- The biochemical molecule responsible for organizing DNA into nucleosome structures is Histones.

- DNA in eukaryotic cells is highly compacted to fit within the confined space of the nucleus. This compaction is achieved by wrapping DNA around proteins called histones, forming a structure known as the nucleosome. Each nucleosome consists of DNA wound around a histone octamer, which includes two copies each of histones H2A, H2B, H3, and H4. This structure serves as the fundamental repeating unit of chromatin, facilitating the efficient packaging of DNA while also regulating gene accessibility.

Other options explained:
- DNA polymerase (Option 2) is involved in DNA synthesis during replication.
- Topoisomerase (Option 3) helps relieve torsional strain during DNA replication and transcription by inducing or removing supercoils.
- RNA polymerase (Option 4) is responsible for synthesizing RNA from a DNA template during transcription.

Thus, the correct answer is Histones, as they directly organize DNA into nucleosomes.

Reference: Molecular Biology of the Cell, 6th Edition, Bruce Alberts, Chapter 5 - The Structure and Function of DNA