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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