Enzyme Kinetics and the Michaelis-Menten Equation

Abstract

Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by doubling, later predominantly in a linear way. Observation of the number of DNA molecules in the experiment becomes possible only when it is substantially larger than initial numbers, and then possibly affected by the randomness in individual replica-tion. Can the initial copy number still be determined? This is a classical problem and, indeed, a concrete special case of the general problem of determining the number of ancestors, mutants or invaders, of a population observed only later. We approach it through a generalised version of the branching process model introduced in Jagers and Klebaner (J Theor Biol 224(3):299-304, 2003. 123 680 P. Chigansky et al. strange way, determination of the initial number turns out to be completely possible if the initial rate v is one, i.e all DNA strands replicate, but only partly so when v < 1, and thus the initial rate or probability of succesful replication is lower than one. Then, the starting molecule number becomes hidden behind a "veil of uncertainty". This is a special case, of a hitherto unobserved general phenomenon in population growth processes, which will be adressed elsewhere.

Label-Free Detection of Doxorubicin in Lake Water by an Electrochemical Aptamer Biosensor

“…This detection mechanism is similar to the catalytic reaction of an enzyme, so we used the Michaelis-Menten equation to fit the calibration curve. Change in DOX concentration with respect to the peak current is in accordance with the Michaelis-Menten equation [35].…”

Developing a three‐dimensional animation for deeper molecular understanding of michaelis–menten enzyme kinetics

“…Enzymes are biological catalysts that increase the rates of cellular reactions by decreasing the activation energies required to transform chemical substrates into products. The study of these reaction rates is called enzyme kinetics, where Michaelis–Menten kinetics is one of the best known kinetic models . This mathematical model describes a simple dynamic system consisting of a binding interaction between an enzyme and a substrate to form an enzyme–substrate complex before the substrate irreversibly converts to a product.…”