How does collaboration on reconstructing metabolic networks work?
A bit of a preface:

A lot of this large scale collaboration (which I would maybe rather describe as the work of a whole [sub]field over a given time frame) often ends up in some sort of database. Really, there A LOT of those in modern biology - and often with minor but sometimes important differences. One of those would be the level of curation: are results gathered automatically from other sources, or always manually checked before being added? Another thing about databases is that (with certain exceptions of course) they often are only relevant for specific sub field, in some cases this can mean that only one lab maintains a website with a databases that is used by a few others, but that's it.
What I'm trying to get to is that there isn't really a 'one size fits all' solution and that especially the size of your field will impact which kind of solutions are both feasible and actually useful.  

Now to answer your actually state question (as far as I can):

Most known biochemical pathways (including the metabolic ones) are described in the KEGG database. Initially this project was started by a single lab (and is still run by that group as far as I can tell), but of course it contains a lot of published information from other sources (I couldn't find information on how they update the networks in the database, you may have to read the papers for this). The database can also be accessed remotely, so it allows people to use the same network for a given reaction, and by incorporating sequence data it also has information on which organisms even contain the given enzymes in the network.
One thing the database does not contain is information about dynamics in the network. In this case I think most groups will generate and publish their own models (e.g. based on ODE's).