Networks and Attractors

The Toggle Switch

Two mutually repressing genes form a Boolean toggle switch.

highlighted = computed this step

Two genes repress each other

A toggle switch has two genes. A represses B, and B represses A. The wiring diagram shows mutual repression with barred arrows.

A⊣B,B⊣AA \dashv B,\quad B \dashv A
Toggle switchA and B repress each other.AB

Each rule is NOT the other gene

The rule for A reads B's current state and flips it. The rule for B reads A's current state and flips it. Those two truth tables are the whole Boolean network.

Anext=NOT⁡B,Bnext=NOT⁡AA_{\text{next}}=\operatorname{NOT} B,\quad B_{\text{next}}=\operatorname{NOT} A
Toggle switchA and B repress each other.AB