Second, negative feedback is useful for protecting cells from perturbations that continuously arise in the cell’s internal environment—due either to random variations in the birth and death of molecules or to fluctuations in environmental variables such as temperature and nutritional supplies. Let us imagine, for example, that βA, the transcription rate constant for gene A, fluctuates by 25% of its value and ask whether and how much the levels of protein R are affected. The results, shown in Figure 8–77, reveal that a change in βA causes a smaller change in the steady-state value of R when the network has negative feedback.
A beautiful thing happens when a negative feedback loop contains some delay mechanism that slows the feedback signal through the loop: rather than generating a new stable state as in a rapid negative feedback loop, a delayed loop generates pulses, or oscillations, in the levels of its components. This can be seen, for example, if the number of components in a negative feedback loop increases, which leads to delays in the amount of time required for the cycle of signals to be completed. Figure 8–78 compares the behavior of two network motifs—one with a three-stage and one with a five-stage negative feedback loop. Using the same kinetic parameters at each stage in the two loops, one finds that stable oscillations arise in the longer loop, while in the shorter loop the same parameters lead to relatively rapid convergence to a stable steady state.
Changes in the parameters of a delayed negative feedback loop—binding affinities, transcription rates, or protein stabilities, for example—can change the amplitude and period of the oscillations, providing a remarkably versatile mechanism for generating all sorts of oscillators that can be used for various purposes in the cell. Indeed, many naturally occurring oscillators, including the calcium oscillators described in Chapter 15 and the cell-cycle network described in Chapter 17, use delayed negative feedback as the basis for biologically important oscillations. Not all of the oscillations observed in cells are thought to have a function, however. Oscillations become inevitable in a highly complex, multicomponent biochemical pathway like glycolysis, due simply to the large number of feedback loops that appear to be required for its regulation.
We have focused thus far on the binding of a single transcription regulator to a single site in a gene promoter. Many promoters, however, contain multiple adjacent binding sites for the same transcription regulator, and it is not uncommon for these regulators to interact with each other on the DNA to form dimers or larger oligomers. These interactions can result in a cooperative form of DNA binding,
Figure 8–77 The effect of fluctuations in kinetic rate constants on a system with negative feedback compared to one without feedback. The plot at left represents the levels of protein R after a sudden activating stimulus, according to the regulatory scheme in Figure 8–76A and determined by the solution of Equation set 8–8 (see Figure 8–76B). A perturbation was induced by changing βA from 4 M/min (red line) to 3 M/min (blue line). The plot at right shows the results when negative feedback was removed. The system with negative feedback deviates less from its normal operation as β changes than does the system with no feedback. Notice that, as in Figure 8–76C, the system with negative feedback also reaches its steady state more rapidly.
such that DNA-binding affinity increases at higher concentrations of the transcription regulator. Cooperativity produces a steeper transcriptional response to increasing regulator concentration than the response that can be generated by the binding of a monomeric protein to a single site. A steep transcriptional response of this sort, when present in conjunction with positive feedback, is an important ingredient for producing systems with the ability to switch between different discrete phenotypic states. To begin to understand how this occurs, we need to modify our equations to include cooperativity.