Abstract
Biological cell networks exhibit complex combinations of both discrete and continuous behaviors: indeed, the dynamics that govern the spatial and temporal increase or decrease of protein concentration inside a single cell are continuous differential equations, while the activation or deactivation of these continuous dynamics are triggered by discrete switches which encode protein concentrations reaching given thresholds. In this paper, we model as a hybrid system a striking example of this behavior in a biological mechanism called Delta-Notch signaling, which is thought to be the primary mechanism of cell differentiation in a variety of cell networks. We present results in both simulation and reachability analysis of this hybrid system.We emphasize how the hybrid system model is computationally superior (for both simulation and analysis) to other nonlinear models in the literature, without compromising faithful modeling of the biological phenomena.
The authors would like to acknowledge Harley McAdams, Mikael Johansson, Da- vid Dill and Henny Sipma. This research is supported by DARPA under the Bio:Info:Micro program, grant MDA972-00-1-0032.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Lewis Wolpert. Principles of Development. Current Biology Ltd and Oxford University Press, 1998.
Julian Lewis. Notch signalling and the control of cell fate choices in vertebrates. Seminars in Cell & Developmental Biology, 9:583–589, 1998.
G. Marnellos, G. A. Deblandre, E. Mjolsness, and C. Kintner. Delta-notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: experimental observations and a gene network model. In Pacific Symposium on Biocomputing, pages 5:326–337, 2000.
Pascal O. Luthi, Bastien Chopard, Anette Preiss, and Jeremy J. Ramsden. A cellular automaton model for neurogenesis in Drosophila. DrosophilaPhysica D, (118):151–160, 1998.
G. Marnellos and E. Mjolsness. A gene network approach to modeling early neurogenesis in Drosophila. In Pacific Symposium on Biocomputing, pages 3:30–41, 1998.
Catherine Haddon, Yun-Jin Jiang, Lucy Smithers, and Julian Lewis. Delta-notch signalling and the patterning of sensory cell differentiation in the zebrafish ear: evidence from the mind bomb mutant. Development, 125:4637–4644, 1998.
Rebecca Crowe, Domingos Henrique, David Ish-Horowicz, and Lee Niswander. A new role for notch and delta in cell fate decisions: pattering the feather array. Development, 125:767–775, 1998.
Stacey S. Huppert, Thomas L. Jacobsen, and Marc A. T. Muskavitch. Feedback regulation is central to delta-notch signalling required for Drosophila wing vein morphogenesis. Development, 124:3283–3291, 1997.
Daniel J. Moloney, Vladislav M. Panin, Stuart H. Johnston, Jihua Chen, Li Shao, Richa Wilson, Yang Wang, Pamela Stanley, Kenneth D. Irvine, Robert S. Haltiwanger, and Thomas F. Vogt. Fringe is a glycosyltransferase that modifies notch. Nature, 406(27):369–375, July 2000.
Sarah Bray. Notch signalling in Drosophila: three ways to use a pathway. Seminars in Cell & Developmental Biology, 9:591–597, 1998.
A. M. Turing. The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. B, 237(641):37–72, August 1952.
George F. Oster. Lateral inhibition models of developmental processes. Mathematical Biosciences, 90:265–286, 1988.
Joanne R. Collier, Nicholas A. M. Monk, Philip K. Maini, and Julian H. Lewis. Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling. J. theor. Biol., (183):429–446, 1996.
Eric Mjolsness, David H. Sharp, and John Reinitz. A connectionist model of development. J. theor. Biol., 152:429–453, 1991.
Harley H. McAdams and Adam Arkin. Simulation of prokaryotic genetic circuits. Annu. Rev. Biophys. Biomol. Struct., 27:199–224, 1998.
John J. Tyson, Bela Novak, Garrett M. Odell, Kathy Chen, and C. Dennis Thron. Chemical kinetic theory: understanding cell-cycle regulation. TIBS, 21:89–96, March 1996.
C. Tomlin, J. Lygeros, and S. Sastry. Controller design for hybrid systems. Proceedings of the IEEE, 88(7), July 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ghosh, R., Tomlin, C.J. (2001). Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_21
Download citation
DOI: https://doi.org/10.1007/3-540-45351-2_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41866-5
Online ISBN: 978-3-540-45351-2
eBook Packages: Springer Book Archive