Combinatorial Control through Allostery

Many
instances of cellular signaling and transcriptional regulation
involve switch-like molecular responses to the presence or absence
of input ligands. To understand how these responses come about and
how they can be harnessed, we develop a statistical mechanical model
to characterize the types of Boolean logic that can arise from allosteric
molecules following the Monod–Wyman–Changeux (MWC) model.
Building upon previous work, we show how an allosteric molecule regulated
by two inputs can elicit AND, OR, NAND, and NOR responses but is unable
to realize XOR or XNOR gates. Next, we demonstrate the ability of
an MWC molecule to perform ratiometric sensinga response behavior
where activity depends monotonically on the ratio of ligand concentrations.
We then extend our analysis to more general schemes of combinatorial
control involving either additional binding sites for the two ligands
or an additional third ligand and show how these additions can cause
a switch in the logic behavior of the molecule. Overall, our results
demonstrate the wide variety of control schemes that biological systems
can implement using simple mechanisms.