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Lambert W function
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In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f = w e w, where w
Plot of the imaginary part of Wn(x + iy) for branches n = −2, −1, 0, 1, 2. The plot is similar to that of the multivalued complex logarithm function e
Plot of the imaginary part of Wn(x + iy) for branches n = −2, −1, 0, 1, 2. The plot is similar to that of the multivalued complex logarithm function except that the spacing between sheets is not constant and the connection of the principal sheet is different
Invert W
Invert W
The range of the W function, showing all branches. The black curves (including the real axis) form the image of the real axis, the orange curves are t
The range of the W function, showing all branches. The black curves (including the real axis) form the image of the real axis, the orange curves are the image of the imaginary axis. The purple curve and circle are the image of a small circle around the point z = 0; the red curves are the image of a small circle around the point z = −1/e.
Michaelis–Menten kinetics
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In biochemistry, Michaelis–Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions involving the transformation of
Lambert W function
…as y ′ ( t ) = a y ( t − 1 ) . In biochemistry, and in particular enzyme kinetics, an opened-form solution for the time-course kinetics analysis of Michaelis–Menten kinetics is described in terms of the Lambert W function. The notation convention chosen here (with W 0 and W − 1 ) follows the canonical reference on the Lambert…
Curve of the Michaelis–Menten equation labelled in accordance with IUBMB recommendations
Curve of the Michaelis–Menten equation labelled in accordance with IUBMB recommendations
Semi-logarithmic plot of Michaelis–Menten data
Semi-logarithmic plot of Michaelis–Menten data
The reaction changes from approximately first-order in substrate concentration at low concentrations to approximately zeroth order at high concentrati
The reaction changes from approximately first-order in substrate concentration at low concentrations to approximately zeroth order at high concentrations.