Fig 4. Broken symmetry circuits function as memory.

AR (first column): The replica symmetry duplication of the AR symmetric circuit results in a network that is analogous to the SR flip-flop circuit. The symmetry between Y and Y’ is broken by the inputs S and R, such that S ≠ R, resulting into a pair logical outputs Q and $\overline{Q}=\mathbf{\text{not}}\left(Q\right)$. FFF (second column): Following the same strategy, we replicate the FFF through a replica symmetry duplication. Note that this operation adds a second level of logic gates to the SR flip-flop. In order to have consistent logic operations, we add an input clock gene CLK in addition to S and R. The resulting circuit is analogous to the Clocked SR flip-flop logic circuit. Fibonacci (third column: The replica symmetry duplication of the Fibonacci Fiber results in a logic circuit which is analogous to the JK flip-flop. For each symmetry breaking class, we show two examples of circuits from the human regulatory network. The external regulator genes, S and R (J and K), provide inputs which are logically processed by the circuit, accordingly to the type of interaction links between the genes, activators (black arrows) or repressors (red flat links). The outputs of the circuits (green genes) regulate the expression levels of other genes (in red) without affecting the circuit functionality. Here, grey arrows correspond to interactions with unknown functionality.