Skip to main content

On Improving the Expressive Power of Chemical Computation

  • Chapter
  • First Online:
Advances in Unconventional Computing

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 22))

Abstract

The term chemical computation describes information processing setups where an arbitrary reaction system is used to perform information processing. The reaction system consists of a set of reactants and a reaction volume that harbours all chemicals. It has been argued that this type of computation is in principle Turing complete: for any computable function a suitable chemical system can be constructed that implements it. Turing completeness cannot be strictly guaranteed due to the inherent stochasticity of chemical reaction dynamics. The computation process can end prematurely or branch off in the wrong direction. The frequency of such errors defines the so-called fail rate of chemical computation. In this chapter we review recent advances in the field, and also suggest a few novel generic design principles which, when adhered to, should enable engineers to build accurate chemical computers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    The results for d \(=\) 2,3 only qualitative since the results are not fully converged with respect to the size of the lattice. This analysis is illustrated briefly in Fig. 26.18.

  2. 2.

    We believe that the \(f_2\) values for \(d=2\) and \(d=3\) should be actually a bit higher due to lack of convergence for two \((d = 2)\) and three \((d = 3)\) dimensions with respect to the number of sites (cells) in the lattice.

  3. 3.

    The same problem with few successful while-loops arises. The specified numbers are for \(v_0=1\).

References

  1. Conrad, M.: Evolutionary learning circuits. J. Theor. Biol. 46, 167–188 (1974)

    Article  Google Scholar 

  2. Rosen, R.: Pattern generation in networks. Prog. Theor. Biol. 6, 161–209 (1981)

    Article  MathSciNet  Google Scholar 

  3. Kampfner, R.R., Conrad, M.: Sequential behavior and stability properties of enzymatic neuron networks. Bull. Math. Biol. 45, 969–980 (1983)

    Article  MATH  Google Scholar 

  4. Kirby, K.G., Conrad, M.: Intraneuronal dynamics as a substrate for evolutionary learning. Phys. D 22, 205–215 (1986)

    Article  MathSciNet  Google Scholar 

  5. Conrad, M.: Rapprochement of artificial-intelligence and dynamics. Eur. J. Op. Res. 30, 280–290 (1987)

    Article  MathSciNet  Google Scholar 

  6. Hjelmfelt, A., Weinberger, E.D., Ross, J.: Chemical implementation of neural networks and turing-machines. Proc. Natl. Acad. Sci. U. S. A. 88, 10983–10987 (1991)

    Article  MATH  Google Scholar 

  7. Hjelmfelt, A., Weinberger, E.D., Ross, J.: Chemical implementation of finite-state machines. Proc. Natl. Acad. Sci. U. S. A. 89, 383–387 (1992)

    Article  Google Scholar 

  8. Aoki, T., Kameyama, M., Higuchi, T.: Interconnection-free biomolecular computing. Computer 25, 41–50 (1992)

    Article  Google Scholar 

  9. Conrad, M.: Molecular computing - the lock-key paradigm. Computer 25, 11–20 (1992)

    Article  Google Scholar 

  10. Hjelmfelt, A., Ross, J.: Chemical implementation and thermodynamics of collective neural networks. Proc. Natl. Acad. Sci. U. S. A. 89, 388–391 (1992)

    Article  Google Scholar 

  11. Hjelmfelt, A., Schneider, F.W., Ross, J.: Pattern-recognition in coupled chemical kinetic systems. Science 260, 335–337 (1993)

    Article  Google Scholar 

  12. Hjelmfelt, A., Ross, J.: Mass-coupled chemical-systems with computational properties. J. Phys. Chem. 97, 7988–7992 (1993)

    Article  Google Scholar 

  13. Rambidi, N.G.: Biomolecular computer: roots and promises. Biosystems 44, 1–15 (1997)

    Article  Google Scholar 

  14. Rambidi, N.G., Maximychev, A.V.: Towards a biomolecular computer. information processing capabilities of biomolecular nonlinear dynamic media. Biosystems 41, 195–211 (1997)

    Article  Google Scholar 

  15. Conrad, M., Zauner, K.P.: Dna as a vehicle for the self-assembly model of computing. Biosystems 45, 59–66 (1998)

    Article  Google Scholar 

  16. Hiratsuka, M., Aoki, T., Higuchi, T.: Enzyme transistor circuits for reaction-diffusion computing. IEEE Trans. Circuits Syst. I-Fundam. Theory Appl. 46, 294–303 (1999)

    Article  Google Scholar 

  17. Stange, P., Zanette, D., Mikhailov, A., Hess, B.: Self-organizing molecular networks. Biophys. Chem. 79, 233–247 (1999)

    Article  MATH  Google Scholar 

  18. Simpson, M.L., Sayler, G.S., Fleming, J.T., Applegate, B.: Whole-cell biocomputing. Trends Biotechnol. 19, 317–323 (2001)

    Article  Google Scholar 

  19. Winfree, E.: Dna computing by self-assembly. Natl. Acad. Eng.: The Bridge 33, 31–38 (2003)

    Google Scholar 

  20. Lizana, L., Konkoli, Z., Orwar, O.: Tunable filtering of chemical signals in a simple nanoscale reaction-diffusion network. J. Phys. Chem. B 111, 6214–6219 (2007)

