Food Searching Strategy of Amoeboid Cells by Starvation Induced Run Length Extension

Food searching strategies of animals are key to their success in heterogeneous environments. The optimal search strategy may include specialized random walks such as Levy walks with heavy power-law tail distributions, or persistent walks with preferred movement in a similar direction. We have investigated the movement of the soil amoebae Dictyostelium searching for food. Dictyostelium cells move by extending pseudopodia, either in the direction of the previous pseudopod (persistent step) or in a different direction (turn). The analysis of ∼4000 pseudopodia reveals that step and turn pseudopodia are drawn from a probability distribution that is determined by cGMP/PLA2 signaling pathways. Starvation activates these pathways thereby suppressing turns and inducing steps. As a consequence, starved cells make very long nearly straight runs and disperse over ∼30-fold larger areas, without extending more or larger pseudopodia than vegetative cells. This ‘win-stay/lose-shift’ strategy for food searching is called Starvation Induced Run-length Extension. The SIRE walk explains very well the observed differences in search behavior between fed and starving organisms such as bumble-bees, flower bug, hoverfly and zooplankton.


Appendix S2. Growth and death at different run length
When a cell moves it will occupy a certain area where it may find food. The food is used for basal cell metabolism and for movement. When more food/energy is found than needed for metabolism and movement the cell will grow, while the cell will die when it used more energy that taken up from the food. We will recognize two situations, when the food is homogeneously distributed around the cell, and when the food is present heterogeneously in small patches, respectively. In both cases dispersion of the cell depends on the diffusion rate constant D and time t, while energy expenditure per unit of time depends on basal metabolism (α), extension of pseudopodia (β) and actual displacement of the cell (γ).

A. Diffusion rate constant during starvation.
Movement of Dictyostelium cells at short time intervals is a persistent random walk, which converts to a random walk after 1-5 minutes. Since we estimate here growth and survival after several hours, movement in two dimensions is accurately described by a random walk with where 2 L is the mean square displacement, and D is the diffusion rate constant.
We determined the diffusion rate constant D and the mean run length <r> for different starvation times (see

B. Food searching in homogeneous environment
We assume that Dictyostelium cells are in a homogeneous environment where they diffuse (thereby visit new area with food), and takes up food proportional to the new area visited and food density ρ.
The food taken up is given by: .55) and <r> is the mean run length.
The food is used for basal metabolism (α), pseudopod extension (β for all pseudopodia) and displacement of the cell (γ for split pseudopodia).
where θ is the pseudopod frequency. The energy balance is then given by We calculated the amount of food that is needed to recover the energy spend during the flight for different values for the mean run length <r>. Figure 2A reveals that cells in a homogeneous environment can make short runs and small displacements at high food density, and still keep a positive energy balance. At a lower foot densities the model suggests that cells must make long runs resulting in large displacements to collect sufficient food.

C. Food searching in heterogeneous environment
We assume that Dictyostelium cells are in an area devoid of food except in a small area at a distance l from the cell. The cell will diffuse and when it reached the food spot will become adsorbed. The cell will have to invest energy for movement, and may recover energy when the food spot is found.
The probably density function (PDF) of the time it takes for a cell that diffuses in two dimensions to become adsorbed at a distance l (see [1]) We calculated the amount of food at the target spot that is needed to recover the energy spend during the flight for different values for the target distance l and the mean run length <r>. The model shows that cells easily recover the investment when food is close by. However when the patches are a little further away, cells must make long runs otherwise they reach the patches too late for survival (Fig 2B).

Figure 2. Death and growth by SIRE, Starvation-Induced
Run-length Extension. Model calculations on the effect of run length on the energy balance of cells in an environment with homogeneous food (A) and food in patches (B) using equations S9 and S11, respectively. Parameter selection: cells take up bacteria that are present at density ρ (in arbitrary energy quanta per µm 2 ), and use energy for basal metabolism (α = 100 min -1 ), pseudopod extension (β = 200 min -1 ) and displacement of the cell (γ = 400 min -1 ). The surface area of the patch is 1000 µm 2 .