1,821 research outputs found
The smallest chemical reaction system with bistability
<p>Abstract</p> <p>Background</p> <p>Bistability underlies basic biological phenomena, such as cell division, differentiation, cancer onset, and apoptosis. So far biologists identified two necessary conditions for bistability: positive feedback and ultrasensitivity.</p> <p>Results</p> <p>Biological systems are based upon elementary mono- and bimolecular chemical reactions. In order to definitely clarify all necessary conditions for bistability we here present the corresponding minimal system. According to our definition, it contains the minimal number of (i) reactants, (ii) reactions, and (iii) terms in the corresponding ordinary differential equations (decreasing importance from i-iii). The minimal bistable system contains two reactants and four irreversible reactions (three bimolecular, one monomolecular).</p> <p>We discuss the roles of the reactions with respect to the necessary conditions for bistability: two reactions comprise the positive feedback loop, a third reaction filters out small stimuli thus enabling a stable 'off' state, and the fourth reaction prevents explosions. We argue that prevention of explosion is a third general necessary condition for bistability, which is so far lacking discussion in the literature.</p> <p>Moreover, in addition to proving that in two-component systems three steady states are necessary for bistability (five for tristability, etc.), we also present a simple general method to design such systems: one just needs one production and three different degradation mechanisms (one production, five degradations for tristability, etc.). This helps modelling multistable systems and it is important for corresponding synthetic biology projects.</p> <p>Conclusion</p> <p>The presented minimal bistable system finally clarifies the often discussed question for the necessary conditions for bistability. The three necessary conditions are: positive feedback, a mechanism to filter out small stimuli and a mechanism to prevent explosions. This is important for modelling bistability with simple systems and for synthetically designing new bistable systems. Our simple model system is also well suited for corresponding teaching purposes.</p
Spatio-temporal correlations can drastically change the response of a MAPK pathway
Multisite covalent modification of proteins is omnipresent in eukaryotic
cells. A well-known example is the mitogen-activated protein kinase (MAPK)
cascade, where in each layer of the cascade a protein is phosphorylated at two
sites. It has long been known that the response of a MAPK pathway strongly
depends on whether the enzymes that modify the protein act processively or
distributively: distributive mechanism, in which the enzyme molecules have to
release the substrate molecules in between the modification of the two sites,
can generate an ultrasensitive response and lead to hysteresis and bistability.
We study by Green's Function Reaction Dynamics, a stochastic scheme that makes
it possible to simulate biochemical networks at the particle level and in time
and space, a dual phosphorylation cycle in which the enzymes act according to a
distributive mechanism. We find that the response of this network can differ
dramatically from that predicted by a mean-field analysis based on the chemical
rate equations. In particular, rapid rebindings of the enzyme molecules to the
substrate molecules after modification of the first site can markedly speed up
the response, and lead to loss of ultrasensitivity and bistability. In essence,
rapid enzyme-substrate rebindings can turn a distributive mechanism into a
processive mechanism. We argue that slow ADP release by the enzymes can protect
the system against these rapid rebindings, thus enabling ultrasensitivity and
bistability
Emergence of switch-like behavior in a large family of simple biochemical networks
Bistability plays a central role in the gene regulatory networks (GRNs)
controlling many essential biological functions, including cellular
differentiation and cell cycle control. However, establishing the network
topologies that can exhibit bistability remains a challenge, in part due to the
exceedingly large variety of GRNs that exist for even a small number of
components. We begin to address this problem by employing chemical reaction
network theory in a comprehensive in silico survey to determine the capacity
for bistability of more than 40,000 simple networks that can be formed by two
transcription factor-coding genes and their associated proteins (assuming only
the most elementary biochemical processes). We find that there exist reaction
rate constants leading to bistability in ~90% of these GRN models, including
several circuits that do not contain any of the TF cooperativity commonly
associated with bistable systems, and the majority of which could only be
identified as bistable through an original subnetwork-based analysis. A
topological sorting of the two-gene family of networks based on the presence or
absence of biochemical reactions reveals eleven minimal bistable networks
(i.e., bistable networks that do not contain within them a smaller bistable
subnetwork). The large number of previously unknown bistable network topologies
suggests that the capacity for switch-like behavior in GRNs arises with
relative ease and is not easily lost through network evolution. To highlight
the relevance of the systematic application of CRNT to bistable network
identification in real biological systems, we integrated publicly available
protein-protein interaction, protein-DNA interaction, and gene expression data
from Saccharomyces cerevisiae, and identified several GRNs predicted to behave
in a bistable fashion.Comment: accepted to PLoS Computational Biolog
A Minimal Model of Burst-Noise Induced Bistability
We investigate the influence of intrinsic noise on stable states of a
one-dimensional dynamical system that shows in its deterministic version a
saddle-node bifurcation between monostable and bistable behaviour. The system
is a modified version of the Schl\"ogl model, which is a chemical reaction
system with only one type of molecule. The strength of the intrinsic noise is
varied without changing the deterministic description by introducing bursts in
the autocatalytic production step. We study the transitions between monostable
and bistable behavior in this system by evaluating the number of maxima of the
stationary probability distribution. We find that changing the size of bursts
can destroy and even induce saddle-node bifurcations. This means that a bursty
production of molecules can qualitatively change the dynamics of a chemical
reaction system even when the deterministic description remains unchanged.Comment: 7 pages, 9 figure
Self-Organization at the Nanoscale Scale in Far-From-Equilibrium Surface Reactions and Copolymerizations
An overview is given of theoretical progress on self-organization at the
nanoscale in reactive systems of heterogeneous catalysis observed by field
emission microscopy techniques and at the molecular scale in copolymerization
processes. The results are presented in the perspective of recent advances in
nonequilibrium thermodynamics and statistical mechanics, allowing us to
understand how nanosystems driven away from equilibrium can manifest
directionality and dynamical order.Comment: A. S. Mikhailov and G. Ertl, Editors, Proceedings of the
International Conference "Engineering of Chemical Complexity", Berlin Center
for Studies of Complex Chemical Systems, 4-8 July 201
Dynamical effects induced by long range activation in a nonequilibrium reaction-diffusion system
We both show experimentally and numerically that the time scales separation
introduced by long range activation can induce oscillations and excitability in
nonequilibrium reaction-diffusion systems that would otherwise only exhibit
bistability. Namely, we show that the Chlorite-Tetrathionate reaction, where
autocatalytic species diffuses faster than the substrates, the spatial
bistability domain in the nonequilibrium phase diagram is extended with
oscillatory and excitability domains. A simple model and a more realistic model
qualitatively account for the observed behavior. The latter model provides
quantitative agreement with the experiments.Comment: 19 pages + 9 figure
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
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