Figure 4.

The LR-CM system is a better shifter than either in isolation. (A) Reaction scheme of a biological network composed of a LR coupled to a CM cycle. The receptor has four possible states: unbound (R), bound to the ligand (RL), bound to the substrate (RS), and bound to both (RLS). RLS is also the enzyme-substrate complex that catalyzes S activation into S*. The enzyme E_d forms a complex with S*, ES* to deactivate it into S, completing the CM cycle. (B,C) For an example parameter set, plot shows the time course and input-output curves (y = (RL = RLS)/R_T), solid lines and z = (S*/S_T), dashed lines) at different times distributed uniformly in log scale from t₀ = 1 to t_f = 10² (using a heatmap color scale). Each curve is normalized by its maximum value at steady-state. (D) For the same example as in (B and C) EC₅₀ vs time for both outputs. Vertical lines mark the time t_ss at which each curve reached ss. Parameter set used in (B–D) a₁ = a₂ = d₁ = d₂ = k₁ = k₂ = E_T = S_T = R_T = 1. Binding rates a₁ and a₂ are in units of ([time] [concentration])⁻¹, unbinding rates d₁, d₂, k₁ and k₂ are in units of [time]⁻¹ and total amounts E_T, S_T and R_T in units of [concentration]. (E) EC_50ssz  for 200 parameter sets sampled randomly within the ranges defined in Table S1 so that K_a [((d₁ + k₁)/(a₁ * S_T))] and K_d [((d₂ + k₂)/(a₂ * S_T))] fell in the ranges indicated. (F) t_ssy vs. t_ssz for the 200 sets shown in (E). (G) The relative speed of the two modules t_ssz/t_ssy negatively correlates with the relative sensitivity (EC_50ssz/EC_50ssy).