Hill function

IGF-1 production is modeled by the Hill function shown in brackets, where Smax = maximum IGF stimulation of kj by rhGH, S50 = rhGH concentration for 50% maximal stimulation of fcf , [GH] = rhGH concentration, y = the Hill coefficient, and = elimination rate of IGF-1. (Modified from Sun YN et al. J Pharmacol Exp Ther 1999 289 1523 2.)... 

Organotransition Metal Chemistry A F Hill Functional Group Chemistry 7 R //aasow Thermodynamics and Statistical Mechanics J D Gale and J M Seddon d- and f-Block Chemistry C Jones Mechanisms in Organic Reactions R A Jackson... 

In Section II, we demonstrate this approach with an equation that incorporates a nonlinear Hill function to model genetic control representing a mutually inhibitory network of two elements [26], and an inhibitory loop of three elements [27]. Although theoretical models of these types of networks have been known for at least 30 years [20, 32, 33], they took on new life in 2000 with the construction of genetic regulatory circuits in bacteria that were well described by the equations. 

In Section III, we show that in the limit when the Hill function control becomes infinitely steep, complex functional control can be represented by logical functions. In this limit the continuous nonlinear differential equation... 

An item about which there is a divergence in viewpoint at present concerns the interactions between non-identical atoms. If we use the Hill function as a vehicle for the discussion (not all workers use this function, but their functions can be recast in this form), there are just two variables to consider a distance parameter (r ) and a hardness parameter (e). Most workers take the sum of the radii of the individual atoms interacting as r, but this is not universally done. The parameter e was taken originally by Hill to be the product of the square roots of the e-values for the interacting atoms, which is what simple physical considerations seem to dictate (Hirschfelder et al.,... 

Another factor that favours oscillations is the steepness of the function characterizing the repression of per transcription by nuclear PER. Such steepness depends on the degree of cooperativity, n, of the repression process, which is described in eqn (11.1a) by a Hill function. In agreement with such a destabilizing role of cooperativity, oscillations in fig. 11.7 were obtained for a value of n = 4 however, periodic behaviour can also occur in the model for n = 2 and for n = 1, but the domain in parameter space where sustained oscillations occur is smaller than for n = 4. 

E. Hille, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, 1948. 

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