Probably the big reason you were unsuccessful in your previous searches is that nobody quite knows exactly how enzymes' 3D structures lead to particular kinetic parameters.
It's wrapped up in the concept of "how the heck do enzymes work, anyway?" -- surprisingly, it's a question we don't really have a good answer to. The leading concept currently - influenced in large part by catalytic antibodies - is the transition state stabilization theory. That is, enzymes work by preferentially stabilizing the transition state, reducing the activation energy of the reaction. (A good overview of the theory can be found in Structure and Mechanism in Protein Science by Alan Fersht, one of the must-reads for anyone interested in enzymes.)
But that's probably not all of how enzymes work, or at the very least "bind the transition state well" is a rather coarse overview of the process. There's thoughts that the precise arrangement of active site sidechains are involved in a quantum mechanical interaction with the transition state. This is the "theozyme" concept put forth by Kendall Houk and colleagues.
The role of enzyme flexibility in catalysis is a highly disputed topic currently. The dynamics of proteins are an important concept for the understanding of the full reaction pathway, but there are some people who think that an important contribution of the protein is funneling vibrational energy into the appropriate bond motions for catalyssi. Nobel prize winner Arieh Warshel is (vocally) against it, though, favoring an electrostatic view of catalysis. (That is, enzymes work by stabilizing the charge distributions found in the catalytic pathways.)
So the long and the short of it is that we really don't understand how enzymes work, so we're rather far from being able to predict how the 3D structure changes the catalytic parameters. There are a number of efforts (particular from David Baker's lab) trying to use computational modeling of 3D enzyme structures to design enzymes, but the results have been rather modest. While such enzymes have been designed, their activities have been modest, and nowhere near the activity of native enzymes.
Doing the reverse - trying to predict the catalytic activity from 3D structures - is difficult, given the lack of knowledge. That's not to say people haven't tried. For example, there's been some efforts to use machine learning to predict catalytic constants from different mutants in a series. The problem with machine learning-type approaches is that the results tend to be only applicable for the particular system they've been trained on, and there's only limited interpretability of the results.