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Unit 3 Assignment 1 Value Chain Analysis Paper

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yielding two equal peaks, as observed in some more complex models (Fig. 2A, scenario 2). If two unequal peaks recruit GTPase equally, then the two unequal peaks would simply coexist (Fig. 2A, scenario 3). To understand how these considerations play out for different peaks, we need to know which peak will recruit more GTPase. To assess how much GTPase would be recruited to a specific peak, consider first the Turing-type model (eqn. 4) in the limit D_v→∞. This model combines a quadratic (in u) activation term with a linear inactivation term (Fig. 2B). Thus, for a fixed value of v, there are two values of u at which activation and inactivation balance each other precisely (i.e. fixed points of the net activation curve F(u,v), Fig. 2C). Given the …show more content…

2D, upper panel), F(u,v) determines whether any given location on the membrane will gain GTPase from the cytoplasm or lose GTPase to the cytoplasm (Fig. 2D, lower panel). At the trough in Fig. 2D, u approaches the lower fixed point of F(u,v), yielding no net gain or loss of GTPase. On the lower flanks of the peak, u values lie between the two fixed points, and inactivation outpaces activation, so there is a net loss of u (Fig. 2B, C). When u rises above the higher fixed point of F(u,v), near the center of the peak, there is net recruitment of GTPase from the cytoplasm. At steady state, the net recruitment in the center (red area) is balanced by net loss from the lower flanks (blue area) (Box1). Additionally, diffusion from the center of the peak to the flanks balances these flows of GTPase, requiring a sharp-topped peak (where negative (∂^2 u)/(∂x^2 ) counteracts net recruitment at the center: eqn. 3a) (Fig. 2D). We could generate a larger peak by increasing the total GTPase content (M) of the system: positive feedback would then drive more GTPase into the peak, so u_max would increase to yield greater net activation in the center of the

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