Hi,
I get the following error with the lyx file in attachment:
lyx: SIGSEGV signal caught
Sorry, you have found a bug in LyX. Please read the bug-reporting
instructions in Help->Introduction and send us a bug report, if
necessary. Thanks !
Bye.
IOT/Abort trap(coredump)
-> actually, lyx crashes when I scroll or go the figures (included as
floats) part of my file.
The differences between the ultimate version of the attached lyx file
and the previous one are some "collapsed" that were true and now are
false.
LyX details:
LyX 1.2.1 of Tue, Aug 20, 2002
Built on Nov 13 2002, 18:11:05
Configuration
Host type: powerpc-ibm-aix5.1.0.0
Special build flags: included-libsigc xforms-image-loader
C Compiler: gcc
C Compiler flags: -g -O2
C++ Compiler: g++ (3.2)
C++ Compiler flags: -O -fno-rtti -fno-exceptions
Linker flags:
Frontend: xforms
libXpm version: 4.11
libforms version: 1.0.0
LyX binary dir: /usr/local/bin
LyX files dir: /usr/local/share/lyx
--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Nicolas FERRE' (PhD)
phone/fax : +39-0577-234278
Dipartimento di Chimica
Universita` di Siena mailto:[EMAIL PROTECTED]
via Aldo Moro
53100 SIENA (Italia) http://ccmaol1.chim.unisi.it/
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#LyX 1.2 created this file. For more info see http://www.lyx.org/
\lyxformat 220
\textclass article
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\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\end_preamble
\language english
\inputencoding auto
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\graphics default
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\paperfontsize 12
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\quotes_language english
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\layout Title
QM/MM parameterization of the Lys296-Retinal-Glu113 part in rhodopsin
\layout Author
Nicolas Ferré and Massimo Olivucci (Siena)
\newline
Alessandro Cembran and Marco Garavelli (Bologna)
\layout Section
Introduction
\layout Standard
The primary chemical reaction in the vision process consists in the ultrafast
photoisomerization of the retinal chromophore in the rhodopsin protein
\begin_inset LatexCommand \cite{math_00_1,kand_01_2}
\end_inset
.
This protein, member of the G-protein coupled receptor family, is composed
of seven transmembrane helices.
The retinal, a long polyenic chain with a terminal
\begin_inset Formula $\beta $
\end_inset
-ionone ring, is in its 11-
\shape italic
cis
\shape default
form in the so-called
\begin_inset Quotes eld
\end_inset
dark state
\begin_inset Quotes erd
\end_inset
of rhodopsin.
After adsorption of a photon, the chromophore isomerizes to the all-
\shape italic
trans
\shape default
state, then forming the first stable intermediate, called
\begin_inset Quotes eld
\end_inset
bathorhodopsin
\begin_inset Quotes erd
\end_inset
, in a few picoseconds.
A transient intermediate has been detected, called
\begin_inset Quotes eld
\end_inset
photorhodopsin
\begin_inset Quotes erd
\end_inset
, it is formed in 200 femtoseconds, that is one of the fastest reaction
found in nature.
The understanding of such a process is far to be complete, although numerous
experimental studies have been carried on the protein in its native form
as well as on rhodopsin mutants.
In particular, the nature of the photorhodopsin has not been yet elucidated,
this is where theoretical calculations can give some insights.
\layout Standard
Computational studies have mainly focused on the retinal itself and the
photoisomerization process is now well established.
Static and dynamical studies have been performed and validate a two-states
two-modes mechanism
\begin_inset LatexCommand \cite{gara_97_1,gara_98_1,gara_99_1,gara_99_2,gonz_00_1}
\end_inset
.
However, the influence of the protein on this mechanism is still largely
unknown.
Only few theoretical works have been published on this topic
\begin_inset LatexCommand \cite{han__95_1,bifo_97_1,yama_02_1,rohr_02_1}
\end_inset
, mainly due to the lack of a reasonable tridimensional structure of rhodopsin.
Recently published, the 2.8
\begin_inset Formula $\textrm{Å}$
\end_inset
resolved structure
\begin_inset LatexCommand \cite{okad_01_2,tell_01_1}
\end_inset
is the first step towards the definition of a computational model of the
protein.
