. 2014 Oct 22;6:plu066. doi: 10.1093/aobpla/plu066

Table 1.

Comparison of the parameters of the Michaelis–Menten equation, and the Holling disc equation. The two models are built from an equation of the same general form (Real 1977) and the two equations model identical processes in plants and animals. This produces interchangeable parameters, where the units of measurement also perfectly translate.

	Parameters	Units	Biological meaning
Holling disc equation	$a = V_{max} / K_{m}$	L g⁻¹ min⁻¹	Effective encounter rate or search efficiency; the maximum volume of nutrients of concentration R (µmol/L) that are encountered per gram of root per minute.
Holling disc equation	$h = 1 / V_{max}$	min g µmol⁻¹	Handling time: the time taken for 1 µmol of nutrient to be captured by a gram of root
Michaelis–Menten equation	$V_{\max} = 1 / h$	µmol g⁻¹ min⁻¹	Maximum theoretical rate of nutrient uptake, per gram of root.
Michaelis–Menten equation	$K_{m} = 1 / a h$	µmol L⁻¹	Half saturation constant or the nutrient concentration where the rate of uptake is half of V_max. This is sometimes called the enzyme affinity for the substrate.