This kind of locomotion is amoeboid movement. It is a crawling-like type of movement accomplished by protrusion of cytoplasm of the cell involving the formation of pseudopodia. Movement occurs when the cytoplasm slides and forms a pseudopodium in front to pull the cell forward.
Microdomain signaling dynamics organize the cytoskeleton and its interaction with the substratum. As microdomains trigger and maintain active polymerization of actin filaments, their propagation and zigzagging motion on the membrane generate a highly interlinked network of curved or linear filaments oriented at a wide spectrum of angles to the cell boundary. Also microdomain interaction marks the formation of new focal adhesion sites at the cell periphery. The interaction of myosin with the actin network then generates membrane retraction/ruffling, retrograde flow, and contractile forces for forward motion.
Other theory includes changes in sol-gel structure of cytoplasm. The protoplasm of the cell is made up of an outer layer termed the ectoplasm which surrounds an inner portion called the endoplasm. The ectoplasm consists of a gelatinous semisolid called plasma gel whereas the endoplasm is made up of a less viscous fluid called plasma sol. The ectoplasm owes its highly viscous state, in part, to the cross-linking actomyosin complex. Locomotion is thought to occur due to the sol-gel conversion of the protoplasm within its cell. Sol-gel conversion describes the contraction and relaxation events which are enforced by osmotic pressure and other ionic charges.