An activator gene follows the Hill activation function with and Hill coefficient

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Genetic circuits, regulation and biological information · Genetic circuits, regulation and biological information

Forces, Machines and Signals, Ch Genetic circuits and biological pattern

Problem

An activator gene follows the Hill activation function

f(x) = \dfrac{(x/K)^{n_H}}{1+(x/K)^{n_H}}

with

K = 200\,\mathrm{nM}

and Hill coefficient

n_H = 3

, where

x

is the concentration of the activating regulator. ((a)) Find the regulator concentration

x_{10}

at which

f = 0.10

and the concentration

x_{90}

at which

f = 0.90

. ((b)) Compute the fold change

x_{90}/x_{10}

and compare it with

81^{1/n_H}

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