They in fact do. Check out a review "Postranslational Protein Modification in Archaea" by Jerry Eichler.
The problem is that took a long time to discover this so it was assumed that they don't have any PTMs but this is wrong.
Post-translational modifications occur in the endoplasmic reticulum and Golgi apparatus, as well as in other cellular compartments. These modifications can include phosphorylation, glycosylation, acetylation, and more, which help to regulate protein function and localization within the cell.
Post-translation or Post-translational regulation refers to the control of the levels of active protein either by means of reversible events (Post-translational modifications, such as Phosphorylation or sequestration) or by means of irreversible events (proteolysis).
The process of protein modifications is typically completed in the Golgi apparatus of the cell. During this process, the proteins undergo various post-translational modifications, such as glycosylation, phosphorylation, and cleavage. These modifications are essential for the proper functioning and localization of the proteins within the cell.
Bacterial translation occurs in the cytoplasm and has fewer post-translational modifications. Eukaryotic translation occurs in the cytoplasm and on the endoplasmic reticulum, and involves more complex regulatory mechanisms and additional processing steps.
Translation, which is the process of protein synthesis, occurs outside of the nucleus in the cytoplasm. Post-translational modifications of proteins, such as phosphorylation and glycosylation, also occur outside of the nucleus. These modifications can alter the function, stability, and localization of proteins.
Post-translational modifications occur in the endoplasmic reticulum and Golgi apparatus, as well as in other cellular compartments. These modifications can include phosphorylation, glycosylation, acetylation, and more, which help to regulate protein function and localization within the cell.
Post-translation or Post-translational regulation refers to the control of the levels of active protein either by means of reversible events (Post-translational modifications, such as Phosphorylation or sequestration) or by means of irreversible events (proteolysis).
Franco A. Taverna has written: 'The role of post-translational modifications in the structure and function of glutamate receptors'
Post-translational modifications of proteins do occur in prokaryotes, but they are generally less complex than in eukaryotes. Prokaryotes lack certain cellular compartments where modifications like glycosylation occur in eukaryotes. Additionally, prokaryotes have simpler metabolic pathways that may not require extensive post-translational modifications for protein function.
Actually, for some uses prokaryotic cells are just fine for eukaryotic gene expression. That said bacteria are deficient in quite a lot of the post-translational modification systems that eukaryotes use, such as glycosylation. Since those post-translational modifications can actually be important to the protein's function you might choose a eukaryotic expression system to preserve them.
The process of protein modifications is typically completed in the Golgi apparatus of the cell. During this process, the proteins undergo various post-translational modifications, such as glycosylation, phosphorylation, and cleavage. These modifications are essential for the proper functioning and localization of the proteins within the cell.
Bacterial translation occurs in the cytoplasm and has fewer post-translational modifications. Eukaryotic translation occurs in the cytoplasm and on the endoplasmic reticulum, and involves more complex regulatory mechanisms and additional processing steps.
Translation, which is the process of protein synthesis, occurs outside of the nucleus in the cytoplasm. Post-translational modifications of proteins, such as phosphorylation and glycosylation, also occur outside of the nucleus. These modifications can alter the function, stability, and localization of proteins.
a protein encoded by a gene that has been cloned in a system that supports expression of the gene and translation of messenger RNA. Modification of the gene by recombinant DNA technology can lead to expression of a mutant protein. Proteins coexpressed in bacteria will not possess post-translational modifications, e.g. phosphorylation or glycosylation; eukaryotic expression systems are needed .
Post translational activation of the proteins
Eukaryotes exhibit control mechanisms at all levels, including transcriptional, transcript processing, translational, and post-translational regulation. These mechanisms work together to finely regulate gene expression and protein production in response to various internal and external signals.
One way to control an enzyme is through post-translational modification such as phosphorylation or glycosylation. Other ways to control enzymes are through enzyme induction, inhibition, or by compartmentalizing the metabolic pathways.