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Dive into the principles of binary counting through chemical reactions, modeled by ordinary differential equations. Explore a fascinating algorithm involving pre-reactants, molecular types, and absence indicators, culminating in a robust final design with future potential extensions. This innovative approach combines molecular computations with signal processing in electronics.
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Binary Counting with Chemical ReactionsAleksandra Kharam, Hua Jiang, Marc Riedel, and KeshabParhi Electrical and Computer Engineering University of Minnesota
Molecular computations Signal In Chemistry In Electronics Input ChemicalReactions Electronics 1100 0010 1010 input output 0111 0101 0110 10, 2, 12, 8, 4, 8, 10, 2, … Output 5, 6, 7, 10, 6, 6, 9, 6, …
Playing by The Rules a c b input output k + a b c • Modeled by Ordinary Differential Equations:
Principles of Binary Counting 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 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
Algorithm ` Xinj 0 0 0
Prereactants and Absence Indicators Molecular Type X Absence indicator ax
Prereactants and Absence Indicators Molecular Type X Absence indicator ax PrereactantXp Prereactant for the next type Yp
Three-Phase Synchronization R But how do we know that a group of molecules is absent r ?
Basic Algorithm Three-Phase Synchronization
zx Mapping to Experimental Chassis Auxiliary Complexes Reactants 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? Thanks to PSB organizers, NSF, BICB, and UROP Biomedical Informatics & Computational BiologyUMN / Mayo Clinic / IBM NSF CAREER Award #0845650 NSF EAGER Grant #0946601
