Biphasic Exponential Decay and Growth

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This Demonstration plots the decay or growth curve of a biphasic process or reaction whose two stages follow first-order kinetics. The parameters of the process are the exponential rate constants of the two stages and the time that marks the transition between them.

Contributed by: Mark D. Normand and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: biphasic decay where the first phase is slower than the second

Snapshot 2: biphasic growth where the first phase is faster than the second

Snapshot 3: biphasic growth where the first phase is slower than the second

Several biochemical reactions and biological processes can be considered biphasic; that is, they have both fast and slow kinetics and a transition between them. If the two phases follow first-order kinetics with exponential rate constants and , and the transition between them occurs at time , then the process's product can be described by if and if . In growth or accumulation processes the terms on the right side of the equation are all positive and in decay or degradation they are negative.

This Demonstration helps the user to visualize the progress of such processes. It plots decay or growth curves by setting the exponential rate constants of the two phases, and , and the transition time, . The user can choose between decay and growth processes with a selector switch and enter the values of the rate constants and the transition time using sliders. The maximum value displayed on the , , and axes is also entered with sliders.

Notice that if is set to 0, then the plot will be of a conventional first-order kinetics having an exponential rate constant . If is set to a value greater than or equal to the axis maximum, then the plot will be of a conventional first-order kinetics having an exponential rate constant .

Reference:

M. A. J. S. von Boekel, Kinetic Modeling of Reactions in Foods, Boca Raton: CRC Press, 2008.

M. G. Corradini, M. D. Normand, and M. Peleg, "Modeling Non-Isothermal Heat Inactivation of Microorganisms Having Biphasic Isothermal Survival Curves," International Journal of Food Microbiology, 116(3), 2007 pp. 391–399.



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