The present paper presents the initial work we have done to derive a suitable
hybrid quantum mechanics (QM)/molecular mechanics (MM) model of the rhodopsin
protein.
It focuses on the definition and parameterization of the Lys296-Retinal-Glu113
part of the protein.
\layout Section
The model
\layout Standard
Inactivated rhodopsin has retinal in its 11-
\shape italic
cis
\shape default
form as chromophore.
The retinal is covalently linked to a lysine residue (Lys296) of the protein
through a protonated Schiff base, which counterion is a glutamate residue
(Glu113).
Beside the interactions between the chromophore and the residues that build
the pocket in which it lies and the long-range electrostatic interactions
with the entire protein-solvent-membrane macromolecular system, this lysine-ret
inal-glutamate (denoted LRG in the following) molecular group is the heart
of the system and is certainly responsible for a large part of the force
that drives the
\shape italic
cis
\shape default
\begin_inset Formula $\rightarrow $
\end_inset
\shape italic
trans
\shape default
photoisomerization.
Thus, deriving a reliable QM/MM model of the rhodopsin protein means first
to focus on this LRG molecular group, i.e.
to propose a computational model which combines both accuracy of the calculated
properties and tractability from the computational resources point of view.
While the rest of the protein will be treated in an approximate fashion,
using a standard MM forcefield, the LRG QM/MM potential must be designed
carefully: size of the QM subsystem with respect to the QM method and the
tractability of the calculation ; design of the QM/MM frontier ; choice
of the MM forcefield ; reparameterization of some QM/MM potentials.
\layout Standard
Concerning the last point, the procedure we retained consists to add or
modify a minimum number of QM/MM classical parameters, in order to reproduce
qualitatively the pure QM forcefield of the LRG group.
This means that the corresponding QM/MM forcefield will be strongly problem-dep
endent.
However, it would be difficult to have a less-specific forcefield, because
we are interested in the description of a chemical process - the photoisomeriza
tion of retinal - that involves at least two energy surfaces, while standard
forcefields, including the usual QM/MM ones, are dealing only with one
surface (usually the ground state).
\layout Standard
The QM/MM forcefield is characterized by a special Hamiltonian which is
the sum of three terms:
\layout Standard
\begin_inset Formula \begin{equation}
\widehat{\mathbf{H}}=\widehat{\mathbf{H}}_{QM}+\widehat{\mathbf{H}}_{MM}+\widehat{\mathbf{H}}_{QM/MM}\label{eq:totalHamiltonian}\end{equation}
\end_inset
On the right hand side,
\begin_inset Formula $\widehat{\mathbf{H}}_{QM}$
\end_inset
is the usual Hamiltonian of the QM part as if it were
\shape italic
in vacuo
\shape default
,
\begin_inset Formula $\widehat{\mathbf{H}}_{MM}$
\end_inset
is actually the classical energy of the MM part and
\begin_inset Formula $\widehat{\mathbf{H}}_{QM/MM}$
\end_inset
takes into account all the interactions between the QM and MM subsystems.
This last term can be splitted in several contributions:
\begin_inset Formula \begin{equation}
\widehat{\mathbf{H}}_{QM/MM}=\sum _{i=1}^{n}\sum _{j=1}^{Q}\frac{-q_{j}}{r_{ij}}+\sum
_{i=1}^{N}\sum
_{j=1}^{Q}\frac{-Z_{i}q_{j}}{r_{ij}}+E_{vdW}+E_{bonded}\label{eq:QM/MMHamiltonian}\end{equation}
\end_inset
The first term means that the QM wavefunction is polarized by all the surroundin
g point charges while the three remaining terms are the nuclei-point charges
electrostatic interactions, the QM/MM van der Waals short-term interactions
and some classical bonded terms (bonds, angles or torsions that involve
two, three or four atoms).
We choose to take into account any classical interaction when at least
one MM atom is involved in it.
We choose to use the Amber94
\begin_inset LatexCommand \cite{corn_95_1}
\end_inset
forcefield as it is coded in Tinker3.9
\begin_inset LatexCommand \cite{tink_39_1}
\end_inset
.
While in Amber electrostatic and van der Waals interactions are considered
when two atoms are separated by at least three bonds, the QM subsystem
feels all the MM point charges (in contrast, we keep the Amber rules for
the van der Waals interactions).
