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A Design Method for Realizing Markov Chains Using Reversible Unimolecular Reactions

A Markov chain and design method technology, applied in the field of chemical reaction network calculation, can solve the problem of not realizing Markov chain calculation, and achieve the effect of reducing the types and the number of reactions

Active Publication Date: 2020-02-18
SOUTHEAST UNIV
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Problems solved by technology

S.A.Salehi et al. first designed a formal chemical reaction network, and M.Cardona et al. used DNA chains to represent the endpoints and edges of Markov chains, but none of the above methods realized the calculation of continuous-time Markov chains.

Method used

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  • A Design Method for Realizing Markov Chains Using Reversible Unimolecular Reactions
  • A Design Method for Realizing Markov Chains Using Reversible Unimolecular Reactions
  • A Design Method for Realizing Markov Chains Using Reversible Unimolecular Reactions

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Embodiment Construction

[0021] Such as figure 1 Shown, realize the design method of Markov chain with unimolecular reversible reaction among the present invention, comprise the following steps:

[0022] (1) Using different reactant species ν i (i=1,2,...,k)ν i , i=1,2,...k represent different states, and set the initial concentration of the reactant according to the initial probability distribution of the target Markov chain (the Markov chain of the steady-state distribution to be solved); that is, the initial concentration of all reactants must be equal to or proportional to the initial state distribution of the target Markov chain;

[0023] (2) Use the reaction rate constant to express the transition probability k ij (i=1,2,...,k j=1,2,...,k), set the value of the reaction rate constant according to the transition probability;

[0024] (3) Reversible unimolecular reaction Indicates a state transition;

[0025] (4) Use the designed reaction to calculate the steady-state distribution of the Ma...

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Abstract

The invention discloses a design method for realizing a Markov chain by using a reversible unimolecular reaction. The final concentration of the reactant is used to characterize the steady-state probability distribution of the Markov chain, which is suitable for discrete-time Markov chains and continuous-time Markov chains. Markov chain. The method of the invention solves the problem that the method for estimating the steady-state distribution of the Markov chain by DNA reaction in the prior art cannot realize the calculation of the continuous time Markov chain, and simultaneously effectively reduces the types of reactants and the number of reactions required.

Description

technical field [0001] The invention belongs to the calculation field of chemical reaction networks (CRNs), in particular to a design method for realizing Markov chains by using reversible unimolecular reactions. Background technique [0002] Typically, Markov chains are used to analyze stochastic processes in chemical reaction networks. However, S.A. Salehi, M.D. Riedel, and K.K. Parhi in the paper "Markov chaincomputations using molecular reactions" published in IEEE International Conference on Digital Signal Processing (DSP), 2015, pp.689–693, and M. Cardona, M. Colomer, J.Conde, J.Miret, J.Miro, and A.Zaragoza, in the paper "Markov chains: Computing limit existence and approximations with DNA" published in Biosystems, vol.81, no.3, pp.261–266, 2005 " did the opposite: using DNA reactions to estimate the steady-state distribution of Markov chains. S.A.Salehi et al. first designed a formal chemical reaction network, and M.Cardona et al. used DNA chains to represent the e...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G16C20/10G16C20/70G06K9/62
CPCG16C20/10G16C20/70G06F18/295
Inventor 沈梓原张川戈璐璐尤肖虎
Owner SOUTHEAST UNIV
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