The results above paint a grim picture for suppression of molecular noise. At first glance this seems contradicted by a wealth of biological counterexamples: molecules are often present in low numbers, signaling cascades where one component affects the rates of another are ubiquitous, and yet many processes are extremely precise. How is this possible if the limits apply universally? First, the transmission of chemical information is not fundamentally limited by the number of molecules present at any given time, but by the number of chemical events integrated over the time-scale of control (i.e., by *N*_{2} rather than <*x*_{2}> above). Second, most processes that have been studied quantitatively in single cells do in fact show large variation, and the anecdotal view of cells as microscopic-yet-precise largely comes from a few central processes where cells can afford a very high number of chemical events at each step, often using post-translational signaling cascades. Just like gravity places energetic and mechanistic constraints on flight but does not confine all organisms to the surface of the earth, the rapid loss of information in chemical networks places hard constraints on molecular control circuits but does not make any level of precision inherently impossible.

It can also be tempting to dismiss physical constraints simply because life seems fine despite them. For example, many cellular processes operate with a great deal of stochastic variation, and central pathways seem able to achieve sufficiently high precision. But such arguments are almost circular. The existence of flight does not make gravity irrelevant, nor do winged creatures simply fly sufficiently well. The challenges are instead to understand the trade-offs involved: what performances are selectively advantageous given the associated costs, and how small fitness differences are selectively relevant?

To illustrate the biological consequences of imperfect signaling we consider systems that must suppress noise for survival and must relay signals through gene expression, where chemical information is lost due to infrequent activation, transcription, and translation. The best characterized examples are the homeostatic copy number control mechanisms of bacterial plasmids that reduce the risk of plasmid loss at cell division. These have been described much like the example above with X

_{1} as plasmids and X

_{2} as plasmid-expressed inhibitors

^{5}, except that plasmids self-replicate with rate

*u*(

*t*)

*x*_{1} and therefore are bound by the quartic root limit for all values of

*N*_{1} and

*N*_{2} (

SI, ). To identify the mechanistic constraints when X

_{1} production is directly inhibited by X

_{2}, rather than by a control demon that is infinitely fast and that delivers the optimal response to every perturbation, we consider a closed toy model:

where X

_{1} degradation is a proxy for partitioning at cell division, and the rate of making X

_{2} is proportional to X

_{1} because each plasmid copy encodes a gene for X

_{2}. We then use the logarithmic gains

^{6}^{,}^{14}
*H*_{12} = −

ln

*u*/

ln

*x*_{2} and

to quantify the percentage responses in rates to percentage changes in levels without specifying the exact rate functions. Parameter

*H*_{12} is similar to a Hill coefficient of inhibition, and

*H*_{22} determines how X

_{2} affects its own rates, increasing when it is negatively auto-regulated and decreasing when it is degraded by saturated enzymes. The ratio

*H*_{12}/

*H*_{22} is thus a total gain, corresponding to the eventual percentage response in

*u* to a percentage change in

*x*_{1}. With

*τ*_{2} as the average lifetime of X

_{2} molecules, stationary fluctuation-dissipation approximations

^{6}^{,}^{15} (linearizing responses,

SI) then give:

where the limit holds for all

*H*_{ij} and

*τ*_{i} (

SI). This reflects a classic trade-off in control theory: higher total gain suppresses spontaneous fluctuations in X

_{1} but amplifies the transmitted fluctuations from X

_{2} to X

_{1}. Numerical analysis confirms that even a Hill-type inhibition function

*u* can get close to the limit (not shown), and thus that direct inhibition can do almost as well as a control demon. However, the parameter requirements can be extreme: the signal molecules must be very short-lived, and the optimal gain

may be so high that introducing any delays or ‘extrinsic’ fluctuations

^{6}^{,}^{16} would destabilize the dynamics. Regardless of the inhibition control network, plasmids thus need to express inhibitors at extraordinarily high rates, and generate strongly nonlinear feedback responses without introducing signaling cascades. Most plasmids indeed take these strategies to the extreme, for example transcribing control genes tens of thousands of times per cell cycle using several gene copies and some of the strongest promoters known. Some plasmids also eliminate many of the cascade steps inherent in gene expression, using small regulatory RNAs, and still create highly nonlinear responses using proofreading-type mechanisms (,

*left*). Others partially avoid indirect control by ensuring that the plasmid copies themselves prevent each others’ replication (,

*right*), or suppress noise without closing control loops

^{17}^{,}^{18} by changing the Poisson nature of the X

_{1} and X

_{2} chemical events (

Eq. (1)). Though such schemes may have limited effects on variances

^{11}, some plasmids seem to take advantage of them

^{5}.