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Negative feedback circuits and robustness

Harold Black, a famous Bell Telephones Laboratories engineer, was met with disbelief when he proposed in the 1930's that negative feedback could play a significant role in amplifiers, other than avoiding singing. The idea behind his negative-feedback amplifier, described in a patent [49], was to reduce distortion by feeding back into the amplifier input the error between the input and a scaled-down portion of the output (this error is known as distortion, and results from uneven amplification of different frequency signals).

Such a use of negative feedback is dynamic: one is not concerned with clamping down system variables to certain values, but to provide adjustments between different, dynamic variables. Many biological systems use negative feedback for this purpose. For example, it is crucial for organisms to maintain a fixed stoichiometry between proteic ribosomal subunits: ribosomes are present in great quantities under favourable growth conditions (40% of total dried cellular mass for E. coli under the most favourable laboratory conditions, [50]), and it would be most wasteful to have components present in too high or too low quantities. It is thus imperative that different subunits be produced in similar quantities (note that this quantity is not fixed for a given prokaryotic cell, but rather a function of the growth rate). Nature has engineered sophisticated coupling mechanisms to ensure the concomitant production of two proteins in similar quantities [51]. Such coupling mechanisms are also present within ribosomal operons in E. coli [50]; however it appears that the number of proteins is too great for their production to be coupled within a single operon, requiring another mechanism, based on negative feedback.

The mechanism, as reviewed in [50], is basically the following: each operon (whose proteins are synthesized in highly similar quantities) is under negative control of one of the proteins it codes for. If a group of protein is not in excess, it is incorporated into neo-synthesized ribosomes; if however it is in excess, proteins will not be sequestered in ribosomes, and then one of the proteins will be available to inhibit translation of the corresponding mRNA. Sequestering of proteins in ribosomes is where the substraction happens. As with the negative-feedback amplifier, the result of the substraction is fed back into the controlling input of the signal/protein generation system.

The beauty of this system is that it would be difficult (if not impossible) without negative feedback to devise ribosomal proteins in such a way as their production rates are exactly the same, especially since these proteins have different lengths and amino-acid contents. The system is freed from the particular kinetics of protein synthesis, and the stoichiometry cannot be ruined by evolutionary changes of these kinetics. More generally, such negative feedback can make it possible to have a varying number of copies of a same gene without its function being affected, a major evolutionary advantage, keeping a same gene functional for homozygotes and heterozygotes, and allowing duplication, a major source of new genes.

Black's negative feedback amplifier was criticised on the grounds that the feedback diminished the gain of the amplifier; while the fact is quite true, the criticism missed the point that it was better to have an amplifier which would be slightly less powerful but which would output a better signal. The same applies to ribosomal synthesis: synthesis rates of different proteins align on the lowest one. But while it is necessary to strive toward higher ribosomal synthesis rates, it is of no use to synthesise some proteins in excess.

Finally, it is interesting to note that electronic engineers and cyberneticians have made an extensive and successful use of negative feedback to render their systems independent of their operating conditions (especially temperature, for electronic systems) and of the imperfections and variabilities inherent to their components. Negative feedback in biological systems might very well lay the same role of guiding a generic system of variable properties toward the correct behaviour, by having it constantly correct itself, and thus of making the system robust against changes in its operating conditions or its internal parameters. From the practical viewpoint of understanding the inner workings of a regulation system, this has the consequence that some parameters may not be important and need not be investigated thoroughly. Considering the great complexity of most biological regulation systems, it is important to be able to concentrate on main parameters, i.e. those to which systems are very sensitive.


next up previous
Next: Conclusion Up: Roles of positive and Previous: Oscillations
Olivier Cinquin 2002-11-04