How does a cell consume a food particle that it too large to pass through a protein channel?

Answer 1

phagocytosis (it's a form of endocytosis)

Phagocytosis is the cellular process of engulfing solid particles by the cell membrane to form an internal phagosome, or "food vacuole." The phagosome is usually delivered to the lysosome, an organelle involved in the breakdown of cellular components, which fuses with the phagosome. The contents are subsequently degraded and either released extracellularly via exocytosis, or released intracellularly to undergo further processing.

Phagocytosis is involved in the acquisition of nutrients for some cells, and in the immune system it is a major mechanism used to remove pathogens and cell debris. Bacteria, dead tissue cells, and small mineral particles are all examples of objects that may be phagocytosed.

Phagocytosis is a specific form of endocytosis involving the vesicular internalization of solid particles, such as bacteria, and is therefore distinct from other forms of endocytosis such as pinocytosis, the vesicular internalization of various liquids.

Answer 2

The cell forms a dimple on its side closest to the food particle, then wraps itself around the food particle engulfing the food particle, then the cell membrane pinches off enclosing the food particle in a vacuole. The vacuole is then flooded with digestive enzymes, which dissolve the food particle. The nutrients released are then absorbed by the cell from the vacuole.

Once the vacuole has served its purpose it merges back into the cell membrane, dumping its indigestible contents outside the cell.