Notes on stochastic (bio)-logic gates: the role of allosteric cooperativity

TL;DR

This paper develops a comprehensive statistical mechanical model of allosteric enzymes to evaluate their potential as biological logic gates, providing insights into their cooperativity and computational capabilities based on biochemical data.

Contribution

It introduces a self-consistent theoretical framework for allosteric enzyme logic gates, linking statistical mechanics with logical operations and revising the concept of cooperativity.

Findings

Revised the concept of cooperativity in allosteric systems.

Quantified the logical capabilities of allosteric enzymes.

Compared allosteric cooperativity with classical models.

Abstract

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called {\em enzyme based logic}) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. The investigation of this field would enormously benefit from a self-consistent, predictive, theoretical framework. Here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express logical operators and/or perform logical operations. Mixing statistical mechanics with logics, and quantitatively our findings with the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).