Correction to Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics
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Correction to Constant pH Molecular Dynamics in Explicit Solvent with λ‑Dynamics Serena Donnini, Florian Tegeler, † Gerrit Groenhof,* and Helmut Grubmü ller* Department of Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, Gö ttingen, Germany Journal of Chemical Theory and Computation 2011, 7, 1962−1978. DOI: 10.1021/ct200061r W ith this erratum, we correct an error in the expressions for V chem (λ 1 ,λ 2 ) (eqs 31 and 32) and V transf (λ 1 ,λ 2 ) (eq 33) for chemically coupled titrating sites, in the aforementioned paper (J. Chem. Theory Comput. 2011, 7, 1962−1978). The correct expressions for V chem (λ 1 ,λ 2 ) are λ λ λ λ λ λ λ λ λ λ = − − Δ + Δ + − Δ + Δ −Δ ̃ V G G G G G ( , ) (1 )[(1 ) ] [(1 ) ] ( , ) chem 1 2 1 2 ref,00 2 ref,01 exp 1 2 ref,10 exp 2 ref,11 exp ref FF 1 2 with Δ = G 0 ref,00 Δ = ⇌ − G RT K (ln 10) (p (00 01) pH) ref,01 exp a,ref Δ = ⇌ − G RT K (ln 10) (p (00 10) pH) ref,10 exp a,ref and Δ = ⇌ − RT K G (ln 10) (p (00 11) pH) ref,11 exp a,ref which replace eqs 31 and 32. The correct expression for V transf (λ 1 ,λ 2 ) is λ λ λ λ λ λ λ λ = − − Δ + Δ + − Δ + Δ + − V G G G G ( , ) (1 )[(1 ) ] [(1 ) ], transf 1 2 1 2 AHH 2 AH 1 2 AH 2 A which replaces eq 33. We note that in our implementation of the constant pH protocol, the expressions for the forces due to V chem (λ 1 ,λ 2 ) and V transf (λ 1 ,λ 2 ) were implemented correctly; thus the trajetories are unaffected. The above corrected expressions are required only to compute the total energy of the system (i.e., the real and λ particles together) during the simulation. As a test, we have computed a 1 ns constant pH trajectory of imidazole in water (≈ 15 700 atoms) in the microcanonical ensemble. In the simulation, nonbonded interactions were evaluated with a 1.3 nm cutoff. Between 1 nm and the 1.3 nm cutoff, forces were smoothly shifted to zero using a shift function. We observed that the total energy of the complete system is constant with an average of −177 723 kJ mol −1 and a standard deviation of 0.3 kJ mol −1 . As the time step was decreased from 0.5 fs to 0.25 fs and 0.1 fs, the standard deviation decreased from 0.3 kJ mol −1 to 0.07 kJ mol −1 and 0.01 kJ mol −1 , respectively, thus establishing proper conservation of total energy. ■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (H.G.), [email protected] (G.G.). Present Address † Institute of Computer Science, Georg August University, Gö ttingen, Germany. Published: June 12, 2013 Erratum pubs.acs.org/JCTC © 2013 American Chemical Society 3261 dx.doi.org/10.1021/ct400439g | J. Chem. Theory Comput. 2013, 9, 3261−3261 Terms of Use
Transcript of Correction to Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics
Correction to Constant pH Molecular Dynamics in Explicit Solventwith λ‑DynamicsSerena Donnini, Florian Tegeler,† Gerrit Groenhof,* and Helmut Grubmuller*
Department of Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, Gottingen, Germany
Journal of Chemical Theory and Computation 2011, 7, 1962−1978. DOI: 10.1021/ct200061r
With this erratum, we correct an error in the expressionsfor Vchem(λ1,λ2) (eqs 31 and 32) and Vtransf(λ1,λ2) (eq
33) for chemically coupled titrating sites, in the aforementionedpaper (J. Chem. Theory Comput. 2011, 7, 1962−1978). Thecorrect expressions for Vchem(λ1,λ2) are
λ λ λ λ λ
λ λ λ
λ λ
= − − Δ + Δ
+ − Δ + Δ
− Δ
V G G
G G
G
( , ) (1 )[(1 ) ]
[(1 ) ]
( , )
chem1 2 1 2 ref,00 2 ref,01
exp
1 2 ref,10exp
2 ref,11exp
refFF
1 2
with
Δ =G 0ref,00
Δ = ⇌ −G RT K(ln 10) (p (00 01) pH)ref,01exp
a,ref
Δ = ⇌ −G RT K(ln 10) (p (00 10) pH)ref,10exp
a,ref
and
Δ = ⇌ −RT KG (ln 10) (p (00 11) pH)ref,11exp
a,ref
which replace eqs 31 and 32.The correct expression for Vtransf(λ1,λ2) is
λ λ λ λ λ
λ λ λ
= − − Δ + Δ
+ − Δ + Δ
+
−
V G G
G G
( , ) (1 )[(1 ) ]
[(1 ) ],
transf1 2 1 2 AHH 2 AH
1 2 AH 2 A
which replaces eq 33.We note that in our implementation of the constant pH
protocol, the expressions for the forces due to Vchem(λ1,λ2) andVtransf(λ1,λ2) were implemented correctly; thus the trajetoriesare unaffected. The above corrected expressions are requiredonly to compute the total energy of the system (i.e., the realand λ particles together) during the simulation. As a test, wehave computed a 1 ns constant pH trajectory of imidazole inwater (≈ 15 700 atoms) in the microcanonical ensemble. In thesimulation, nonbonded interactions were evaluated with a 1.3nm cutoff. Between 1 nm and the 1.3 nm cutoff, forces weresmoothly shifted to zero using a shift function. We observedthat the total energy of the complete system is constant with anaverage of −177 723 kJ mol−1 and a standard deviation of 0.3 kJmol−1. As the time step was decreased from 0.5 fs to 0.25 fs and0.1 fs, the standard deviation decreased from 0.3 kJ mol−1 to0.07 kJ mol−1 and 0.01 kJ mol−1, respectively, thus establishingproper conservation of total energy.
■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] (H.G.), [email protected](G.G.).Present Address†Institute of Computer Science, Georg August University,Gottingen, Germany.
Published: June 12, 2013
Erratum
pubs.acs.org/JCTC
© 2013 American Chemical Society 3261 dx.doi.org/10.1021/ct400439g | J. Chem. Theory Comput. 2013, 9, 3261−3261
Terms of Use
