but how can preventing that secretion of MMPs via Doxycycline strengthen the ligament again?
Nothing in the body is static, everything is in a dynamic state of turnover. Processes that break down substances are usually balanced by other processes which build up or repair those same substances. So if you inhibit the break down process, you shift the dynamic balance to towards build up and repair.
In the case of connective tissue,
fibroblast cells embedded in the tissue secrete collagen and elastin to build up the tissue. Thus these fibroblasts will help rebuild and strengthen the connective tissue if the break down processes can be reduced.
Though whether MMP enzymes secreted by immune cells are the cause of the ligament connective tissue weakening in CCI of course is not known (I've not seen any studies that have found elevated MMP enzymes in patients with infection-triggered CCI). If they are not, then MMP inhibitors like doxycycline may not help CCI much.
It's interesting that fibroblasts can become chronically infected with coxsackievirus B, a virus often found in ME/CFS. So I wonder whether such infected fibroblasts might malfunction because of the presence of the virus within them, leading to reduced secretion collagen and elastin, which might then cause connective tissue weakening and CCI. In other words, CCI might not be due to an overactive connective tissue break down, but by underactive connective tissue repair.
If underactive repair is the problem in CCI, then another speculative approach to treating CCI might be drugs or supplements that stimulate collagen and elastin secretion and connective tissue repair. Such substances include: the peptide BPC 157 (body protection compound 157) and the peptide TB-500 (thymosin beta 4). These are available to buy without prescription at peptide sellers such as
www.peptidesciences.com