At this point, no considerations about the frontier between the QM and
the MM subsystems have been made.
\layout Standard
Because our target is to use a multireference
\shape italic
ab initio
\shape default
level (like CASSCF or CASPT2) for the calculation of the QM part, it is
out of reach to include the whole LRG group in the QM subsystem.
Obviously, the minimal QM part is the whole
\begin_inset Formula $\pi $
\end_inset
system, i.e.
the retinal, while lysine and glutamate are treated at the MM level.
However, it could be difficult to design a QM/MM frontier directly on the
PSB nitrogen atom, due to its involvement in the
\begin_inset Formula $\pi $
\end_inset
system, and it would certainly require a sophisticated scheme.
Therefore we choose to cut the next bond on the lysine side-chain, i.e.
between C
\begin_inset Formula $\delta $
\end_inset
and C
\begin_inset Formula $\varepsilon $
\end_inset
, thus including in the QM subsystem the whole retinal and the last bond
of the lysine residue (see figure
\begin_inset LatexCommand \ref{fig: QM/MM partition}
\end_inset
).
Another reason to cut this bond is that such a carbon-carbon bond is more
appropriate for using a simple QM/MM frontier scheme like the Link Atom
(LA) one: when this carbon-carbon covalent bond is cut, an electron remains
unpaired on the QM side, that is not realistic.
Consequently, the C
\begin_inset Formula $\varepsilon $
\end_inset
atom is saturated with an hydrogen atom which position is restrained on
the C
\begin_inset Formula $\delta $
\end_inset
-C
\begin_inset Formula $\varepsilon $
\end_inset
line at 1
\begin_inset Formula $\textrm{Å}$
\end_inset
from the QM carbon atom.
Numerous QM/MM studies have shown that in this case, the simple LA scheme
is enough accurate to design a smooth QM/MM frontier.
According to a recent study
\begin_inset LatexCommand \cite{ferr_02_4}
\end_inset
, we choose to let interact the LA with all MM point charges, whereas no
van der Waals or bonded terms are included between the LA and the MM atoms.
\layout Standard
The remaining of the LRG group and the rest of the rhodopsin protein are
treated with the Amber forcefield.
While the Glu113 residue is entirely MM, Lys296 is now a mixed QM/MM residue,
for which a special set of parameters should be derived.
Moreover, Amber6 does not contain any parameter to describe the retinal.
Therefore, the first part of this work will be about the derivation of
such parameters for retinal and lysine.
\layout Standard
The QM/MM calculations are performed using a modified version of Gaussian98
\begin_inset LatexCommand \cite{gaus_98_1}
\end_inset
, linked with a modified version of Tinker3.9
\begin_inset LatexCommand \cite{tink_39_1}
\end_inset
.
\layout Section
Parameterization
\layout Subsection
Selection of the QM/MM parameters
\layout Standard
As mentioned previously, the Lys296 residue is now a mixed QM/MM molecular
group which MM parameters should be adapted to reflect this hybrid situation.
First, the corresponding MM point charges may be changed.
While the original Amber lysine residue has a net charge of +1, the MM
side of the Lys296 residue must now have a 0 total charge because the positive
charge belongs to the QM part.
Moreover, as we are using the LA scheme, we choose to set to zero the C
\begin_inset Formula $\delta $
\end_inset
point charge to 1) not overpolarize the QM/MM frontier and 2) keep unchanged
the classical parameters of the frontier (see below).
Finally, in order to keep a minimum of consistency with the Amber forcefield,
the modified point charges are chosen to be close as possible to the original
ones.
With all these requirements in mind, we propose the set of modified point
charges listed in table
\begin_inset LatexCommand \ref{table: charges}
\end_inset
.
While all charges corresponding to the side-chain remain unchanged (apart
from C
\begin_inset Formula $\delta $
\end_inset
set to 0), the point charges carried by the carbonyl and the amino groups
are changed by about
\begin_inset Formula $\pm $
\end_inset
0.05 electrons only.
\layout Standard
The QM/MM van der Waals interactions are really important to keep a realistic
placement of the QM subsystem with respect to the protein cavity in which
it lies.
We have therefore to develop a set of atomic parameters for all the retinal
atoms.
