The response of the incoherent feed-forward motif will vary, depending on the parameters of the system. Suppose, for example, that the transcription activator protein A binds more weakly to the gene regulatory region than does the transcription repressor protein R (KA < KR). In this case, there will be a transient burst of protein synthesized by the affected gene (gene X) in response to a sudden activating input (Figure 8–85B). In contrast, the output will be more sustained if KA is much larger than KR, because the repression will be too weak to overcome the gene activation (Figure 8–85C). Other properties of this network, such as the dependence of the amplitude of the pulse on the various rate constants in the system, can be explored with the same computational tools. Thus, our intuitive guess about how this system would behave was only partially correct; even the simplest of networks depends on precise interaction strengths, demonstrating yet again why mathematics is needed to complement cartoon drawings.
In the bacterium E. coli, the sugar arabinose is only consumed when the preferred sugar, glucose, is scarce. The strategy that cells use to assess the presence of arabinose and absence of glucose involves a feed-forward arrangement that is different from the one just described. In this case, depletion of glucose causes an increase of cAMP, which is sensed by the CAP transcription activator protein, as described previously. In this case, however, CAP also induces the synthesis of a second transcription activator, AraC. Both activator proteins are necessary to activate arabinose metabolic genes (the AND logic function in Figure 8–83B).
Figure 8–85 How an incoherent feed-forward motif can generate a brief pulse of gene activation in response to a sustained input. (A) Diagram of an incoherent feed-forward motif in which the transcription activator A and the repressor R control the expression of gene X using the AND NOT logic of Figure 8–83A.
(B) When KA « KR, this motif generates a pulse of protein X expression, such that the output goes back down even if the input remains high. (C) When KA » KR, the same motif responds to a sustained input by generating a sustained output.
This arrangement, known as a coherent feed-forward motif, has the interesting characteristics illustrated in Figure 8–86. Imagine that two activators, A1 and A2, are both required to initiate transcription of a gene. The input to the network activates A1 directly, but only activates A2 through this A1 activation. Thus, for a protein to be synthesized from this gene, long-term inputs are required that allow both A1 and A2 to be produced in active form. Brief input pulses are either ignored or produce small outputs. The requirement for a long input is important if assurances about a signal are needed before a costly cellular program is triggered. For example, glucose is the sugar on which E. coli cells grow best. Before cells trigger arabinose metabolism in the example above, it might be beneficial to be sure that glucose has been depleted (a sustained CAP pulse), rather than inducing the arabinose program during a transient glucose fluctuation.
The Same Network Can Behave Differently in Different Cells Due to Stochastic Effects
Up to this point, we have assumed that all cells in a population produce identical behaviors if they contain the same network. It is important, however, to account for the fact that cells often show considerable individuality in their responses. Consider a situation in which a single mother cell divides into two daughter cells of equal volume. If the mother cell has only one molecule of a given protein, then only one daughter will inherit it. The daughters, though genetically identical, are already different. This variability is most pronounced for molecules that are present in small numbers. Nevertheless, even when there are many copies of a particular protein (or RNA), it is very unlikely that both daughter cells will end up with exactly the same number of molecules.