176 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
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 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
Efficient Parallel Statistical Model Checking of Biochemical Networks
We consider the problem of verifying stochastic models of biochemical
networks against behavioral properties expressed in temporal logic terms. Exact
probabilistic verification approaches such as, for example, CSL/PCTL model
checking, are undermined by a huge computational demand which rule them out for
most real case studies. Less demanding approaches, such as statistical model
checking, estimate the likelihood that a property is satisfied by sampling
executions out of the stochastic model. We propose a methodology for
efficiently estimating the likelihood that a LTL property P holds of a
stochastic model of a biochemical network. As with other statistical
verification techniques, the methodology we propose uses a stochastic
simulation algorithm for generating execution samples, however there are three
key aspects that improve the efficiency: first, the sample generation is driven
by on-the-fly verification of P which results in optimal overall simulation
time. Second, the confidence interval estimation for the probability of P to
hold is based on an efficient variant of the Wilson method which ensures a
faster convergence. Third, the whole methodology is designed according to a
parallel fashion and a prototype software tool has been implemented that
performs the sampling/verification process in parallel over an HPC
architecture
Multiple verification in computational modeling of bone pathologies
We introduce a model checking approach to diagnose the emerging of bone
pathologies. The implementation of a new model of bone remodeling in PRISM has
led to an interesting characterization of osteoporosis as a defective bone
remodeling dynamics with respect to other bone pathologies. Our approach allows
to derive three types of model checking-based diagnostic estimators. The first
diagnostic measure focuses on the level of bone mineral density, which is
currently used in medical practice. In addition, we have introduced a novel
diagnostic estimator which uses the full patient clinical record, here
simulated using the modeling framework. This estimator detects rapid (months)
negative changes in bone mineral density. Independently of the actual bone
mineral density, when the decrease occurs rapidly it is important to alarm the
patient and monitor him/her more closely to detect insurgence of other bone
co-morbidities. A third estimator takes into account the variance of the bone
density, which could address the investigation of metabolic syndromes, diabetes
and cancer. Our implementation could make use of different logical combinations
of these statistical estimators and could incorporate other biomarkers for
other systemic co-morbidities (for example diabetes and thalassemia). We are
delighted to report that the combination of stochastic modeling with formal
methods motivate new diagnostic framework for complex pathologies. In
particular our approach takes into consideration important properties of
biosystems such as multiscale and self-adaptiveness. The multi-diagnosis could
be further expanded, inching towards the complexity of human diseases. Finally,
we briefly introduce self-adaptiveness in formal methods which is a key
property in the regulative mechanisms of biological systems and well known in
other mathematical and engineering areas.Comment: In Proceedings CompMod 2011, arXiv:1109.104
Programmable models of growth and mutation of cancer-cell populations
In this paper we propose a systematic approach to construct mathematical
models describing populations of cancer-cells at different stages of disease
development. The methodology we propose is based on stochastic Concurrent
Constraint Programming, a flexible stochastic modelling language. The
methodology is tested on (and partially motivated by) the study of prostate
cancer. In particular, we prove how our method is suitable to systematically
reconstruct different mathematical models of prostate cancer growth - together
with interactions with different kinds of hormone therapy - at different levels
of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104
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