PMC:1570349 / 24859-26740 JSONTXT

{"project":"2_test","denotations":[{"id":"16859561-15231543-1688457","span":{"begin":828,"end":830},"obj":"15231543"}],"text":"4.3.1 Example 1: engineer irreversibility\nFirst, we mention a number of main species and their interactions. The regulatory system consists of a core double inhibitor-activator module as well as several positive-feedback loops. The transcription factor E2F1 activates itself as well as pRB, a tumor suppressor. In turn, pRB inhibits itself as well as E2F1. The following equations describe this core module:\nAnother important collection of species is AP-1, which is used to denote a family of transcription factors that mediate the mitogenic signal Fm . The family AP-1 is also activated by E2F1, with feedback strength k25. The dynamics for the concentration of the family [AP-1] is modelled as:\nIn the first example, we consider the construction of an irreversible gene switch via parameter changes. It has been demonstrated [28] that for some value of k25 in (8), the G1/S transition becomes irreversible. That is, if Fm is increased beyond a certain point, a subsequent decrease to zero will not lead to a G0 state with a low level of E2F1.\nGeometrically, the inverse problem is to find the value of k25 such that the x-abscissa of the upper saddle node (SN2) is as close to zero as possible. As inequality constraints, we take 0.1 ≤ k25 ≤ 1.5. The result of the inverse analysis shows that the feedback strength should increase from its initial value of k25 = 0.9 to k25 = 1.099, resulting in a change of bifurcation diagram shown in Figure 12. Row 1 of Table 3 shows the number of optimization iterations as well as the number of functional evaluations (which in this case equals the number of one-parameter continuations) required to reach a tolerance of 10-3 on the function value.\nFigure 12 Example 1: initial and optimized gene switches.\nTable 3 Iteration summary\nOptim. iter. Func. eval.\nExample 1: irreversibility 6 14\nExample 2: irreversibility, fixed G1/S 9 22"}