Complete integrability of information processing by biochemical reactions.
Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling - based on spin systems - has been proved to be accurate for a wide class of systems matching classical (e.g. Michaelis-Menten, Hill, Adair) scenarios in the infinite-size approximation. However, the current research in biochemical information processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid. Here we show that the whole statistical mechanical description of reaction kinetics can be re-formulated via a mechanical analogy - based on completely integrable hydrodynamic-type systems of PDEs - which provides explicit finite-size solutions, matching recently investigated phenomena (e.g. noise-induced cooperativity, stochastic bi-stability, quorum sensing). The resulting picture, successfully tested against a broad spectrum of data, constitutes a neat rationale for a numerically effective and theoretically consistent description of collective behaviors in biochemical reactions.
Dipartimento di Matematica, Sapienza Università di Roma, Italy.|Istituto Nazionale d'Alta Matematica (GNFM-INdAM), Rome (IT).
Elena
E
Agliari
Department of Computer Science, Sapienza Università di Roma, Italy.|Istituto Nazionale d'Alta Matematica (GNFM-INdAM), Rome (IT).
Adriano
A
Barra
Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität Bonn, Germany.
Lorenzo
L
Dello Schiavo
Department of Mathematics and Information Science, University of Northumbria Newcastle, United Kingdom.
Antonio
A
Moro