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Matrix Metalloproteinase (MMP) Regulation

The controlled degradation and remodeling of the extracellular matrix (ECM). MMPs, such as MMP-1 and MMP-9, balance tissue breakdown with synthesis, crucial for wound contraction.
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The statement of the theorem

Define the concentration of active MMPs, [MMP][MMP], and the concentration of the substrate, [ECM][ECM]. The balance is described by the rate of degradation and the regulatory feedback loop:\nd[ECM]dt=ksynth[Collagen]−kMMP[MMP][ECM]+kremodel(1−[ECM][ECM]eq)\frac{d[ECM]}{dt} = k_{synth} [\text{Collagen}] - k_{MMP} [MMP] [ECM] + k_{remodel} (1 - \frac{[ECM]}{[ECM]_{eq}}) \nd[MMP]dt=kind[Cytokines]−kinact[MMP][TIMP]−kclear[MMP]\frac{d[MMP]}{dt} = k_{ind} [\text{Cytokines}] - k_{inact} [MMP] [\text{TIMP}] - k_{clear} [MMP] \nwhere [TIMP][TIMP] represents Tissue Inhibitors of Metalloproteinases, establishing the critical [MMP]/[TIMP][MMP]/[TIMP] ratio.