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Issue No. 06 - Nov.-Dec. (2012 vol. 9)
ISSN: 1545-5963
pp: 1607-1620
A. Abate , Delft Center for Syst. & Control, Delft Univ. of Technol., Delft, Netherlands
S. Vincent , Ecole Normale Super. de Lyon, Lyon, France
R. Dobbe , Delft Center for Syst. & Control, Delft Univ. of Technol., Delft, Netherlands
A. Silletti , Dept. of Inf. Eng., Univ. of Padova, Padua, Italy
N. Master , Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA
J. D. Axelrod , Dept. of Pathology, Stanford Univ., Stanford, CA, USA
C. J. Tomlin , Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA
ABSTRACT
Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution, we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).
INDEX TERMS
Cells (biology), Computational modeling, Finite element methods, Mechanical factors, Mathematical model, Biological system modeling,morphogenesis, Epithelium, cellular network, nonlinear dynamical model, spring-damper system, discrete element method, early dorsal closure
CITATION
A. Abate, S. Vincent, R. Dobbe, A. Silletti, N. Master, J. D. Axelrod, C. J. Tomlin, "A Mathematical Model to Study the Dynamics of Epithelial Cellular Networks", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. , pp. 1607-1620, Nov.-Dec. 2012, doi:10.1109/TCBB.2012.126
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