The architecture of viral capsids based on tiling theory.
The Effect of Bacteria on Epidermal Wound Healing
Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an...
The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response
We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some...
The electrokinetic model of matter transport through biological barriers
The onset of necrosis in a 3D cellular automaton model of EMT6 multi-cellular spheroids
A 3-dimensional (3D) extension to a previously reported scaled 2-dimensional Cellular Automaton (CA) model of avascular multi-cellular spheroid growth is presented and analysed for the EMT6/Ro cell line. The model outputs are found to compare favourably with reported experimentally obtained data for in vitro spheroids of the same cell line. Necrosis (unprogrammed central cell death) is observed to be delayed when compared with the experimental data. Furthermore, it is found that necrosis arises...
The role of cell motility in metastatic cell dominance phenomenon: Analysis by a mathematical model.
The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts
Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...
The Use of CFSE-like Dyes for Measuring Lymphocyte Proliferation : Experimental Considerations and Biological Variables
The measurement of CFSE dilution by flow cytometry is a powerful experimental tool to measure lymphocyte proliferation. CFSE fluorescence precisely halves after each cell division in a highly predictable manner and is thus highly amenable to mathematical modelling. However, there are several biological and experimental conditions that can affect the quality of the proliferation data generated, which may be important to consider when modelling dye...
Thymic presentation of autoantigens and the efficiency of negative selection.
Towards Sub-cellular Modeling with Delaunay Triangulation
In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...
Transport equations in cell population dynamics. I.
Transport equations in cell population dynamics. II.
Transport in a molecular motor system
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
Transport in a molecular motor system
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.