Molecular Computation :
RNA solutions to chess problems
Dirk Faulhammer, Anthony R. Cukras, Richard J.
Lipton, and Laura F. Landweber
PNAS 2000; vol. 97: no. 4: 1385-1389
2004.11.20 Summarized by Seong Hwan Kim
Table of Contents
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“Knight Problem”
Key features
Preparation before experiment
Experiment
Result
Discussion
Knight Problem in Chess Game(1/2)
• ‘Knight ’ in chess game ?
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A piece in the game, depicted as a horse’s head
Plays and captures alternatively on white and black square
“Jumping” available  ignore any pieces in its moving path
Powerful at the center position rather than edge
Knight Problem in Chess Game(2/2)
• ‘Knight Problem ’ ?
– Knight tour problem
– Hamiltonian path problem in graph theory
• a variant of knight problem
– Asking a configuration of knights on a n x n chess board
– such as ‘no knight is attacking any other knight on the board ’
Key features
• Applying molecular computation algorithm
– To a 3x3 chessboard problem
– Using RNA library
– Searching RNA strands that fit the constraints
• Destructive algorithm with RNase H
– Instead of conventional hybridization extraction
– Hydrolyze RNA strands inappropriate for the solution constraints
– Using hybridization of RNA and complementary bit DNA
oligonucleotides as a hydrolysis marking
Preparation(1/6) : problem expression
• Knight problem expression
– 9 positions of 3x3 chessboard
– ‘no knight is attacking any other knight on the board ’
simplifying
Preparation(2/6) : solution expression
• RNA library
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Made through synthesis of DNA “Half Libraries”
A RNA strand means 10-bit solution
Contain 1024 different strands
10-bit library for a instance of a 9-bit problem
 Ignore any position that computes less reliably
Preparation(3/6) : Sequence Design
• 3 criteria
1) different bit encodings
– Maximizing Hamming Distances between different strands as
well as between different parts of individual strand
– <= 5 matches over a 20-nt window, both within and between
all 210 possible strands
– Average melting temperature of 45 ℃
2) Biased to avoid secondary structure
– Each bit position, equally accessible to the enzyme and DNA
– Using a three-letter alphabet : A, C, and U for the bits and
for the bits and spacers in the library
– Eliminating potential of G-C pair (G:U in RNA) as well as G
stacking
Preparation(4/6) : Sequence Design
• 3 criteria (Cont’d)
3) constraint for hybridization
– Avoid hybridization to themselves or to any other library
strands by more than 7 consecutive base pairs
– To avoid the interference made by inaccessibility of reagents
to the regions
• Computer program for design
– PERMUTE
– Published as supplemental material on the PNAS web site,
www.pnas.org
Preparation(5/6) : Sequence Design
• Sequence Design Result
1) sequence for each bit and spacer of the DNA library
Preparation(6/6) : Sequence Design
• Sequence Design Result (Cont’d)
2) sequence for each DNA bit oligonucleotide
Experiment (1/6) : Library Synthesis
1)
Synthesis of a 10-bit DNA library
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2)
Recursive mix and split strategy
Mix half libraries
Primer extension
Synthesis of a 10 bit RNA library
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From the previously synthesized DNA library
Synthesized by in vitro T7-transcription
Experiment (2/6) : Library Synthesis (Cont’d)
 Modular construction of
the combinatorial DNA library
from two half-libraries
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One half
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From bit ‘f’ through ‘a’ to ‘prefix’
The other half
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From reverse complementary ‘f’
through ‘j’ to ‘suffix’
White box for “true”, or “1”
Black box for “false”, or “0”
Shadowed box for prefix, suffix,
and spacer sequences
Experiment (3/6) : RNA algorithm
<Algorithm>
1)
Prepare a test tube containing RNA pool
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2)
Bit operation for a clause in the rule
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3)
Dividing the initial RNA library into two test tubes
One for RNA of having a value ‘1’ at a specific bit position
The other for ‘0’
Target digestion by RNase H
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4)
5)
Initially encodes all 1024 possible 10-bit string
‘1’ or ‘0’ assigned to a specific bit position
Destroying inappropriate RNA strands in each tube
Combining resulting two tubes
repeat 2)~3) for the next OR clause in the rule
Readout the surviving strands
Experiment (4/6) : RNA algorithm
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Diagram for RNA algorithm
which illustrating start
from the proposition
followed by other
successive OR clauses
in the rule
Experiment (5/6) : RNA algorithm
<Experimental Methods>
Digestion of the RNA library by thermostable RNase H
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RNase H digests RNA strands in the presence of combination of DNA bit
oligonucleotides (a0,f1,h1;b0,g1,i1;…)
Spin-column chromatography and gel purification
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3)
Remove DNA bit oligonucleotides and short RNA digestion products
Remaining full-length RNA strands are purified by polyacrylamide gel
Reverse transcription and PCR
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Recovered RNA strands are reverse transcribed
Amplified by no more than five PCR cycles to reduce recombination events
Half of resulting DNA are transcribed in vitro for the next step in the algorithm
Readout by colony PCR followed multiplex linear PCR
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Creates a “bar code” for each strand
Allow rapid screening and recovery of individual library strands
Experiment (6/6) : RNA algorithm
<Experimental Methods> (Cont’d)
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Multiplex colony PCR readout
Result (1/3) : RNA solution
• Analysis
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43 clones are randomly chosen and interpreted by readout PCR
42 of them, solution for this version of “knight problem”
10 solutions occur more than once
Acquire 31 different solutions of unique board configuration with 1
illegal solution
• similar distribution as a random sampling of all 94 possible
solutions (higher numbers of knights modestly preferred)
• Other 64 solution are all variants of 30 solutions
Result (2/3) : RNA solution
• Analysis (Cont’d)
 31 unique boards
 Expected and observed
frequencies of boards
Result (3/3) : RNA solution
• Analysis (Cont’d)
• Illegal solution results from ineffective RNase H cleavage because
of an adjacent deletion and point mutation in bit 9
(TCCACTACTACCTA instead of TCCACCAACTACCTA)
• Main source of error is clusters of mutations in the same bit
positions
• Accurate size purification needed to reduce prevalence of such
deletion
Discussion
• 250 ~ 1015 : number of RNA molecules that in vitro
selection protocols can currently search
• Upper bound for the size of DNA or RNA computing
experiments that can use exhaustive search algorithm
• Same order as many interesting problem in computer
science
• Further works : Knight tour problem, rule finding