Fig 4. Designed signalling cycle motif and parameter space for adaptation and ultrasensitivity.

(A) Cartoon showing the designed signalling cycle motif with a sequestering protein. The sequestrating protein (T) binds both the kinase (K) and phosphatase (P), which catalyse the phosphorylation and dephosphorylation of unphosphorylated (S) and phosphorylated (S_p) substrate respectively. (B) The values of key parameters for achieving ultrasensitive (> 0.8) and adaptive (>0.3) responses, when assuming an enzyme-saturated regime ([S_total] = 1, [P_total] = 0.1). Panels on the left show the distribution of Michaelis-Menten constants, for kinase: K_M,K = (k₂+k₃)/k₁ (x-axis) and phosphatase K_M,P = (k₅+k₆)/k₄ (y-axis). Panels on the right show the distribution of affinities of sequestrating protein T with kinase and phosphatase: K_D,K = k₈/k₇ and K_D,P = k₁₀/k₉ Note that all four panels are plotted on the same logarithmic range. Each black dot represents a parameter set and the colours shows density of parameters.