Here's the hook: similar substrate binding sites in the chaperone domains of Clp and Lon.
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Wickner
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Maurizi
D049069:ATP-Dependent Proteases; D000251:Adenosine Triphosphatases / Q000737:chemistry*; D001665:Binding Sites; D049071:Endopeptidase Clp; D004926:Escherichia coli / Q000201:enzymology*; D029968:Escherichia coli Proteins; D006360:Heat-Shock Proteins / Q000737:chemistry*; D018832:Molecular Chaperones / Q000737:chemistry*; D049070:Protease La; D011485:Protein Binding; D011487:Protein Conformation; D017510:Protein Folding; D012697:Serine Endopeptidases / Q000737:chemistry*; D013379:Substrate Specificity; D019895:Transposases / Q000378:metabolism
D029968:Escherichia coli Proteins; D006360:Heat-Shock Proteins; D018832:Molecular Chaperones; C114697:mu transposase; D019895:Transposases; D049069:ATP-Dependent Proteases; D012697:Serine Endopeptidases; C483567:Lon protein, E coli; D049070:Protease La; D049071:Endopeptidase Clp; D000251:Adenosine Triphosphatases