're interested in. By selecting

primers that flank the section of DNA you want to amplify, the polymerase

preferentially amplifies the DNA between these primers, doubling theamount of DNA containing this sequence. After many iterations of PCR, the

DNA you're working on is amplified exponentially. So to selectively

amplify the itineraries that start and stop with our cities of interest, we use

primers that are complimentary to LA and NY. What we end up with after

PCR is a test tube full of double stranded DNA of various lengths, encoding

itineraries that start with LA and end with NY.

Part III: Select itineraries that contain the correct number of

cities.

Strategy : Sort the DNA by length and select the DNA whose length

corresponds to 5 cities.

Our test tube is now filled with DNA encoded itineraries that start

with LA and end with NY, where the number of cities in between LA and

NY varies. We now want to select those itineraries that are five cities long.

To accomplish this we can use a technique called Gel Electrophoresis ,

which is a common procedure used to resolve the size of DNA. The basic

principle behind Gel Electrophoresis is to force DNA through a gel matrix

by using an electric field. DNA is a negatively charged molecule under mostconditions, so if placed in an electric field it will be attracted to the positive

potential. However since the charge density of DNA is constant (charge per

length) long pieces of DNA move as fast as short pieces when suspended in

a fluid. This is why you use a gel matrix. The gel is made up of a polymer


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that forms a meshwork of linked strands. The DNA now is forced to thread

its way through the tiny spaces between these strands, which slows down the

DNA at different rates depending on its length. What we typically end up

with after running a gel is a series of DNA bands, with each bandcorresponding to a certain length. We can then simply cut out the band of

interest to isolate DNA of a specific length. Since we known that each city is

encoded with 6 base pairs of DNA, knowing the length of the itinerary gives

us the number of cities. In this case we would isolate the DNA that was 30

base pairs long (5 cities times 6 base pairs).

Part IV: Select itineraries that have a complete set of cities

Strategy : Successively filter the DNA molecules by city, one city at a

time. Since the DNA we start with contains five cities, we will be left with

strands that encode each city once.

DNA containing a specific sequence can be purified from a sample of

mixed DNA by a technique called affinity purification . This is

accomplished by attaching the compliment of the sequence in question to a

substrate like a magnetic bead. The beads are then mixed with the DNA.

DNA, which contains the sequence you're after then hybridizes with the

complement sequence on the beads. These beads can then be retrieved and

the DNA isolated.

So we now affinity purifies fives times, using a different city

complement for each run. For example, for the first run we use L.A.'-beads

(where the ' indicates compliment strand) to fish out DNA sequences which

contain the encoding for L.A. (which should be all the DNA because of step


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3), the next run we use Dallas'-beads, and then Chicago'-beads, Miami'-

beads, and finally NY'-beads. The order isnt important. If an itinerary is

missing a city, then it will not be "fished out" during one of the runs and will

be removed from the candidate pool. What we are left with are the itinerariesthat start in LA, visit each city once, and end in NY. This is exactly what we

are looking for. If the answer exists we would retrieve it at this step.

Reading out the answer

One possible way to find the result would be to simply sequence the

DNA strands. However, since we already have the sequence of the cityencodings we can use an alternate method called graduated PCR . Here we

do a series of PCR amplifications using the primer corresponding to L.A.,

with a different primer for each city in succession. By measuring the various

lengths of DNA for each PCR product we can piece together the final

sequence of cities in our itinerary. For example, we know that the DNA

itinerary starts with LA and is 30 base pairs long, so if the PCR product for

the LA and Dallas primers was 24 base pairs long, you know Dallas is the

fourth city in the itinerary (24 divided by 6). Finally, if we were careful in

our DNA manipulations the only DNA left in our test tube should be DNA

itinerary encoding LA, Chicago, Miami, Dallas, and NY. So if the

succession of primers used is LA & Chicago, LA & Miami, LA & Dallas,

and LA & NY, then we would get PCR products with lengths 12, 18, 24, and

30 base pairs.

The incredible thing is that once the DNA sequences had been created

he simply "just added water" to initiate the "computation". The DNA strands

then began their highly efficient process of creating new sequences based on


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the input sequences.

