"Some of the proteins in differentiated cells are found in all cells of the organism" is the only true statement.
Cells of different types express different transcription factors, and they're never the same from one cell type to another.
- It is true that different cells expression some different TFs, but the statement is false because there are some genes that all cells transcribe (eg. GAPDH, which is used for glycolysis; these genes are often those that are fundamental to cellular function), so different cells would still have the same TFs.
Once a cell has differentiated, it can no longer change its gene expression.
- False, because cells can change their gene expression when cell signaling cascades happen, and a GPCR that has been activated produce cAMP, which activates PKA, which then goes into the nucleus and activates a TF through phosphorylation (thereby changing gene expression). Hormones may also diffuse through the plasma membrane, bind to an intracellular receptor, which may act as a TF as well.
Once a cell has differentiated, it no longer needs to transcribe RNA
- A cell being differentiated means that it became a specific cell type from a stem cell (which has the potential to be a wide range of cells). But to stay alive and keep all the cellular functions going, the cell still needs to make protein, and to make protein, you first need to transcribe RNA.