Final answer:
Shotgun sequencing is the method that uses random fragmentation to produce overlapping DNA segments for sequencing large DNA molecules. It involves sequencing the fragments and assembling the contig based on overlaps, akin to piecing together a torn-up photograph.
Step-by-step explanation:
The sequencing approach that employs fragmentation to produce random but overlapping pieces for sequencing large DNA molecules is called Shotgun sequencing. In this method, numerous copies of a DNA molecule are randomly fragmented into smaller pieces. These segments are then sequenced using chain termination techniques. After sequencing, the overlapping ends of these fragments are analyzed and assembled into a continuous stretch of DNA sequence, also known as a contig. This method is akin to reconstructing a torn-up photograph from overlapping pieces, where one can determine the entire picture, such as a mountain behind a lake with a cabin on its shore, by examining the overlaps. Shotgun sequencing has advanced with technologies like pairwise-end sequencing to handle the complexities of larger genomes. Despite the evolution of sequencing technologies, shotgun sequencing remains a fundamental strategy for assembling DNA sequences.
Next-generation sequencing (NGS), which is often used for its high throughput capabilities, does employ a similar concept of sequencing random fragments and assembling them together. However, the key distinction between shotgun and next-generation sequencing lies in the scale and automation of the process. NGS technologies can sequence millions of fragments simultaneously and utilize different methodologies such as synthesis sequencing.
Therefore, the correct answer to the question about the method which uses random fragmentation and overlapping pieces to sequence large DNA molecules is Shotgun sequencing. This approach played a vital role in the sequencing of complex genomes and has influenced the development of newer sequencing strategies, including those used in current NGS platforms.