Stochastic Computing with Biomolecular Automata

1. Stochastic Computing with Biomolecular Automata Advanced Artificial Intelligence Cho, Sung Bum

2. Contents • Introduction • Material & Methods • Results & Discussion

3. Introduction • Why stochastic computing ? • Deterministic Vs Stochastic finite automata • Deterministic finite automata through biomolecular computation • Goal of this article

4. Stochastic Computing • The core recurring step of stochastic computation ->choice between several alternative computation paths, each with a prescribed probability • Useful in the analysis of biological information • Digital computers→ realized stochastic choice in a costly and indirect way

5. Deterministic Vs Stochastic finite automata • Deterministic finite automata • Stochastic finite automata

7. Biomolecular DFA • Benenson et al. 2001, 2003 • Hardware – restriction enzyme ( FokI ) Software – input, software, output sequences

10. Goal of This Study • Designing principle for stochastic computer with unique properties of biomolecular computer • To realize the intended probability of each transition by the relative molar concentration of the software molecule encoding that transition

11. Material & Methods • Assembly of Components • Calibration Reaction • Computation Reaction • Calculation of Transition Probabilities • Determining the Deviation of Predicted Results

12. Assembly of the Components • Software & Input molecule ; single stranded synthetic oligonucleotides • Label molecule carboxyfluorescein at 3’ end CY5 at 5’ end

13. Calibration Reaction • To determine the relationship between concentration of transition molecule and probabilities of transition • Sequences for calibration ; aaab, bbba

14. Calibration Reaction • O.1 uM of four symbol inputs • O.5 uM of tested transition molecule (1.5 for deterministic & 0.5 for stochastic) • 2.0 uM of FokI enzyme • Detection of terminal state ; TYPHOON SCANNER CONTROL & IMAGEQUANT V 5.2 software

15. Computation Reaction • Input, software and hardware molecule → 0.1 : 2 :2 • Each pair of competing transition molecules → maintained at 0.5 uM • Software and hardware molecule → preincubated with FokI enzyme • Scanning CY 5 labeled band ( 16 ~ 17 nt long)

17. Calculation of Transition Probabilities • By using measured output distribution • Equation set for each given program, with transition possibilities as unknown variables. • A solution is an optimal set of transition probabilities minimizing the discrepancy between the calculated and the measured final state distribution • Program 1,2,3 for training set => 450 times of optimization & additional 449 optimizations with random initial values →among the calculated transitional probabilities, the most consistent triplet-of-transition probability set was selected

18. Determining the Deviation of Predicted Results • Determination of the standard deviation of the predicted output ratio → by simulating all possible independent pipetting errors of 5 % with the same possibilities • Discrete deviations of –5%, 0%, and 5% form the nominal volume of each software molecule solution • 6,561 (38) different combination → the average of the set was very close to the predicted value with no deviation

19. Results & Discussion -1 • The main idea of this study ; the probability to obtain a particular final state can be measured directly from the relative concentration of the output molecule encoding this state • The key problem ; determine the function linking relative concentrations of competing transition molecules to the probability of a chosen transition

20. Results of Calibration Reaction -1 • T4 & T8 software molecule→ higher reaction rate than T3 & T7:reason for convexity • The mistake of FokI →cleave one nt further than expected : S1 to S0, S0 to dead-end

21. Results of Calibration Reaction -2 • Experiment for verifying that the system is in-sensitive to the concentration of input molecule • The computation is insensitive to the different input molecule concentration

22. Results of Calibration Reaction -3 • Experiment for ensuring that the transition probability is not affected by absolute molecular concentration • Transition probability → insensitive to concentration of transition molecule

23. Results of Computation Reaction-1 • Four programs with the same structure & different transition probabilities on nine inputs

24. Results of Computation Reaction-2 • Good correlation was observed between predicted and measured results by using measured transition probabilities

26. Results of Computation Reaction-3 • A number of measured results fell outside of the expected error range and were consistently lower than the prediction • Not solely pitteting error, but rather tosome error in the method of direct probability measurement • A strong correlation existbetween the SD of predicted output probability and the difference between measured and predicted output probabilities

28. Conclusion • A good fit between predicted and measured computation output using calculated probabilities • The transition probability associated with a given relative concentration of a software molecule is a dependable programming tool