Figure 4

In Silico Evolution. Simulations of the bestmodels derived from in silico evolution of the systemwithout regulation and the system with negative feedback. (a) Evolution to minimize protein standard deviation. The regulated system can achieve about 21% improvement over the unregulated system, with the standard deviation reduced from 10.4 to 8.2 for a protein abundance of 100 molecules per cell. The evolved parameters for the unregulated system are: k _m = 1.0s^-1; k _p = 0.00387s^-1; γ _m = 0.0664s^-1; γ _p = 0.000572s^-1. The evolved parameters for the negatively regulated system are: k _off = 0.256s^-1; k _m = 0.835s^-1; k _p = 0.294s^-1 γ _m = 1.783s^-1; γ _p = 000282s^-1. (b) Evolution to minimize first passage time to 50% of mean protein abundance. The regulated system only achieves an improvement of 18% over the unregulated system with the rise time (of 20 repeats of the best model) reduced from 16.9s to 13.9s. The evolved parameters for the unregulated system are: k _m = 1.0s^-1; k _p = 1.0s^-1; γ _m = 0.0591s^-1; γ _p = 0.163s^-1. The evolved parameters for the negatively regulated system are: k _off = 0.0664s^-1; k _m = 1.0s^-1; k _p = 1.0s^-1; γ _m = 0.0494s^-1; γ _p = 0.0146s^-1. (c) Evolution to minimize first passage time to mean protein abundance. The regulated system achieves an improvement of 53% over the unregulated system with the rise time (of 20 repeats of the best model) reduced from 42.6s to 20.0s. The evolved parameters for the unregulated system are: k _m = 0.903s^-1; k _p = 1.0s^-1; γ _m = 0.101s^-1; γ _p = 0.0916s^-1. The evolved parameters for the negatively regulated system are: k _off = 0.000648s^-1; k _m = 1.0s^-1; k _p = 1.0s^-1; γ _m = 0.00139s^-1; γ _p = 0.0183s^-1. (d) Evolution to minimize mRNA usage. The regulated system is able to achieve a 71% improvement over the unregulated system, reducing mean mRNA levels from 0.069 to 0.020 molecules per cell to achieve a protein abundance of 100 molecules per cell. The evolved parameters for the unregulated system are: k _m = 0.000641s^-1; k _p = 0.468s^-1; γ _m = 0.0148s^-1; γ _p = 0.000200s^-1. The evolved parameters for the negatively regulated system are: k _off = 0.0942s^-1; k _m = 0.270s^-1; k _p = 1.0s^-1; γ _m = 1.168s^-1; γ _p = 0.000200s^-1. Note that the systems that minimize noise and mRNA usage evolve stable proteins while the systems that minimize response times evolve more rapidly turned-over proteins.