Modeling Notch Signaling: A Practical Tutorial
Theoretical and computational approaches for understanding different aspects of Notch signaling and Notch dependent patterning are gaining popularity in recent years. These in silico methodologies can provide dynamic insights that are often not intuitive and may help guide experiments aimed at elucidating these processes. This chapter is an introductory tutorial intended to allow someone with basic mathematical and computational knowledge to explore new mathematical models of Notch-mediated processes and perform numerical simulations of these models. In particular, we explain how to define and simulate models of lateral inhibition patterning processes. We provide a Matlab code for simulating various lateral inhibition models in a simple and intuitive manner, and show how to present the results from the computational models. This code can be used as a starting point for exploring more specific models that include additional aspects of the Notch pathway and its regulation.
Key wordsMathematical modeling Simulations Lateral inhibition Notch signaling Cis-interactions Cell-to-cell communication Pattern formation
The code used in this manuscript was loosely based on a code written together with Michael Elowitz, Amit Lakhanpal, and Jordi Garcia-Ojalvo. We would like to thank Iftach Nachman and Oren Shaya for their instructive comments of the manuscript. D. S. would like to thank the support of the Community under a Marie Curie European Reintegration Grant and a grant from the Israel Science Foundation (grant 1021/11).
- 13.Formosa-Jordan P, Ibañes M (2009) Diffusible ligand and lateral inhibition dynamics for pattern formation. J Stat Mech Theor E 2009, P03019Google Scholar
- 25.Alon U (2007) An introduction to systems biology: design principles of biological circuits. CRC Press, Boca Raton, FLGoogle Scholar
- 26.Murray JD (2002) Mathematical biology. Springer, New YorkGoogle Scholar
- 29.Fiuza U, Klein T, Martinez Arias A et al (2010) Mechanisms of ligand-mediated inhibition in Notch signaling activity in Drosophila. Dev Dyn 239:798–805Google Scholar
- 30.Formosa-Jordan P, Ibañes M (2014) Competition in Notch Signaling with Cis Enriches Cell Fate Decisions. PLoS One 9:e95744Google Scholar
- 43.Gardiner C (2004) Handbook of stochastic methods: for physics, chemistry & the natural sciences, vol 13, Series in synergetics. Springer, New YorkGoogle Scholar
- 47.Petrovic J, Formosa-Jordan P, Luna-Escalante JC et al (2014) Ligand-dependent Notch signaling strength orchestrates lateral induction and lateral inhibition in the developing inner ear. Development 141:2313–2324Google Scholar
- 49.Garcia-Ojalvo J (2011) Physical approaches to the dynamics of genetic circuits: a tutorial. Contemp Phys 52:439–464Google Scholar
- 51.Strogatz S (2001) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Westview Press, CambridgeGoogle Scholar
- 52.Formosa-Jordan P (2013) Pattern formation through lateral inhibition mediated by Notch signaling. University of Barcelona, BarcelonaGoogle Scholar