Matrix-Chain Multiplication Based on Combinatorial Allosteric DNA Strand Displacement

DNA computing has gained widespread attention for leveraging the unique properties of DNA molecules to perform computational operations. As a fundamental tool for analyzing data and optimizing models, matrix operation plays an important role in intensive computational tasks and is a focus of DNA-based numerical computation. However, complex computing tasks are often achieved through transmitting and processing signals successively, which requires matrix operation to perform calculations sequentially. Therefore, it is important to find a way to perform successive matrix operation to ensure computational sustainability in molecular computing. In this paper, we present a successive DNA matrix operation method based on the mechanism of combinatorial allosteric DNA strand displacement. In this mechanism, the input signal and the output signal are completely decoupled in the base arrangement of the DNA domain, which makes it easy to implement successive DNA matrix operation and easily realize the connection of DNA signal processing units. Based on this mechanism, some basic DNA logic gates, such as AND gate, OR gate, and INHIBIT gate, were constructed first, then Boolean matrix multiplication was realized and, finally, matrix-chain multiplication was completed to illustrate successive DNA matrix operation. This study provides a new way to implement successive DNA matrix operation and enriches the toolbox for achieving intensive computational tasks through molecular computing.