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

2 Neuron and Analog Computing Neuron Analog Computing

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

Hopfield Model

5 DNA Computing as a Spin Glass Microbes in deep sea P ∝ Exp (-ΣJ ij S i S j ) Many DNA neighbor molecules in 3D enables the system to resemble the spin glass.

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

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 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.

10 Theory (2/2) We adopted above evolutionary algorithm for simulating the hybridization of DNA molecules. We used only four parameters, ∆H G-C = 9.0 kcal/MBP (mole base pair), ∆H A-T = 7.2 kcal/MBP, ∆H other = 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 Inspect the number of target dsDNA and the number of bonds.

12 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’)

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  ㄱ p 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 ( ㄱ Q V ㄱ P V R) Λ Q  ㄱ P V R