63 research outputs found
Algebraic and Topological Indices of Molecular Pathway Networks in Human Cancers
Protein-protein interaction networks associated with diseases have gained
prominence as an area of research. We investigate algebraic and topological
indices for protein-protein interaction networks of 11 human cancers derived
from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a
strong correlation between relative automorphism group sizes and topological
network complexities on the one hand and five year survival probabilities on
the other hand. Moreover, we identify several protein families (e.g. PIK, ITG,
AKT families) that are repeated motifs in many of the cancer pathways.
Interestingly, these sources of symmetry are often central rather than
peripheral. Our results can aide in identification of promising targets for
anti-cancer drugs. Beyond that, we provide a unifying framework to study
protein-protein interaction networks of families of related diseases (e.g.
neurodegenerative diseases, viral diseases, substance abuse disorders).Comment: 15 pages, 4 figure
Scaling behavior of drug transport and absorption in in silico cerebral capillary networks
Drug delivery to the brain is challenging due to the presence of the blood-brain barrier. Mathematical modeling and simulation are essential tools for the deeper understanding of transport processes in the blood, across the blood-brain barrier and within the tissue. Here we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids. We apply our model to the delivery of L-Dopa, the primary drug used in the therapy of Parkinson\u27s Disease. Our model replicates observed blood flow rates and ratios between plasma and tissue concentrations. We propose an optimal network grain size for the simulation of tissue volumes of 1 cm3 that allows to make reliable predictions with reasonable computational costs
Predicting the Drug Release Kinetics of Matrix Tablets
In this paper we develop two mathematical models to predict the release
kinetics of a water soluble drug from a polymer/excipient matrix tablet. The
first of our models consists of a random walk on a weighted graph, where the
vertices of the graph represent particles of drug, excipient and polymer,
respectively. The graph itself is the contact graph of a multidisperse random
sphere packing. The second model describes the dissolution and the subsequent
diffusion of the active drug out of a porous matrix using a system of partial
differential equations. The predictions of both models show good qualitative
agreement with experimental release curves. The models will provide tools for
designing better controlled release devices.Comment: 17 pages, 7 figures; Elaborated at the first Workshop on the
Application of Mathematics to Problems in Biomedicine, December 17-19, 2007
at the University of Otago in Dunedin, New Zealan
Partial differential equation models for intranuclear diffusion, inverse problems in nanobiology and cell cycle specific effects of anticancer drugs
Corrigendum to "Pathogen evolution in switching environments: A hybrid dynamical system approach" [Math. Biosci. 240 (2012) 70-75]
A mathematical model quantifies proliferation and motility effects of TGF-- on cancer cells
Transforming growth factor (TGF) is known to have properties of both
a tumor suppressor and a tumor promoter. While it inhibits cell proliferation,
it also increases cell motility and decreases cell--cell adhesion. Coupling
mathematical modeling and experiments, we investigate the growth and motility
of oncogene--expressing human mammary epithelial cells under exposure to
TGF--. We use a version of the well--known Fisher--Kolmogorov equation,
and prescribe a procedure for its parametrization. We quantify the simultaneous
effects of TGF-- to increase the tendency of individual cells and cell
clusters to move randomly and to decrease overall population growth. We
demonstrate that in experiments with TGF-- treated cells \textit{in
vitro}, TGF-- increases cell motility by a factor of 2 and decreases
cell proliferation by a factor of 1/2 in comparison with untreated cells.Comment: 15 pages, 4 figures; to appear in Computational and Mathematical
Methods in Medicin
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