A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.
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