Energetics of Infinite Homopolypeptide Chains - A

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

E. Penev et al. [email protected]

52nd Biophysical Society Meeting • Long Beach


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




“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.




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. [email protected]



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Helical domain: Ireta et al., JACS 127, 17241 (2005) Complete PES: Ireta et al., unpublished E. Penev et al. [email protected]



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. [email protected]



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)


4



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


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



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.)


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



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


∆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



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. [email protected]



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. [email protected]
