P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS - PowerPoint PPT Presentation

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS Chris Chipot Laboratoire International Associé CNRS-UIUC, Unité Mixte de Recherche n° 7565, Université de Lorraine Beckman Institute for Advanced Science and Technology, Department of Physics University of Illinois at Urbana-Champaign H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS O UTLINE T HE LONG - STANDING PROTEIN - LIGAND PROBLEM T HE ALCHEMICAL ROUTE T HE GEOMETRICAL ROUTE R ELATIVE BINDING FREE ENERGIES A LANINE SCANNING B EYOND PROTEIN - LIGAND BINDING H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS O UTLINE T HE LONG - STANDING PROTEIN - LIGAND PROBLEM T HE ALCHEMICAL ROUTE T HE GEOMETRICAL ROUTE R ELATIVE BINDING FREE ENERGIES A LANINE SCANNING B EYOND PROTEIN - LIGAND BINDING H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS T HE LONG - STANDING PROTEIN - LIGAND PROBLEM drugs shape recognition constant computational investment rigid docking flexible docking free energy Chipot, C.; Rozanska, X.; Dixit, S. B. J. Comput. Aided Mol. Des. 2005 , 19 , 765-770. Shirts, M. R.; Mobley, D. L.; Chodera, J. D. Annual Reports Comput. Chem. 2007 , 3, 41-59. Chipot, C. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014 , 4 , 71-89. H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS T HE LONG - STANDING PROTEIN - LIGAND PROBLEM The computational microcalorimeter T HEORETICAL BACKGROUND K eq K eq = [protein : ligand] protein : ligand protein + ligand [protein][ligand] which can readily be determined by experiment: K d = k o ff k on response units — A single event is evidently not enough. — Brute-force simulations are limited by k on and k off . Kollman, P.A. Chem. Rev. 1993 , 93 , 2395-2417 Gilson, M. K. et al. Biophys. J. 1997 , 72 , 1047-1069 Chipot, C.; Pohorille, A. Free-energy calculations. Springer 2007 . Karlsson, R.; Larsson, A. Methods Mol. Biol. 2004 , 248 , 389-415 Buch, I.; Giorgino, T.; Fabritiis, G. D. Proc. Natl. Acad. Sci. U. S. A. 2011 , 108 , 10184-10189 H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS T HE LONG - STANDING PROTEIN - LIGAND PROBLEM T HEORETICAL BACKGROUND K eq K eq = [protein : ligand] protein : ligand protein + ligand [protein][ligand] p 1 [protein] tot 1 p 1 K eq = = [ligand] p 0 [protein] tot [ligand] p 0 8 Z Z Z Z d x e − β U d 1 d 2 . . . d N > > 1 < site bulk bulk K eq = Z Z Z Z [ligand] d x e − β U d 1 d 2 . . . d N > > : bulk bulk bulk N ligands Z Z Z Z d x e − βU d 1 d 2 . . . d N bulk site bulk + + · · · Z Z Z Z d x e − βU d 1 d 2 . . . d N bulk bulk bulk [protein] = p 0 [protein] tot Z Z Z Z 9 d x e − βU d 1 d 2 . . . d N > > [protein : ligand] = p 1 [protein] tot = bulk bulk site + Z Z Z Z d x e − βU d 1 d 2 . . . d N > > ; bulk bulk bulk Shoup, D.; Szabo, A. Biophys. J. 1982 , 40 , 33-39 Woo, H. J.; Roux, B. Proc. Natl. Acad. Sci. USA 2005 , 102, 6825-6830 H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS T HE LONG - STANDING PROTEIN - LIGAND PROBLEM T HEORETICAL BACKGROUND Z Z Z Z d x e − β U d 1 d 2 . . . d N N 1 site bulk bulk K eq = Z Z Z Z [ligand] d x e − β U d 1 d 2 . . . d N bulk bulk bulk Z Z d x e − βU d 1 N 1 site = Z Z [ligand] d x e − βU d 1 x ∗ bulk 1 Z Z d x e − βU d 1 N 1 site = Z Z [ligand] d x e − βU d 1 δ ( x 1 − x ∗ 1 ) V bulk bulk [ligand] = N/V bulk alchemical route Z Z d x e − βU d 1 site K eq = Z Z d x e − βU d 1 δ ( x 1 − x ∗ 1 ) bulk geometrical route Shoup, D.; Szabo, A. Biophys. J. 1982 , 40 , 33-39 Woo, H. J.; Roux, B. Proc. Natl. Acad. Sci. USA 2005 , 102, 6825-6830 H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS O UTLINE T HE LONG - STANDING PROTEIN - LIGAND PROBLEM T HE ALCHEMICAL ROUTE T HE GEOMETRICAL ROUTE R ELATIVE BINDING FREE ENERGIES A LANINE SCANNING B EYOND PROTEIN - LIGAND BINDING H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS T HE ALCHEMICAL ROUTE T HE DOUBLE - ANNIHILATION STRATEGY Couple reversibly the ligand to the binding site of the protein - Floating ligand problem. - Corpora non agunt nisi fixata. Paul Ehrlich - Definition of a set of restraints. Δ G 0 - The loss of translational, orientational and conformational protein + ligand 0 protein:ligand 0 entropies contributes to the free energy. site bulk Δ G c Δ G c bulk site bulk site Δ G a Δ G o Δ G o Δ G a site bulk Δ G p Δ G p Δ G * protein + nothing 0 protein + ligand * protein:nothing 0 protein:ligand * bulk site Δ G a Δ G a protein + nothing * protein:nothing * Gilson, M. K. et al. Biophys. J., 1997 , 72 , 1047-1069 Hermans, J.; Wang, L. J. Am. Chem. Soc. 1997 , 119 , 2707-2714 H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS T HE ALCHEMICAL ROUTE T HE DOUBLE - ANNIHILATION STRATEGY Z Z Z Z d x e − β ( U 0 + u c + u o ) d x e − β U 1 d 1 δ ( x 1 − x ∗ 1 ) d 1 bulk site K eq = × Φ Z Z Z Z d x e − β ( U 0 + u c ) d x e − β ( U 1 + u c ) d 1 δ ( x 1 − x ∗ 1 ) d 1 Θ bulk site Z Z d x e − β ( U 1 + u c ) r d 1 site Ψ × Z Z Z Z d x e − β ( U 1 + u c + u o ) d 1 d x e − β ( U 0 + u c ) θ d 1 δ ( x 1 − x ∗ 1 ) site bulk × Z Z Z Z d x e − β ( U 1 + u c ) d 1 δ ( x 1 − x ∗ 1 ) ϕ d x e − β ( U 1 + u c + u o ) d 1 bulk site × Z Z d x e − β ( U 1 + u c + u o + u p ) d 1 site site Z Z Z Z d x e − β ( U 1 + u c ) d x e − β ( U 1 + u c + u o + u p ) d 1 δ ( x 1 − x ∗ 1 ) d 1 bulk site × × Z Z Z Z d x e − βU 1 d x e − β ( U 1 + u c + u o + u p + u r ) d 1 δ ( x 1 − x ∗ 1 ) d 1 bulk site Z Z d x e − β ( U 1 + u c + u o + u p + u r ) d 1 site × Z Z d x e − β ( U 0 + u c + u o + u p + u r ) d 1 site Z Z d x e − β ( U 0 + u c + u o + u p + u r ) d 1 bulk × Z Z d x e − β ( U 0 + u c + u o ) d 1 δ ( x 1 − x ∗ 1 ) bulk bulk Deng, Y.; Roux, B. J. Phys. Chem. B 2009 , 113 , 2234-2246 H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018

P ROTEIN -L IGAND S TANDARD B INDING F REE -E NERGY C ALCULATIONS O UTLINE T HE LONG - STANDING PROTEIN - LIGAND PROBLEM T HE ALCHEMICAL ROUTE T HE GEOMETRICAL ROUTE R ELATIVE BINDING FREE ENERGIES A LANINE SCANNING B EYOND PROTEIN - LIGAND BINDING H ANDS -O N W ORKSHOP ON E NHANCED S AMPLING AND F REE -E NERGY C ALCULATIONS NIH C ENTER FOR M ACROMOLECULAR M ODELING & B IOINFORMATICS , U RBANA , I LLINOIS , S EPTEMBER 2018