Synthesizing Markov Chain with Reversible Unimolecular Reactions

It is prevalently known that Markov chains have been successfully applied to many fields such as digital communications, queuing theory, and finance. However, when the system becomes massive and complex, the computational load will become too heavy to be handled by conventional approaches. To address this issue, molecular computation, which is inherently parallel, has been considered in this paper to synthesize Markov chain. Here, a succinct and systematic approach based on reversible unimolecular reactions is proposed for any time-homogeneous Markov chain, no matter it is discrete or continuous. For the chemical reaction networks (CRNs), molecular concentrations at time t reflect the probability distribution of the continuous-time Markov chain at time t. The final concentrations indicate the steady state of the Markov chain. Numerical results based on deterministic mass action kinetics have demonstrated the robustness and accuracy of this method. It is worth noting that an already mathematically-proven conclusion, which states that nearly an arbitrary set of uni-or bimolecular reactions can be implemented by DNA strand displacement reactions, ensures the meaningfulness of our work.