An evolutionary Monte Carlo algorithm for predicting DNA hybridization

1. An evolutionary Monte Carlo algorithm for predicting DNA hybridization JoonShik Kim et al. (2008) 11.05.06.(Fri) Computational Modeling of Intelligence JoonShik Kim

2. Neuron and Analog Computing Analog Computing Neuron

3. Spin glass system Spin Glass <S>= Tanh(J<S>+Ø) :Mean field theory

4. Hopfield Model

5. DNA Computing as a Spin Glass P∝Exp(-ΣJijSiSj) Many DNA neighbor moleculesin 3D enables the system to resemble thespin glass. Microbes in deep sea

6. Adaptive steepest descent Evolutionary MCMC for DNA Boltzmann machine Natural gradient Hopfield model Simulated annealing Deterministic steepest descent Stochastic annealing Spin glass Ising model

7. I. Simulating the DNA hybridization with evolutionary algorithm of Metropolis and simulated annealing.

8. 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.

9. Theory (1/2) • Boltzmann distribution is the one that • maximizes the sum of entropies ofboth • 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.

10. 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)

11. 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.

12. Target dsDNA (double stranded DNA) • 6 types of ssDNA Sequence (from 5’ to 3’) Axiom ㄱQ V ㄱP V R CGTACGTACGCTGAA CTGCCTTGCGTTGAC TGCGTTCATTGTATG Q V ㄱT V ㄱS TTCAGCGTACGTACG TCAATTTGCGTCAAT TGGTCGCTACTGCTT S AAGCAGTAGCGACCA T ATTGACGCAAATTGA P GTCAACGCAAGGCAG ㄱR CATACAATGAACGCA • Target dsDNA (The arrows are from 5’ to 3’)

13. Simulation Results (1/2) • The number of bonds vs. temperature

14. Simulation Results (2/2) • The number of target dsDNA • (double stranded DNA) vs. temperature

15. Wet-Lab experiment results (1/2) • SYBR Green I fluorescent intensity • as the cooling of the system

16. Wet-Lab experiment results (2/2) • Gel electrophoresis of cooled DNA solution

17. Why theorem proving? • Resolution refutation • p→q  ㄱp v q • S Λ T → Q, P Λ Q →R, S, T, P then R? 1. Negate R 2. Make a resolution on every axioms. 3. Target dsDNA is a null and its existence proves the theorem

18. Resolution refutation • Resolution tree • (ㄱQ V ㄱP V R) Λ Q ㄱP V R