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Hill Equation

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Hill function; Hill kinetics


Several molecular interactions in cellular systems exhibit sigmoidal response curve to variations in the input concentrations. Such a response curve is typically represented by Hill equation as given below.

$$ Y = \left( {\frac{{{I^{{{n_H}}}}}}{{K_{{0.5}}^{{{n_H}}} + {I^{{{n_H}}}}}}} \right) $$

where Y is the output response and I is the input concentration. Hill equation involves two parameters, Hill Coefficient \( ({n_H}) \) and half-saturation constant (K 0.5). While Hill coefficient characterizes the sensitivity of the response, the half-saturation constant quantifies the threshold concentration required for 50% output response. Hill equation is typically used to quantify cooperativity, where the initial binding of an effecter molecule (ligand, activator) to the receptor enhances the binding of the forthcoming effecter molecules (Goldbeter and Dupont 1990). This is observed in allosteric regulation of enzymes and of ligands...

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Hill Equation, Fig. 1
Hill Equation, Fig. 2


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Somvanshi, P.R., Venkatesh, K.V. (2013). Hill Equation. In: Dubitzky, W., Wolkenhauer, O., Cho, KH., Yokota, H. (eds) Encyclopedia of Systems Biology. Springer, New York, NY.

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