Mesosomes are the invaginations of the plasma membrane that can form into vesicles. They are found to be present in both gram-positive and gram-negative bacteria. Mesomes are only found in prokaryotic cells. Mesosomes may play a role in cell wall formation during cell division and/or chromosome replication and distribution and/or electron transfer systems of respiration. Electron transport chains are found within the mesosome producing 32-34ATP. They act as an anchor to bind and pull apart daughter chromosomes during cell division. There is some evidence that bacterial mesosomes may be artifacts formed during the process of chemical fixation  of bacteria for electron microscopy and thus they actually may not exist in reality. 
- <Bacterial mesosomes. Real structures or artifacts?, Silva et al.; Biochim Biophys Acta. 1976 Aug 4;443(1):92-105.
- Bacterial mesosomes: Method dependent artifacts; Ebersold, Cordier and Lüthy, Archives of Microbiology, vol. 130:19-22 (1981)