65,413 research outputs found
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relatively small number of units, where this approximation is no longer valid.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.Comment: 24 pages, 10 figures; accepted for publication in Scientific Report
Complex Reaction Kinetics in Chemistry: A unified picture suggested by Mechanics in Physics
Complex biochemical pathways or regulatory enzyme kinetics can be reduced to
chains of elementary reactions, which can be described in terms of chemical
kinetics. This discipline provides a set of tools for quantifying and
understanding the dialogue between reactants, whose framing into a solid and
consistent mathematical description is of pivotal importance in the growing
field of biotechnology. Among the elementary reactions so far extensively
investigated, we recall the socalled Michaelis-Menten scheme and the Hill
positive-cooperative kinetics, which apply to molecular binding and are
characterized by the absence and the presence, respectively, of cooperative
interactions between binding sites, giving rise to qualitative different
phenomenologies. However, there is evidence of reactions displaying a more
complex, and by far less understood, pattern: these follow the
positive-cooperative scenario at small substrate concentration, yet
negative-cooperative effects emerge and get stronger as the substrate
concentration is increased. In this paper we analyze the structural analogy
between the mathematical backbone of (classical) reaction kinetics in Chemistry
and that of (classical) mechanics in Physics: techniques and results from the
latter shall be used to infer properties on the former
Mesoscopic Biochemical Basis of Isogenetic Inheritance and Canalization: Stochasticity, Nonlinearity, and Emergent Landscape
Biochemical reaction systems in mesoscopic volume, under sustained
environmental chemical gradient(s), can have multiple stochastic attractors.
Two distinct mechanisms are known for their origins: () Stochastic
single-molecule events, such as gene expression, with slow gene on-off
dynamics; and () nonlinear networks with feedbacks. These two mechanisms
yield different volume dependence for the sojourn time of an attractor. As in
the classic Arrhenius theory for temperature dependent transition rates, a
landscape perspective provides a natural framework for the system's behavior.
However, due to the nonequilibrium nature of the open chemical systems, the
landscape, and the attractors it represents, are all themselves {\em emergent
properties} of complex, mesoscopic dynamics. In terms of the landscape, we show
a generalization of Kramers' approach is possible to provide a rate theory. The
emergence of attractors is a form of self-organization in the mesoscopic
system; stochastic attractors in biochemical systems such as gene regulation
and cellular signaling are naturally inheritable via cell division.
Delbr\"{u}ck-Gillespie's mesoscopic reaction system theory, therefore, provides
a biochemical basis for spontaneous isogenetic switching and canalization.Comment: 24 pages, 6 figure
The thermodynamics of computational copying in biochemical systems
Living cells use readout molecules to record the state of receptor proteins,
similar to measurements or copies in typical computational devices. But is this
analogy rigorous? Can cells be optimally efficient, and if not, why? We show
that, as in computation, a canonical biochemical readout network generates
correlations; extracting no work from these correlations sets a lower bound on
dissipation. For general input, the biochemical network cannot reach this
bound, even with arbitrarily slow reactions or weak thermodynamic driving. It
faces an accuracy-dissipation trade-off that is qualitatively distinct from and
worse than implied by the bound, and more complex steady-state copy processes
cannot perform better. Nonetheless, the cost remains close to the thermodynamic
bound unless accuracy is extremely high. Additionally, we show that
biomolecular reactions could be used in thermodynamically optimal devices under
exogenous manipulation of chemical fuels, suggesting an experimental system for
testing computational thermodynamics.Comment: Accepted versio
Collective behaviours: from biochemical kinetics to electronic circuits
In this work we aim to highlight a close analogy between cooperative
behaviors in chemical kinetics and cybernetics; this is realized by using a
common language for their description, that is mean-field statistical
mechanics. First, we perform a one-to-one mapping between paradigmatic
behaviors in chemical kinetics (i.e., non-cooperative, cooperative,
ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics
(i.e., paramagnetic, high and low temperature ferromagnetic,
anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a
unified, broad theory for all scenarios and, in particular, Michaelis-Menten,
Hill and Adair equations are consistently recovered. This framework is then
tested against experimental biological data with an overall excellent
agreement. One step forward, we consistently read the whole mapping from a
cybernetic perspective, highlighting deep structural analogies between the
above-mentioned kinetics and fundamental bricks in electronics (i.e.
operational amplifiers, flashes, flip-flops), so to build a clear bridge
linking biochemical kinetics and cybernetics.Comment: 15 pages, 6 figures; to appear on Scientific Reports: Nature
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