Computing Beyond Silicon Valley Summer School at Caltech

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Computing Beyond Silicon Valley Summer School at
Caltech

• Science undergraduate students were brought
  together to interact and understand the
  connections between computer science and other
  disciplines
• Gestalt principle
• Physics of Computation, Molecular Computing,
  Biomolecular Computing, and Quantum Computing
• A month in Pasadena

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Branching in Biological Models of Computation

• Blair Andres-Beck, Vera Bereg, Stephanie Lee,
• Mike Lindmark, Wojciech Makowiecki

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Branching in DNA Computation

• Chose several models of DNA computation (in
  particular the sticker model and DNA solution to
  small SAT problems)
• Examined the implementation of ifelse statements
  and looping
• Branching allows easier mapping of conventional
  algorithms

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Design Criteria

• Any change must preserve the existing
  functionality of the model
• Branching
• Operation selection based on current data and
  instruction
• Looping
• Further instructions based on test condition
• Nested loops that is, looping that doesnt rely
  on a single marker

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The Sticker Model

• Presented in A Sticker Based Model for DNA
  Computation (1996)
• Two types of ssDNA molecules
• memory strand
• complimentary stickers
• Four operations allow universal computation
• set, clear, separate and combine
• Parallel processing/computation
• Robotic assistance needed

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Bit Representation
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Set and Clear
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Combine and Separate
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Simple branching and looping in the Sticker Model

• Idea use current mechanical operations to do
  branching (if else) and looping

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Branching with existing operations

• Perform a separate operation based on evaluation
  of branch condition
• Act on each vial independently
• If statement carried out on true, else on
  false
• Recombine vials after if statement
• Note a vial is a small beaker

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Branching and Looping procedures
Example of usage Minimal Set Cover problem
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Looping with existing operations

• Test for loop condition
• Fluorescent markers
• Can be detected by the robotic assistant
• Can have more than one type, allowing nested
  looping
• Choose next instruction based on presence or
  absence of fluorescence
• Problems
• Slow (as the separate operation is difficult and
  slow)
• Reliance on intervention outside the beaker
  (cant mix, shake and get the answer)
• Experimental error (eg. some florescence already
  present)

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Branching through DNA Transcriptional Logic

• Idea use an OR gate for branching ?

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DNA Transcriptional Logic

• How it works
• Transcription factor binds to the promoter region
• Activated by enzyme RNA Polymerase RNAP
• Unwinds DNA, makes RNA until terminator is
  reached
• input and output are programmable!

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Implementation of Branching

• The OR gate allows the if-else statement to end
  and the program to continue

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Definition of Branching

• Branching allows for conditional if-else
  statements
• if (condition)
• output 1
• else
• output 2
• continuation

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Properties of the Branching

• Pros
• Programmable input
• Easy to track progress (by taking a sample and
  approximating the concentrations of outputs)
• Does not require outside intervention
• Cons
• Does not allow parallelism
• Inefficient and fairly slow (although speed can
  be controlled)
• Requires large number of promoter -transcription
  factor pairs

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Smart drug or DNA automata combined with
Sticker Model
Idea use if else statements from Smart drug
model (with stickers instead of drugs)
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Automata

• Automata
• Machine that accepts strings over specific
  alphabet that are in its language
• Computation terminates on processing last string
  symbol
• Accepts input if terminates in accepting state

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Smart Drug

• Basic Idea transport diagnosis and drug delivery
  (suppression) stages into the cell
  
  
• No robotic intervention what-so-ever
• Basic if else statements, thus can do
  branching! ?
• Automata with
• Hardware (restriction nuclease, ligase, FolkI)
• Software and input (dsDNA molecules and dsDNA
  with a hairpin structure at end)
• In vitro

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Smart Drug
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Smart drug and Sticker Model

• Sticker model
• Memory strand with on/off regions for bits
• Drug model
• Coded instructions plus coded input with a
  sticker as hairpin (software and input)
• Reusable rules (hardware)
• If (ruletrue) ? release sticker
• Can do anti-stickers to clear off bits as well ?
• Thus SISD model
• By varying code and subset of rules can change
  the outcome of the computation

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Pros and Cons

• Less mechanical operations used
• Separation procedure might not be needed
• Could possibly get rid of them all together?
• Eliminates one of the positive sides of sticker
  model (no enzymes), but our enzymes are reusable
  (hardware)
• Have SISD, can do MIMD?
• How to ensure that each code is related to its
  specific data molecule?
• Do we need to ensure this at all?
  Randomize?
• Do the environments fit?

