Mathematical modeling accurately predicts the dynamics and scaling of nuclear growth in discrete cytoplasmic volumes.

Scaling of nuclear size with cell size has been observed in many species and cell types. In this work we formulate a modeling framework based on the limiting component hypothesis. We derive a family of spatio-temporal mathematical models for nuclear size determination based on different transport and growth mechanisms. We analyse model properties and use in vitro experimental data to identify the most probable mechanism. This suggests that nuclear volume scales with cell volume and that a nucleus controls its import rate as it grows. We further test the model by comparing to data of early frog development, where rapid cell divisions set the relevant time scales.

Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation.

We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between the self-propelled particles and the obstacles, for which we assume large tether stiffness. The result is a coupled system of nonlinear, non-local partial differential equations. Linear stability analysis shows that patterning is expected if the interactions are strong enough and allows for the predictions of pattern size from model parameters. The macroscopic equations reveal that the obstacle interactions induce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs are attractive or repulsive.

Mathematical modeling of Myosin induced bistability of Lamellipodial fragments.

For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton dynamics. In this work, the Filament Based Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum model for the dynamics of the actin filament network in lamellipodia, is extended by a new description of actin-myosin interaction. For appropriately chosen parameter values, the resulting model has bistable dynamics with stable states showing the qualitative features observed in experiments. This is demonstrated by numerical simulations and by an analysis of a strongly simplified version of the FBLM with rigid filaments and planar lamellipodia at the cell front and rear.

Substrate specificity of the phosphorylated fructose-1,6-bisphosphatase dephosphorylating protein phosphatase from Saccharomyces cerevisiae.

Enzymatic dephosphorylation of the phosphorylated forms of five different yeast enzymes has been studied: fructose-1,6-bisphosphatase, glycogen phosphorylase, neutral trehalase, NAD-glutamate dehydrogenase and 6-phosphofructo-2-kinase. Phosphorylated fructose-1,6-bisphosphatase and phosphorylated 6-phosphofructo-2-kinase were present in extracts of starved yeast cells which had been incubated for 10 min with glucose. Phosphorylated glycogen phosphorylase, neutral trehalase and NAD-glutamate dehydrogenase were obtained by incubation of yeast extract with ATP, cyclic AMP and Mg2+. After incubation with commercially available preparations of alkaline phosphatase, all five phosphorylated enzymes studied showed the changes in catalytic activity that would be expected as a consequence of dephosphorylation. The recently purified yeast enzyme which dephosphorylates phosphorylated fructose-1,6-bisophosphatase (Horn and Holzer (1987) however, was found to be active only with the phosphorylated fructose-1,6-bisphosphatase, but not with the other four phosphorylated enzymes studied. By contrast, a crude extract from yeast showed dephosphorylating activity towards all five substrates. Substrate specificity with the five phosphorylated enzymes studied of different phosphoprotein phosphatases from yeast prepared by others is discussed.

Sensitivity of yeast glycolytic enzymes to chloroquine.

Chloroquine at pH 8.0 and 1mM [corrected] concentration inhibits about 30% glucose consumption and ethanol formation in yeast cells. Out of the 11 glycolytic enzymes assayed, phosphoglycerate kinase and pyruvate decarboxylase have been found to be most sensitive to chloroquine. Next sensitive are hexokinase, glyceraldehyde-3-phosphate dehydrogenase and pyruvate kinase. Kinetic studies with the three kinases studied revealed competitive inhibition of chloroquine with ATP (hexokinase, phosphoglycerate kinase) or ADP (pyruvate kinase).