Final answer:
The Michaelis-Menten equation models the hyperbolic relationship between the rate of an enzyme-catalyzed reaction and substrate concentration. It describes how the reaction velocity approaches a maximum (Vmax) as substrate concentration increases, with the Michaelis constant (Km) representing the substrate concentration at half-maximal velocity. It is based on theoretical assumptions that align with the observed kinetics of enzymatic reactions.
Step-by-step explanation:
The Michaelis-Menten equation describes the hyperbolic relationship between the rate of an enzyme-catalyzed reaction and the concentration of the substrate. The relationship is given by the equation V = Vmax[S] / (Km + [S]), where V is the reaction velocity, Vmax is the maximum velocity achieved by the system, [S] is the substrate concentration, and Km is the Michaelis constant, a value that represents the substrate concentration at which the reaction velocity is half of Vmax. This hyperbolic plot signifies that as [S] increases, the reaction velocity (V) approaches Vmax, indicating that all enzyme active sites are saturated with substrate. When substrate concentration is so high that [S]>>(Km), the equation simplifies and the velocity reaches Vmax, showing no further increase with additional substrate due to enzyme saturation.
The Michaelis-Menten equation is derived based on assumptions detailed by Michaelis, Menten, Briggs, and Haldane. These assumptions are made to solve previous rate equations that did not account for the hyperbolic kinetics observed in enzymatic reactions. For practical applications, the Lineweaver-Burk plot can be used, which linearizes the Michaelis-Menten equation to help determine Km and Vmax more precisely.