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Combinatorial Gene Regulation Using Auto-Regulation
Figure 5
NAND gates at increasing selection pressure on response speed.
On the one hand, the sensitivity of the response function of a NAND gate is improved by auto-activation. On the other hand, the response speed of the gate is enhanced by auto-repression. Consequently, if selection acts both on the response function and the response time, the simulation results are a compromise and depend critically on the relative magnitudes of the two selection pressures. The figure shows representative response functions and promoter designs of NAND gates resulting from four values of the parameter 
, which controls the weight of the response speed in the total fitness function 
. (The irrelevant constant 
merely serves to ensure that 
.) The average values of the measures 
(measuring the response time in arbitrary units 
) and 
(the deviation of the response function from the goal function in units 
) for each condition are also plotted. By definition, low values of 
and 
correspond to good performance. For the lowest value 
the response function is optimized and shows an excellent NAND gate. Due to strong, cooperative auto-regulation, the response is very sharp and almost bistable in the transition region, but the response speed is low. At 
the result is a compromise: the quality of the response function is clearly reduced but the response speed is higher. Still auto-activation evolves, but it is weaker and non-cooperative and combined with weak auto-repressing binding sites. At 
auto-repression fully takes over; the response function is crippled but the response speed is high. If the selection pressure on response time is increased even further (
) the response speed is fully optimized by disabling the response altogether.
doi: https://doi.org/10.1371/journal.pcbi.1000813.g005