Linear Algebra - Least Squares Approximation - 10 - Fitting data to the Michaelis--Menten equation
Channel: Arthur Parzygnat
Date: 2023-01-31

We go through another example to illustrate how least squares works for more general functions. In this case, we go through the Michaelis--Menten equation from biochemistry. We do this first abstractly and then explicitly with numbers (real data borrowed from my friend!) using Mathematica. The Michaelis--Menten equation is used to model the reaction rate for a particular enzyme reaction to take place as a function of the substrate concentration. One of the subtle points about using our setup of fitting data to curves is that the form of the Michaelis--Menten equation is not provided as a linear combination of functions in the independent variable. In this video, I illustrate one approach towards fitting data to this curve (I believe there are better methods, and I hope to revisit this topic in the future). 

This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.

The next video on Special Topics in Linear Algebra changes to an independent topic, which is on Hamming's error correcting codes https://youtu.be/1DN2zDg5ew8

The previous video on Special Topics in Linear Algebra is fitting data to more general functions example: https://youtu.be/KThg6-XLWx8

An earlier video on fitting data to more general functions: https://youtu.be/w_pqFOfLiP0

These videos were created during the 2019 Spring semester at the UConn CETL Lightboard Room.