Genes as Switches

A Gene as a Switch

Each gene is ON or OFF, and a rule sets its next state; a self-repressing gene oscillates.

highlighted = computed this step

A gene is a switch with a rule

In a Boolean model each gene is either ON (1) or OFF (0). A rule says what the gene's next state is, given its regulators. Here gene A represses itself: it is ON next only when it is OFF now.

Anext=NOT⁡AA_{\text{next}} = \operatorname{NOT} A
A repression ruleGene A turns OFF when its regulator is ON.AA next0110

Self-repression cannot settle

Applying the rule each step flips A: OFF becomes ON, ON becomes OFF, forever. The wiring uses a barred arrow for repression. A single self-repressing gene has no stable state — it oscillates.

…→0→1→0→1→…\ldots \to 0 \to 1 \to 0 \to 1 \to \ldots
Self-repressionA represses itself.A

The transition table shows the cycle

The state table lists each state and its successor. Both states belong to one cycle of length 2, so neither is a fixed point.

0→1,1→00 \to 1, \quad 1 \to 0
It never settlesEach step flips the gene.StateNextType0→1cycle1→0cycle