From owner-chemistry@ccl.net Wed Jul 7 17:50:00 2021 From: "Andrew DeYoung andrewdaviddeyoung#,#gmail.com" To: CCL Subject: CCL: Wisdom on mixing (combination) rules in MD simulations Message-Id: <-54426-210707174754-29558-aaDUj9UZEfjEkzLElTdzkQ~!~server.ccl.net> X-Original-From: Andrew DeYoung Content-Type: multipart/alternative; boundary="0000000000004f100005c68f7d11" Date: Wed, 7 Jul 2021 17:47:37 -0400 MIME-Version: 1.0 Sent to CCL by: Andrew DeYoung [andrewdaviddeyoung|gmail.com] --0000000000004f100005c68f7d11 Content-Type: text/plain; charset="UTF-8" Hi, I'm wondering if someone can help me gain some wisdom about mixing (combination) rules in MD simulations. The classical simple point charge models for water -- SPC and SPC/E -- seem to be widely used to the present day in MD simulations of aqueous systems. At the same time, it seems that there are two widely used sets of mixing (combination) rules for calculating Lennard-Jones (LJ) interaction parameters for the interaction of different atomic species. If I understand correctly, these two most common sets are: (1) Lorentz-Berthelot mixing rules: arithmetic for sigma [ sigma_ij = 1 / 2 * (sigma_i + sigma_j) ], geometric for epsilon [ epsilon_ij = \sqrt{epsilon_i * epsilon_j} ] (2) Geometric mixing rules: geometric for sigma [ sigma_ij = \sqrt{sigma_i * sigma_j} ], geometric for epsilon [ epsilon_ij = \sqrt{epsilon_i * epsilon_j} ] and the Lennard-Jones (LJ) interaction I am referring to is U_LJ(r_ij) = 4 epsilon_ij * [(sigma_ij / r_ij)^12 - (sigma_ij / r_ij)^6]. Many of the papers reporting MD simulations of SPC-only or SPC/E-only systems (mostly from the 1980s, 1990s, and 2000s) state that they used the Lorentz-Berthelot mixing rules (1). However, in the case of SPC or SPC/E water, epsilon for the hydrogens is 0, so (1) and (2) will give the same result. However, the situation becomes less straightforward when one introduces, for example, Na and Cl ions modeled by the OPLS-AA force field. OPLS-AA uses mixing rules (2) above: geometric combination for both sigma and epsilon, as described in the second page of the Jorgensen group's classic paper (Jorgensen et al., JACS 1996, 118, 45, 11225--11236): https://doi.org/10.1021/ja9621760 So, my question is, if I have an OPLS-modeled solute in SPC or SPC/E water, do I use mixing rules (1) or (2) above? One possible lead is this paper from the Frenkel group (Espinosa et al., J. Chem. Phys. 2018, 149, 224501): https://doi.org/10.1063/1.5054056 In that paper, they state, "As OPLS/AA has been parameterized for being used in combination with SPC, TIP3P, and TIP4P water models, we have chosen these models for simulating water despite them being less accurate than other models in reproducing the behavior of pure water." Sure enough, when I look at what appears to be the original OPLS paper -- albeit united-atom, not all-atom -- Jorgensen et al. state, "The potential functions have the simple Coulomb plus Lennard-Jones form and are compatible with the widely used models for water, TIP4P, TIP3P, and SPC" (Jorgensen & Tirado-Rives, JACS 1988, 110, 1657--1666: https://doi.org/10.1021/ja00214a001 ) But I'm still a little confused... does the discussion above mean it is legitimate to use mixing rules (2) when simulating an OPLS solute in SPC or SPC/E water? As far as I know, most people, and most MD codes, use either mixing rules (1) or mixing rules (2) -- not a "mixture" of mixing rules (1) and (2), so to speak. Does anyone have wisdom on this? Thank you very much for your time! Andrew DeYoung, PhD Department of Chemistry Carnegie Mellon University --0000000000004f100005c68f7d11 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hi,=

I'm wondering if someone can help me gain= some wisdom about mixing (combination) rules in MD simulations.=C2=A0 The = classical simple point charge models for water -- SPC and SPC/E -- seem to = be widely used to the present day in MD simulations of aqueous systems.=C2= =A0 At the same time, it seems that there are two widely used sets of mixin= g=20 (combination) rules for calculating Lennard-Jones (LJ) interaction parameters for the int= eraction of different atomic species.=C2=A0 If I understand correctly, thes= e two most common sets are:

