380 research outputs found
A Minimal Model of Signaling Network Elucidates Cell-to-Cell Stochastic Variability in Apoptosis
Signaling networks are designed to sense an environmental stimulus and adapt
to it. We propose and study a minimal model of signaling network that can sense
and respond to external stimuli of varying strength in an adaptive manner. The
structure of this minimal network is derived based on some simple assumptions
on its differential response to external stimuli. We employ stochastic
differential equations and probability distributions obtained from stochastic
simulations to characterize differential signaling response in our minimal
network model. We show that the proposed minimal signaling network displays two
distinct types of response as the strength of the stimulus is decreased. The
signaling network has a deterministic part that undergoes rapid activation by a
strong stimulus in which case cell-to-cell fluctuations can be ignored. As the
strength of the stimulus decreases, the stochastic part of the network begins
dominating the signaling response where slow activation is observed with
characteristic large cell-to-cell stochastic variability. Interestingly, this
proposed stochastic signaling network can capture some of the essential
signaling behaviors of a complex apoptotic cell death signaling network that
has been studied through experiments and large-scale computer simulations. Thus
we claim that the proposed signaling network is an appropriate minimal model of
apoptosis signaling. Elucidating the fundamental design principles of complex
cellular signaling pathways such as apoptosis signaling remains a challenging
task. We demonstrate how our proposed minimal model can help elucidate the
effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a
cell-type independent manner. We also discuss the implications of our study in
elucidating the adaptive strategy of cell death signaling pathways.Comment: 9 pages, 6 figure
Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
Biodiversity is essential to the viability of ecological systems. Species
diversity in ecosystems is promoted by cyclic, non-hierarchical interactions
among competing populations. Such non-transitive relations lead to an evolution
with central features represented by the `rock-paper-scissors' game, where rock
crushes scissors, scissors cut paper, and paper wraps rock. In combination with
spatial dispersal of static populations, this type of competition results in
the stable coexistence of all species and the long-term maintenance of
biodiversity. However, population mobility is a central feature of real
ecosystems: animals migrate, bacteria run and tumble. Here, we observe a
critical influence of mobility on species diversity. When mobility exceeds a
certain value, biodiversity is jeopardized and lost. In contrast, below this
critical threshold all subpopulations coexist and an entanglement of travelling
spiral waves forms in the course of temporal evolution. We establish that this
phenomenon is robust, it does not depend on the details of cyclic competition
or spatial environment. These findings have important implications for
maintenance and evolution of ecological systems and are relevant for the
formation and propagation of patterns in excitable media, such as chemical
kinetics or epidemic outbreaks.Comment: Final submitted version; the printed version can be found at
http://dx.doi.org/10.1038/nature06095 Supplementary movies are available at
http://www.theorie.physik.uni-muenchen.de/lsfrey/images_content/movie1.AVI
and
http://www.theorie.physik.uni-muenchen.de/lsfrey/images_content/movie2.AV
Intrinsic noise alters the frequency spectrum of mesoscopic oscillatory chemical reaction systems
Mesoscopic oscillatory reaction systems, for example in cell biology, can exhibit stochastic oscillations in the form of cyclic random walks even if the corresponding macroscopic system does not oscillate. We study how the intrinsic noise from molecular discreteness influences the frequency spectrum of mesoscopic oscillators using as a model system a cascade of coupled Brusselators away from the Hopf bifurcation. The results show that the spectrum of an oscillator depends on the level of noise. In particular, the peak frequency of the oscillator is reduced by increasing noise, and the bandwidth increased. Along a cascade of coupled oscillators, the peak frequency is further reduced with every stage and also the bandwidth is reduced. These effects can help understand the role of noise in chemical oscillators and provide fingerprints for more reliable parameter identification and volume measurement from experimental spectra
A Stochastic Differential Equation Inventory Model
© 2018, The Author(s). Inventory for an item is being replenished at a constant rate whilst simultaneously being depleted by demand growing randomly and in relation to the inventory level. A stochastic differential equation is put forward to model this situation with solutions to it derived when analytically possible. Probabilities of reaching designated a priori inventory levels from some initial level are considered. Finally, the existence of stable inventory states is investigated by solving the Fokker–Planck equation for the diffusion process at the steady state. Investigation of the stability properties of the Fokker–Planck equation reveals that a judicious choice of control strategy allows the inventory level to remain in a stable regime
Particle simulation approach for subcellular dynamics and interactions of biological molecules
BACKGROUND: Spatio-temporal dynamics within cells can now be visualized at appropriate resolution, due to the advances in molecular imaging technologies. Even single-particle tracking (SPT) and single fluorophore video imaging (SFVI) are now being applied to observation of molecular-level dynamics. However, little is known concerning how molecular-level dynamics affect properties at the cellular level. RESULTS: We propose an algorithm designed for three-dimensional simulation of the reaction-diffusion dynamics of molecules, based on a particle model. Chemical reactions proceed through the interactions of particles in space, with activation energies determining the rates of these chemical reactions at each interaction. This energy-based model can include the cellular membrane, membranes of other organelles, and cytoskeleton. The simulation algorithm was tested for a reversible enzyme reaction model and its validity was confirmed. Snapshot images taken from simulated molecular interactions on the cell-surface revealed clustering domains (size ~0.2 μm) associated with rafts. Sample trajectories of raft constructs exhibited "hop diffusion". These domains corralled the diffusive motion of membrane proteins. CONCLUSION: These findings demonstrate that our approach is promising for modelling the localization properties of biological phenomena
