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An evolutionary Monte Carlo algorithm for predicting DNA hybridization
Joon Shik Kim et al. (2008)11.05.06.(Fri)
Computational Modeling of IntelligenceJoon Shik Kim
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Neuron and Analog Computing
Neuron Analog Computing
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Spin glass system
Spin Glass
<S>=Tanh(J<S>+Ø):Mean field theory
Hopfield Model
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DNA Computing as a Spin Glass
Microbes in deep sea
P Exp∝ (-ΣJijSiSj)
Many DNA neighbormolecules in 3Denables the system toresemble the spin glass.
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Ising model
Spin glass
Stochasticannealing
Deterministicsteepestdescent
Simulated annealing
Boltzmann machine
Evolutionary MCMC for DNA
Hopfield model
Natural gradient
Adaptive steepestdescent
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I. Simulating the DNA hybridization with evolutionary algorithm of Metropolis and simulated annealing.
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Introduction
• We devised a novel evolutionary algorithm applicable to DNA nanoassembly, biochip, and DNA computing.
• Silicon based results match well the fluorometry and gel electrophoresis biochemistry experiment.
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Theory (1/2) • Boltzmann distribution is the one that maximizes the sum of entropies of both the system and the environment.
• Metropolis algorithm drives the system into Boltzmann distribution and simulated annealing drives the system into lowest Gibbs free energy state by slow cooling of the whole system.
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Theory (2/2)
• We adopted above evolutionary algorithm for simulating the hybridization of DNA molecules.
• We used only four parameters, ∆HG-C = 9.0 kcal/MBP (mole base pair), ∆HA-T = 7.2 kcal/MBP, ∆Hother = 5.4 kcal/MBP, ∆S = 23 cal/(MBP deg).From (Klump and Ackermann, 1971)
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Algorithm
• 1. Randomly choose i-th and j-th ssDNA (single stranded DNA).• 2. Randomly try an assembly with Metropolis acceptance min(1, e-∆G/kT).• 3. We take into account of the detaching process also with Metropolis acceptance.• 4. If whole system is in equilibrium then decrease the temperature and repeat process 1-3.• 5. Inspect the number of target dsDNA and the number of bonds.
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Target dsDNA (double stranded DNA)
ㄱ Q V ㄱ P V R CGTACGTACGCTGAA CTGCCTTGCGTTGAC TGCGTTCATTGTATG Q V ㄱ T V ㄱ S TTCAGCGTACGTACG TCAATTTGCGTCAAT TGGTCGCTACTGCTT S AAGCAGTAGCGACCA T ATTGACGCAAATTGA P GTCAACGCAAGGCAG ㄱ R CATACAATGAACGCA
Axiom Sequence (from 5’ to 3’)• 6 types of ssDNA
• Target dsDNA (The arrows are from 5’ to 3’)
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Simulation Results (1/2)
• The number of bonds vs. temperature
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Simulation Results (2/2)
• The number of target dsDNA (double stranded DNA) vs. temperature
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Wet-Lab experiment results (1/2)
• SYBR Green I fluorescent intensity as the cooling of the system
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Wet-Lab experiment results (2/2)
• Gel electrophoresis of cooled DNA solution
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Why theorem proving?
Resolution refutation
p→q ㄱ p v q
S Λ T → Q, P Λ Q →R, S, T, P then R?1. Negate R2. Make a resolution on every axioms.3. Target dsDNA is a null and its existence proves the theorem
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Resolution refutationResolution tree
( ㄱ Q V ㄱ P V R) Λ Q ㄱ P V R