If an "answer" to the problem for a given set of inputs existed then it

should amongst these trillions of sequences. The next (difficult) step was to

isolate the "answer" sequences. To do this Adleman used a range of DNAtools. For example, one technique can test for the correct start and end

sequences, indicating that the strand has a solution for the start and end

cities. Another step involved selecting only those strands which have the

correct length, based on the total number of cities in the problem

(remembering that each city is visited once).

Finally another technique was used to determine if the sequence for each

city was included in the strand. If any strands were left after these processes

then:

A solution to the problem existed, and

The answer(s) would be in the sequence(s)

on the remaining strands.

His attempt at solving a seven-city, 14 flight map took seven days of

lab work. This particular problem can be manually solved in a few minutes

but the key point about Adleman's work is that it will work on a much larger

scale, when manual or conventional computing techniques become

overwhelmed. "The DNA computer provides enormous parallelism... in one

fiftieth of a teaspoon of solution approximately 10 to the power 14 DNA

'flight numbers' were simultaneously concatenated in about one second".


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Caveats

Adleman's experiment solved a seven city problem, but there are two

major shortcomings preventing a large scaling up of his computation. The

complexity of the traveling salesman problem simply doesnt disappear

when applying a different method of solution - it still increases

exponentially. For Adlemans method, what scales exponentially is not the

computing time, but rather the amount of DNA. Unfortunately this places

some hard restrictions on the number of cities that can be solved; after the

Adleman article was published, more than a few people have pointed out

that using his method to solve a 200 city HP problem would take an amount

of DNA that weighed more than the earth. Another factor that places limits

on his method is the error rate for each operation. Since these operations are

not deterministic but stochastically driven (we are doing chemistry here),

each step contains statistical errors, limiting the number of iterations you can

do successively before the probability of producing an error becomes greater

than producing the correct result. For example an error rate of 1% is fine for 10 iterations, giving less than 10% error, but after 100 iterations this error

grows to 63%.

Conclusions of Experiment

So will DNA ever be used to solve a traveling salesman problem with

a higher number of cities than can be done with traditional computers? Well,considering that the record is a whopping 13,509 cities, it certainly will not

be done with the procedure described above. It took this group only three

months, using three Digital Alpha Server 4100s (a total of 12 processors)

and a cluster of 32 Pentium-II PCs. The solution was possible not because of


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brute force computing power, but because they used some very efficient

branching rules. This first demonstration of DNA computing used a rather

unsophisticated algorithm, but as the formalism of DNA computing becomes

refined, new algorithms perhaps will one day allow DNA to overtakeconventional computation and set a new record.

On the side of the "hardware" (or should I say "wetware"),

improvements in biotechnology are happening at a rate similar to the

advances made in the semiconductor industry. For instance, look at

sequencing ; what once took a graduate student 5 years to do for a PhD

thesis takes Celera just one day. With the amount of government funded

research dollars flowing into genetic-related R&D and with the large

potential payoffs from the lucrative pharmaceutical and medical-related

markets, this isn't surprising. Just look at the number of advances in DNA-

related technology that happened in the last five years. Today we have not

one but several companies making "DNA chips," where DNA strands are

attached to a silicon substrate in large arrays (for example Affymetrix's genechip). Production technology of MEMS is advancing rapidly, allowing for

novel integrated small scale DNA processing devices. The Human Genome

Project is producing rapid innovations in sequencing technology. The future

of DNA manipulation is speed, automation, and miniaturization.

And of course we are talking about DNA here, the genetic code of life

itself. It certainly has been the molecule of this century and most likely the

next one. Considering all the attention that DNA has garnered, it isnt too

hard to imagine that one day we might have the tools and talent to produce a

small integrated desktop machine that uses DNA, or a DNA-like

biopolymer, as a computing substrate along with set of designer enzymes.
http://www.affymetrix.com/http://www.affymetrix.com/


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Perhaps it wont be used to play Quake IV or surf the web -- things that

traditional computers are good at -- but it certainly might be used in the

study of logic, encryption, genetic programming and algorithms, automata,

language systems, and lots of other interesting things that haven't even beeninvented yet.

The Restricted Model:

Since Adleman's original experiment, several methods to reduce error

and improve efficiency have been developed. The problems with

implementing a DNA computer can be separated into two types:

o Physical obstructions: difficulties with large scale

systems and coping with errors

o Logical obstructions: concerning the versatility of

molecular computers and their capacity to

efficiently accommodate a wide variety of

computational problems

The Restricted model of DNA computing solves several physical

problems with the unrestricted model. The Restricted model simplifies the

physical obstructions in exchange for some additional logical considerations.

