Here's how it works:
1. Formation of the FtsZ ring: A protein called FtsZ assembles into a ring-like structure at the future division site in the middle of the elongated cell.
2. Assembly of the divisome: The FtsZ ring acts as a scaffold for other proteins to assemble, forming a complex called the "divisome". This complex includes proteins that will help to synthesize new cell wall material.
3. Inward growth of the cell wall: The divisome directs the synthesis of new cell wall material, which starts to grow inwards from the periphery of the cell, constricting the cell in the middle.
4. Cell separation: As the new cell wall material grows, it eventually pinches off the cell completely, resulting in two separate daughter cells.
So, it's not a single pinch but a gradual process of cell wall synthesis and constriction that eventually leads to the separation of the two cells.