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Branching in the Sticker Model using DNA
Instructions

• The Idea Store the program with the data, run
  all the programs independently.

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Basic Ideas

• Encode instructions into DNA
• Create a DNA program counter
• Each DNA computes cycle
• Separate strands based on next instruction
• Perform operation
• Increment PC

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Changes to the Sticker Model

• Instruction strand head instruction
  data connector
• Instruction instr code operand code

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Changes to the Sticker Model

• Add connector to data strand
• Addition of PC strands

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Changes to the Sticker Model

• Introduction of halt
• No explicit combine or separate operations
• Use of operation selectors

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Adding Looping

• Looping by restarting the PC
• Loop operation
• Clears off PC using complement PC strands
• if (stage1)
• if (NOT done)
• loop
• stage1 false

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Adding Branching

• Add IF instruction code
• Use End-If IF operation
• Operation selectors with solid-bound stickers
• Trapped strands enter branching cycle
• Addition of excess PC and Step strands (excluding
  PC End-If IF strands)
• Flow by End-If IF selectors
• Return trapped strands

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The Strands
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Advantages

• Reusability of data, pc, start, step, and
  selector strands
• Simple programmability
• Imagine building strand from instruction pieces
• Ability to run more than one program concurrently
• Thousands of problems at the same time

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Disadvantages

• Large error rate vs. long cycle time
• Must perform several separations per cycle
• No ability to do error correction
• Large number of unique sequences needed

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Exploring Branching in SAT problems

• Idea use ssDNA as clauses for the SAT problem
  (Adelman et al)

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Exploring Branching in SAT problems

• Works in parallel checking all the solutions at
  once
• If the solution is not valid (the variables in it
  contradict each other and thus the clause can not
  be resolved) then folds on itself
• An if statement acts on each clause at the same
  time!
• Disadvantages
• high error rates (esp. with increase of
  variables)
• can not be done past 20 variables

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Conclusion and future goals/work

• Have tried to list and describe different ways
  that branching in DNA computing can be thought of
  and realized as.
• There are limitations and barriers that each one
  of the described here models has, however, they
  all have their advantages, benefits and purposes.
  
• Moving beyond convertional computers and applying
  Gestalte principle whenever possible
• Have fun.

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References

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  solutions to combinatorial problems." Science.
  226 (1994) 1021--1024.
• .Adelman, Leonard, et al. Solutions of
  20-Variable 3-SAT Problem on a DNA Computer.
  Science. 296(2002) 499--502.
• .Benenson, Yaakov, et al. An autonomous
  molecular computer for logical control of gene
  expression. Nature. 429(2004) 423428.
• .Benenson, Yaakov, et al. Programmable and
  autonomous computing machine made of
  biomolecules. Nature. 414(2001) 430434.
• .Campbell, Neil A., Jane B. Reece, and Lawrence
  G. Mitchell. Biology, 5th edition. Menlo Park
  Benjamin Cummings, 1999.
• .Condon, Anne. Automata make antisense. Nature.
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• .Karp, R, et al. Error-resilient DNA
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• .Lauria, Mario, Kaustubh Bhalerao, Muthu M.
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  biochemical CPU based on DNA transcription
  logic." 3rd Workshop on Non-Silicon Computation
  (NSC-3), Munich, June 2004.
• .Lipton, C. et al. DNA Based Computers II
  DIMACS. 44(1999) 163170.
• .Lipton, R. Using DNA to Solve NP-Complete
  Problems. Science. 268(1995) 542--545.
• .Liu, Q, et al. DNA computing on surfaces.
  Nature. 403(2000) 175.
• .Lloyd et al. DNA computing on a chip. Nature.
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• .Roweis, Sam, et al. A Sticker Model for DNA
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• .Tan, W, et al. Molecular beacons for DNA
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