The purpose of this restructuring is to simplify biochemical operations and

reduce the errors due to physical obstructions.


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The Restricted model of DNA computing:

o Separate: isolate a subset of DNA from a sample

o Merging: pour two test tubes into one to perform

union

o Detection: Confirm presence/absence of DNA in a

given test tube

Despite these restrictions, this model can still solve NP-complete

problems such as the 3-colourability problem, which decides if a map can be

colored with three colors in such a way that no two adjacent territories havethe same color.

Certain assumptions must be made about the oligonucleotides used in

the manipulations:

o Under easily achievable conditions (temperature,

pH, etc.) each oligonucleotide reliably forms stable

hybrids with its Watson-Crick complement

o Under easily achievable conditions, each

oligonucleotide reliably dissociates from its

Watson-Crick complement

o Under neither of the conditions above does any

oligonucleotide form hybrids with itself or another

oligonucleotide (except its complement), nor

another oligonucleotide's Watson-Crick

complement


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Error control is achieved mainly through logical operations, such as

running all DNA samples showing positive results a second time to reduce

false positives. Some molecular proposals, such as using DNA with a

peptide backbone for stability, have also been recommended.


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Sequence of DNA Representation


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Image of DNA representation

Bit Representation Using DNA


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6. Comparison of DNA & Silicon

DNA, with its unique data structure and ability to perform many

parallel operations, allows you to look at a computational problem from a

different point of view. Transistor-based computers typically handle

operations in a sequential manner. Of course there are multi-processor

computers, and modern CPUs incorporate some parallel processing, but in

general, in the basic von Neumann architecture computer, instructions are

handled sequentially. A von Neumann machine, which is what all modernCPUs are, basically repeats the same "fetch and execute cycle" over and

over again; it fetches an instruction and the appropriate data from main

memory, and it executes the instruction. It does these many, many times in a

row, really, really fast. The great Richard Feynman, in his Lectures on

Computation, summed up von Neumann computers by saying, "the inside of

a computer is as dumb as hell, but it goes like mad!" DNA computers,

however, are non-von Neuman, stochastic machines that approach

computation in a different way from ordinary computers for the purpose of

solving a different class of problems.

Typically, increasing performance of silicon computing means faster

clock cycles (and larger data paths), where the emphasis is on the speed of

the CPU and not on the size of the memory. For example, will doubling theclock speed or doubling your RAM give you better performance? For DNA

computing, though, the power comes from the memory capacity and parallel

processing. If forced to behave sequentially, DNA loses its appeal. For

example, let's look at the read and write rate of DNA. In bacteria, DNA can


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be replicated at a rate of about 500 base pairs a second. Biologically this is

quite fast (10 times faster than human cells) and considering the low error

rates, an impressive achievement. But this is only 1000 bits/sec, which is a

snail's pace when compared to the data throughput of an average hard drive.But look what happens if you allow many copies of the replication enzymes

to work on DNA in parallel. First of all, the replication enzymes can start on

the second replicated strand of DNA even before they're finished copying

the first one. So already the data rate jumps to 2000 bits/sec. But look what

happens after each replication is finished - the number of DNA strands

increases exponentially (2^n after n iterations). With each additional strand,

the data rate increases by 1000 bits/sec. So after 10 iterations, the DNA is

being replicated at a rate of about 1Mbit/sec; after 30 iterations it increases

to 1000 Gbits/sec. This is beyond the sustained data rates of the fastest hard

drives.

Now let's consider how you would solve a nontrivial example of the

traveling salesman problem (# of cities > 10) with silicon vs. DNA. With avon Neumann computer, one naive method would be to set up a search tree,

measure each complete branch sequentially, and keep the shortest one.

Improvements could be made with better search algorithms, such as pruning

the search tree when one of the branches you are measuring is already longer

than the best candidate. A method you certainly would not use would be to

first generate all possible paths and then search the entire list. Why? Well,

consider that the entire list of routes for a 20 city problem could theoretically

take 45 million GBytes of memory (18! routes with 7 byte words)! Also for

a 100 MIPS computer, it would take two years just to generate all paths

(assuming one instruction cycle to generate each city in every path).


