Prokaryotes like Neisseria do not have mebrane bound organelles, including nuclei. Their DNA is stored in the cytosol without the benefit of extensive sequestration.

Post-transcriptional modifications, such as the splicing out of introns, only occur in eukaryotic cells. They cannot occur in prokaryotes because in those cells, trancription and translation happen concurrently in the cytoplasm.

Both types of cell contain ribosomes, so this answer does not fulfill the question criteria. Cells that lack membrane-bound organelles and a nuclear membrane are prokaryotes, not eukaryotes. Similarly, only prokaryotes are capable of coupled transcription and translation mechanisms. Finally, the choice that references external plasmids also describes prokaryotes.

All of the answer choices are tenets of the Cell Theory, except for the one concerning organelles. Not every cells has membrane-bound organelles (e.g. prokaryotic cells). 

E. Coli is a type of bacteria. Because bacteria are prokaryotes, they do not contain membrane-bound organelles. A nucleus is a membrane-bound organelle and therefore would not be found in bacteria.

The chief difference between prokaryotic and eukaryotic cells is the presence of membrane-bound organelles. Mitochondria and Golgi bodies are examples of such organelles, and are only found in eukaryotes. Nucleoids are only found in prokaryotes, while eukaryotes use membrane-bound nuclei.

Cell walls can be found in either prokaryotes or eukaryotes. Many prokaryotic bacteria use cell walls as protection from the external environment, while eukaryotic plants cells use cell walls to help maintain rigidity and prevent water loss.

Ribosomes are not membrane-bound organelles. All of the other organelles are membrane-bound, and are thus only found in eukaryotes. Ribosomes, which are the site of protein synthesis, are found in both prokaryotes and eukaryotes.

This question has several components for understanding what it is asking, and what the answer is. The first clue is the use of the word "energy," which is often code for ATP in biology. In eukaryotes, ATP is generated in the mitochondria through a long multi-step process, in which a proton gradient is established to produce ATP from glucose metabolism in the presence of oxygen. Note that even autotrophs require mitochondria in conjunction with chloroplasts; photosynthesis does not negate the necessity of an ion gradient for ATP synthesis.

Prokaryotes do not have mitochondria, but do generate ATP to carry out many biomolecular functions. Because there are no membrane-bound organelles, in order to complete bacterial metabolism prokaryotes must generate a proton gradient between the intra- and extra-cellular spaces, generally between the plasma membrane and the cell wall. This allows an electron transport chain to function along the cell membrane, using the proton gradient between the membrane and the bacterial cell wall to generate ATP.

All three statements are false.

Bacteria are prokaryotic organisms that do not contain any membrane-bound organelles; however, they do contain a cell wall and a plasma membrane as outer coverings for containment. The bacterial plasma membrane is analogous to the plasma membrane found in eukaryotes because both are made up of a phospholipid bilayer. Bacterial plasma membranes are mostly made up of phospholipids, not triglycerides. Recall that triglycerides are also a type of lipid, but their primary function is to store energy.

Gram staining is a lab procedure that is widely used to classify bacteria. A bacterium can be either gram positive or gram negative. The difference between the two classifications lies in the thickness of the cell wall. A thicker cell wall, found in gram positive cells, retains the gram stain whereas a thinner cell wall, found in gram negative cells, allows the gram stain to leave the cell. This leads to a discrepancy in the stained cell’s color (purple for gram positive and pink for gram negative), which can be used to classify the bacterium. Gram staining is irrelevant for cell membranes. Remember that all bacterial cells (whether gram positive or gram negative) have cell membranes. 

It is true that bacterial cells do not contain membrane-bound organelles, such as the nucleus. Instead of a nucleus, bacterial cells contain a region called the nucleoid that houses the genetic material of the bacterial cell; however, the nucleoid is not a membrane-bound structure.

The main difference between a gram positive and a gram negative bacterial species is the thickness of their cell walls: gram positive bacteria have thicker cell walls than gram negative bacteria. The interior of each bacterium, however, contains the same types of structures. Recall that bacteria, in general, have no membrane-bound organelles; therefore, both gram positive and gram negative bacteria will have zero membrane-bound organelles. The internal structures of each bacterial class are essentially indistinguishable.

Round bacterial cells are considered cocci. In this case, with two cells, it would be classified specifically as a diploccocus.