# Combinatorial Control through Allostery

## TL;DR

This paper models allosteric molecules to understand how they produce various logical responses, revealing their capabilities and limitations in cellular signaling and regulation.

## Contribution

It introduces a statistical mechanical framework for analyzing Boolean logic in allosteric molecules, extending understanding of their control schemes.

## Key findings

- Allosteric molecules can implement AND, OR, NAND, NOR logic gates.
- They cannot realize XOR or XNOR gates.
- Additional binding sites or ligands can switch the logic behavior.

## Abstract

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.