Stochastic Computing with BStochastic Computing with Biomolecular Automataiomolecular Automata

Advanced Artificial IntelligenceAdvanced Artificial IntelligenceCho, Sung BumCho, Sung Bum

ContentsContents

• Introduction Introduction

•Material & MethodsMaterial & Methods

•Results & DiscussionResults & Discussion

IntroductionIntroduction

• Why stochastic computing ?

• Deterministic Vs Stochastic finite automata

• Deterministic finite automata through biomolecular computation

• Goal of this article

Stochastic ComputingStochastic Computing

• The core recurring step of stochastic computation -> choice between several choice between several alternative computation paths, each with alternative computation paths, each with a prescribed probabilitya prescribed probability

• Useful in the analysis of biological Useful in the analysis of biological informationinformation

• Digital computers →→ realized stochastic realized stochastic choice in a costly and indirect way choice in a costly and indirect way

Deterministic Vs Deterministic Vs Stochastic finite Stochastic finite

automataautomata

• Deterministic finite automata

• Stochastic finite automata

Biomolecular DFABiomolecular DFA

• Benenson et al. 2001, 2003

• Hardware – restriction enzyme ( FokI ) Software – input, software, output sequences

Goal of This StudyGoal 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 concenby the relative molar concentration of the software moleculetration of the software molecule encoding that transition

Material & MethodsMaterial & Methods

• Assembly of ComponentsAssembly of Components

• Calibration ReactionCalibration Reaction

• Computation ReactionComputation Reaction

• Calculation of Transition ProbabilitiesCalculation of Transition Probabilities

• Determining the Deviation of Determining the Deviation of Predicted ResultsPredicted Results

Assembly of the Assembly of the ComponentsComponents

• Software & Input molecule ; single stranded synthetic oligonucleotides

• Label molecule carboxyfluorescein at 3’ end CY5 at 5’ end

Calibration ReactionCalibration Reaction

• To determine the relationship between concentration of transition molecule and probabilities of transition

• Sequences for calibration ; aaab, bbba

Calibration ReactionCalibration 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 Computation ReactionReaction

• Input, software and hardware molecule → 0.1 : 2 :20.1 : 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 Calculation of Transition ProbabilitiesTransition 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

• Program 1,2,3 for training set => 450 times of optimization450 times of optimization & additional 449 optimizations with random initial valuesadditional 449 optimizations with random initial values →among the calculated transitional probabilities, the most among the calculated transitional probabilities, the most

consistent triplet-of-transition probability set was selectedconsistent triplet-of-transition probability set was selected

Determining the Determining the Deviation of Predicted Deviation of Predicted

ResultsResults• Determination of the standard deviation of the predict

ed output ratio → by simulating all possible independby simulating all possible independent pipetting errors of 5 % with the same possibilitiesent 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 close to the predicted value with no deviationwith no deviation

Results & Discussion Results & Discussion -1-1

• The main idea of this study The main idea of this study ; ; the probability to obtain a particular the probability to obtain a particular

final state can be measured directly final state can be measured directly from the relative concentration of the from the relative concentration of the output molecule encoding this stateoutput molecule encoding this state

• The key problem The key problem ; ; determine the functiondetermine the function linking linking

relative concentrations of competing relative concentrations of competing transition molecules to the transition molecules to the probability of a chosen transition probability of a chosen transition

Results of Calibration Results of Calibration Reaction -1Reaction -1

• T4 & T8 software molecule → higher reaction rate thigher reaction rate than T3 & T7:reason for cohan T3 & T7:reason for convexitynvexity

• The mistake of FokI →clecleave one nt further than exave one nt further than expectedpected : S1 to S0, S0 to dead-end

Results of Calibration Results of Calibration Reaction -2Reaction -2

• Experiment for Experiment for verifying that the verifying that the system is in-system is in-sensitive to the sensitive to the concentration of concentration of input moleculeinput molecule

• The computation The computation is is insensitive to insensitive to the different input the different input molecule molecule concentrationconcentration

Results of Results of Calibration Reaction Calibration Reaction

-3-3• Experiment for

ensuring that the transition probability is not affected by absolute molecular concentration

• Transition probability → insensitive to insensitive to concentration of concentration of transition moleculetransition molecule

Results of Computation Results of Computation Reaction-1Reaction-1

• Four programs with the same structure & different transition probabilities on nine inputs

Results of Computation Results of Computation Reaction-2Reaction-2

• Good correlation Good correlation was observedwas observed between between predicted and predicted and measured results measured results by using by using measured measured transition transition probabilitiesprobabilities

• 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 to some some error in the method of direct probability measerror in the method of direct probability measurementurement

• A strong correlation exist between the SD of between the SD of predicted output probability and the differencpredicted output probability and the difference between measured and predicted output pre between measured and predicted output probabilitiesobabilities

Results of Computation Results of Computation Reaction-3Reaction-3

ConclusionConclusion

• A good fit between predicted and A good fit between predicted and measured computation output measured computation output using calculated probabilities using calculated probabilities

• The transition probability The transition probability associated with a given relative associated with a given relative concentration of a software concentration of a software molecule is a dependable molecule is a dependable programming toolprogramming tool