MONTE CARLO SIMULATION OF WATER
INTERACTION WITH GRAMICIDIN A
TRANSMEMBRANE CHANNEL : HYDROGEN
BOND ANALYSIS
S. Fornili, M. Migliore, D. Vercauteren, E. Clementi
To cite this version:
S. Fornili, M. Migliore, D. Vercauteren, E. Clementi. MONTE CARLO SIMULATION OF WATER INTERACTION WITH GRAMICIDIN A TRANSMEMBRANE CHANNEL : HYDROGEN BOND ANALYSIS. Journal de Physique Colloques, 1984, 45 (C7), pp.C7-219-C7-223.
<10.1051/jphyscol:1984724>. <jpa-00224289>
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Submitted on 1 Jan 1984
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JOURNAL D E PHYSIQUE
Colloque C7,supplement au n09, Tome 45, septembre 1984
page C7-219
MONTE CARL0 SIMULATION OF WATER INTERACTION WITH GRAMICIDIN A
TRANSMEMBRANE CHANNEL : HYDROGEN BOND ANALYSIS
S.L. Fornili',
M. Migliore*, D.P. Vercauteren
++
and E. Clementi
IBM Corp., P.O. Box 390, Dept. 0 5 5 , BZdg. 701-2, Poughkeepsie,
New York 12602, U.S.A.
*IAIF-CAR, Via Archirafi 36, 1-90123 Palerrno, Italy
-
~gsum; La simulation, par la me/thode Monte Carlo, de la structure conformationelle de mol6cules d'eau, dans et aux extr&mit&s dd'n canal transmembranairedutype Gramicidin A, nous permet de montrer la persistance de liaisons hydrogenes entre les mol6cules d'eau. Le mcme type d'analyse est ensuite
applique/au cas :o diffe'rents cations monovalents sont placgs dans une position fixde a l'inte'rieur du canal.
-
The conformational structure of water molecules inside and close
Abstract
to the ends of the Gramicidin A transmembrane channel is examined by a statistical method which determines the persistence, over the Monte Carlo generated configurations, of hydrogen bonds among water molecules. The same kind
of analysis is applied to results of simulation experiments in which monovalent cations are placed in a fixed position inside the channel.
As it is well known, selective control of ion flow through membranes is essential to
the behaviour of biological cells. Ion transport may take place by migration through
a transmembrane molecular channel/l/, as it occurs, e.g., in the electrical excitation of neurons/2/. The pentadecapeptide antibiotic Gramicidin A (GA) forms transmembrane channels with high single channel conductance, which are selective for monovalent cations 131. Further, GA has a relatively simple chemical structure 141 and
detailed molecular models for GA channel are available 15-71. For all these reasons,
a large amount of work has been done on GA channel, which is now considered a prototype transmembrane channel 18-101.
Water may play a remarkable role in ion transport through membranes, since a substantial reduction of Born energy barrier for an ion crossing-a membrane is caused even
by a single file of 8-12 water molecules filling the transmembrane channel 111-131.
In a previous paper, results have been reported on Monte Carlo simulations of water
interaction with GA channel, modeled according to Urry's atomic coordinates, by using
atom-atom pair-potentials derived by ab initio calculations/l4/. In particular, we
have determined the number and the conformational structure of the water molecules
inside and at the extremes of the GA channel, and their interaction energy among
themselves and r~iththe GA channel.
In the present paper we discuss further features of water molecules interacting with
GA channel, that have been evidenced by a statistical method which analyzes the Monte
Carlo generated water configurations in terms of permanence of hydrogen bonding.
The Metropolis Monte Carlo simulations 115,161 were carried out according to a previously described procedure 1141, which is here summarized. Eighty one water molecules
+present add., Physics Dept. and IAIF-CNR, Via Archirafi 36, 1-90123 Pal~rmo,
++Italy.
