Abstract
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processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid.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.
Highlights
Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions
Hereafter we review main concepts of chemical kinetics, statistical mechanics and cybernetics, which we will be needed in the following; we refer to classical textbooks for a more extensive treatment
If we look at the expression for the system’s energy (Eq (44)), a key point is that when J > 0, the contribution 2JY(1 −Y) provides a boost for the system’s response, further stabilizing the states Y = 0 and Y = 1. The usefulness of this Condorcet-like mechanism at work in biochemistry becomes evident already in the paradigmatic case of hemoglobin: when in the lungs, hemoglobin uses cooperativity to bind to as much oxygen as possible; when in the tissues it uses cooperativity to get rid of it, releasing oxygen in the tissue. In this manuscript we deepened our translation of biochemical kinetics into a statistical mechanical scaffold started in refs 34,35 and that allows a straightforward cybernetic interpretation of these phenomenologies
Summary
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. As recently observed in the case of large systems[34,35], the statistical mechanical approach plays the role of a general stochastic framework that naturally highlights the structural and conceptual analogies between response functions in biochemical reaction kinetics and transfer functions in cybernetics (see Figs 1 and 2), tacitely working as a translator between these two worlds, that is crucial to show how information is handled by these biochemical systems. The current research in biochemical information processing has been recently attributing particular importance to systems involving a relatively small number of units and this implies that the standard statistical mechanical picture, given in the thermodynamic limit (where the role of intrinsic noise can be suppressed36), is www.nature.com/scientificreports/
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