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A computational framework for testing the effects of cytotoxic molecules, specific to a
given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The
model is based on a cellular automaton to describe tumour cell states transitions from
proliferation to death. It is coupled with a model describing the tumour vasculature and
its adaptation to the blood rheological constraints when alterations are induced by VDAs
treatment....
In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the...
Many cancer-associated genes and pathways remain to be identified in order to clarify the
molecular mechanisms underlying cancer progression. In this area, genome-wide
loss-of-function screens appear to be powerful biological tools, allowing the accumulation
of large amounts of data. However, this approach currently lacks analytical tools to
exploit the data with maximum efficiency, for which systems biology methods analyzing
complex cellular networks...
To model the dynamics of discrete deterministic systems, we extend the Petri nets framework by a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The aim of this paper is to gain some insight into the structure of this conflict graph and to characterize a class of suitable orientations by an analysis in the context of hypergraph theory.
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and...
The calculus of looping sequences is a formalism for describing the
evolution of biological systems by means of term rewriting rules. In
this paper we enrich this calculus with a type discipline which
preserves some biological properties depending on the minimum and
the maximum number of elements of some type requested by the present elements. The type
system enforces these properties and typed reductions guarantee that
evolution preserves them. As an example, we model the hemoglobin
structure...
HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic
mechanisms are manifold and mediated through a range of positive and negative feedback
regulations of immune and physiological processes engaged in virus-host interactions. The
fundamental questions towards understanding the pathogenesis of HIV infection are now
shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally
disrupted? (ii)...
The paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including...
Cell-based, mathematical models help
make sense of morphogenesis—i.e. cells organizing into
shape and pattern—by capturing cell behavior in simple, purely
descriptive models. Cell-based models then predict the
tissue-level patterns the cells produce collectively. The first
step in a cell-based modeling approach is to isolate
sub-processes, e.g. the patterning capabilities of one or a
few cell types in cell cultures. Cell-based models can then
identify the mechanisms responsible for patterning in...
Two main approaches have been considered for modelling the dynamics of the SIS model on
complex metapopulations, i.e, networks of populations connected by migratory flows whose
configurations are described in terms of the connectivity distribution of nodes (patches)
and the conditional probabilities of connections among classes of nodes sharing the same
degree. In the first approach migration and transmission/recovery process alternate
sequentially,...
In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a...
Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneously
bind a single receptor. This result if often employed to interpret the Hill coefficient as
the number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibrium
states of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively and
in a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate,
but only an upper...
This paper proposes a quantitative model of the reaction-diffusion type to examine the
distribution of interferon-α (IFNα) in a lymph node
(LN). The numerical treatment of the model is based on using an original unstructured mesh
generation software Ani3D and nonlinear finite volume method for diffusion equations. The
study results in suggestion that due to the variations in hydraulic conductivity of
various zones of the secondary lymphoid organs...
This paper investigates the output controllability problem of temporal Boolean networks with inputs (control nodes) and outputs (controlled nodes). A temporal Boolean network is a logical dynamic system describing cellular networks with time delays. Using semi-tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems. Some necessary and sufficient conditions on the output controllability via two kinds of inputs are obtained by providing...
In this paper we build and analyze networks using the statistical and programming
environment R and the igraph package. We investigate random, small-world, and scale-free
networks and test a standard problem of connectivity on a random graph. We then develop a
method to study how vaccination can alter the structure of a disease transmission network.
We also discuss a variety of other uses for networks in biology.
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...
In proteomics study, Imaging Mass Spectrometry (IMS) is an emerging and very promising
new technique for protein analysis from intact biological tissues. Though it has shown
great potential and is very promising for rapid mapping of protein localization and the
detection of sizeable differences in protein expression, challenges remain in data
processing due to the difficulty of high dimensionality and the fact that the number of
input variables in...
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