Figure 2
Schematic diagram for theoretical framework and its application on Rac1-RhoA regulatory circuit.
(a) Schematic diagram of the regulation of a typical Rho family GTPase (denoted as Rho). The inactive GDP-bound state of Rho (Rho-GDP) and the active GTP-bound state of Rho (Rho-GTP) both bind to the membrane. They can interconvert through the regulations of GAPs (at rate J[I1]) or GEFs (at rate B[I2]), which may be activated by some external input signals (I1 and I2). Rho-GDP can be released from the membrane by binding to a GDI molecule (at rate gdi_R) and revert to its membrane-bound state by releasing GDI (at rate dgdi_R). Rho-GDP and Rho-GTP degrade at rate KR and 
respectively, while the degradation of Rho-GDI was not considered, because GDI binding can stabilize the Rho protein21. (b) The RhoA-Rac1 regulatory circuit (Details in Supplementary Table S1). The GTP-bound states of RhoA or Rac1 can promote GTP loading of its own and meanwhile activate the GTP hydrolysis of the other. RhoA-GTP is also transcriptionally self-activated. Grb2 induces the GTP loading of Rac1, while Gab1 induces that of both Rac1 and RhoA. (c) The effective (reduced Rac1/RhoA) circuit. In terms of Rac1-GTP and Rho-GTP, their mutual inhibitions form a non-canonical toggle switch with positive auto-regulations. A solid arrow denotes activation, a solid bar indicates repression and the wavy line represents regulation by external signals. The solid double line represents the GTP loading or hydrolysis process while the dashed double one represents the binding or unbinding process of GDI molecules. The dashed-dot lines indicate the indirect regulations on GTP loading or hydrolysis process via GEFs or GAPs. (d) Typical values of the B and the J functions with respect to the concentrations of the GTPases. The B and J functions represent the GTP loading and hydrolysis rates of both Rac1 and RhoA respectively. Both functions increase with the level of GTP-bound Rac1 and RhoA. The parameters for the two functions were listed in Supplementary Table S2.
