Lamins are intermediate filaments found inside the nucleus. Lamins attach to nuclear proteins and form a layer underneath the nuclear envelope (nuclear membrane) called the nuclear lamina. The nuclear lamina functions to position nuclear pores to let molecules pass between the cytoplasm and the nucleoplasm. It also functions to break and resynthesize the nuclear envelope during mitosis. Recall that the nuclear envelope is broken down during the prophase of mitosis; therefore, lack of lamins will directly affect this phase of mitosis.

In addition to the aforementioned functions, lamins are also involved in maintaining the integrity of chromosomes. Lack of lamins will decrease the stability of chromosomes. Cholesterol and most other lipids are synthesized in the smooth endoplasmic reticulum; therefore, lamins are irrelevant to cholesterol synthesis. Since they are involved in positioning nuclear pores, lamins are important for exchanging molecules between the nucleus and cytoplasm. Lack of lamins will decrease this trafficking.

The central dogma of molecular biology states that genetic information flows from DNA to RNA to protein. The first step is the replication of the genetic material, DNA, during the S phase of the cell cycle. The second step is the conversion of DNA to RNA. This process is called transcription and involves several enzymes that convert the DNA to mRNA. The final step is called translation, which involves the conversion of mRNA to protein.

DNA replication and transcription occur inside the nucleus because the enzymes required to carry out these processes are found in the nucleoplasm. Translation, on the other hand, occurs on ribosomes in the cytoplasm or on ribosomes on the rough endoplasmic reticulum. 

Genetic information that codes for ribosomes is found on the nucleolus. Recall that the nucleolus is a specialized structure found inside the nucleus that functions to assemble ribosomes from proteins and ribosomal RNA (rRNA). The DNA that encodes for rRNA is on the nucleolus or in the vicinity of the nucleolus.

The periplasm is the space between the inner and outer cell membrane in gram-negative bacteria; it is irrelevant to this question. The nuclear envelope is the phospholipid bilayer that covers the nucleus. It does not contain any genetic information. Histones are proteins that organize and structure DNA strands; they don’t have any genetic information. 

In the nucleolus, the transcripts synthesized are rRNA molecules. The unique aspect of rRNA molecules is that they are never converted to proteins; therefore, they never undergo translation. The rRNA molecules synthesized by the nucleolus are assembled with other proteins to create ribosomes; they themselves never undergo translation.

Transcription in the rest of the nucleus produces mRNA molecules that enter the cytoplasm and undergo translation to create proteins.

The nucleolus has genes for transcribing ribosomal RNA. RNA polymerase I in the nucleolus transcribes the gene for ribosomal RNA and causes formation of ribosomal complexes. mRNA and tRNA are transcribed elsewhere in the nucleus and use RNA polymerase II and III, respectively. Arachidonic acid is an omega-6 polyunsaturated fatty acid, which plays roles in cell-signaling, prostaglandin synthesis, and the immune response, and is synthesized in the cytosol.

The electron transport chain (ETC) is located on the inner mitochondrial membrane. It is composed of a set of cytochromes which function in creating a proton (H⁺) gradient which provides the energy for ATP synthase to make ATP.

Note that the prokaryotic electron transport chain occurs on the plasma membrane with a proton gradient generated between two outer membranes or between the membrane and cell wall.

Red blood cells, although they are eukaryotic cells, do not contain mitochondria. This is because red blood cells function in transporting oxygen. Mitochondria, on the other hand, require oxygen in order to make ATP. If red blood cell had mitochondria, they would use up the oxygen that the cells are trying to transport.

Though all of the answer choices are correct statements, only one provides support for the endosymbiotic theory. This commonly supported theory proposes that mitochondria arose as single-celled prokaryotes that were engulfed by larger cells. These cells developed a symbiotic relationship that eventually led to current eukaryotic cells. So, for a statement to support this theory, it must make a connection between mitochondria and the prokaryotes from which they arose—such as the fact that they have similar DNA structures.

Mitochondria have all of the above qualities, except most of their ATP is produced via oxidative phosphorylation.

Mitochondria do not have the full prokaryotic genetic complement. Over the eons since they were originally free living, most of their genes have been transferred to their host cells, reducing the mitochondrial genome.

All other statements are true.