By Uri Alon
Provides layout ideas that govern the constitution and behaviour of organic networks comparable to gene circuits, highlighting basic, ordinary circuit parts that make up the community. This e-book presents a quantitative thought for which circuits are present in a given atmosphere and a mathematical framework for figuring out organic circuits.
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Extra resources for An Introduction to Systems Biology: Design Principles of Biological Circuits
5) (See color insert following page 112). , 2002; Beer and Tavazoie, 2004). The functional form of input functions can be readily changed by means of mutations in the promoter of the regulated gene. , 2006). It appears that the precise form of the input function of each gene is under selection pressure during evolution. 5 (See color insert following page 112) Two-dimensional input functions. (a) Input function measured in the lac promoter of E. coli, as a function of two input signals, the inducers cAMP and IPTG.
The higher n is, the weaker the dependence of the steady state on b. In other words, robustness to variations in production rates increases with the Hill coefficient. For Hill coefficient n = 4, for example, S(Xst, b) = 1/5, which means that a 10% change in b yields only a 2% change in Xst. In the limit of very high n, the steadystate does not depend at all on production or degradation rates, Xst = K. This is the steady-state solution found in the main text for the logic input function. Simple regulation is equivalent to n = 0, so that S(Xst, b) = 1.
4a). Typically, input functions are moderately steep, with n = 1 – 4. As do many functions in biology, the Hill function approaches a limiting value at high levels of X*, rather than increasing indefinitely. This saturation of the Hill function at high X* concentration is fundamentally due to the fact that the probability that the activator binds the promoter cannot exceed 1, no matter how high the concentration of X*. The Hill equation often describes empirical data with good precision. 4 (a) Input functions for activator X described by Hill functions with Hill coefficient n = 1, 2, and 4.
An Introduction to Systems Biology: Design Principles of Biological Circuits by Uri Alon