This PDF file includes:

• fig. S1. Position of the Y51A mutation in PCquad.
  
• fig. S2. Crystallographic density maps of PCquad as found in PDB entry 4QF0.
  
• fig. S3. Testing the concentration dependence of the cage systems.
  
• fig. S4. Scattering profiles and their fits.
  
• fig. S5. Heat map and force plot analysis using V_R and χ².
  
• fig. S6. Comparing RMSD changes measured from atomic models to the similarity of SAXS calculated from the same atomic models.
  
• fig. S7. Purity of PCtrip and PCquad after affinity purification and SEC.
  
• fig. S8. PCtrip multimerization as a function of pH as probed by SEC.
  
• fig. S9. Minimalist ensembles with nearly equivalent fits to SAXS data.
  
• table S1. SAXS-related parameters estimated from crystal structures.
  
• table S2. Summary of buffer effects on SAXS parameters of PCtrip.
  
• table S3. Summary of buffer effects on SAXS parameters of PCquad.
  
• table S4. Multimeric composition from fitting SAXS results from PCtrip.
  
• table S5. Multimeric composition from fitting SAXS results from PCquad.

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Other Supplementary Material for this manuscript includes the following:

• movie S1 (.mp4 format). Structural morphing between idealized symmetric structure and most compact asymmetric crystal structure.