Limits
2 problems · hints, answers and solutions shown beside each one
Consider the Michaelis-Menten kinetics where the speed of an enzyme-catalyzed reaction is given by .
Explain the statement that “when is large there is a horizontal asymptote” and find the value of to which that asymptote approaches.
Determine the reaction speed when and explain why the constant is sometimes called the “half-max” concentration.
– half the maximum rate
Hill functions are sometimes used to represent a biochemical “switch,” that is a rapid transition from one state to another. Consider the functions:
where .
Where do these functions intersect?
What are the asymptotes of these functions?
Which of these functions increases fastest near the origin?
Which is the sharpest “switch” and why?
Both have horizontal asymptotes at
(reasoning not provided)
These questions are adapted from Keshet, Chapter 1. Note that text does not provide entire solutions.
From the UBC Math 100 open textbook project, © Joel Feldman, Andrew Rechnitzer, Elyse Yeager and others. Licensed CC BY-NC-SA 4.0; this HTML adaptation is released under the same licence. Full attribution.
