The concentration dynamics of quorum sensing molecules such as AHL during bacterial growth; when do bacteria start to produce QS compounds? When is the QS compound consumed by bacteria? Does the QS compound decline or disappear at a late time?
To get a complete picture for a specific system, you are going to have to look up the details of your organism but the general scheme is this:
1) Bacteria have some basal, low level of autoinducer production.
2) As the concentration of the autoinducer increases (often when population density increases), the cell reacts to it causing an increased production of the autoinducer. This is called positive feedback.
3) At some concentration, gene expression is even more altered within the organism.
On top of this simple scheme, you can add layers of complication. You can imagine a system where the autoinducer is only ever produced under some environmental condition. Autoinducer molecules could also be degraded by the cell or by other cells of different types (some think of this as microbial warfare and there are some pretty interesting reviews going over this kind of communication).
For a comprehensive review that has at least some details of specific systems, I would google Bonnie Bassler - most of her papers relate to this and her reviews are nice. She is one of the big dogs in the field. As far as dynamics go, you might want to check some of the modeling that has been done on some of the more well-characterized systems.
As far as I know, most study suggest the production of QS signal molecules are growth-phase dependent, peaking at the later mid-exponential phase. However, to measure/evaluate the exact concentration dynamics is much complex. the secretion of signal molecules is either related to the cell density or influenced by medium.
more intriguingly, the indirect assay of signal molecules is restrained by multiple factors, e.g the luminescent assay of AI-2 is inhibited by both acid and glucose, while stimulated by boron. A more objective method may be examining their (or their chemical modified derivants) concentrations at different time points. Regarding the uptake of signal molecules by bacteria, some strains are proposed to utilize them as carbon source when sugars are in short supply, commonly after the stationary phase. To be frankly, if one of any question posted by you can be answered, a nice paper is completed.