# how to tell MATLAB to rewrite a complex equation into a michaelis-menten form equation?

I'm using MATLAB to derive rate equations for enzyme kinetic mechanisms. These rate equations are usually very large and contain lots of k-values (k1, k2, k3,...). The simplest output that matlab generates is an equation like this:

v = -k3*k1*s/(-k2-k3-k1*s)

I would like to tell MATLAB to rewrite this equation into the standard michaelis-menten type equation: v = vm*s/(km+s), where vm and km stand for the k-values. In this simple case this would yield:

v = k3*s/((k2+k3)/k1+s)

Does anyone know how to do this? thanks!

## Answers

Here’s something you could try:

syms vm km s pattern = vm*s/(km+s); values = solve(v == pattern, vm, km); subs(pattern, values)

I don’t think there’s any reason to switch to a different system, really, unless of course you prefer another system for other reasons. MATLAB does this sort of manipulations just fine (with the Symbolic Math Toolbox, in this case, but from your question, I kind of assumed you have that).