title: Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity.
abstract: Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called 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. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: 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 noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on 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).
authors.affiliation: Dipartimento di Fisica, Sapienza Università di Roma, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Agliari
authors.affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Italy.
authors.forename: Matteo
authors.initials: M
authors.lastname: Altavilla
authors.affiliation: Dipartimento di Fisica, Sapienza Università di Roma, Italy.
authors.forename: Adriano
authors.initials: A
authors.lastname: Barra
authors.affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Dello Schiavo
authors.affiliation: Department of Chemistry and Biomolecular Science, Clarkson University, New York, USA.
authors.forename: Evgeny
authors.initials: E
authors.lastname: Katz
mesh_terms: D000465:Algorithms; D000494:Allosteric Regulation; D039301:Computers, Molecular; D007700:Kinetics; D008128:Logic; D015233:Models, Statistical; D013269:Stochastic Processes