How motile, free unicellular organisms maximize the rate at which they encounter resources and develop optimal search strategies remains largely unknown. In fact, cell foraging is a very complex activity in which unicellular organisms integrate a diversity of external cues and develop efficient systemic movements to localize nourishment. These foraging strategies are critical when cells face conditions of scarce resources or they don't possess information on where food is located. Here, in order to determine whether nuclear activity is directly involved in cell migration, we placed single, well-isolated, enucleated and non-enucleated starved Amoeba proteus on nutrient-free petri dishes, and we then analyzed their trajectories of movement using non-linear dynamic tools. We found that despite being enucleated, the systemic responses of the protoplasm exhibited typical biological behaviors, moving with apparent normality, creeping along the substrate, developing pseudopodia and gobbling up prey. Our quantitative studies show that both the non-enucleated and enucleated amoebas display a similar migration structure, characterized by super-diffusivity, non-trivial long-term correlations and move-step fluctuations with scale invariant properties. In conclusion, the nuclear activity does not seem to directly control the systemic cellular movements involved in locating sparse resources.