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Biophys J, May 2002, p. 2304-2316, Vol. 82, No. 5
*Structural Biology and Biochemistry, Hospital for Sick Children,
and Department of Biochemistry, University of Toronto, Toronto, Ontario
M5G 1X8, Canada; and Biochemistry Department, Weill
Medical College of Cornell University, New York, New York 10021 USA
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
CONCLUSIONS AND PERSPECTIVES
REFERENCES
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The conduction of protons in the hydrogen-bonded chain of water molecules (or "proton wire") embedded in the lumen of gramicidin A is studied with molecular dynamics free energy simulations. The process may be described as a "hop-and-turn" or Grotthuss mechanism involving the chemical exchange (hop) of hydrogen nuclei between hydrogen-bonded water molecules arranged in single file in the lumen of the pore, and the subsequent reorganization (turn) of the hydrogen-bonded network. Accordingly, the conduction cycle is modeled by two complementary steps corresponding respectively to the translocation 1) of an ionic defect (H+) and 2) of a bonding defect along the hydrogen-bonded chain of water molecules in the pore interior. The molecular mechanism and the potential of mean force are analyzed for each of these two translocation steps. It is found that the mobility of protons in gramicidin A is essentially determined by the fine structure and the dynamic fluctuations of the hydrogen-bonded network. The translocation of H+ is mediated by spontaneous (thermal) fluctuations in the relative positions of oxygen atoms in the wire. In this diffusive mechanism, a shallow free-energy well slightly favors the presence of the excess proton near the middle of the channel. In the absence of H+, the water chain adopts either one of two polarized configurations, each of which corresponds to an oriented donor-acceptor hydrogen-bond pattern along the channel axis. Interconversion between these two conformations is an activated process that occurs through the sequential and directional reorientation of water molecules of the wire. The effect of hydrogen-bonding interactions between channel and water on proton translocation is analyzed from a comparison to the results obtained previously in a study of model nonpolar channels, in which such interactions were missing. Hydrogen-bond donation from water to the backbone carbonyl oxygen atoms lining the pore interior has a dual effect: it provides a coordination of water molecules well suited both to proton hydration and to high proton mobility, and it facilitates the slower reorientation or turn step of the Grotthuss mechanism by stabilizing intermediate configurations of the hydrogen-bonded network in which water molecules are in the process of flipping between their two preferred, polarized states. This mechanism offers a detailed molecular model for the rapid transport of protons in channels, in energy-transducing membrane proteins, and in enzymes.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
CONCLUSIONS AND PERSPECTIVES
REFERENCES
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The control of proton fluxes across biomembranes
constitutes one of the most complex and fundamental properties of
living systems. To achieve biological energy conversion
(bioenergetics), membrane-spanning protein assemblies use energy
provided by photochemical or redox reactions to pump protons against an
electrochemical gradient, 
µH+. In turn, the
flow of H+ in the direction of the
electrochemical gradient drives ATP synthesis (Saraste, 1999
). This
"chemiosmotic coupling" is the cornerstone of bioenergetics
(Mitchell, 1961). Despite the importance of proton transport phenomena,
detailed molecular mechanisms have remained elusive. A high level of
detail is required to understand proton-pumping mechanisms
(Wikström, 1998; Sjogren et al., 2000; Lanyi, 2000). In general,
it is particularly challenging to understand the forces driving proton
movement in enzymes, because it requires knowledge, at the atomic
level, of three equilibrium properties that are intimately coupled to
each other: 1) the protonation state of all titratable groups in the
protein; 2) the electronic (charge) state of the protein; and 3) the
equilibrium distribution of conformational states of the enzyme.
Furthermore, these properties must be characterized at each stage of
the catalytic cycle. This is a formidable undertaking for the complex
membrane-bound protein assemblies involved in energy transduction
and/or proton pumping, as illustrated in the cases of
bacteriorhodospin, a light-driven proton pump (Lanyi, 1999), of
bacterial photosynthetic reaction centers (Okamura et al., 2000), and
of cytochrome c oxidase, a redox-coupled proton pump
(Zaslavsky and Gennis, 2000).
