DNA Computing Units Based on Fractional Coding

  • Sayed Ahmad SalehiEmail author
  • Peyton Moore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)


Fractional encoding has been recently proposed as a promising convention to represent information in molecular computing systems. This paper presents new 2-input molecular computing units based on unipolar fractional representation. The units calculate simple computational equations that can be used for the computation of more complex functions. The design of these molecular computing units is inspired by fan-in 2 logic gates in the field of stochastic computing. Each computing unit consists of four chemical reactions with two reactants and one product. We design the DNA reactions implementing the chemical reactions of each unit based on the toehold-mediated DNA strand-displacement mechanism. Every unit is designed by four input strands and eight fuel gate strands of DNA. Since DNA molecules related to the input and output of the units have the same form of domain-toehold-domain-toehold, output molecules of each unit can be used as input for other units and this provides the cascading of the units for designing complex circuits. The whole DNA pathway for each unit is composed of twenty DNA reactions. The simulation results by Visual DSD show that the DNA implementations follow the theoretically expected computations of each unit with the maximum of 9.33% error.


DNA computing Fractional coding DNA strand-displacement 



This work was supported by the “UK ECE Undergraduate Research Fellowship”.


  1. 1.
    Chen, H., Doty, D., Soloveichik, D.: Rate-independent computation in continuous chemical reaction networks. In: Conference on Innovations in Theoretical Computer Science, pp. 313–326 (2014)Google Scholar
  2. 2.
    Cardelli, et al.: Chemical reaction network designs for asynchronous logic circuits. Nat. Comput. 17, 109–130 (2018)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Salehi, S.A., Parhi, K.K., Riedel, M.D.: Chemical reaction networks for computing polynomials. ACS Synth. Biol. 6(1), 76–83 (2017)CrossRefGoogle Scholar
  4. 4.
    Chen, H.L., Doty, D., Soloveichik, D.: Deterministic function computation with chemical reaction networks. Nat. Comput. 13, 517–534 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chalk, C., Kornerup, N., Reeves, W., Soloveichik, D.: Composable rate-independent computation in continuous chemical reaction networks. In: 16th International Conference on Computational Methods in Systems Biology (CMSB) (2018)CrossRefGoogle Scholar
  6. 6.
    Doty, D., Hajiaghayi, M.: Leaderless deterministic chemical reaction networks. Natural Comput. 14(2), 213–223 24 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cummings, R., Doty, D., Soloveichik, D.: Probability 1 computation with chemical reaction networks. Nat. Comput. 15(2), 245–261 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chen, H.L., Cummings, R., Doty, D., Soloveichik, D.: Speed faults in computation by chemical reaction networks. Distrib. Comput. 30(5), 373–390 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chou, C.T.: Chemical reaction networks for computing logarithm. Synthetic Biol. 2(1), ysx002 (2017)CrossRefGoogle Scholar
  10. 10.
    Qian, L., Soloveichik, D., Winfree, E.: Efficient turing-universal computation with dna polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 2010. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011). Scholar
  11. 11.
    Salehi, S.A., Liu, X., Riedel, M.D., Parhi, K.K.: Computing mathematical functions using DNA via fractional coding, Scientific Reports, vol. 8, Article 8312, May 2018Google Scholar
  12. 12.
    Gaines, B.R.: Stochastic Computing. In: Proceedings of AFIPS Spring Joint Computer Conference, pp. 149–156. ACM (1967)Google Scholar
  13. 13.
    Poppelbaum, W.J., Afuso, C., Esch. J.W.: Stochastic computing elements and systems. In: Proceedings of the Joint Computer Conference, AFIPS 1967 (Fall), pp. 635–644. ACM, New York (1967)Google Scholar
  14. 14.
    Gaines, B.R.: Stochastic computing systems. In: Tou, J.T. (ed.) Advances in Information Systems Science, pp. 37–172. Springer, Boston (1969). Scholar
  15. 15.
    Salehi, S.A., Liu, Y., Riedel, M., Parhi, K.K.: Computing polynomials with positive coefficients using stochastic logic by DoubleNAND expansion. In: Proceedings of the 2017 ACM Great Lakes Symposium on VLSI (GLSVLSI), pp. 471–474 (2017)Google Scholar
  16. 16.
    Yurke, B., Turberfeld, A.J., Mills, A.P., Simmel, F.C., Neumann, J.L.: A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000)CrossRefGoogle Scholar
  17. 17.
    Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. PNAS 107(12), 5393–5398 (2010)CrossRefGoogle Scholar
  18. 18.
    Lakin, M.R., Youssef, S., Polo, F., Emmott, S., Phillips, A.: Visual DSD: a design and analysis tool for DNA strand displacement systems. Bioinformatics 27, 3211–3213 (2011)CrossRefGoogle Scholar
  19. 19.
  20. 20.
    Chen, Y.J., et al.: Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8, 755–762 (2013)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.University of KentuckyLexingtonUSA

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