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A Mathematical Model to Study the Dynamics of Epithelial Cellular Networks
Nov.-Dec. 2012 (vol. 9 no. 6)
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
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:
zoology,biological tissues,biomechanics,cellular biophysics,physiological models,germband retraction,mathematical model,epithelial cellular network dynamics,connected cells,sheets,animal kingdom,single-layered epithelial tissues,mechanical systems,point masses,mechanical properties,network topology,actual cellular geometry extraction,mechanical structure,mechanical dynamics,spring-damper elements,morphogenesis,Drosophila melanogaster embryo,dorsal epithelium,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. 6, pp. 1607-1620, Nov.-Dec. 2012, doi:10.1109/TCBB.2012.126
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