Molecular computing for Markov chains
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Molecular computing for Markov chains Chuan Zhang1
•
Ziyuan Shen1 • Wei Wei2 • Jing Zhao2 • Zaichen Zhang1 • Xiaohu You1
Ó Springer Nature B.V. 2019
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. Keywords Molecular computing DNA strand displacement Markov chain Mass action kinetics Gillespie algorithm
1 Introduction 1.1 Brief introduction By far, the exploitation and application of traditional computing equipment, such as silicon-based devices, has reached its peak. This urges the need of new material for Chuan Zhang and Ziyuan Shen have contributed equally to this work. & Chuan Zhang [email protected] Ziyuan Shen [email protected] Wei Wei [email protected] Jing Zhao [email protected] 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
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
possibly better computation performance or different application scenarios. Capable of exhibiting abundant dynamic behaviors, chemical reaction networks (CRNs) turn out to be a programmable language, prompting molecular scale material to become a highly promising candidate. As a parallel system in nature, CRNs possess the potential to handle large-scale and sophisticated computations. The past few decades have seen a groundswell of interest in molecular computing no matter concerning academy or industry (Bennett 1982; Stemmer 1995; Pun and Rozenberg 2002; Lund et al. 2010), with scientists trying to reveal the natural programmability of CRNs. A wealth of research is of primary interest in exploring the potential computational power of biological molecules by implementing digital logic, signal processing and functions (Chen et al. 2014; Jiang et al. 2013a, b, 2011; Khara
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