Mathematical modeling of the lambda switch: a fuzzy logic approach.
Gene regulation plays a central role in the development and functioning of living organisms. Gaining a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the 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 Lambda switch.
Laschov
Dmitriy
D
School of Electrical Engineering-Systems, Tel Aviv University, 69978 Tel Aviv, Israel.
Margaliot
Michael
M
D000818:Animals; D010582:Bacteriophage lambda / Q000235:genetics* / Q000502:physiology; D044127:Epigenesis, Genetic / Q000502:physiology; D017143:Fuzzy Logic; D015967:Gene Expression Regulation, Viral / Q000502:physiology*; D053263:Gene Regulatory Networks / Q000502:physiology; D008957:Models, Genetic