Research on Three-Order Matrix–Vector Multiplication Using DNA Strand Displacement

In recent years, with the rapid development of DNA strands technology, the application of DNA strand displacement is gaining more and more attention in numerical calculations. In this study, we design a third-order matrix vector combined with mathematical theory based on DNA strand displacement. The idea of the novel approach is to realize the higher-order matrix vector multiplicative in biological computer logic operations. The third-order matrix vector multiplication is first designed via a biological mechanism; for this reason, this paper provides a novel complex logic operation for third-order matrix–vector multiplication, in which the matrix is a compound circuit with a series of strands structures, and the vector is represented by a single-strand structure. Moreover, a novel dual-rail theory with high-precision operation is used for this multiplication. Subsequently, the multiplication circuit is transformed into a biological circuit with multiple logic gates. During the calculation, a threshold is set, and if the threshold is exceeded, the circuit will select forward calculation; otherwise, no calculation will be performed. Finally, a professional bio-circuit simulation software called Visual DSD is used to perform online simulation of multiplier logic circuits through a high-performance computer. By changing the input parameters of the multiplication matrix vector, different calculation results are obtained and displayed by the simulation software, the results show that the design of the output of the third-order matrix vector multiplication results in the biological mechanism is reliable and stable, and can be applied to perform logical operations in biological chip making, nanocomputer, numerical computation, nanomedicine, nanorobot and other fields.