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Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity

Fig 6

Input-output curves (bifurcation diagrams) for the reduced reciprocal allosteric regulation system in Fig 2(c) (that is, with κ₂ = κ₅ = 0 for simplicity).

The following parameters are fixed: κ₁ = 1, κ₃ = 1, κ₇ = 1, κ₈ = 1, κ₉ = 1, κ₁₀ = 0.1, L_tot = 72, K_tot = 62, S_tot = 426. In (a)-(d), the bifurcation parameter t, which can be negative, describes a path for . Subfigures (a)-(c) show the bifurcation diagrams for the concentration of S_p, K and L at steady state. In the intervals with three steady states, the one in the middle is unstable. Subfigure (d) shows the path in the three-dimensional space (K₂, P_tot, κ₆). The blue regions indicate the region of the path that belongs to the multistationarity region, and the displayed plane κ₆ = 1 separates the two regions. Subfigures (e)-(f) show the multistationarity regions when we fix κ₆ = 9.5 and κ₆ = 0.195 respectively. These are two slices of the two path-connected components, obtained by keeping only two free parameters.

doi: https://doi.org/10.1371/journal.pcbi.1010970.g006