Following the philosophy of the Amber forcefield, we will distinguish only
three kinds of atoms in the chromophore: the carbon atoms involved in the
\begin_inset Formula $\pi $
\end_inset
system, the other carbon atoms and the hydrogen atoms.
Moreover, to restrict the parameterization, we keep the same
\begin_inset Formula $\varepsilon $
\end_inset
values found in the original Amber forcefield for
\begin_inset Formula $\mathrm{sp}^{2}$
\end_inset
carbon (0.0860),
\begin_inset Formula $\mathrm{sp}^{3}$
\end_inset
carbon (0.1094) and hydrogen (0.0157).
\layout Standard
Next are the frontier bonded potentials.
They include the bond term of the QM/MM frontier bond, the angle terms
N-C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
, H
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
, C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
-H
\begin_inset Formula $\delta $
\end_inset
and C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
-C
\begin_inset Formula $\gamma $
\end_inset
.
The torsion terms involve rotations around three bonds (N-C
\begin_inset Formula $\varepsilon $
\end_inset
, C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
and C
\begin_inset Formula $\delta $
\end_inset
-C
\begin_inset Formula $\gamma $
\end_inset
) and are sketched in figure
\begin_inset LatexCommand \ref{fig: QM/MM torsions}
\end_inset
.
All these potentials are already parameterized in Amber, with the exception
of the dihedral C(Ret)-N-C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
that involves a retinal atom.
In order to limit the reparameterization process, it would be interesting
to keep the same set of parameters in the QM/MM simulation.
As mentioned previously, the charge of the C
\begin_inset Formula $\delta $
\end_inset
atom is set to zero, thus it allows to not change the parameters of the
frontier bond potential as only this potential acts between the two atoms
that make the bond.
Concerning the bond angles, they involve MM atoms with null or very little
charges, we can therefore hope that the original angle parameters are still
adapted to the hybrid situation.
\layout Standard
The torsion potentials are the most critical to set up because such dihedrals
must be described enough accurately to let the molecular geometry adapt
itself correctly during the photoisomerization process.
However, as all these QM/MM torsions (minus one) are already parameterized
in Amber and involve MM atoms with little charge values, we decide to determine
the C(Ret)-N-C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
torsion parameters and the retinal van der Waals parameters together, in
order to correctly reproduce the torsional behavior around the N-C
\begin_inset Formula $\varepsilon $
\end_inset
(
\begin_inset Formula $\phi $
\end_inset
angle) and the C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
(
\begin_inset Formula $\psi $
\end_inset
angle) bonds for both ground state (S0) and first singlet excited state
(S1).
\layout Subsection
Fitting procedure and resulting parameters
\layout Standard
Reproducing correctly the S0 and S1 energy surfaces means calculating these
surfaces at the QM level only.
Actually, it consists to sample the (
\begin_inset Formula $\phi $
\end_inset
,
\begin_inset Formula $\psi $
\end_inset
) space, i.e.
to calculate the S0 and S1 energies for each pair of (
\begin_inset Formula $\phi $
\end_inset
,
\begin_inset Formula $\psi $
\end_inset
) values.
Because performing such calculations for the entire retinal+lysine molecular
system would ask a lot of computer times and powers, we adopt a model of
this system in which the retinal is replaced by three conjugated double
bonds linked to a lysine-like residue that contains only three bonds in
the side-chain (instead of five).
The model and the (
\begin_inset Formula $\phi $
\end_inset
,
\begin_inset Formula $\psi $
\end_inset
) angles are displayed in figure
\begin_inset LatexCommand \ref{fig: model}
\end_inset
.
The starting structure results from an optimization of the geometry of
the model at the RHF/6-31G* level, leading to
\begin_inset Formula $\phi =-120.726^{\circ }$
\end_inset
and
\begin_inset Formula $\psi =179.704^{\circ }$
\end_inset
.
Then a grid of 96 different structures is built, varying
\begin_inset Formula $\phi $
\end_inset
from
\begin_inset Formula $-120.726^{\circ }$
\end_inset
to
\begin_inset Formula $44.274^{\circ }$
\end_inset
with a step of
\begin_inset Formula $15^{\circ }$
\end_inset
and
\begin_inset Formula $\psi $
\end_inset
from
\begin_inset Formula $179.704^{\circ }$
\end_inset
to
\begin_inset Formula $74.704^{\circ }$
\end_inset
with a step of
\begin_inset Formula $-15^{\circ }$
\end_inset
.
