217 research outputs found
Stochastic modeling of cargo transport by teams of molecular motors
Many different types of cellular cargos are transported bidirectionally along
microtubules by teams of molecular motors. The motion of this cargo-motors
system has been experimentally characterized in vivo as processive with rather
persistent directionality. Different theoretical approaches have been suggested
in order to explore the origin of this kind of motion. An effective theoretical
approach, introduced by M\"uller et al., describes the cargo dynamics as a
tug-of-war between different kinds of motors. An alternative approach has been
suggested recently by Kunwar et al., who considered the coupling between motor
and cargo in more detail. Based on this framework we introduce a model
considering single motor positions which we propagate in continuous time.
Furthermore, we analyze the possible influence of the discrete time update
schemes used in previous publications on the system's dynamic.Comment: Cenference proceedings - Traffic and Granular Flow 1
A case study in model-driven synthetic biology
We report on a case study in synthetic biology, demonstrating the modeldriven
design of a self-powering electrochemical biosensor. An essential result of
the design process is a general template of a biosensor, which can be instantiated
to be adapted to specific pollutants. This template represents a gene expression network
extended by metabolic activity. We illustrate the model-based analysis of this
template using qualitative, stochastic and continuous Petri nets and related analysis
techniques, contributing to a reliable and robust design
Stronger computational modelling of signalling pathways using both continuous and discrete-state methods
Starting from a biochemical signalling pathway model expresses in a process algebra enriched with quantitative information, we automatically derive both continuous-space and discrete-space representations suitable for numerical evaluation. We compare results obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results
Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions
A stochastic model of autocatalytic chemical reactions is studied both
numerically and analytically. The van Kampen perturbative scheme is
implemented, beyond the second order approximation, so to capture the non
Gaussianity traits as displayed by the simulations. The method is targeted to
the characterization of the third moments of the distribution of fluctuations,
originating from a system of four populations in mutual interaction. The theory
predictions agree well with the simulations, pointing to the validity of the
van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Towards Probabilistic Model Checking on P Systems Using PRISM
This paper presents the use of P systems and π-calculus to
model interacting molecular entities and how they are translated into a
probabilistic and symbolic model checker called PRISM.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58
Analysis of Petri Net Models through Stochastic Differential Equations
It is well known, mainly because of the work of Kurtz, that density dependent
Markov chains can be approximated by sets of ordinary differential equations
(ODEs) when their indexing parameter grows very large. This approximation
cannot capture the stochastic nature of the process and, consequently, it can
provide an erroneous view of the behavior of the Markov chain if the indexing
parameter is not sufficiently high. Important phenomena that cannot be revealed
include non-negligible variance and bi-modal population distributions. A
less-known approximation proposed by Kurtz applies stochastic differential
equations (SDEs) and provides information about the stochastic nature of the
process. In this paper we apply and extend this diffusion approximation to
study stochastic Petri nets. We identify a class of nets whose underlying
stochastic process is a density dependent Markov chain whose indexing parameter
is a multiplicative constant which identifies the population level expressed by
the initial marking and we provide means to automatically construct the
associated set of SDEs. Since the diffusion approximation of Kurtz considers
the process only up to the time when it first exits an open interval, we extend
the approximation by a machinery that mimics the behavior of the Markov chain
at the boundary and allows thus to apply the approach to a wider set of
problems. The resulting process is of the jump-diffusion type. We illustrate by
examples that the jump-diffusion approximation which extends to bounded domains
can be much more informative than that based on ODEs as it can provide accurate
quantity distributions even when they are multi-modal and even for relatively
small population levels. Moreover, we show that the method is faster than
simulating the original Markov chain
A Monte Carlo study of temperature-programmed desorption spectra with attractive lateral interactions
We present results of a Monte Carlo study of temperature-programmed
desorption in a model system with attractive lateral interactions. It is shown
that even for weak interactions there are large shifts of the peak maximum
temperatures with initial coverage. The system has a transition temperature
below which the desorption has a negative order. An analytical expression for
this temperature is derived. The relation between the model and real systems is
discussed.Comment: Accepted for publication in Phys.Rev.B15, 10 pages (REVTeX), 2
figures (PostScript); discussion about Xe/Pt(111) adde
On P Systems as a Modelling Tool for Biological Systems
We introduce a variant of P systems where rules have associated
a real number providing a measure for the “intrinsic reactivity”of
the rule and roughly corresponding to the kinetic coefficient which, in
bio-chemistry, is usually associated to each molecular reaction. The behaviour
of these P systems is then defined according to a strategy which,
in each step, randomly selects the next rule to be applied depending upon
a certain distribution of probabilities. As an application, we present a P
system model of the quorum sensing regulatory networks of the bacterium
Vibrio Fischeri. In this respect, a formalisation of the network
in terms of P systems is provided and some simulation results concerning
the behaviour of a colony of such bacteria are reported. We also
briefly describe the implementation techniques adopted by pointing out
the generality of our approach which appears to be fairly independent
from the particular choice of P system variant and the language used to
implement it.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems
This paper investigates the dynamics of biomass in a marine ecosystem. A
stochastic process is defined in which organisms undergo jumps in body size as
they catch and eat smaller organisms. Using a systematic expansion of the
master equation, we derive a deterministic equation for the macroscopic
dynamics, which we call the deterministic jump-growth equation, and a linear
Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von
Foerster equation, used in previous studies, is shown to be a first-order
approximation, appropriate in equilibrium systems where predators are much
larger than their prey. The model has a power-law steady state consistent with
the approximate constancy of mass density in logarithmic intervals of body mass
often observed in marine ecosystems. The behaviours of the stochastic process,
the deterministic jump-growth equation and the McKendrick--von Foerster
equation are compared using numerical methods. The numerical analysis shows two
classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change
A computational group theoretic symmetry reduction package for the SPIN model checker
Symmetry reduced model checking is hindered by two problems: how to identify state space symmetry when systems are not fully symmetric, and how to determine equivalence of states during search. We present TopSpin, a fully automatic symmetry reduction package for the Spin model checker. TopSpin uses the Gap computational algebra system to effectively detect state space symmetry from the associated Promela specification, and to choose an efficient symmetry reduction strategy by classifying automorphism groups as a disjoint/wreath product of subgroups. We present encouraging experimental results for a variety of Promela examples
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