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