Figure 4. Numerical results of the information-thermodynamics bound on the robustness.

We compare the robustness (red line), the information-thermodynamic bound (green line) and the conventional thermodynamic bound (blue line). The initial condition is the stationary state with , fixed ligand signal βl_t = 0, and noise intensity T^a = 0.005. We numerically confirmed that holds for the six transition processes. These results imply that, for the signal transduction model, the information-thermodynamic bound is tighter than the conventional thermodynamic bound. The parameters are chosen as τ^a = 0.02, τ^m = 0.2, α = 2.7 and to be consistent with the real parameters of E. coli bacterial chemotaxis 7,14,16. We discuss the six different types of input signals βl_t (red solid line) and noises (green dashed line). (a) Step function: βl_t = 0.01 and for t > 0. (b) Sinusoidal function: βl_t = 0.01 sin(400t) and for t > 0. (c) Linear function: βl_t = 10t and for t > 0. (d) Exponential decay: βL_t = 0.01[1−exp(−200t)] and for t > 0. (e) Square wave: and for t > 0, where denotes the floor function. (f) Triangle wave: and for t > 0.