ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

A MATHEMATICAL MODEL FOR CELL DEFORMATION UNDER
CHEMOTAXIS INDUCED CELL MOTION
1. ABSTRACT
F.J. Vermolen 1 and A. Gefen 2
We present a three-dimensional model for cell deformation and motion under the
influence of a chemo-attractant. The model, describing the temporal evolution of the
cell geometry, is applied to determine qualitatively and quantitatively the impact of
cellular defects, like the cell stiffness and motility, on the time needed to engulf
bacteria. Our formalism is able to quantify the influence of cellular diseases on the
immunity system of an organism.
2. INTRODUCTION
Cells are well-known to migrate and to deform under chemical stimulation. An
important example is our immunity system, where the immunity response is initiated
by, amongst others, a bacterial secretion of chemicals that activate cells like phagocytes,
macrophages, or lymphocytes to move towards the bacteria and subsequently neutralize
them by engulfment. Next to immunity responses, one can think of processes like
wound healing, tumor growth and organ development where cells migrate, deform,
proliferate, differentiate or decease. In all the aforementioned processes, cell
deformation is an important issue on the smallest cellular scale. The aforementioned
processes are modeled at several scales: (1) the cellular scale, with examples of
modeling studies in [1,2], (2) cell colony scale with several hundreds or thousands of
cells, with examples of modeling studies in [3,4], and on the (3) tissue scale, where the
cells are not modeled individually, but merely by means of average quantities such as
cell densities using continuum models based on (systems of) partial differential
equations, for studies about these models, we refer to references [5,6].
In the present paper, we consider cell deformation on the cellular scale, where the
evolution of the cell-shape and position are modeled in the course of time. First, we
present the model hypotheses, and refer to [1] for more details concerning the
mathematical relations, then we briefly discuss the numerical implementation. Further,
some computed results in terms of an example of several snapshots of the temporal
evolution of the cell-shape are presented. Here, we also quantify the influence of
cellular defects that deteriorate the cell stiffness and mobility. We end up with a brief
discussion and some conclusions. The main innovation of the present conference paper
is the application of the model formulated in [1] to bacterial sources and the
quantification of the variation of several parameters like the cell stiffness and motility
1
Associate Professor, Delft Institute of Applied Mathematics, Delft University of Technology,
Mekelweg 4, 2628 CD Delft, The Netherlands
2
Associate Professor, Department of Biomedical Engineering , University of Tel Aviv, 69978
Tel Aviv, Israel