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: hgrubmu@gwdg.de (H.G.), ggroenh@gwdg.de(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

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