    Article  Google Scholar 

  21. Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Nat. Comput. 7, 615–633 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Soloveichik, D., Seelig, G., Winfree, E.: Dna as a universal substrate for chemical kinetics. Proc. Natl. Acad. Sci. 107, 5393–5398 (2010)

    Article  Google Scholar 

  23. Jiang, H., Riedel, M.D., Parhi, K.K.: Digital logic with molecular reactions. 2013 IEEE/Acm International Conference on Computer-Aided Design. ICCAD-IEEE ACM International Conference on Computer-Aided Design, pp. 721–727. IEEE, New York (2013)

    Google Scholar 

  24. Cummings, R., Doty, D., Soloveichik D.: Probability 1 computation with chemical reaction networks. In: Murata, S., Kobayashi, S., (eds.) DNA Computing and Molecular Programming, Lecture Notes in Computer Science, vol. 8727, pp. 37–52. Springer International Publishing, Berlin (2014)

    Google Scholar 

  25. Sienko, T., Adamatzky, A., Rambidi, N.G., Conrad, M.: Molecular Computing. MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  26. Cardelli, L.: On process rate semantics. Theor. Comput. Sci. 391, 190–215 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Krivine, J., Danos, V., Benecke, A.: Modelling epigenetic information maintenance: A kappa tutorial. In: Bouajjani, A., Maler, O. (eds.) Computer Aided Verification. Proceedings, volume 5643 of Lecture Notes in Computer Science, pp. 17–32. Springer, Berlin (2009)

    Chapter  Google Scholar 

  28. Degano, P., Bracciali, A.: Process calculi, systems biology and artificial chemistry. Handb. Nat. Comput. 3, 1863–1896 (2012)

    Article  Google Scholar 

  29. Liekens, A.M.L., Fernando, C.T.: Turing complete catalytic particle computers. In: Costa, F.A.E., Rocha, L.M., Costa, E., Harvey, I., Coutinho, A. (eds.) Advances in Artificial Life, Proceedings, volume 4648 of Lecture Notes in Artificial Intelligence, pp. 1202–1211 (2007)

    Google Scholar 

  30. Cardelli, L., Zavattaro, G.: On the computational power of biochemistry. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds.) Algebraic Biology. Proceedings, volume 5147 of Lecture Notes in Computer Science, pp. 65–80. Springer, Berlin (2008)

    Chapter  Google Scholar 

  31. Liekens, A., Fernando, T: Turing Complete Catalytic Computers. In: Advances in Artificial life, vol. 4648, pp. 1202–1211. Springer, Berlin (2007)

    Google Scholar 

  32. Konkoli, Z.: Diffusion controlled reactions, fluctuation dominated kinetics, and living cell biochemistry. Int. J. Softw. Inform. 7, 675 (2013)

    Google Scholar 

  33. Konkoli, Z.: Modeling reaction noise with a desired accuracy by using the x level approach reaction noise estimator (xarnes) method. J. Theor. Biol. 305, 1–14 (2012)

    Article  MathSciNet  Google Scholar 

  34. Singh, A., Hespanha, J.P.: A derivative matching approach to moment closure for the stochastic logistic model. Bull. Math. Biol. 69, 1909–1925 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. Privman, V.: Nonequilibrium Statistical Mechanics in One Dimension. Cambridge Univ. Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  36. Brookshear, G., Brylow, D.: Computer Science: An Overwiew, 11th edn. Addison-Wesley, Boston (2003)

    Google Scholar 

  37. Van Kampen, N.G.: Stochastic Processes in Physics and Chemistry, 1st edn. Elsevier Science, Amsterdam (2003)

    MATH  Google Scholar 

  38. Elf, J., Donĉić, A., Ehrenberg, M.: Mesoscopic reaction-diffusion in intracellular signaling. Proc. SPIE 5110, 114–124 (2003)

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by Chalmers University of Technology. A part of the work has been done for meeting the master’s degree requirements at Chalmers University of Technology.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zoran Konkoli .

Editor information

Editors and Affiliations

Appendix: Convergence Tests

Appendix: Convergence Tests

We studied how the number of lattice sites affects the simulation data. Extensive convergence tests were performed which consisted of analyzing how the graphs presented in this section change when the number of lattice sites is increased. A few examples are shown in Fig. 26.18.

The conclusions are as follows. For one \((d = 1)\) the convergence has been achieved and these results are quantitative. The results for two \((d = 2)\) dimensions are only qualitative. To obtain better results, the lattice size should be increased. This could not be done due to the usual hardware limitations. In these types of simulations the CPU speed is the most limiting factor.

Fig. 26.18
figure 18

Convergence tests of the fail rate versus number of nodes. The system is a minimal while loop implementation with \(k_1/k_2=10^6\) and \(v_0=1\). On the x-axis is the length in nodes of the domain. In panel a is the convergence test for one dimension, this yields that the x-axis also correspond to the total number of nodes. Panel b corresponds to two dimensions with the total number of nodes then being the x-axis value squared. Panel c consequently corresponds to three dimensions. Since the domain used has been \(5\times 5\times 4\) for three dimensions, the total number of nodes is the x-axis value cubed times a factor \(0.8\) due to the non-symmetry

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Bergh, E., Konkoli, Z. (2017). On Improving the Expressive Power of Chemical Computation. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-33924-5_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-33924-5_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33923-8

  • Online ISBN: 978-3-319-33924-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics