modeling and predicting the structure of transmembrane
play

. Modeling and predicting the structure of transmembrane proteins - PowerPoint PPT Presentation

Feb 08, 2024 •99 likes •1.23k views

. Modeling and predicting the structure of transmembrane proteins uhl 123 , Jean-Marc Steyaert 2 J er ome Waldisp Jerome.Waldispuhl@polytechnique.edu 1 Department of Biology, Boston College, USA 2 LIX, Ecole polytechnique, France 3

  1. ✕ ☎ ✟ ✏ ✂ ✌ ☞ ☛ ✁ ✆ ✠ ✝ ✞ ☞ ☛ ✁ ✟ ☞ ✜ ✡ ✞ ☛✧ ✓ ✡ ✞ ✝ ✆ ☎ ☛✧ ☎ ✓ ✆ ✝ ✞ � ✁ ✆ ☎ ✢ ✠ ✝ ✟ ✝ ✔ ✂ ✓ ✑ ✏ ☎ ✆ ✞ ✓ ✍ ✂ ✓ ✟ ✘ ✠ ✆ ✔ ✂ ☎✆ ✓ ✏ ✂ ✌ ✠ ✛ ✟ ✙ ✔ ✙ ✞ ✝ ✆ ☛ ✕ ✙ ✑ ✚ ✢ ✣ ✪ ✟ ✍ ✁ � ✞ ✝ ✠ ✡ ☛ ★ ✁ ✡ ✞ ✝ ✆ ☎ ✆ ✟ ✠ ✁ ✞ � ✠ ✩ ✟ ✆ ✏ ✡ ✝ ✡ ✆ ☎ ✢ ☛ ✓ ☛ ✙ ✏ ☛ ✡ ✠ ✤ ✏ ✡ ✠ ✤ ✟ ✏ ☎ ✞ ☛ ✝ ✆ ☎ ☎✥ ✚ ✏ ☎ ✤ ✙ ✓ ✚ ✠ ✚ ☛ ☛✧ ✚ ✍ ✁ � ✦ ✚ ✟ ✙ ✏ ✡ ✞ ✝ ✚ ☛ ✟ ✔ ✠ ✁ ✖ ✞ ✝ ☎✆ ✆ ☛ ☛ ✝ ✁ ✂ ✆ ✝ ✌ ✝✍ ✄ ✕ ✟ ✆ ✆ ✟ ✓ ✕ ✔ ✞ ✝ ☎ ✗ ✆ ✑ ✫ ✓ ✕ ✔ ✠ ☎ ✝ ✠ ✝ ✌ ✟ ✝ ✁ ✎ ✞ ✆ ✖ ☎ ✄ ✍ ✝ ✁ ✏✑ ✎ ✠ ✒ ✞ ✒ ✌ ✝✍ ✟ ✌ ✠ ✠ ✟ ✝✓ ✓ ✝ ✒ ✞ ✝ ✆ ☎ ✔ ✝ ✁ ✫ ✝ ☎✆ ☎ ✂ ✁ ✆ ✑ ☎ ✕ ✚ ✬ ✭ ✠ ✟ ✭ ✏ ✂ � ✞ ✝ ☎✆ ✄ ✂ ✁ � ✫ ✞ ✝ ✞ ✟ ✝ ☎ ✠ ✖ ✟ ✑ ✓ ✚ ✏ ✖ ✞ ✝ ✆ ✂ ✆ ✠ ✟ ✭ ✠ ✁ � ✚✬ ✖ ✑ ✓ Definition of a protein The 20 amino acids : H H H H H H H H H H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH + NH + NH + NH + NH + NH + NH + NH + NH + NH + C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H CH 3 CH CH 2 H C CH 3 CH 2 H C OH CH 2 CH 2 CH 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH 3 . . . . . . . . . . CH 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH CH 2 OH CH 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . C CH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH 3 . . . . . . . . . . . . CH 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH CH 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H . . . . . . . . . . H H H H H H H H H . . . . . . . . . . . . . . . . . . NH + C α COO − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH + NH + NH + NH + NH + NH + NH + NH + NH + . . . . . . . . C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − C α COO − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 3 3 3 3 3 3 CH 2 CH 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH 2 . . . . CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH 2 . . . . . . . . . . . . . . . . O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH 2 CH 2 CH 2 CH 2 CH 2 COO − SH C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH 2 . . . . . . . . . . . . . . . . O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH . . . . . . NH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH 2 CH 2 COO − S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N CH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CH 2 C NH 2 CH 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH + NH 2 3 Notions of biology – p. 14/62

  2. Definition of a protein The peptid bond : H H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH + NH + C α COO − C α COO − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R 1 R 2 Notions of biology – p. 14/62

  3. Definition of a protein The peptid bond : H H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH + · · · + H 2 O C α CONH C α COO − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R 1 R 2 Notions of biology – p. 14/62

  4. Structure of proteins Kynase C Notions of biology – p. 15/62

  5. α -helix α -helix 3 . 6 amino acids per turn, hydrogen bond between residus n and n + 4 . Notions of biology – p. 16/62

  6. β -sheet β -sheet composed of β -strands 2 amino acids per turn, hydrogen bond between residues of paired β -strands. Notions of biology – p. 17/62

  7. Transmembrane channels Bacteriorhodopsin Porin Notions of biology – p. 18/62

  8. Transmembrane channels Bacteriorhodopsin Porin Notions of biology – p. 18/62

  9. Transmembrane channel Why ? Notions of biology – p. 19/62

  10. Transmembrane channel Why ? Simple topologies (only parallel or anti-parallel pairings) , strong contraints from the environment, Some parameters are (much) more important than the others (hydrophobicity) Notions of biology – p. 19/62

  11. Transmembrane channel Why ? Simple topologies (only parallel or anti-parallel pairings) , strong contraints from the environment, Some parameters are (much) more important than the others (hydrophobicity) Interest ? Notions of biology – p. 19/62

  12. Transmembrane channel Why ? Simple topologies (only parallel or anti-parallel pairings) , strong contraints from the environment, Some parameters are (much) more important than the others (hydrophobicity) Interest ? nearly 40 % of the proteome, functional importance (allows communication between inner and outer milieu of cell) , difficult to be observe experimentaly. Notions of biology – p. 19/62

  13. Approximate physical model for transmembrane channels Approximate physical model for α -transmembrane channels Modeling the overall structure of α -channel, modeling anti-parallel pairing of α -helices, modeling the local structure of α -helices, pseudo folding energy of α -channels. Approximate physical model – p. 20/62

  14. Modeling the overall structure of α -channel Approximate physical model – p. 21/62

  15. Modeling the overall structure of α -channel Approximate physical model – p. 21/62

  16. Modeling the overall structure of α -channel Approximate physical model – p. 21/62

  17. Modeling the overall structure of α -channel Approximate physical model – p. 21/62

  18. Modeling the overall structure of α -channel Approximate physical model – p. 22/62

  19. Modeling the overall structure of α -channel Approximate physical model – p. 22/62

  20. Modeling the overall structure of α -channel Description of α -channels with only simple anti-parallel pairings. Approximate physical model – p. 22/62

  21. Modeling the overall structure of α -channel An α -channel is a concatenation of simple anti-parallel pairings. Approximate physical model – p. 22/62

  22. Modeling anti-parallel pairing of α -helices Let’s go back to a linear description : Approximate physical model – p. 23/62

  23. Modeling anti-parallel pairing of α -helices Let’s go back to a linear description : Approximate physical model – p. 23/62

  24. modeling anti-parallel pairing of α -helices Approximate physical model – p. 24/62

  25. modeling anti-parallel pairing of α -helices Approximate physical model – p. 24/62

  26. modeling anti-parallel pairing of α -helices I O I O I O I O O I O I O I O I Approximate physical model – p. 24/62

  27. ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ✁ O I Modeling the local structure of α -helices turn, consecutive amino acids of a helix A helical face is a subsequence of turn around the helix axis, dues corresponding to a complete A helix turn is a sequence of resi- A helix is a stacking of helix turns, face O is opposed to pairing. face I is involved in pairing, Approximate physical model – p. 25/62

  28. ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ✁ O I Modeling the local structure of α -helices I I O O I I O O I Approximate physical model – p. 25/62 O O I

  29. ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ✁ O I Modeling the local structure of α -helices On average, 3 . 6 residus per turn. acids, A helical face has 1 or 2 amino consecutive amino acids, A helix turn is composed by 3 or 4 residues belonging to a I or O face, A helix is an alternate sequence of Approximate physical model – p. 25/62

  30. Pseudo folding energy 2 1 2 MEMBRANE MEMBRANE EXTERIEUR 3 Approximate physical model – p. 26/62

  31. Pseudo folding energy 2 1 2 1. E contact residu interaction MEMBRANE MEMBRANE energy, EXTERIEUR 3 n λ j · λ j ′ � f ( I k i , I k +1 ) , où f ( I k i , I k +1 � � E contact = ) = · i i � i · # I k +1 # I k i =0 ω j ∈ I k ω j ′ ∈ I k +1 i i i Approximate physical model – p. 26/62

  32. Pseudo folding energy 2 1 2 1. E contact residu interaction MEMBRANE MEMBRANE energy, 2. E memb membrane interaction energy, EXTERIEUR 3 � E memb = K memb · λ i ω i ∈ O k i Approximate physical model – p. 26/62

  33. Pseudo folding energy 2 1 2 1. E contact residu interaction MEMBRANE MEMBRANE energy, 2. E memb membrane interaction energy, 3. E turn turn energy. EXTERIEUR 3 n � E turn = T ( n − m ) + K cyt/per · λ i i = m Approximate physical model – p. 26/62

  34. Modeling the overall structure of α -channel Approximate physical model – p. 27/62

  35. Modeling the overall structure of α -channel Approximate physical model – p. 28/62

  36. Modeling the overall structure of α -channel Approximate physical model – p. 28/62

  37. Modeling the overall structure of α -channel A β -channel is a concatenation of anti-parallel pairings of β -strands. Approximate physical model – p. 28/62

  38. Grammatical modeling Grammatical modeling of Transmembrane channels Local structure of the secondary structures : rational grammar Secondary structure pairing : context-free grammar Overall structure of a TM channel : multi-tape context-free grammar pseudo folding energy : attributes Grammatical modeling – p. 29/62

  39. MTCFG des canaux α Grammatical modeling of TM α -channels Regular grammar for α -helix, Context-free grammar for α -helix pairings, Multi-tape context-free grammar for α -channel, Muti-tape S-attribute grammar for α -channel, Grammatical modeling – p. 30/62

  40. Regular grammar for α -helix A helix is an alternate se- quence of residues belon-  S helice → I 0 | I 1 | O 0 | O 1 ging to a I or O face,     A helix turn is composed by I 0 → • I 1 | • O 0     3 or 4 consecutive amino  P helice = I 1 → • O 0 | • O 1 acids,   O 0 → • O 1  A helical face has 1 or 2     amino acids, O 1 → • I 0   On average, 3 . 6 residus per turn. Grammatical modeling – p. 31/62

  41. Regular grammar for α -helix A helix is an alternate se- quence of residues belon- ging to a I or O face, A helix turn is composed by 3 or 4 consecutive amino I 0 I 1 O 0 O 1 acids, A helical face has 1 or 2 amino acids, On average, 3 . 6 residus per turn. Grammatical modeling – p. 31/62

  42. CFG for α -helix anti-parallel pairings I O I O I O I O O I O I O I O I Grammatical modeling – p. 32/62

  43. CFG for α -helix anti-parallel pairings I O I O I O I O O I O I O I O I  S α F α O | F α →  ap I    F α I F α O I | C α cyt | C α  →  per I    F α O F α I O | C α cyt | C α P ap = → per O  C α i C α  → cyt | i  cyt     C α o C α → per | o   per Grammatical modeling – p. 32/62

  44. CFG for α -helix anti-parallel pairings  S α F α O | F α →  ap I    F α I F α O I | C α cyt | C α  →  per I    F α O F α I O | C α cyt | C α P ap = → per O  C α i C α  → cyt | i  cyt     C α o C α → per | o   per Grammatical modeling – p. 32/62

  45. CFG for α -helix anti-parallel pairings  S α F α O | F α →   ap I S helice → I 0 | I 1 | O 0 | O 1      F α I F α O I | C α cyt | C α   →   I 0 → • I 1 | • O 0 per I       F α O F α I O | C α cyt | C α P ap = → P helice = I 1 → • O 0 | • O 1 per O   C α i C α   O 0 → • O 1 → cyt | i   cyt       O 1 → • I 0   C α o C α → per | o   per Grammatical modeling – p. 32/62

  46. CFG for α -helix anti-parallel pairings  F 1 , 1 | F 1 , 1 S ap → 1  I O     F 1 , 1 • • F 1 , 1 • • | • F 2 , 1 • • | • • F 1 , 2 • | • F 1 , 1  • | C α → 2   cyt I O O O O     F 2 , 1 • • F 1 , 1 • • | • • F 1 , 2 • | C α  → 3   cyt I O O     F 1 , 2 • • F 1 , 1 • • | • F 2 , 1  • • | C α → 4   cyt I O O     F 2 , 2 • • F 2 , 2  • • | C α → 5   cyt I O P α ap = F 1 , 1 • • F 1 , 1 • • | • F 2 , 1 • • | • • F 1 , 2 • | • F 2 , 2 • | C α → 6   cyt O I I I I     F 2 , 1 • • F 1 , 1 • • | • • F 1 , 2 • | C α  → 7   cyt O I I     F 1 , 2 • • F 1 , 1 • • | • F 2 , 1 • • | C α  → 8   cyt O I I     F 2 , 2 • • F 1 , 1 • • | C α  → 9   cyt O I     C α • C α  → cyt | • 10  cyt Grammatical modeling – p. 33/62

  47. MTCFG for α -channels A TM-channel is represented by a 2-tape word : ))))))iii))))))oo))))))ii))))))ooo)))))) ((((((iii((((((oo((((((ii((((((ooo(((((( Grammatical modeling – p. 34/62

  48. MTCFG for α -channels A TM-channel is represented by a 2-tape word : ))))))------iii))))))------oo))))))------ii))))))------ ------((((((iii------((((((oo------((((((ii------(((((( Grammatical modeling – p. 34/62

  49. MTCFG for α -channels  � t ) � �  � − | T α seq,cyt | T α  S α → S α 1  seq,per − t (        T α T α cyt T α seq,per | T α → 2   seq,cyt cyt        T α T α per T α seq,cyt | T α → 3  seq,per per      � t ) � � P canal = − � T α T α | C α → 4 cyt cyt cyt t ( −     � t ) � �  − �  T α T α | C α → 5  per per per  t ( −      � i cyt | � i  � � C α C α  → 6  cyt i i      � o per | � o   � � C α C α → 7   per o o Grammatical modeling – p. 35/62

  50. MTCFG for α -channels S α S α S α S α S α S α T α seq,cyt T α seq,per T α T α per seq,cyt T α T α T α cyt per cyt T α T α T α cyt per cyt T α T α T α cyt per cyt T α T α T α cyt per cyt T α C α T α cyt per cyt C α C α C α cyt per cyt C α C α C α cyt per cyt � i � i � � t ) �� t ) �� t ) �� t ) �� t ) � o � o � o � � t ) �� t ) �� t ) �� t ) �� t ) � i � i � � t ) �� t ) �� t ) �� t ) �� t ) �� t ) �� t ) �� t ) �� t ) �� t ) � − � − � − � − � − � − � − � − � − � − � − � − � − � − � − � − � − � − � − � − � � � � � � � � � � � � � � � � � � � � � � � � � � � t ( t ( t ( t ( t ( t ( t ( t ( t ( t ( i i − − − − − t ( t ( t ( t ( t ( o o o − − − − − t ( t ( t ( t ( t ( i i − − − − − − − − − − Grammatical modeling – p. 36/62

  51. MTCFG for α -channels How to integrate the pairing rules ? ))))iii))))oo))))ii))))oo)))) ((((iii((((oo((((ii((((oo(((( Grammatical modeling – p. 37/62

  52. MTCFG for α -channels How to integrate the pairing rules ? MPPMMPMMPPMMiiiPPMPPMMPMMPPooMMPPMMPMMPMMiiPPMPPMMPMMPPooMMPMMPMMPPMM PMMPPMMPPMMPiiiMPPMMPMMPPMMooPMMPPMPPMMPPiiMPPMMPPMMPPMooMPPMMPPMPPMM Grammatical modeling – p. 37/62

  53. MTCFG for α -channels  F 1 , 1 | F 1 , 1 S ap → 1  I O     F 1 , 1 • • F 1 , 1 • • | • F 2 , 1 • • | • • F 1 , 2 • | • F 1 , 1  • | C α → 2   I O O O O     F 2 , 1 • • F 1 , 1 • • | • • F 1 , 2 • | C α  → 3   I O O     F 1 , 2 • • F 1 , 1 • • | • F 2 , 1  • • | C α → 4   I O O     F 2 , 2 • • F 2 , 2  • • | C α → 5   I O P α ap = F 1 , 1 • • F 1 , 1 • • | • F 2 , 1 • • | • • F 1 , 2 • | • F 2 , 2 • | C α → 6   O I I I I     F 2 , 1 • • F 1 , 1 • • | • • F 1 , 2 • | C α  → 7   O I I     F 1 , 2 • • F 1 , 1 • • | • F 2 , 1 • • | C α  → 8   O I I     F 2 , 2 • • F 1 , 1 • • | C α  → 9   O I    • C α | •  C α  → 10  Grammatical modeling – p. 38/62

  54. MTCFG for α -channels  � � � � ε • S α → S α | Canal 1  ε •     F 1 , 1 Canal | F 1 , 1 Canal | F 1 , 1 | F 1 , 1 → 2 Canal   I O I O    � �� � � �� � | � � � �� � | � �� � � � | � � � � F 1 , 1 F 1 , 1 F 2 , 1 F 1 , 2 F 2 , 2 ε ε ε ε ε ε | C α • • • • • •  → 3  I O ε ε O ε ε O ε O ε • • • • • •    � �� � � �� � | � �� � � �  F 2 , 1 ε ε F 1 , 1 ε ε F 1 , 2 | C α • • • → 4  ε ε ε  I O O • • • •    � �� � � �� � | � � � �� � F 1 , 2 F 1 , 1 F 2 , 1 ε ε ε | C α  • • • • → 5  ε ε ε ε I O O • • •   P α = � �� � � �� � F 2 , 2 F 1 , 1 ε ε | C α • • → 6 ε ε I O • •   � �� � � �� � | � � � �� � | � �� � � � | � � � � F 1 , 1 ε ε F 1 , 1 ε F 2 , 1 ε ε F 1 , 2 ε F 2 , 2 | C α • • • • • •  → 7  O I ε ε I ε ε I ε I ε • • • • • •    � �� � � �� � | � �� � � �  F 2 , 1 F 1 , 1 F 1 , 2 ε ε ε ε | C α • • • → 8  ε ε ε  O I I • • • •    � �� � � �� � | � � � �� � F 1 , 2 F 1 , 1 F 2 , 1 ε ε ε | C α  • • • • → 9  ε ε ε ε O I I • • •    � �� � � �� �  F 2 , 2 F 1 , 1 ε ε | C α • • → 10   O I ε ε • •    � � C α | � � C α  • • → 11 • =1 • =1 Grammatical modeling – p. 38/62

  55. MTSAG for α -channels Multi-tape S-attribute grammar for α -channels To each production rule, associate a functions which allows a recursive computation of the energy. Grammatical modeling – p. 39/62

  56. MTSAG for α -channels f energy � ( uvxyz ) = x. energy → � �� � � �� F 1 , 1 F 1 , 1 ε ε • • ε ε O I • • f energy  x. energy + ( u. hp + v. hp ) · ( y. hp + z. hp ) � ( uxyz ) = x. energy f energy � ( uvxyz ) = → � � � �� F 1 , 1 ε F 2 , 1 • •  → � �� � � �� 2 F 1 , 1 F 1 , 1 ε ε  • • O I ε ε •  ε ε I O • •  f energy  � ( uvxy ) = x. energy x. energy + ( u. hp ) · ( y hp + z. hp ) f energy  → � �� � � � ( uxyz ) = F 1 , 1 ε ε F 1 , 2  √ •  → � � � �� F 1 , 1 ε F 2 , 1 2 ε • • O • • I   I O ε ε • f energy  � ( uxy ) = x. energy  x. energy + ( u. hp + v. hp ) · ( y. hp ) f energy → � � �  � ( uvxy ) = F 1 , 1 F 2 , 2 ε √ •  → � �� � � F 1 , 1 F 1 , 2 2  ε ε ε • O I •  ε I • • O  f energy  → Cα ( x ) = x. energy  f energy F 1 , 1 � ( uxy ) = x. energy + u hp · y. hp  → � � �  F 1 , 1 F 2 , 2 ε O •   ε f energy I O • � ( uvxyz ) = x. energy  → � �� � � ��  f energy F 2 , 1 ε ε F 1 , 1 • •  → Cα ( x ) = x. energy  ε ε F 1 , 1 O I • •   I f energy  � ( uvxy ) = x. energy x. energy + ( u. hp + v. hp ) · ( y. hp + z. hp )  f energy → � �� � � � ( uvxyz ) = F 2 , 1 ε ε F 1 , 2  •  2 → � �� � � �� F 2 , 1 ε ε F 1 , 1 • • ε  O • • I  I O ε ε • •  f energy → Cα ( x ) = x. energy x. energy + ( u. hp + v. hp ) · ( y. hp ) F α f energy F 2 , 1 ap = � ( uvxy ) = √ → � �� � � F 2 , 1 ε ε F 1 , 2 2 O • ε f energy  I • • O � ( uvxyz ) = x. energy  → � �� � � ��  F 1 , 2 F 1 , 1 f energy ε ε • • → Cα ( x ) = x. energy  ε ε  F 2 , 1 O • • I   I f energy � ( uxyz ) = x. energy  x. energy + ( u. hp + v. hp ) · ( y. hp + z. hp ) f energy  → � � � �� � ( uvxyz ) = F 1 , 2 F 2 , 1 ε  • • 2 → � �� � � ��  F 1 , 2 F 1 , 1 ε ε ε ε • • O I •   ε ε I • • O f energy  → Cα ( x ) = x. energy x. energy + ( u. hp ) · ( y hp + z. hp )  f energy F 1 , 2  � ( uxyz ) = √  → � � � �� 2 F 1 , 2 ε F 2 , 1 O  • •  ε ε f energy I O  • � ( uvxyz ) = x. energy  → � �� � � �� f energy F 2 , 2 ε ε F 1 , 1  • • → Cα ( x ) = x. energy  F 1 , 2 O I ε ε  • •  I f energy  → Cα ( x ) = x. energy  x. energy + ( u. hp + v. hp ) · ( y. hp + z. hp ) f energy F 2 , 2  � ( uvxyz ) =  2 → � �� � � �� F 2 , 2 ε ε F 1 , 1 O  • •  f energy I O ε ε  • • ( xy ) = x. hp · K milieu + y. energy  Cα → � �  f energy • Cα → Cα ( x ) = x. energy  • =1 F 2 , 2  I f energy � ( x ) = x. hp · K milieu Cα → � • • =1 Grammatical modeling – p. 39/62

  57. MTSAG for α -channels An example ! Grammatical modeling – p. 40/62

  58. MTSAG for α -channels Periplasme Q G L V I A L R M C D V I L L D H L G A L A P Cytoplasme D E Grammatical modeling – p. 41/62

  59. MTSAG for α -channels S α , 115 . 64 S α , 115 . 64 S α , 115 . 64 S α , 115 . 64 S α , 115 . 64 S α , 115 . 64 S α , 115 . 64 Canal cyt , 77 . 54 Canal per , 35 . 31 F 1 , 1 F 1 , 1 O,cyt , 41 . 77 O,per , 35 . 31 F 1 , 1 F 1 , 1 I,cyt , 41 . 77 I,per , 35 . 31 F 1 , 2 F 2 , 1 O,cyt , 9 . 19 O,per , 23 . 99 F 2 , 1 F 1 , 1 I,cyt , 9 . 19 I,per , 23 . 99 F 1 , 1 F 1 , 2 O,cyt , 9 . 78 O,per , 2 . 81 C α C α cyt , 9 . 78 per , 2 . 81 C α C α cyt , 3 . 62 per , 2 . 81 � A � V � L � L � I � G � A � ε � ε � ε � ε � ε � ε � ε � D � E � P � D � L � H � C � L � R � ε � ε � ε � ε � ε � ε � ε � G � Q � M � I � V � L � G � A � L � ε � ε � ε � ε � ε � ε � ε � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Q ε ε ε ε ε ε ε A V L L I G A D E ε ε ε ε ε ε ε P D L H C L R G ε ε ε ε ε ε ε M I V L G A L 0 . 22 4 . 67 5 . 66 5 . 66 4 . 67 0 . 00 0 . 22 0 . 22 4 . 67 5 . 66 5 . 66 4 . 77 0 . 00 0 . 22 − 3 . 08 − 1 . 81 − 2 . 23 − 3 . 08 5 . 66 0 . 46 4 . 07 5 . 66 1 . 42 − 2 . 23 − 3 . 08 5 . 66 0 . 46 4 . 07 5 . 66 1 . 42 0 . 00 − 2 . 81 4 . 23 4 . 77 4 . 67 5 . 66 0 . 00 0 . 00 5 . 66 4 . 23 4 . 77 4 . 67 5 . 66 0 . 00 0 . 22 5 . 66 Grammatical modeling – p. 41/62

  60. ✡ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ✌ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ✌ ✌ ☞ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✌ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✍ ✌ ✌ ✌ ☞ ☞ ✎ ✡ ☛ ☛ ☛ ☛ ☛ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ☛ ✡ ✡ � ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ✡ ☛ ☛ ☞ ☛ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ☛ ✍ ✎ ✡ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✒ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✒ ✒ ✑ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✒ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✒ ✒ ✒ ✑ ✑ ✎ ✎ ✏ ✏ ✏ ✏ ✏ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✏ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✎ ✏ ✏ ✑ ✏ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✡ ✡ ✠ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✄ ✄ ✂ ☎ ☎ ☎ ☎ ☎ ☎ ☎ ☎ ✠ ☎ ☎ ☎ ☎ ☎ ☎ ✄ ☎ ☎ ☎ ☎ ☎ ☎ ☎ ☎ ✄ ✄ ✄ ✄ ✄ ✂ ✂ ☎ � ✁ ✁ ✁ � � � � � � � � � � ✁ � � � � � � � � � � � � � ✁ ✁ ✂ ✁ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ☎ ☎ ✆ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✞ ✞ ✆ ✞ ✞ ✞ ✞ ✞ ✞ ✞ ✟ ✟ ✞ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✟ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✠ ✟ ✟ ✟ ✟ ✞ ✞ ✞ ✆ ✝ ✝ ✝ ✝ ✆ ✆ ✆ ✞ ✆ ✆ ✆ ✆ ✆ ✝ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✆ ✝ ✆ ✝ ✝ ✞ ✞ ✞ ✞ ✞ ✝ ✞ ✞ ✞ ✞ ✞ ✝ ✝ ✞ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ ✝ V C K A L V L L P Periplasme Cytoplasme H I Q W C F A M I E MTSAG for β -channels W V G D Grammatical modeling – p. 42/62 L L

  61. MTSAG for β -channels S β , 71 . 92 S β O , 71 . 92 S β I , 70 . 75 S β O , 70 . 23 S β I , 66 . 34 T β seq,cyt , 61 . 63 T β seq,per , 37 . 13 T β seq,cyt , 21 . 12 T β cyt , 21 . 12 T β T β F O cyt , 24 . 50 per , 16 . 01 cyt , 21 . 12 F O F O F I cyt , 24 . 50 per , 16 . 01 cyt , 19 . 86 F I F I F O cyt , 20 . 40 per , 12 . 54 cyt , 16 . 25 F O F O F I cyt , 20 . 34 per , 9 . 10 cyt , 14 . 93 F I F I F O cyt , 15 . 74 per , 7 . 53 cyt , 10 . 9 F O F O F I − cyt , 11 . 71 per , 6 . 99 cyt , 9 . 78 F I + F I C β cyt , 10 . 54 per , 2 . 59 per , 9 . 78 C β C β C β cyt , 10 . 54 per , 2 . 59 per , 6 . 16 C β C β C β cyt , 4 . 46 per , − 0 . 22 per , 0 . 00 � C � A � V � L � ε � ε � ε � ε � K � P � V � I � L � H � L � ε � ε � ε � ε � ε � Q � A � F � M � W � I � C � ε � ε � ε � ε � ε � E � D � G � L � V � L � W � ε � ε � ε � ε � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ε ε ε ε C A V L K P ε ε ε ε ε V I L H L Q A ε ε ε ε ε F M W I C E D G ε ε ε ε L V L W 4 . 07 0 . 22 4 . 67 5 . 66 4 . 07 0 . 22 4 . 67 5 . 66 − 3 . 04 − 2 . 23 4 . 67 4 . 77 5 . 66 0 . 46 5 . 66 4 . 67 4 . 77 5 . 66 0 . 46 5 . 66 − 2 . 81 0 . 22 4 . 44 4 . 23 1 . 04 4 . 77 4 . 07 4 . 44 4 . 23 1 . 04 4 . 77 4 . 07 − 1 . 81 − 3 . 08 0 . 00 5 . 66 4 . 67 5 . 66 1 . 04 5 . 66 4 . 67 5 . 66 1 . 04 Grammatical modeling – p. 42/62

  62. MTSAG for TM channels What has not been said : TM-channel closure, TM α -helix selection, turn selection (between secondary structures), constraints on the overlapping of the motifs. Grammatical modeling – p. 43/62

  63. Performance evaluation Performance evaluation How to realize a structure prediction ? How to evaluate a prediction ? Results. Performance evaluation – p. 44/62

  64. How to realize a structure prediction ? syntax analysis (GCP algorithm), implementation using mtsag2c (F . Lefebvre), software tmmtsag ... and now ASTRiD (web interface). Performance evaluation – p. 45/62

  65. How to realize a structure prediction ? Example of an α -channel : Bacteriorhodopsin QAQITGRPEWIWLALGTALMGLGTLYFLVKGMGVSDPDAKKFYAITTLVPAIAFTMYLSMLLGYGLTMVPFGGEQNPIYWARYADWLFTTPLLLLDLALL .......TTHHHHHHHHHHHTTHHHHHHHHSS..S.HHHHHHHHHHHHTHHHHHHHHHHHHTT.....SSS.SSS....STTHHHHTTTHHHHTTTTSTT ............MMMMMMMMMMMMMMMMMMMMMMiiiiiiiPPMPPMPPMMPPMMPPMMPPMMPPMMPPooooooooPPMPPMPPMPPMMPPMPPMPPMP ............PMMPMMPMMPMMPMMPMMPMMPiiiiiiiPMMPMMPPMMPPMMPPMMPPMMPPMMPPooooooooPPMMPPMMPPMMPPMMPMMPMMP VDADQGTILALVGADGIMIGTGLVGALTKVYSYRFVWWAISTAAMLYILYVLFFGFTSKAESMRPEVASTFKVLRNVTVVLWSAYPVVWLIGSEGAGIVP TT..HHHHHHHHHHHHHHHHHHHHHHS..SSS.HHHHHHHHHHHHHHHHHHHTTTTTTT..TT.SHHHHTTHHHHHHHHHHHHHHHHHHTTTTSSSSSS. PiiiiiiPPMPPMPPMPPMPPMPPMMPoooPPMMPPMMPPMMPPMMPPMMPPMMPPiiiiiiPPMMPMMPPMPPMMPMMPPMMPPMPPMPPooooooPPM PiiiiiiPPMPPMPPMPPMPPMPPMMPoooPMMPPMPPMPPMPPMPPMPPMPPMMPiiiiiiPPMMPPMMPMMPMMPMMPPMMPPMPPMPPooooooMMM LNIETLLFMVLDVSAKVGFGLILLRSRAIFGEAEAPEPSAGDGAAATS SHHHHHHHHHHHHHHTHHHHTTTT........................ PPMPPMPPMPPMPPMMPMMPPMPP........................ MMMMMMMMMMMMMMMMMMMMMMMM........................ pseudo folding energy : 1583.92 Performance evaluation – p. 46/62

  66. How to realize a structure prediction ? tape 1 PPMPPMPPMPPMPPMPPMMPoooPPMMPPMMPPMMPPMMPPMMPPMMPPiiiiiiPPMMPMMPPMPPMMPMMPPMMPPMPPMPP tape 2 PPMPPMPPMPPMPPMPPMMPoooPMMPPMPPMPPMPPMPPMPPMPPMMPiiiiiiPPMMPPMMPMMPMMPMMPPMMPPMPPMPP helice k−1 helice k+1 helice k Performance evaluation – p. 46/62

  67. How to realize a structure prediction ? Example of a β -channel : Porin MAPKDNTWYTGAKLGWSQYHDTGLINNNGPTHENKLGAGAFGGYQVNPYVGFEMGYDWLGRMPYKGSVENGAYKAQGVQLTAKLGYPITDDLDIYTRLGG ....TT.EEEEEEEEEES.S.....SS.......EEEEEEEEEEE.BTTEEEEEEEEEEEE.....SS....EEEEEEEEEEEEEEESSSSEEEEEEEEE ...............EEEEEEEEEEooooooooooCBCBCBCBCiiiiiiBCBCBCBCBCBCooooooooooooooBCBCBCBCBiiiiiiiiBCBCBCB ...............CBCBCBCBCBooooooooooBCBCBCBCBiiiiiiBCBCBCBCBCBCooooooooooooooBCBCBCBCBiiiiiiiiCBCBCBC MVWRADTYSNVYGKNHDTGVSPVFAGGVEYAITPEIATRLEYQWTNNIGDAHTIGTRPDNGMLSLGVSYRFG EEEEEEE..SSS..EEEEEEEEEEEEEEEEESSSSEEEEEEEEEE......SS........EEEEEEEEEE. CBCBCooooooooooooooCBCBCBCBCiiiCBCBCBCBCBCoooooooooooooooooooBCBCBCBCBC. BCBCBooooooooooooooCBCBCBCBCiiiCBCBCBCBCBCoooooooooooooooooooEEEEEEEEEE. pseudo folding energy : 402.15 Performance evaluation – p. 46/62

  68. How to evaluate a prediction ? observed : ......HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHH........ predition : ..HHHHHHHHHHHHHHH.........HHHHHHHHHHH.............HHHHHHHHHHHHHHH... Definition A secondary structure is said to be predicted, if it intersects one and only one observed secondary structure. Definition A structure is correctly predicted if all its secondary structures are predicted, almost predicted if the non-predicted secondary structures do not intersect any observed secondary structures, and non-predicted otherwise. Performance evaluation – p. 47/62

  69. How to evaluate a prediction ? ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. ..HHHHHHHHHHHHHHHHH.........HHHHHHHHHHHHH...............HHHHHHHHHHHHHHH........ Performance evaluation – p. 48/62

  70. How to evaluate a prediction ? t c e r ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. r o ..HHHHHHHHHHHHHHHHH.........HHHHHHHHHHHHH...............HHHHHHHHHHHHHHH........ C Performance evaluation – p. 48/62

  71. How to evaluate a prediction ? t c e r ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. r o ..HHHHHHHHHHHHHHHHH.........HHHHHHHHHHHHH...............HHHHHHHHHHHHHHH........ C ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. ..HHHHHHHHHHHHHHHHH..............HHHHHHHHHHHHHHHHHH............................ Performance evaluation – p. 48/62

  72. How to evaluate a prediction ? t c e r ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. r o ..HHHHHHHHHHHHHHHHH.........HHHHHHHHHHHHH...............HHHHHHHHHHHHHHH........ C t s o ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. m l ..HHHHHHHHHHHHHHHHH..............HHHHHHHHHHHHHHHHHH............................ A Performance evaluation – p. 48/62

  73. How to evaluate a prediction ? t c e r ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. r o ..HHHHHHHHHHHHHHHHH.........HHHHHHHHHHHHH...............HHHHHHHHHHHHHHH........ C t s o ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. m l ..HHHHHHHHHHHHHHHHH..............HHHHHHHHHHHHHHHHHH............................ A ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. ..HHHHHHHHHHHHHHHHH.................HHHHHHHHHHHHHHHHHHHHHH....HHHHHHHHHHHHHHH.. Performance evaluation – p. 48/62

  74. How to evaluate a prediction ? t c e r ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. r o ..HHHHHHHHHHHHHHHHH.........HHHHHHHHHHHHH...............HHHHHHHHHHHHHHH........ C t s o ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. m l ..HHHHHHHHHHHHHHHHH..............HHHHHHHHHHHHHHHHHH............................ A o ........HHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHHH...HHHHHHHHHHHHHHHHH............. N ..HHHHHHHHHHHHHHHHH.................HHHHHHHHHHHHHHHHHHHHHH....HHHHHHHHHHHHHHH.. Performance evaluation – p. 48/62

  75. How to evaluate a prediction ? Estimator for the secondary structure element prediction Q ok = 100 · number of correctly predicted structures number of proteins = 100 · number of TM segments correctly predited Q % obs stm number of TM segment observed = 100 · number of TM segments correctly predited Q % pred stm number of TM segment predicted Performance evaluation – p. 49/62

  76. How to evaluate a prediction ? Estimator for the secondary structure assignment prediction Q 2 = 100 · number of correctly predicted residus number of residus = 100 · number of correctly predicted residus in TM segment Q % obs 2 T number of residus observed in TM segments = 100 · number of correctly predicted residus in TM segment Q % pred 2 T number of residus predicted in TM segments = 100 · number of correctly predicted residus in non-TM segment Q % obs 2 N number of residus observed in non-TM segments = 100 · number of correctly predicted residus in non-TM segment Q % pred 2 N number of residus predicted in non-TM segments Performance evaluation – p. 50/62

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