How much detail is sufficient? A comparison of non-polarizable and - PowerPoint PPT Presentation

How much detail is sufficient? A comparison of non-polarizable and polarizable force fields for protein folding Anthony Hazel July 12, 2018 NAMD Workshop DICP , Dalian, CN

Free Energy Landscapes Free energy: G = H - TS • Protein folding landscapes are narrower at the bottom; there are few low-energy, native- like conformations and many more open unfolded structures. • Random steps that are mostly incrementally downhill in energy Unfolded Local States Structures Native Global Structure State Wolynes, Onuchic, Thirumalai. Navigating the folding routes. Science 267: 1619-1620 (1995).

Umbrella Sampling Potential of Mean Force (PMF) k 1 ( ξ - ξ 1 ) 2 k 2 ( ξ - ξ 2 ) 2 N independent simulations k N ( ξ - ξ N ) 2 k N-1 ( ξ - ξ N-1 ) 2 Kumar et al. J. Comput. Chem. 13:1011 (1992). Park et al. J. Chem. Phys. 119:3559 (2003).

WHAM Equations Unbiased Bias Hamiltonian Potential … convergence of f m ’s Unbiased Biased Arbitrary constant Subtract PMF PMF for each simulation bias Initial guess of constants (f m = 0)

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Replica Exchange Umbrella Sampling (REUS) Sampling Toy Model: U(x,y) Free Energy P(y|x) US REUS aREUS Park & Im. J. Chem. Theory Comput. 10:2719-2728 (2014).

B1 domain of streptococcal protein G (GB1) PDB: 1GB1 C-terminal hairpin of GB1 (G41-E56) 56 residues A. All residues B. Hydrogen bonds C. Hydrophobic core

GB1 as a model for β -sheet folding Commonly used to calibrate force fields and enhanced sampling techniques 30-50% folded @ 298/300K Folds in ~6 μ s Munoz et al. Nature. 149:072317 (1997). Best and Mittal. Proteins. 79:1318-1328 (2011). Fesinmeyer et al. J. Am. Chem. Soc. 126:7238-7243 (2004).

CHARMM Drude Polarizable Force Field Non-polarizable FFs tend to be overpolarized in order to mimic a solvent environment Drude Lysine Drude oscillator polarizable FF splits each heavy atom into a (+) parent Polarizability atom and a (—) Drude particle, Drude connected by a stiff spring ( k D ) α = q D2 / k D Particle Parent Drude model allows for polarization of Atom molecule from environment, not just SWM4-DNP molecular geometry Water 1-fs timestep drude on drudeTemp 1 drudeDamping 20.0 drudeBondLen 0.25 drudeHardWall on drudeNBTHOLEcut 5.0 LJcorrection yes Lone Pairs Lopes et al. J. Chem. Theory Comput. 9:5430 − 5449 (2013). Huang and MacKerell, Jr. Biophys. J. 107:991–997 (2014).

Folding PMFs of the GB1 β -hairpin 89-100 REUS windows 12-20ns/window Δ G fold (exp) = 0.0-0.5 kcal/mol Δ G fold = -7.2±2.2 Δ G fold = -1.7±2.2 Δ G fold = +2.8±1.7 C36 greatly overestimates Δ G fold C22* slightly overestimates Δ G fold Drude slightly underestimates Δ G fold

Side chain hydration free energies show room for improvement in the non-polarizable and polarizable models 40-stage Weeks–Chandler– Anderson (WCA)- decomposition free-energy perturbation (FEP) procedure Y. Deng and B. Roux. J. Phys. Chris Rowley Chem. B. 108:16567 (2004). Y. Deng and B. Roux. J. Phys. Chem. B. 113:2234 (2009). The Drude model underestimates hydroxyl, overestimates some charged, and improves sulfur-containing and amide hydration free energies. Improved backbone hydration needs to be compensated by improved N-H—O=C hydrogen bonding or peptide will unfold. Also, while backbone (NMA) hydration is improved in the Drude model over C36, further improvements could still be implemented.

Examining backbone polarization in the Drude model C36 C22* Drude 16 150 Protein Dipole moments are enhanced in the 120 14 − − − − 90 12 60 Drude model 10 Dipole Moment (D) 30 8 0 6 R G (Å) 4 30 Backbone 24 14 N-H bonds significantly polarize 18 12 12 10 during intrapeptide hydrogen 6 8 0 6 bonding, but not when hydrogen 4 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 6 N hb bonding with water hb hb C D 0.9 60 N − DN N − DN N − DN N − DN 0.8 55 14 14 HBonds Other HBonds Other C=O bonds behave in the opposite 0.7 50 12 12 0.6 45 10 10 0.5 40 manner, only polarizing significantly 8 8 0.4 35 6 6 when hydrogen bonding with water 4 0.4 4 60 Dipole Moment (D) C − DC C − DC C − DC C − DC 55 14 14 Angle (deg) HBonds Other HBonds Other 50 12 12 R G (Å) R G (Å) 0.3 45 10 10 40 Unlike water-peptide hydrogen 8 8 0.2 35 6 6 bonding, intrapeptide hydrogen 4 0.3 4 85 O − DO O − DO O − DO O − DO 75 14 14 HBonds Other HBonds Other 65 12 12 bonding aligns parent-drude bond 0.2 55 10 10 45 8 8 with chemical bond 0.1 35 6 6 4 4 0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 0 1 2 3 4 5 6 N hb N hb