期刊
BIOESSAYS
卷 31, 期 10, 页码 1110-1115出版社
WILEY
DOI: 10.1002/bies.200900072
关键词
feedback; gene network; liar paradox; oscillator; systems biology
资金
- European Commission [FP6 Netsensor-012948, FP6 Integra-29025, FP7 ERC Zinc-hubs-201249]
- Spanish Ministry of Science (MEC) [SAF2007-61422]
Network motifs are small patterns of connections, found over-represented in gene regulatory networks. An example is the negative feedback loop (e.g. factor A represses itself). This opposes its own state so that when 'on' it tends towards 'off' - and vice versa. Here, we argue that such self-opposition, if considered dimensionlessly, is analogous to the liar paradox: 'This statement is false'. When 'true' it implies 'false' - and vice versa. Such logical constructs have provided philosophical consternation for over 2000 years. Extending the analogy, other network topologies give strikingly varying outputs over different dimensions. For example, the motif 'A activates B and A. B inhibits A' can give switches or oscillators with time only, or can lead to Turing-type patterns with both space and time (spots, stripes or waves). It is argued here that the dimensionless form reduces to a variant of 'The following statement is true. The preceding statement is false'. Thus, merely having a static topological description of a gene network can lead to a liar paradox. Network diagrams are only snapshots of dynamic biological processes and apparent paradoxes can reveal important biological mechanisms that are far from paradoxical when considered explicitly in time and space.
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