  Information processing relying on biochemical interactions in the cellular
environment is essential for biological organisms. The implementation of
molecular computational systems holds significant interest and potential in the
fields of synthetic biology and molecular computation. This two-part article
aims to introduce a programmable biochemical reaction network (BCRN) system
endowed with mass action kinetics that realizes the fully connected neural
network (FCNN) and has the potential to act automatically in vivo. In part I,
the feedforward propagation computation, the backpropagation component, and all
bridging processes of FCNN are ingeniously designed as specific BCRN modules
based on their dynamics. This approach addresses a design gap in the
biochemical assignment module and judgment termination module and provides a
novel precise and robust realization of bi-molecular reactions for the learning
process. Through equilibrium approaching, we demonstrate that the designed BCRN
system achieves FCNN functionality with exponential convergence to target
computational results, thereby enhancing the theoretical support for such work.
Finally, the performance of this construction is further evaluated on two
typical logic classification problems.