For each structure, four energy calculations are performed: CAS(6,6)/6-31G*
on the ground state and on the first singlet excited state and CAS(6,6)/6-31G*
+ Amber on the same states.
The difference between the QM and QM/MM relative energies (where relative
means with respect to their minimum) is then minimized by running MM calculatio
ns taking into account only van der Waals interactions between the QM and
MM parts and also the C(Ret)-N-C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
torsion, using parameters resulting from a simplex minimization of the
energy difference (QM-QM/MM) root mean square.
The resulting optimized van der Waals atomic parameters are (R* in
\begin_inset Formula $\textrm{Å}$
\end_inset
;
\begin_inset Formula $\varepsilon $
\end_inset
in kcal/mol): (1.8700 ; 0.0860) for a carbon atom in the conjugated
\begin_inset Formula $\pi $
\end_inset
system ; (1.8700 ; 0.1094) for the other carbon atoms and (0.9200 ; 0.0157)
for an hydrogen atom.
The C(Ret)-N-C
\begin_inset Formula $\varepsilon $
\end_inset
-C
\begin_inset Formula $\delta $
\end_inset
torsional potential is given by:
\layout Standard
\begin_inset Formula \begin{equation}
0.750\left[1+cos(\phi -0)\right]\label{eq:torsion}\end{equation}
\end_inset
Then QM/MM energies are re-calculated using the new parameters.
The QM and QM/MM potential energy surfaces for both S0 and S1 states are
reported in figure
\begin_inset LatexCommand \ref{fig: surfaces}
\end_inset
.
Differences between QM and QM/MM energies exceed 3 kcal/mol for only 11
structures in S0 and 9 structures in S1 (for a total number of 96 structures),
these structures have very high relative energies and should never be reached
during a geometry optimization.
\layout Standard
We have now designed a QM/MM Lys296-Ret in order to reproduce efficiently
the torsional behavior of the lysine side-chain at the QM/MM frontier.
The next step in the building of the QM/MM LRG molecular system, is to
pay attention to the retinal-Glu113 interactions, when the glutamate counterion
is replaced with Amber point charges.
\layout Section
Ret-Glu113 (BOLOGNA)
\layout Section
LRG (SIENA/BOLOGNA)
\layout Section
Conclusions
\layout Standard
\pagebreak_top
\begin_inset LatexCommand \BibTeX[aip]{/home/ferre/BIBTEX/niko}
\end_inset
\layout Standard
\pagebreak_top
\begin_inset FloatList table
\end_inset
\layout Standard
\begin_inset Float table
wide false
collapsed false
\layout Caption
RESP and QM/MM Lys296 point charges.
MM modified values are given in bold.
\layout Standard
\added_space_top medskip \align center
\begin_inset Tabular
<lyxtabular version="3" rows="18" columns="3">
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\layout Standard
Atom
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
RESP
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
QM/MM
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
N
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
-0.3479
\end_inset
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\begin_inset Text
\layout Standard
\series bold
-0.39805
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<row>
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\layout Standard
C
\begin_inset Formula $\alpha $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\family roman
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-0.2400
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<cell alignment="center" valignment="top" topline="true" leftline="true"
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\begin_inset Text
\layout Standard
-0.2400
\end_inset
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<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
C
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.7341
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true"
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\begin_inset Text
\layout Standard
\series bold
0.68395
\end_inset
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<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.2747
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\series bold
0.22455
\end_inset
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</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
O
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
-0.5894
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true"
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\begin_inset Text
\layout Standard
\series bold
-0.63955
\end_inset
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</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\begin_inset Formula $\alpha $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.1426
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\begin_inset Text
\layout Standard
0.1426
\end_inset
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</row>
<row>
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\begin_inset Text
\layout Standard
C
\begin_inset Formula $\beta $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
-0.0094
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\begin_inset Text
\layout Standard
-0.0094
