Binary Counting with Chemical Reactions Aleksandra Kharam, Hua Jiang, Marc Riedel, and Keshab Parhi Electrical and Computer Engineering University of Minnesota
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Binary Counting with Chemical Reactions
Aleksandra Kharam, Hua Jiang, Marc Riedel, and Keshab Parhi
Binary Counting with Chemical Reactions
Aleksandra Kharam, Hua Jiang, Marc Riedel, and Keshab Parhi
Electrical and Computer Engineering University of Minnesota
Signal
10, 2, 12, 8, 4, 8, 10, 2, …
5, 6, 7, 10, 6, 6, 9, 6, …
1010 010100101100 01100111
input outputElectronicsChemicalReactions
Molecular computations
In ElectronicsIn Chemistry
Input
Output
Modeled by Ordinary Differential Equations:
input output
a c
Playing by The Rules
+k
b
cba
Principles of Binary Counting
Z Y X 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0
Z Y X 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0
Intuitive Model
Algorithm`
Xinj
Z Y X 0 0 0
Prereactants and Absence Indicators
Molecular Type X
Absence indicator ax
Prereactants and Absence Indicators
Molecular Type X
Absence indicator ax
Prereactant Xp
Prereactant for the next type Yp
Modified Algorithm
Three-Phase Synchronization
But how do we know that agroup of molecules is absent
?
R
r
Basic Algorithm Three-Phase Synchronization
Three-Phase Synchronization
Final Design
Simulation Results
zx Mapping to Experimental Chassis Mapping to Experimental Chassis
Auxiliary ComplexesReactants Products
* D. Soloveichik et al: “DNA as a Universal Substrate for Chemical Kinetics.” PNAS, Mar 2010
Conclusion
Robustness: - the design is rate independent.
Future and related work: - generalizing to n-bit counter;
- borrowing idea from digital logic (edge triggered clock );
- computing variety of functions
Questions?Questions?Thanks to PSB organizers,Thanks to PSB organizers,
NSF, BICB, and UROPNSF, BICB, and UROP
NSF CAREER Award #0845650NSF EAGER Grant #0946601
Biomedical Informatics & Computational Biology
UMN / Mayo Clinic / IBM
Some additional slidesSome additional slides
Synchronization
Three-Phase Synchronization
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