Present add., Laboratoire de Chimie Thgorique Appliquge, Facultgs Universitaires,
Notre Dame de la Paix, Rue de Bruxelles 61, B-5000 Namur, Belgium.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984724
JOURNAL DE PHYSIQUE
C7-220
surroundiag the GA channel, were confined within a cylindrical volume 48
high and
with 5.5 A base radius. The cylinder axis was taken parallel to the long axis of the
channel ( Z axis). In some experiments a monovalent cation (Li+, ~ a +or k)was added
at a fixed position (at the center of the channel which coincides with the cylinder
center).
The sim ated temperature was 300 OK. For each experiment, we have considered about 4x10 different Monte Carlo moves per water molecules, after the end of
the equilibration phase. We recall that each Monte Carlo configuration is obtained
from a previous one by random selection of one water molecule and b a random displacement (the displacements are for distances not longer than 0.3
and for rotations not larger than about 18 degres).
9
f
For the water-water interaction, we have used the MCY potential reported elsewhere
1171. The GA-water'interactionenergy has been expressed in terms of atom-atom pairpotentials
where i represents an atom in the GA channel belonging to "class" a and j refers to
either H or 0 atom of water molecules, which belongs to the class designated by the
index b. We recall that the atoms of a molecule can be grouped into classes/l8/. A
class contains all the atoms of a given atomic number that are in similar molecular
environments. The latter are defined by (1) same number of bonds, (2) same (gross)
charge, as defined by Mulliken's population analysis 1191, and (3) same molecular orbital valency state (MOVS) energy /20/. The assumed form for V(i,j;a,b) is
where r(i,j) is the distance between atoms i and j, and q(i) and q(j) are the net
charges of the same atoms. The constants A(a,b),
B(a,b) and C(a,b) are fitting parameters previously reported 1141 for the 16 classes that were found necessary t
describe the water interaction with the GA channel. For the water-Li+,-~a+ and -K9
pair-potentials we have used the fitting constants reported in Ref. 14.
Two main algorithms have been implemented for statistical analyses of the Monte Carlo
generated configurations of water molecules. The first one, which has been already
used in the previous paper 1141, gives the probability distribution, P, of the oxygen
and hydrogen atoms (heavier and lighter lines, respectively, in Figs. 1 and 2, top
insets) of water molecules along the channel axis. In the second kind of analysis the
hydrogen bonds among every water molecule and all the other water molecules belonging
to the same Monte Carlo configuration are searched for. Two water molecules are supposed to be linked if at least one of the distances between the oxygen atom of either
water molecule and the hydrogen atoms of the other is not greater than 2.1 8. This
analysis can be carried out for a selectable number of Monte Carlo water configurations.
The resulting link matrix can be worked out and used for various purposes. One of
them is shown in the middle insets of Figs. 1 and 2, where the information stored in
the link matrix is combined with results obtained from a statistical analysis which
determines the average positions, over the Monte Carlo configurations, of the oxygen
atoms of water molecules. In these plots a segment represents a link between two water molecules, which is present not less than the indicated percentage of the Monte
Carlo configurations. The end points of the segment represent the average positions
of the oxygen atoms of the two hydrogen bonded water molecules.
Another possible use of the information contained in the link matrix is to select and
visualize only "filaments" of links connecting two selectable water molecules. This
to analyze hydration features of solute molecular
application is useful, e.g.,
groups.
Further, this kind of analysis has been proven extremely useful as a diagnostic tool,
e.g., to monitor the evolution of the equilibration phase or to catch abnormal
behaviours of the system, which usually cause the appearance of anomalous link structures.
Also, by using 3-D subroutines of the Tektronix Plot-10 package, a program has been
developed which rotates the link pattern around a selectable axis, to visualize on a
Tektronix 4115B color monitor the spatial distribution of the statistical hydrogen
bond network.
