TY - CHAP
T1 - Mathematical modeling of the λ switch
T2 - A fuzzy logic approach
AU - Laschov, Dmitriy
AU - Margaliot, Michael
PY - 2009
Y1 - 2009
N2 - Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The λ switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the λ switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the λ switch.
AB - Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The λ switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the λ switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the λ switch.
UR - http://www.scopus.com/inward/record.url?scp=84898503464&partnerID=8YFLogxK
U2 - 10.4018/978-1-60566-685-3.ch024
DO - 10.4018/978-1-60566-685-3.ch024
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AN - SCOPUS:84898503464
SN - 9781605666853
SP - 573
EP - 603
BT - Handbook of Research on Computational Methodologies in Gene Regulatory Networks
PB - IGI Global
ER -