Energetics of Infinite Homopolypeptide Chains
Energetics of Infinite Homopolypeptide Chains A New Look at Commonly Used Force Fields Evgeni Penev1 1 Department
Joel Ireta2
Joan-Emma Shea1
of Chemistry & Biochemistry, University of California Santa Barbara
2 Departamento
de Qu´ımica, Universidad Aut´ onoma Metropolitana, M´ exico
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52nd Biophysical Society Meeting • Long Beach
Energetics of Infinite Homopolypeptide Chains
Motivation Current method of choice for simulations : Molecular Dynamics & empirical force fields fixed partial-charge: AMBER, CHARMM, OPLS, GROMOS, . . . polarizable: AMOEBA, . . .
Big diversity ➜ calls for better understanding of differences and similarities among the potentials Infinite chains ➜ New method to compare the ”gas-phase” part of the common force fields
E. Penev et al.
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52nd Biophysical Society Meeting • Long Beach
Energetics of Infinite Homopolypeptide Chains
“Gold standard” for benchmarking (φ, ψ)-Ramachandran map of dipeptides (Ala, Gly,. . . ) Ala φ
ψ
Nme Ace Computationally tractable but results may not be transferable to larger systems Intrinsic limitations: description of long-range interactions; hydrogen bond cooperativity.
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Energetics of Infinite Homopolypeptide Chains
A non-standard approach: Ireta et al. (DFT) C N O Cα,i +1
r
L θ Cα,i
Use infinite polypeptide chain: Ala∞ , “supercell” + PBC Use twist θ, pitch L as geometry descriptors Map Potential Energy Surface in (L, θ) ( L(R) = Li ∆E (Li , θi ) = min E (R) − E0 , R θ(R) = θi Modeling package: Tinker 4.2 Force fields: AMBER99/99SB, CHARMM27, OPLS-AA/L, AMOEBApro
Cβ E. Penev et al.
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Energetics of Infinite Homopolypeptide Chains
Ala∞ conformations in vacuum from DFT kcal/mol/residue
θ
α
(degrees)
FES
27
π
L (Angstroms)
310
Helical domain: Ireta et al., JACS 127, 17241 (2005) Complete PES: Ireta et al., unpublished E. Penev et al.
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Energetics of Infinite Homopolypeptide Chains
Force-field PES’s in (L, θ) 285
AMBER99SB
245 205
310 165
twist θ (deg)
125
α π 2 7 FES
85 45 0.8 285
1.3
1.8
2.3
2.8
245 205
310 125
α π
85 45 0.8
2 7 FES 1.3
1.8
2.3
2.8
285
CHARMM27
245 205 165 125
α π
85
27
45 0.8
3.3
OPLS−AA/L
165
8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
285
1.3
2.3
2.8
3.3
AMOEBApro
245 205 165 125
α π 2 7 FES
85 45 0.8
3.3
1.8
FES
1.3
1.8
2.3
2.8
6 kcal/mol/residue 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8
9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5
3.3
pitch L (Å) E. Penev et al.
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Energetics of Infinite Homopolypeptide Chains
Minimum energy pathway s(L, θ) 6 4 2 ∆E (kcal/mol)
FES
27 π
0
α
310
-2 AMBER99SB AMBER99 CHARMM27 OPLS-AA/L AMOEBApro DFT
-4 -6 -8 0
1 2 3 path length s (arbitrary units)
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52nd Biophysical Society Meeting • Long Beach
Energetics of Infinite Homopolypeptide Chains
Minimum energy pathway s(L, θ) 6 4 27
2 ∆E (kcal/mol)
FES
π
0
α
310
-2 AMBER99SB AMBER99 CHARMM27 OPLS-AA/L AMOEBApro DFT
-4 -6 -8 0
1 2 3 path length s (arbitrary units)
4
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Five (meta)stable minima with increasing L: π, α, 310 , 27 , FES helical domain (π, α, 310 ) transition region L ≃ 2.5 ˚ A extended region (27 , FES) Helical domain for all force fields - more stable than DFT Quite different stabilization energies ∆E , but helices structurally similar
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Energetics of Infinite Homopolypeptide Chains
Nonbonded components along s(L, θ)
energy (kcal/mol)
energy (kcal/mol)
E = Estr + Ebend + Etors + EvdW + Eel 6 4 2 0 -2 -4 -6 -8 6 4 2 0 -2 -4 -6 -8
AMBER99SB
π
α
310
27
FES
OPLS-AA/L
0
1
2 3 40 path length s (a. u.)
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6 4 2 0 -2 -4 -6 -8 6 AMOEBApro 4 2 0 -2 -4 -6 -8 1 2 3 4 path length s (a. u.) EvdW Eel Etors Etot
CHARMM27
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Energetics of Infinite Homopolypeptide Chains
energy (kcal/mol)
energy (kcal/mol)
Nonbonded components along s(L, θ) 6 4 2 0 -2 -4 -6 -8 6 4 2 0 -2 -4 -6 -8
AMBER99SB
π
α
310
27
FES
OPLS-AA/L
0
1
2 3 40 path length s (a. u.)
6 4 2 0 -2 -4 -6 -8 6 AMOEBApro 4 2 0 -2 -4 -6 -8 1 2 3 4 path length s (a. u.) EvdW Eel Etors Etot
CHARMM27
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∆E similar, but individual contributions may differ considerably All conformations are local minima only for Eel π- and α-helices local min. for both Etors and EvdW 310 -helix not stable for CHARMM27 and AMOEBApro ➜ unfavorable bonding terms
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Energetics of Infinite Homopolypeptide Chains
Energetic convergence: AlaN ➜ Ala∞
How large a finite helix should be to fully include long-range interactions? Ace-AlaN -Nme, truncated from Ala∞ ; εN = EN − EN−1 − E0 cooperativity: ∆∆EN = εN − εN−1 α-helix E. Penev et al.
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52nd Biophysical Society Meeting • Long Beach
Energetics of Infinite Homopolypeptide Chains
Summary New method for comparing the long-range part of common force fields (gas-phase, max. cooperative nonbonded interactions) ∞-chains make identification of helical minima easy Valuable reference limit case in improving force-field parameterization Expedient model to compare first-principles vs. force-field methods AMBER99/99SB in closest agreement with DFT, reproducing π-, α-, and 310 -helices
Funding: David and Lucile Packard Foundation, NSF E. Penev et al.
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52nd Biophysical Society Meeting • Long Beach