30,594 research outputs found
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
Noise Induced Phenomena in the Dynamics of Two Competing Species
Noise through its interaction with the nonlinearity of the living systems can
give rise to counter-intuitive phenomena. In this paper we shortly review noise
induced effects in different ecosystems, in which two populations compete for
the same resources. We also present new results on spatial patterns of two
populations, while modeling real distributions of anchovies and sardines. The
transient dynamics of these ecosystems are analyzed through generalized
Lotka-Volterra equations in the presence of multiplicative noise, which models
the interaction between the species and the environment. We find noise induced
phenomena such as quasi-deterministic oscillations, stochastic resonance, noise
delayed extinction, and noise induced pattern formation. In addition, our
theoretical results are validated with experimental findings. Specifically the
results, obtained by a coupled map lattice model, well reproduce the spatial
distributions of anchovies and sardines, observed in a marine ecosystem.
Moreover, the experimental dynamical behavior of two competing bacterial
populations in a meat product and the probability distribution at long times of
one of them are well reproduced by a stochastic microbial predictive model.Comment: 23 pages, 8 figures; to be published in Math. Model. Nat. Phenom.
(2016
Resilience, reactivity and variability : A mathematical comparison of ecological stability measures
In theoretical studies, the most commonly used measure of ecological
stability is resilience: ecosystems asymptotic rate of return to equilibrium
after a pulse-perturbation or shock. A complementary notion of growing
popularity is reactivity: the strongest initial response to shocks. On the
other hand, empirical stability is often quantified as the inverse of temporal
variability, directly estimated on data, and reflecting ecosystems response to
persistent and erratic environmental disturbances. It is unclear whether and
how this empirical measure is related to resilience and reactivity. Here, we
establish a connection by introducing two variability-based stability measures
belonging to the theoretical realm of resilience and reactivity. We call them
intrinsic, stochastic and deterministic invariability; respectively defined as
the inverse of the strongest stationary response to white-noise and to
single-frequency perturbations. We prove that they predict ecosystems worst
response to broad classes of disturbances, including realistic models of
environmental fluctuations. We show that they are intermediate measures between
resilience and reactivity and that, although defined with respect to persistent
perturbations, they can be related to the whole transient regime following a
shock, making them more integrative notions than reactivity and resilience. We
argue that invariability measures constitute a stepping stone, and discuss the
challenges ahead to further unify theoretical and empirical approaches to
stability.Comment: 35 pages, 7 figures, 2 table
A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
We propose a dynamical matrix product ansatz describing the stochastic
dynamics of two species of particles with excluded-volume interaction and the
quantum mechanics of the associated quantum spin chains respectively. Analyzing
consistency of the time-dependent algebra which is obtained from the action of
the corresponding Markov generator, we obtain sufficient conditions on the
hopping rates for identifing the integrable models. From the dynamical algebra
we construct the quadratic algebra of Zamolodchikov type, associativity of
which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are
obtained directly from the dynamical matrix product ansatz.Comment: 19 pages Late
Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
We study the general properties of stochastic two-species models for
predator-prey competition and coexistence with Lotka-Volterra type interactions
defined on a -dimensional lattice. Introducing spatial degrees of freedom
and allowing for stochastic fluctuations generically invalidates the classical,
deterministic mean-field picture. Already within mean-field theory, however,
spatial constraints, modeling locally limited resources, lead to the emergence
of a continuous active-to-absorbing state phase transition. Field-theoretic
arguments, supported by Monte Carlo simulation results, indicate that this
transition, which represents an extinction threshold for the predator
population, is governed by the directed percolation universality class. In the
active state, where predators and prey coexist, the classical center
singularities with associated population cycles are replaced by either nodes or
foci. In the vicinity of the stable nodes, the system is characterized by
essentially stationary localized clusters of predators in a sea of prey. Near
the stable foci, however, the stochastic lattice Lotka-Volterra system displays
complex, correlated spatio-temporal patterns of competing activity fronts.
Correspondingly, the population densities in our numerical simulations turn out
to oscillate irregularly in time, with amplitudes that tend to zero in the
thermodynamic limit. Yet in finite systems these oscillatory fluctuations are
quite persistent, and their features are determined by the intrinsic
interaction rates rather than the initial conditions. We emphasize the
robustness of this scenario with respect to various model perturbations.Comment: 19 pages, 11 figures, 2-column revtex4 format. Minor modifications.
Accepted in the Journal of Statistical Physics. Movies corresponding to
Figures 2 and 3 are available at
http://www.phys.vt.edu/~tauber/PredatorPrey/movies
A Low Dimensional Approximation For Competence In Bacillus Subtilis
The behaviour of a high dimensional stochastic system described by a Chemical
Master Equation (CME) depends on many parameters, rendering explicit simulation
an inefficient method for exploring the properties of such models. Capturing
their behaviour by low-dimensional models makes analysis of system behaviour
tractable. In this paper, we present low dimensional models for the
noise-induced excitable dynamics in Bacillus subtilis, whereby a key protein
ComK, which drives a complex chain of reactions leading to bacterial
competence, gets expressed rapidly in large quantities (competent state) before
subsiding to low levels of expression (vegetative state). These rapid reactions
suggest the application of an adiabatic approximation of the dynamics of the
regulatory model that, however, lead to competence durations that are incorrect
by a factor of 2. We apply a modified version of an iterative functional
procedure that faithfully approximates the time-course of the trajectories in
terms of a 2-dimensional model involving proteins ComK and ComS. Furthermore,
in order to describe the bimodal bivariate marginal probability distribution
obtained from the Gillespie simulations of the CME, we introduce a tunable
multiplicative noise term in a 2-dimensional Langevin model whose stationary
state is described by the time-independent solution of the corresponding
Fokker-Planck equation.Comment: 12 pages, to be published in IEEE/ACM Transactions on Computational
Biology and Bioinformatic
- …