Biotechnological expertise and related tools (required e.g. for drug synthesis) increases daily mainly driven by a continuum of tumultuous experimental breakthroughs . In particular, recently, scientists have been able to build in-vitro reaction kinetics ( among enzymatic proteins and their ligands{\em  ) which code for two-inputs logic gates mimicking the stochastic AND ( NAND) and the stochastic OR ( NOR), beyond simpler and already known single-input gates (  as YES and NOT),  the whole triggering prompt effort even from the theoretical counterpart. To this task, several allosteric receptor-ligand systems are hereby described according to the Monod-Wyman-Changeaux model: with the purpose of exploring their concrete functional capabilities to express logical operators and/or perform logical operations , we revise the concept of cooperativity  for allosteric systems trough an extensive treatment of their statistical mechanical formulation ( with particular emphasis on the ranges and scaling of the involved parameters actually missing in the Literature) and we show how these reactions may successfully encode logical computing, beyond the YES and NOT gates, playing also as stochastic version of the AND (NAND) and the OR (NOR)operators .
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) .
R
Biotechnological expertise and related tools (required e.g. for drug synthesis) increases daily mainly driven by a continuum of tumultuous experimental breakthroughs . In particular, recently, scientists have been able to build
Recent experimental breakthroughs have finally allowed to implement
R
among enzymatic proteins and their ligands
the so called
A
enzyme based logic
R
mimicking
and mimic
R
NAND) and
and NAND) as well as
R
NOR), beyond simpler and already known
and NOR). This accomplishment, together with the already-known
A
performing
A
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
D
whole triggering prompt effort even from the theoretical counterpart. To this task, several allosteric receptor-ligand systems are hereby described according to the
R
model:
allosteric model for both single and double ligand systems,
R
concrete functional
practical
R
, we
. Mixing statistical mechanics with logics, and quantitatively our findings with the available biochemical data, we successfully
A
(and anti-cooperativity)
R
trough an extensive treatment of their statistical mechanical formulation (
,
R
the
its computational capabilities, the related
R
actually missing in the Literature) and we show how these reactions may successfully encode logical computing, beyond the YES and NOT gates, playing also as stochastic version of the AND (NAND) and the OR (NOR)operators
and its differences with classical cooperativity (and anti-cooperativity)