In addition to these equilibrium properties, the structure and function
of well-defined pathways for proton translocation, without which leaks
resulting in the loss of proton activity would occur, must be
elucidated. The transient events (nonequilibrium properties) involved
in proton movement present a special challenge in their own right.
Unlike that of other ions, the transport of protons does not require
the net diffusion of atomic or molecular species, but may instead take
place according to a Grotthuss relay mechanism involving the chemical
exchange of hydrogen nuclei along successive hydrogen-bond donor and
acceptor groups forming extensive networks and the subsequent
reorganization of these networks (Grotthuss, 1806; Nagle and
Morowitz, 1978; Knapp et al., 1980; Agmon, 1995) (Fig.
1). Such pathways constitute "proton
wires" mediating H+ displacement over long
distances.
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Although the molecular structures of such important proton pumps as
bacteriorhodopsin and cytochrome c oxidase are known, the
detailed nature of proton pathways and the molecular mechanisms leading
to proton translocation are still unclear. In addition to
proton-relaying amino acid residues, energy-transducing proteins, like
ion channels, appear to use water wires. Models for the relay of
H+ by buried water molecules have been
substantiated in several systems of bioenergetic interest. In
particular, there is now abundant evidence for the involvement of
buried water molecules in bacteriorhodopsin (for recent reviews, see
Dencher et al., 2000; Luecke, 2000; Kandori, 2000). However,
high-resolution structures of intermediates in the pumping cycle
suggest that although several water molecules reside in the protein
interior, they may not at all times form a continuous hydrogen-bonded
chain (Lanyi, 2000). Thus, water wires make up extended but incomplete
tracts of the proposed H+ pathways, underlining
the importance of conformational changes and dynamic fluctuations in
proton transport. This, in turn, raises further questions: do water
chains function as passive units, or are they involved in the
controlled access, blockage, and gating of proton flow? Understanding
the properties governing proton transport in hydrogen-bonded networks
containing water molecules is a prerequisite to achieving full
description of both ion permeation and energy-transduction mechanisms.
To this end, the study of simple proton wires can help in
characterizing the fundamental principles governing proton translocation.
Gramicidin constitutes a model of choice for the study of proton
conduction in much more complex proteins (Quigley et al., 1999;
Cukierman, 2000; DeCoursey and Cherny, 1999). With the notable exception provided by the potassium channel KcsA (Doyle et al., 1998),
it is to this day the only ion channel for which detailed structure-function relationships have been characterized, both experimentally (Tian and Cross, 1999) and theoretically (Roux and
Karplus, 1994). The relative structural and functional simplicity of
gramicidin A (gA) permits one to approach the proton transport mechanism "in isolation." In its active form, gA assembles as a
head-to-head homodimer of pentadecapeptides in lipid bilayers (Arseniev
et al., 1985). Its alternating L- and D-amino
acids adopt a right-handed 
6.3-helix
structure, which leaves its hydrophobic side chains facing out into the
bilayer and its peptide backbone lining the interior of a cylindrical
pore 4 Å in diameter (Fig. 2). This
hydrophilic pore accommodates a single file of water molecules and
mediates the translocation of monovalent cations such as
H+, Cs+,
Na+, and K+ (Finkelstein,
1987). The partial dehydration of cations upon entry into the
single-file region is partly compensated by the channel backbone.
Whereas permeation of other ions necessitates the net diffusion of the
single-file water column, the absence of streaming potentials during
H+ permeation through gramicidin (Levitt et al.,
1978) indicates that the long-range translocation of
H+ arises from a Grotthuss mechanism (Akeson and
Deamer, 1991).
