51,776 research outputs found
Switching Dynamics in Reaction Networks Induced by Molecular Discreteness
To study the fluctuations and dynamics in chemical reaction processes,
stochastic differential equations based on the rate equation involving chemical
concentrations are often adopted. When the number of molecules is very small,
however, the discreteness in the number of molecules cannot be neglected since
the number of molecules must be an integer. This discreteness can be important
in biochemical reactions, where the total number of molecules is not
significantly larger than the number of chemical species. To elucidate the
effects of such discreteness, we study autocatalytic reaction systems
comprising several chemical species through stochastic particle simulations.
The generation of novel states is observed; it is caused by the extinction of
some molecular species due to the discreteness in their number. We demonstrate
that the reaction dynamics are switched by a single molecule, which leads to
the reconstruction of the acting network structure. We also show the strong
dependence of the chemical concentrations on the system size, which is caused
by transitions to discreteness-induced novel states.Comment: 11 pages, 5 figure
Discreteness-induced Transition in Catalytic Reaction Networks
Drastic change in dynamics and statistics in a chemical reaction system,
induced by smallness in the molecule number, is reported. Through stochastic
simulations for random catalytic reaction networks, transition to a novel state
is observed with the decrease in the total molecule number N, characterized by:
i) large fluctuations in chemical concentrations as a result of intermittent
switching over several states with extinction of some molecule species and ii)
strong deviation of time averaged distribution of chemical concentrations from
that expected in the continuum limit, i.e., . The origin of
transition is explained by the deficiency of molecule leading to termination of
some reactions. The critical number of molecules for the transition is obtained
as a function of the number of molecules species M and that of reaction paths
K, while total reaction rates, scaled properly, are shown to follow a universal
form as a function of NK/M
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
Publishing Grou
Growth states of catalytic reaction networks exhibiting energy metabolism
All cells derive nutrition by absorbing some chemical and energy resources
from the environment; these resources are used by the cells to reproduce the
chemicals within them, which in turn leads to an increase in their volume. In
this study, we introduce a protocell model exhibiting catalytic reaction
dynamics, energy metabolism, and cell growth. Results of extensive simulations
of this model show the existence of four phases with regard to the rates of
both the influx of resources and the cell growth. These phases include an
active phase with high influx and high growth rates, an inefficient phase with
high influx but low growth rates, a quasi-static phase with low influx and low
growth rates, and a death phase with negative growth rate. A mean field model
well explains the transition among these phases as bifurcations. The
statistical distribution of the active phase is characterized by a power law
and that of the inefficient phase is characterized by a nearly equilibrium
distribution. We also discuss the relevance of the results of this study to
distinct states in the existing cells.Comment: 21 pages, 5 figure
DNA as a universal substrate for chemical kinetics
Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka–Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior
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
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