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

Contents IntroductionIntroduction Material & MethodsMaterial & Methods Results & DiscussionResults & Discussion

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

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

Deterministic Vs Stochastic finite automata Deterministic finite automata Stochastic finite automata

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

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

Material & Methods Assembly of ComponentsAssembly of Components Calibration ReactionCalibration Reaction Computation ReactionComputation Reaction Calculation of Transition ProbabilitiesCalculation of Transition Probabilities Determining the Deviation of Predicted ResultsDetermining the Deviation of Predicted Results

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

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

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

Computation Reaction Input, software and hardware molecule 0.1 : 2 :2 → 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)

Calculation of Transition Probabilities By using measured output distributionBy 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 450 times of optimizationProgram 1,2,3 for training set => 450 times of optimization additional 449 optimizations with random initial values & additional 449 optimizations with random initial values among the calculated transitional probabilities, the most consistent triplet-of-transition probability set was selected →among the calculated transitional probabilities, the most consistent triplet-of-transition probability set was selected

Determining the Deviation of Predicted Results by simulating all possible independent pipetting errors of 5 % with the same possibilitiesDetermination 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 close to the predicted value with no deviation6,561 (3 8 ) different combination → the average of the set was very close to the predicted value with no deviation

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

Results of Calibration Reaction -1 higher reaction rate than T3 & T7:reason for convexityT4 & T8 software molecule → higher reaction rate than T3 & T7:reason for convexity cleave one nt further than expectedThe mistake of FokI →cleave one nt further than expected : S1 to S0, S0 to dead-end

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

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

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

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

A number of measured results fell outside of the expected error range and were consistently lower than the prediction some error in the method of direct probability measurementNot solely pitteting error, but rather to some error in the method of direct probability measurement between the SD of predicted output probability and the difference between measured and predicted output probabilitiesA strong correlation exist between the SD of predicted output probability and the difference between measured and predicted output probabilities Results of Computation Reaction-3

Conclusion A good fit between predicted and measured computation output using calculated probabilitiesA 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 toolThe transition probability associated with a given relative concentration of a software molecule is a dependable programming tool