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Molecular computing for Markov chains

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Abstract

In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing chemical reaction networks as a programmable language, molecular concentrations serve to denote both input and output values. One reaction network is elaborately designed for each chain. The evolution of species’ concentrations over time well matches the transient solutions of the target continuous-time Markov chain, while equilibrium concentrations can indicate the steady state probabilities. Additionally, second-order Markov chains are considered for implementation, with bimolecular reactions rather than unary ones. An original scheme is put forward to compile unimolecular systems to DNA strand displacement reactions for the sake of future physical implementations. Deterministic, stochastic and DNA simulations are provided to enhance correctness, validity and feasibility.

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Acknowledgement

This work is supported in part by NSFC under grants 61871115 and 61501116, Jiangsu Provincial NSF for Excellent Young Scholars under grant BK20180059, the Six Talent Peak Program of Jiangsu Province under grant 2018-DZXX-001, the Distinguished Perfection Professorship of Southeast University, the Fundamental Research Funds for the Central Universities, the SRTP of Southeast University, and the Project Sponsored by the SRF for the Returned Overseas Chinese Scholars of MoE.

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  1. Chuan Zhang and Ziyuan Shen have contributed equally to this work.

Authors and Affiliations

  1. Lab of Efficient Architectures for Digital-Communication and Signal-Processing (LEADS), Quantum Information Center of Southeast University, National Mobile Communications Research Laboratory, Southeast University, Nanjing, China

    Chuan Zhang, Ziyuan Shen, Zaichen Zhang & Xiaohu You

  2. State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing, China

    Wei Wei & Jing Zhao

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  1. Chuan Zhang
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  2. Ziyuan Shen
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  3. Wei Wei
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  4. Jing Zhao
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  5. Zaichen Zhang
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  6. Xiaohu You
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Correspondence to Chuan Zhang.

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Zhang, C., Shen, Z., Wei, W. et al. Molecular computing for Markov chains. Nat Comput 19, 593–608 (2020). https://doi.org/10.1007/s11047-019-09736-8

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