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.

翻译：依赖于细胞环境中生化相互作用的信息处理对生物体至关重要。分子计算系统的实现在合成生物学和分子计算领域具有重要的研究价值和潜力。本文分两部分介绍一种具有质量作用动力学的可编程生化反应网络系统，该系统能够实现全连接神经网络，并具备在体内自动运行的潜力。在第一部分中，前向传播计算、反向传播组件以及全连接神经网络的所有桥接过程，均基于其动力学特性被巧妙设计为特定的生化反应网络模块。该方法解决了生化赋值模块和判断终止模块的设计空白，并为学习过程提供了一种新颖、精确且稳健的双分子反应实现方案。通过平衡逼近方法，我们证明了所设计的生化反应网络系统能够以指数级收敛速度逼近目标计算结果，实现全连接神经网络功能，从而增强了此类研究的理论支撑。最后，我们通过两个典型的逻辑分类问题进一步评估了该构建的性能。