In Fig. 1 and in Fig. 2 we report results of Monte Carlo simulations of water
molecules interacting with GA channel. In Fig. 1 ( A ) , results are shown for a computer
experiment involving only water molecules. In Fig.l(B), and in+Fig.+2 resul s are reported of simulations in which a fixed monovalent cation (Na , Li and K , respectively) is added at the center of the channel. In both Fig. 1 and Fig. 2, the top insets show the probability distribution of oxygen and hydrogen atoms of water
molecules along the channel axis; the bottom insets show one of the Monte Carlo water
configurations, where hydrogen bonds have been indicated, and the middle insets report results of the statistical hydrogen bond analysis, which has been carried out as
outlined in the previous section. The latter plots show hydrogen bonds which are
present in at least 25, 50 and 75 %, respectively, of the Monte Carlo generated water
configurations.
4
Fig. 1. (A) Top: oxygen and hydrogen probability distributions (heavy and light
lines, respectively) of water molecules along the GA-channel Z axis (in 2). Middle:
plots of hydrogen bonds among water molecules along the Z axis, which are present in
at least 25, 50 and 75%, respectively, of the Monte Carlo configurations. Bottom: a
statistically significant Monte Carlo water configuration (with indication of hydrogen bonding). (B) The same as in (A), for a Monte Carlo simulation in which a fixed
Na ion is placed at Z=0.
The top inset of Fig. 1(A) shows a well defined peak pattern in the probability distributions of the oxygen and hydrogen atoms of water molecules inside the channel
(approximatly from Z=-12 to Z=12 2) , suggesting that, as previously pointed out /14/,
a single file of about nine water molecules fills the channel. This result, which is
in agreement with experimental findings /11/, is clearly evidenced by the hydrogen
C7-222
JOURNAL DE PHYSIQUE
bond permanence plots (Fig.1 middle insets). Further, the similarity among the water
distribution of the bottom inset of Fig. 1 and the 25% and 50% link patterns suggests
that the movements of water molecules inside and close to the extremes of the channel
are rather hindered. This agrees with the energy profile for water-GA interaction reorted in the previous paper /14/, which shows deep energy minima in regions 12 to 14
distant from the center of the channel. Nevertheless, some rotational freedom of
the water molecules inside the channel seems to be compatible at 300 OK even with a
completely static channel conformation, as it has been assumed in the present simulation experiments. In fact, the position of the breakage point of link filaments inside the channel, which corresponds to an inversion of the relative position of 0 and
H probability distributions (Fig. 1, top inset), slightly fluctuates, if results of
different Monte Carlo experiments are compared.
g
As a further feature of water conformational structure inside the channel, which has
been evidenced by the 3-D-rotation version of the statistical link analysis mentioned
in the previous section, the oxygen average positions of water molecules connecting a
channel extreme to the link breakage point appear to lay approximately on a same
plane. This plane seems to be different for the two halves of the channel and it
seems determined by the water molecules clustered at the channel entrances, where the
energy minima for water-GA channel interaction are located. We recall that according
to the Urry's model / 5 / , the GA channel is formed by two head-to-head hydrogen bonded
GA molecules.
Fig. 2. (A) and (B): same as in Fig. 1(B) for ~ i +and K+, respectively.
Results shown in Fig. 1(B) and in Fig. 2 confirm and extend findings previously reported /14/ on the effects due to the presence of monyvalent cations on the conformational structure of water molecules inside the GA channel. As the probability distributions shown in the top insets suggest, the two main effects are i) a strong polarization of the water molecules closest to the ion, and ii) a strong electrostriction
induced by the ion on the single file of water molecules inside the channel, which
causes stretching of link filaments and appearance of gaps, as clearly shown by the
results reported in the link pattern insets. These gaps occurr since, as previously
mentioned, water molecules at the channel entrances feel strong energy interaction
with GA channel. As clearly shown by Fig. 1(B) and Fig. 2, these effects increase
with decreasing ion radius. A consistent picture is given by the Monte Carlo water
configurations shown in the bottom insets.
We thank Prof. M.U. Palma and Prof. M.B. Palma-Vittorelli for useful discussions, Mr.
M. Lapis and Mr. A. La Gattuta for technical help, and Ms. M. Genova-Baiamonte and
Ms. M. Giannola for typescript preparation. General indirect support from CRRNSM and
MPI is also acknowledged.
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