Computational limits to binary genes

We analyse the trade-off between the speed with which a gene can propagate information, the noise of its output and its metabolic cost. Our main finding is that for any given level of metabolic cost there is an optimal trade-off between noise and processing speed. Any system with a non-vanishing leak expression rate is suboptimal, i.e. it will exhibit higher noise and/or slower speed than leak-free systems with the same metabolic cost. We also show that there is an optimal Hill coefficient h which minimizes noise and metabolic cost at fixed speeds, and an optimal threshold K which minimizes noise.