Design Principles of Life, Disease, and Aging

# Network motifs: the recurring circuits of biology *Evidence guide: Primary experimental results and mathematical circuit models. Motif enrichment and a demonstrated function are separate findings.* First, what is a network? Nodes are components, such as genes. Directed edges are interactions. In a transcription network, an arrow means that a transcription factor activates a gene, and a bar means that it represses it. The known transcription network of E. coli has hundreds of such interactions. To ask whether a pattern is special, you need a fair comparison. Alon's group compared each real network with many randomized versions that keep the same nodes, and the same number of incoming and outgoing edges for every node, but shuffle who connects to whom. A network motif is a small pattern that occurs significantly more often in the real network than in these randomized networks. Over-representation is the definition. So not every small circuit is a motif, and a network is not made only of motifs. The simplest motif is negative autoregulation: a transcription factor X represses its own gene. In E. coli, more than forty percent of known transcription factors do this. What does it buy? Picture X switched on. Without autoregulation, X rises slowly, at a pace set by dilution and degradation. With autoregulation, X can be made at a high initial rate, then shut itself down as it nears its target. Experiments with synthetic circuits in E. coli showed that this shortened the rise time about five-fold. Next, the coherent feed-forward loop. X activates Y, and both X and Y are needed to activate Z. There are two paths from X to Z: a direct, fast one, and an indirect, slower one through Y. Suppose a short pulse of signal arrives. Y has no time to build up, so Z barely responds. A sustained signal lets Y accumulate, and Z turns on after a delay. It works like a rule: do not react until the signal persists. Measurements in the E. coli arabinose system showed a delay of this kind when the signal turned on, but not when it turned off. The incoherent feed-forward loop has the opposite logic. X activates Z directly, but X also activates Y, which represses Z. So Z first rises, then Y catches up and pushes it back down. Depending on its parameters, this circuit can generate a pulse, as shown in a synthetic circuit, or speed up a response, as measured in the E. coli galactose system. Some versions can respond to relative, fold changes in a signal. So one motif class does not always perform exactly the same function. Notice also that over-representation alone does not prove function. In each case, a function had to be predicted with a model and then tested in living cells. Sources: [shenorr2002](https://doi.org/10.1038/ng881), [alon2007](https://doi.org/10.1038/nrg2102), [milo2002](https://doi.org/10.1126/science.298.5594.824), [rosenfeld2002](https://doi.org/10.1016/s0022-2836(02)00994-4), [mangan2003jmb](https://doi.org/10.1016/j.jmb.2003.09.049), [mangan2003pnas](https://doi.org/10.1073/pnas.2133841100), [basu2004](https://doi.org/10.1073/pnas.0307571101), [mangan2006](https://doi.org/10.1016/j.jmb.2005.12.003), [goentoro2009](https://doi.org/10.1016/j.molcel.2009.11.018).