The what and where of adding channel noise to the Hodgkin-Huxley equations
One of the most celebrated successes in computational biology is the
Hodgkin-Huxley framework for modeling electrically active cells. This
framework, expressed through a set of differential equations, synthesizes the
impact of ionic currents on a cell's voltage -- and the highly nonlinear impact
of that voltage back on the currents themselves -- into the rapid push and pull
of the action potential. Latter studies confirmed that these cellular dynamics
are orchestrated by individual ion channels, whose conformational changes
regulate the conductance of each ionic current. Thus, kinetic equations
familiar from physical chemistry are the natural setting for describing
conductances; for small-to-moderate numbers of channels, these will predict
fluctuations in conductances and stochasticity in the resulting action
potentials. At first glance, the kinetic equations provide a far more complex
(and higher-dimensional) description than the original Hodgkin-Huxley
equations. This has prompted more than a decade of efforts to capture channel
fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of
these approaches, while intuitively appealing, produce quantitative errors when
compared to kinetic equations; others, as only very recently demonstrated, are
both accurate and relatively simple. We review what works, what doesn't, and
why, seeking to build a bridge to well-established results for the
deterministic Hodgkin-Huxley equations. As such, we hope that this review will
speed emerging studies of how channel noise modulates electrophysiological
dynamics and function. We supply user-friendly Matlab simulation code of these
stochastic versions of the Hodgkin-Huxley equations on the ModelDB website
(accession number 138950) and
http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl
Kinetic modelling of competition and depletion of shared miRNAs by competing endogenous RNAs
Non-conding RNAs play a key role in the post-transcriptional regulation of
mRNA translation and turnover in eukaryotes. miRNAs, in particular, interact
with their target RNAs through protein-mediated, sequence-specific binding,
giving rise to extended and highly heterogeneous miRNA-RNA interaction
networks. Within such networks, competition to bind miRNAs can generate an
effective positive coupling between their targets. Competing endogenous RNAs
(ceRNAs) can in turn regulate each other through miRNA-mediated crosstalk.
Albeit potentially weak, ceRNA interactions can occur both dynamically,
affecting e.g. the regulatory clock, and at stationarity, in which case ceRNA
networks as a whole can be implicated in the composition of the cell's
proteome. Many features of ceRNA interactions, including the conditions under
which they become significant, can be unraveled by mathematical and in silico
models. We review the understanding of the ceRNA effect obtained within such
frameworks, focusing on the methods employed to quantify it, its role in the
processing of gene expression noise, and how network topology can determine its
reach.Comment: review article, 29 pages, 7 figure
Stochastic Drift in Mitochondrial DNA Point Mutations: A Novel Perspective Ex Silico
The mitochondrial free radical theory of aging (mFRTA) implicates Reactive Oxygen Species (ROS)-induced mutations of mitochondrial DNA (mtDNA) as a major cause of aging. However, fifty years after its inception, several of its premises are intensely debated. Much of this uncertainty is due to the large range of values in the reported experimental data, for example on oxidative damage and mutational burden in mtDNA. This is in part due to limitations with available measurement technologies. Here we show that sample preparations in some assays necessitating high dilution of DNA (single molecule level) may introduce significant statistical variability. Adding to this complexity is the intrinsically stochastic nature of cellular processes, which manifests in cells from the same tissue harboring varying mutation load. In conjunction, these random elements make the determination of the underlying mutation dynamics extremely challenging. Our in silico stochastic study reveals the effect of coupling the experimental variability and the intrinsic stochasticity of aging process in some of the reported experimental data. We also show that the stochastic nature of a de novo point mutation generated during embryonic development is a major contributor of different mutation burdens in the individuals of mouse population. Analysis of simulation results leads to several new insights on the relevance of mutation stochasticity in the context of dividing tissues and the plausibility of ROS ”vicious cycle” hypothesis
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics
Estimation of Isolation Times of the Island Species in the Drosophila simulans Complex from Multilocus DNA Sequence Data
Background: The Drosophila simulans species complex continues to serve as an important model system for the study of new species formation. The complex is comprised of the cosmopolitan species, D. simulans, and two island endemics, D. mauritiana and D. sechellia. A substantial amount of effort has gone into reconstructing the natural history of the complex, in part to infer the context in which functional divergence among the species has arisen. In this regard, a key parameter to be estimated is the initial isolation time (t) of each island species. Loci in regions of low recombination have lower divergence within the complex than do other loci, yet divergence from D. melanogaster is similar for both classes. This might reflect gene flow of the lowrecombination loci subsequent to initial isolation, but it might also reflect differential effects of changing population size on the two recombination classes of loci when the low-recombination loci are subject to genetic hitchhiking or pseudohitchhiking Methodology/Principal Findings: New DNA sequence variation data for 17 loci corroborate the prior observation from 13 loci that DNA sequence divergence is reduced in genes of low recombination. Two models are presented to estimate t and other relevant parameters (substitution rate correction factors in lineages leading to the island species and, in the case of the 4-parameter model, the ratio of ancestral to extant effective population size) from the multilocus DNA sequence data. Conclusions/Significance: In general, it appears that both island species were isolated at about the same time, here estimated at,250,000 years ago. It also appears that the difference in divergence patterns of genes in regions of low an
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