Stochastic Computing with
Biomolecular Automata
Advanced Artificial Intelligence
Cho, Sung Bum
Contents
• Introduction
• Material & Methods
• Results & Discussion
Introduction
• Why stochastic computing ?
• Deterministic Vs Stochastic finite
automata
• Deterministic finite automata through
biomolecular computation
• Goal of this article
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
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
• To realize the intended probability of
each transition by the relative molar
concentration of the software molecule
encoding that transition
Material & Methods
• Assembly of Components
• Calibration Reaction
• Computation Reaction
• Calculation of Transition Probabilities
• Determining 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
• 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 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
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
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
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
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
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
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
probabilities
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 to some
error in the method of direct probability
measurement
• A strong correlation exist between the SD of
predicted output probability and the
difference between measured and predicted
output probabilities
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