Mechanics and control of the cytoskeleton in Amoeba proteus

Many models of the cytoskeletal motility of Amoeba proteus can be formulated in terms of the theory of reactive interpenetrating flow (Dembo and Harlow, 1986). We have devised numerical methodology for testing such models against the phenomenon of steady axisymmetric fountain flow. The simplest workable scheme revealed by such tests (the minimal model) is the main preoccupation of this study. All parameters of the minimal model are determined from available data. Using these parameters the model quantitatively accounts for the self assembly of the cytoskeleton of A. proteus: for the formation and detailed morphology of the endoplasmic channel, the ectoplasmic tube, the uropod, the plasma gel sheet, and the hyaline cap. The model accounts for the kinematics of the cytoskeleton: the detailed velocity field of the forward flow of the endoplasm, the contraction of the ectoplasmic tube, and the inversion of the flow in the fountain zone. The model also gives a satisfactory account of measurements of pressure gradients, measurements of heat dissipation, and measurements of the output of useful work by amoeba. Finally, the model suggests a very promising (but still hypothetical) continuum formulation of the free boundary problem of amoeboid motion. by balancing normal forces on the plasma membrane as closely as possible, the minimal model is able to predict the turgor pressure and surface tension of A. proteus. Several dynamical factors are crucial to the success of the minimal model and are likely to be general features of cytoskeletal mechanics and control in amoeboid cells. These are: a constitutive law for the viscosity of the contractile network that includes an automatic process of gelation as the network density gets large; a very vigorous cycle of network polymerization and depolymerization (in the case of A. proteus, the time constant for this reaction is approximately 12 s); control of network contractility by a diffusible factor (probably calcium ion); and control of the adhesive interaction between the cytoskeleton and the inner surface of the plasma membrane.