The Michaelis-Menten constant, often denoted by Km, is a fundamental concept in enzyme kinetics. It quantitatively analyzes how enzymes act as biological catalysts to speed up the rate of biochemical reactions.
The Km is the substrate concentration at which an enzyme reaches half of its maximum rate of reaction, or Vmax/2. It is determined experimentally from measurements of enzyme activity at various substrate concentrations and using a combination of the Michaelis-Menten equation and the Lineweaver-Burk plot.
Mathematically, Km values can be defined in terms of the rate constants of the enzyme kinetics. If k1 is the rate constant for the reaction of enzyme E and substrate S to form the enzyme-substrate complex ES, and k-1 is the rate constant for the reverse reaction (dissociation of ES back to E + S), then
Km = (k-1 + k2) / k1
where k2 is the rate constant for the conversion of ES to E and product P.
Importantly, Km provides information about the affinity of an enzyme for its substrate; a lower Km value indicates higher affinity because less substrate is needed for the enzyme to reach half of its maximum rate of reaction.
if Km is higher then K1 will lower
So the rate of complex formation is very low i.e enzyme has lower affinity to the substrate.