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However, using DNA computing, this method becomes feasible! 10^15 is

just a nanomole of material, a relatively small number for biochemistry.

Also, routes no longer have to be searched through sequentially. Operations

can be done all in parallel.


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7. Conclusion

A Successor to Silicon

Silicon microprocessors have been the heart of the computing world

for more than 40 years. In that time, manufacturers have crammed more and

more electronic devices onto their microprocessors. In accordance with

Moore's Law , the number of electronic devices put on a microprocessor has

doubled every 18 months. Moore's Law is named after Intel founder Gordon

Moore, who predicted in 1965 that microprocessors would double incomplexity every two years. Many have predicted that Moore's Law will

soon reach its end, because of the physical speed and miniaturization

limitations of silicon microprocessors.

DNA computers have the potential to take computing to new levels,

picking up where Moore's Law leaves off. There are several advantages to

using DNA instead of silicon:

As long as there are cellular organisms, there will always

be a supply of DNA.

The large supply of DNA makes it a cheap resource.

Unlike the toxic materials used to make traditional

microprocessors, DNA biochips can be made cleanly .

DNA computers are many times smaller than today's

computers.

DNA's key advantage is that it will make computers smaller than any

computer that has come before them, while at the same time holding more


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data. One pound of DNA has the capacity to store more information than all

the electronic computers ever built; and the computing power of a teardrop-

sized DNA computer, using the DNA logic gates, will be more powerful

than the world's most powerful supercomputer. More than 10 trillion DNAmolecules can fit into an area no larger than 1 cubic centimeter (0.06 cubic

inches). With this small amount of DNA, a computer would be able to hold

10 terabytes of data, and perform 10 trillion calculations at a time. By

adding more DNA, more calculations could be performed.

Unlike conventional computers, DNA computers perform calculations

parallel to other calculations. Conventional computers operate linearly,

taking on tasks one at a time. It is parallel computing that allows DNA to

solve complex mathematical problems in hours, whereas it might take

electrical computers hundreds of years to complete them.

The first DNA computers are unlikely to feature word processing,

e-mailing and solitaire programs. Instead, their powerful computing power

will be used by national governments for cracking secret codes, or by

airlines wanting to map more efficient routes. Studying DNA computers

may also lead us to a better understanding of a more complex computer --

the human brain.


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8. Bibliography

Books

1. Adleman, L. 1994. Molecular computation of solutions to

combinatorial problems. Science 266:1021-1024.

2. Lipton, R. J. Speeding up computations via molecular biology.

(unpublished manuscript)

3. Boneh, D., Lipton, R. J. Making DNA computers error

resistant. (unpublished manuscript )

4. Kari, L. 1997. DNA computing: the arrival of biological

mathematics. (Unpublished manuscript).

5. Adleman, L. 1995. On constructing a molecular computer.

(unpublished manuscript )

Web Sites

1. www.usc.edu/dept/molecular-science/fm-papers.htm

2. www.arstechnica.com/reviews/2q00/dna

3. www.brooklynuniv.molacular.edu/dna_computer.html

4. www.hypography.com/article.cfm/32402.html

5. www.howstuffworks.com/computer/future

6. www.bioplanet.com/chat/discuss/messages/1095.htm

7. www.4tpgi.com.au/users/aoaug/dna_comp.html
http://www.usc.edu/dept/molecular-science/fm-papers.htmhttp://www.arstechnica.com/reviews/2q00/dnahttp://www.brooklynuniv.molacular.edu/dna_computer.htmlhttp://www.hypography.com/article.cfm/32402.htmlhttp://www.howstuffworks.com/computer/futurehttp://www.bioplanet.com/chat/discuss/messages/1095.htmhttp://www.4tpgi.com.au/users/aoaug/dna_comp.htmlhttp://www.usc.edu/dept/molecular-science/fm-papers.htmhttp://www.arstechnica.com/reviews/2q00/dnahttp://www.brooklynuniv.molacular.edu/dna_computer.htmlhttp://www.hypography.com/article.cfm/32402.htmlhttp://www.howstuffworks.com/computer/futurehttp://www.bioplanet.com/chat/discuss/messages/1095.htmhttp://www.4tpgi.com.au/users/aoaug/dna_comp.html


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Documents

Dna Final Report