(1)=20 Lorentz-Berthelot mixing rules: arithmetic for sigma [ sigma_ij =3D 1 / 2 *= (sigma_i + sigma_j) ], geometric for epsilon [ epsilon_ij =3D \sqrt{epsilo= n_i * epsilon_j} ]
(2) Geometric mixing rules: geometric for sigm= a=20 [ sigma_ij =3D \sqrt{sigma_i * sigma_j} ],=20 geometric for epsilon [ epsilon_ij =3D \sqrt{epsilon_i * epsilon_j} ]
<= /div>

and the=20 Lennard-Jones (LJ) interaction I am referring to is

U_LJ(r_ij) =3D 4 epsilon_ij * [(sigma_ij / r_ij)^12 - (sigma_ij / r_= ij)^6].

Many of the papers reporting MD simulation= s of SPC-only or SPC/E-only systems (mostly from the 1980s, 1990s, and 2000= s) state that they used the=20 Lorentz-Berthelot mixing rules (1).=C2=A0 However, in the case of SPC or=20 SPC/E water, epsilon for the hydrogens is 0, so (1) and (2) will give the s= ame result.

However, the situation becomes less st= raightforward when one introduces, for example, Na and Cl ions modeled by t= he OPLS-AA force field.=C2=A0 OPLS-AA uses mixing rules (2) above: geometri= c combination for both sigma and epsilon, as described in the second page o= f the Jorgensen group's classic paper (Jorgensen et al., JACS 1996, 118= , 45, 11225--11236): https://doi.org/10.1021/ja9621760

= So, my question is, if I have an OPLS-modeled solute in SPC or SPC/E water,= do I use mixing rules (1) or (2) above?

One possi= ble lead is this paper from the Frenkel group (Espinosa et al., J. Chem. Ph= ys. 2018, 149, 224501): https://doi.org/10.1063/1.5054056=C2=A0 In that paper, the= y state, "As OPLS/AA has been parameterized for being used in combinat= ion with SPC, TIP3P, and TIP4P water models, we have chosen these models fo= r simulating water despite them being less accurate than other models in re= producing the behavior of pure water."=C2=A0 Sure enough, when I look = at what appears to be the original OPLS paper -- albeit united-atom, not al= l-atom -- Jorgensen et al. state, "The potential functions have the si= mple Coulomb plus Lennard-Jones form and are compatible with the widely use= d models for water, TIP4P, TIP3P, and SPC" (Jorgensen & Tirado-Riv= es, JACS 1988, 110, 1657--1666: https://doi.org/10.1021/ja00214a001 )
=
But I'm still a little confused... does=C2=A0the discuss= ion above mean it is legitimate to use mixing rules (2) when simulating an = OPLS solute in=20 SPC or SPC/E water?=C2=A0 As far as I know, most people, and most MD codes,= use either mixing rules (1) or mixing rules (2) -- not a "mixture&quo= t; of mixing rules (1) and (2), so to speak.

Does = anyone have wisdom on this?=C2=A0 Thank you very much for your time!
<= div>
Andrew DeYoung, PhD
Department of Chemistry
Carneg= ie Mellon University
--0000000000004f100005c68f7d11-- From owner-chemistry@ccl.net Wed Jul 7 19:39:00 2021 From: "Mezei, Mihaly mihaly.mezei{}mssm.edu" To: CCL Subject: CCL: Wisdom on mixing (combination) rules in MD simulations Message-Id: <-54427-210707193415-23035-wfcIGHYwNJVC7Civrm2snQ a server.ccl.net> X-Original-From: "Mezei, Mihaly" Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset="iso-8859-1" Date: Wed, 7 Jul 2021 23:34:04 +0000 MIME-Version: 1.0 Sent to CCL by: "Mezei, Mihaly" [mihaly.mezei . mssm.edu] Greetings, strictly speaking, both the mixing rules and the solvent model are part of the parametrization. Thus using SPC water with OPLS violates the OPLS parametrization - would you use OPLS for hydrophobic residues and Amber for the rest?. It may not matter too much since TIP3P and SPC are rather similar, but still. So the question of mixing rules for OPLS-SPC system is like asking if I walk across the street when the light is red do I have to watch out for bicycles going the wrong way? Mihaly Mezei Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai Voice: (212) 659-5475 Fax: (212) 849-2456 WWW (MSSM home): http://icahn.mssm.edu/profiles/mihaly-mezei WWW (Lab home - software, publications): https://mezeim01.u.hpc.mssm.edu WWW (Department): http://www.mssm.edu/departments-and-institutes/pharmacology-and-systems-therapeutics