The capacity to retain and precisely release historical data at the right moments is typically managed by sequential logic circuits within computer systems. However, this functionality is notably absent in the realm of DNA computing. To bridge this gap, we have engineered a novel series of sequential logic circuits. These circuits, which encompass SR-latches composed of NOR and NAND gates as well as D-latches, are designed with simplicity, autonomy, and reusability. Furthermore, we have successfully constructed addition, subtraction, and reversible counters leveraging these foundational circuits. The principles and functionalities of these latches have been ingeniously extended to applications such as toxin detection and dynamic ATP imaging within cellular environments.