Final answer:
The statement is false because only proteins that are meant to be transported out of the nucleus have nuclear export signals. Cytosolic proteins may have various other signals that direct them to different organelles, not necessarily requiring export from the nucleus.
Step-by-step explanation:
False. Not all cytosolic proteins have nuclear export signals for removal from the nucleus post-mitosis. Cytosolic proteins synthesized in the cytoplasm are intended for different organelles and contain traffic signals necessary for their correct localization. Nuclear export signals (NES) are specific sequences that allow proteins to be transported out of the nucleus through nuclear pores. However, not every cytosolic protein enters the nucleus or contains an NES.
Instead, proteins that function within the cytoplasm or other organelles would have respective targeting signals such as mitochondrial signal peptides or endoplasmic reticulum signal sequences, in contrast to nuclear localization signals (NLS) that direct proteins into the nucleus. During mitosis, nuclear envelope breakdown permits proteins to mix with the cytoplasm, but afterward, only proteins with an NES are actively exported out of the reformed nucleus.