Boolean networks are qualitative hypotheses, and synchronous update is a modelling choice.

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Boolean models are qualitative

A Boolean model keeps only ON and OFF. It leaves out expression levels, rates, and delays, so it is a qualitative hypothesis about regulatory logic rather than a quantitative model.

ON/OFF logicexpression level\text{ON/OFF logic} \ne \text{expression level}
Toggle state tableEach state maps to its synchronous successor.StateNextType0011cycle0101fixed point1010fixed point1100cycle

Synchronous update is a modelling choice

Updating all genes at once is an idealization. The toggle's 00 to 11 oscillation is a synchronous artifact: a real toggle switch is bistable, with stable memory states 01 and 10. Asynchronous dynamics can give different attractors.

synchronous choiceguaranteed biology\text{synchronous choice} \ne \text{guaranteed biology}
Toggle state tableEach state maps to its synchronous successor.StateNextType0011cycle0101fixed point1010fixed point1100cycle