Computation of Natural Logarithm Using Abstract Chemical Reaction Networks

Recent researches has focused on nucleic acids as a
substrate for designing biomolecular circuits for in situ monitoring
and control. A common approach is to express them by a set of
idealised abstract chemical reaction networks (ACRNs). Here, we
present new results on how abstract chemical reactions, viz., catalysis,
annihilation and degradation, can be used to implement circuit
that accurately computes logarithm function using the method of
Arithmetic-Geometric Mean (AGM), which has not been previously
used in conjunction with ACRNs.

Authors:

• Iuliia Zarubiieva
• Joyun Tseng
• Vishwesh Kulkarni

Keywords:

• Abstract chemical reaction network
• DNA strand displacement
• natural logarithm.

References:

[1] Seelig, G., Soloveichik, D., Zhang, D.Y., & Winfree, E. (2006).
Enzyme-free nucleic acid logic circuits. Science, 314, 1585-1588.
[2] Zhang, D.Y., Turberfield, A.J., Yurke, B. & Winfree, E. (2007).
Engineering entropy-driven reactions and networks catalyzed by DNA.
Science, 318, 1121-1125.
[3] Padirac, A., Fujii, T., & Rondelez, Y. (2013). Nucleic acids for the
rational design of reaction circuits. Current Opinion of Biotechnology,
24, 575-580.
[4] Yordanov, B., Kim, J., Petersen, R.L., Shudy, A., Kulkarni, V.V., &
Philips, A. (2014). Computational design of nucleic acid feedback control
circuits. ACS Synthetic Biology, 3, 600-616.
[5] Zhang, D.Y. (2011). Towards domain-based sequence design for
DNA strand displacement reactions. DNA Computing and Molecular
Programming, Springer Berlin Heidelberg, 162-175.
[6] Montagne, K., Plasson, R., Sakai, Y., Fujii, T., & Rondelez, Y. (2011).
Programming an in vitro DNA oscillator using a molecular networking
strategy. Molecular Systems Biology, 7, 466.
[7] Kim, J., & Winfree, E. (2011). Synthetic in vitro transcriptional
oscillators. Molecular Systems Biology, 7, 465.
[8] Chen, Y.-J., Dalchau, N., Srinivas, N., Philips, A., Cardelli, L.,
Soloveichik, D., & Seelig, G. (2013). Programmable chemical controllers
made from DNA. Nature Nanotechnology, 8, 755-762.
[9] Fujii, T., & Rondelez, Y. (2013). Predator-prey molecular ecosystems.
ACS Nano, 7, 27-34.
[10] Soloveichik, D., Seelig, G., Winfree, E. (2010). DNA as a universal
substrate for chemical kinetics. Proceedings of National Academy of
Sciences, USA, 12, 5393-5398.
[11] Alberts, B. and Johnsosn, A. and Lewis, J. and Raff, M. and Roberts,
K. and Walter, P. (2007). Molecular Biology of the Cell (5th Edition).
Garland Science, New York, NY.
[12] Lim, W. and Mayer, B. and Pawson, T. (2014). Cell Signaling. Garland
Science, New York, NY.
[13] Ma, K.C. and Perli, S.D. and Lu, T.K. (2016). Foundations and emerging
paradigms for computing in living cells. Journal of Molecular Biology,
428, pp. 893-915.
[14] Chou, C. T. (2017) Chemical reaction networks for computing logarithm.
Synthetic Biology, 2(1), ysx002.
[15] Oishi, K., & Klavins, E. (2011). Biomolecular implementation of linear
I/O systems. IET Systems Biology, 5, 252-260.
[16] Brent, R. P. (2018). Fast Algorithms for High-Precision Computation of
Elementary Functions, 5.
[17] Zarubiieva, I., Tseng, J.Y. and Kulkarni, V. (2018). Accurate Ratio
Computation using Abstract Chemical Reaction Networks. IAENG
WCE 2018: International Association of Engineers World Congress on
Engineering.