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</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\begin_inset Formula $\beta $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0362
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0362
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
C
\begin_inset Formula $\gamma $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0187
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0187
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\begin_inset Formula $\gamma $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0103
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0103
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
C
\begin_inset Formula $\delta $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
-0.0479
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0000
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\begin_inset Formula $\delta $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0621
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0.0621
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
C
\begin_inset Formula $\varepsilon $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
-0.0143
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\begin_inset Formula $\varepsilon $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.1135
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
N
\begin_inset Formula $\zeta $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
-0.3854
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
</row>
<row bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
H
\begin_inset Formula $\zeta $
\end_inset
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0.3400
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
</row>
<row bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\shape italic
Total charge
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\shape italic
+1
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true"
rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\shape italic
0
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset LatexCommand \label{table: charges}
\end_inset
\end_inset
\layout Standard
\pagebreak_top
\begin_inset FloatList figure
\end_inset
\layout Standard
\begin_inset Float figure
wide false
collapsed false
\layout Caption
QM/MM partition of the LRG group in the rhodopsin protein
\layout Standard
\begin_inset ERT
status Collapsed
\layout Standard
\backslash
vspace*{10mm}
\end_inset
\layout Standard
\align center
\begin_inset Graphics FormatVersion 1
filename LRG2.eps
display default
size_type 0
rotateOrigin center
lyxsize_type 0
\end_inset
\begin_inset LatexCommand \label{fig: QM/MM partition}
\end_inset
\end_inset
\layout Standard
\begin_inset Float figure
wide false
collapsed false
\layout Caption
QM/MM torsions (curved arrows)
\layout Standard
\begin_inset ERT
status Collapsed
\layout Standard
\backslash
vspace*{10mm}
\end_inset
\layout Standard
\align center
\begin_inset Graphics FormatVersion 1
filename LRG3.eps
display default
size_type 0
rotateOrigin leftBaseline
lyxsize_type 0
\end_inset
\begin_inset LatexCommand \label{fig: QM/MM torsions}
\end_inset
\end_inset
\layout Standard
\begin_inset Float figure
wide false
collapsed true
\layout Caption
Model system for the fitting procedure of the Lys296-Retinal parameters
\layout Standard
\begin_inset ERT
status Collapsed
\layout Standard
\backslash
vspace*{10mm}
\end_inset
\layout Standard
\align center
\begin_inset Graphics FormatVersion 1
filename LRG4.eps
display default
size_type 0
rotateOrigin leftBaseline
lyxsize_type 0
\end_inset
\begin_inset LatexCommand \label{fig: model}
\end_inset
\end_inset
\layout Standard
\begin_inset Float figure
wide false
collapsed true
\layout Caption
Potential energy surfaces (the red axe corresponds to the
\begin_inset Formula $\phi $
\end_inset
angle, the blue axe corresponds to the
\begin_inset Formula $\psi $
\end_inset
angle, the green axe corresponds to the energy relative to its minimum
at
\begin_inset Formula $\phi =-120.726^{\circ }\: ;\: \psi =179.704^{\circ }$
\end_inset
).
\layout Standard
\begin_inset ERT
status Collapsed
\layout Standard
\backslash
vspace*{10mm}
\end_inset
\layout Standard
\align left
\begin_inset Graphics FormatVersion 1
filename gs_qm.eps
display none
subcaption
subcaptionText "QM ground state"
size_type 1
width 8cm
keepAspectRatio
rotateOrigin leftBaseline
lyxsize_type 0
\end_inset
\begin_inset Graphics FormatVersion 1
filename gs_qmmm.eps
display none
subcaption
subcaptionText "QM/MM ground state"
size_type 1
width 8cm
keepAspectRatio
rotateOrigin leftBaseline
lyxsize_type 0
\end_inset
\hfill
\layout Standard
\align left
\begin_inset Graphics FormatVersion 1
filename exc_qm.eps
display none
subcaption
subcaptionText "QM excited state"
size_type 1
width 8cm
keepAspectRatio
rotateOrigin leftBaseline
lyxsize_type 0
\end_inset
\begin_inset Graphics FormatVersion 1
filename exc_qmmm.eps
display none
subcaption
subcaptionText "QM/MM excited state"
size_type 1
width 8cm
keepAspectRatio
rotateOrigin leftBaseline
lyxsize_type 0
\end_inset
\begin_inset LatexCommand \label{fig: surfaces}
\end_inset
\end_inset
\the_end