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In recent years, theoretical studies of proton transport by
hydrogen-bonded networks of water molecules have opened the way to the
study of biological proton wires. The molecular basis for the
hop-and-turn mechanism has been investigated in bulk water (Tuckerman
et al., 1995; Vuillemier and Borgis, 1998, 1999; Schmitt and Voth,
1999), in single-file water chains or "water wires" embedded in
model channels (Pomès and Roux, 1995, 1996a, 1998; Pomès,
1999; Drukker et al., 1998; Decornez et al., 1999; Mei et al., 1998;
Sadeghi and Cheng, 1999; Brewer et al., 2001), and in gA (Pomès
and Roux, 1996b; Sagnella et al., 1996). These studies have uncovered
important aspects of the hop and turn mechanism at the molecular level.
In particular, the respective roles of thermal fluctuations and of
nuclear quantum effects arising form the light mass of
H+, and the modulation of proton-transport
properties by a protein matrix have been explored in simple, yet
biologically-relevant systems.
The Grotthuss mechanism in protonated chains of water molecules forming
a linear hydrogen-bonded array in nonpolar channels was the object of
several computational studies (Pomès and Roux, 1995, 1996a, 1998;
Pomès, 1999; Drukker et al., 1998; Decornez et al., 1999; Mei et
al., 1998; Sadeghi and Cheng, 1999; Brewer et al., 2001). The hopping
of H+ was found to be dominated by structural
fluctuations modulating donor-acceptor separations in the
hydrogen-bonded chain that take place spontaneously at 300 K. These
fluctuations drive the exchange between
OH3+-like and
O2H5+-like
species (Pomès and Roux, 1995). The translocation of protons across several water molecules may occur in subpicosecond time scales
(Pomès and Roux, 1996a; Sadeghi and Cheng, 1999). Nuclear quantum
effects (zero-point energy and quantum tunneling of hydrogen nuclei) on
the equilibrium structure of hydrogen-bonded chains of water molecules
have been studied with discretized Feynman path integral for the
treatment of exchanging protons. These effects, although significant,
do not govern the transfer process in equilibrium conditions
(Pomès and Roux, 1995, 1996a; Mei et al., 1998; Brewer et al.,
2001). By contrast, under nonequilibrium initial conditions mimicking
the effect of an external electric field (Drukker et al., 1998) and of
hydrogen-bonding partners restricting the displacements of water
molecules (Decornez et al., 1999), nuclear tunneling and nonadiabatic
transitions may play an important role in the translocation.
Studies of bulk water (Tuckerman et al., 1995) and gramicidin
(Pomès and Roux, 1996b) have revealed how structural fluctuations of the hydrogen-bonded network fundamentally dominate the rapid, passive relay of H+. More specifically, changes
in the hydrogen-bond connectivity of water molecules control the
progress of ionic translocation in these systems. In bulk water, such
changes consist of making and breaking hydrogen bonds in the second
hydration shell of H+. In gA, proton hopping
appears to be limited by the migration of defects in the polarization
of the wire. These defects result from hydrogen bond interactions
between water molecules and carbonyl oxygen atoms lining the pore
interior. Accordingly, comparisons between the proton translocation
mechanism in gA and in model hydrophobic pores suggest that the
Grotthuss mechanism is highly sensitive to the detail of
hydrogen-bonding and electrostatic interactions between the water wire
and the channel (Pomès and Roux, 1996b; Pomès, 1999).
Finally, calculations of the free energy or potential of mean force
(PMF) for both hop and turn steps of the Grotthuss mechanism in
nonpolar channels indicated that the reorientation of the wire, unlike
hopping, is a thermally activated process (Pomès and Roux, 1998),
suggesting that the reorganization of the wire, not the passage of
H+ itself, limits the rate of proton
translocation in these simplified models.
In this article, the molecular mechanism governing both ionic and bonding translocation steps in gA is investigated. The molecular dynamics and free energy simulation approaches used previously are applied to the chain of water molecules embedded in gA. The structure, dynamic fluctuations, and thermodynamic properties of the hydrogen-bonded network formed by the water molecules are computed successively with and without an excess proton. The present study focuses on the effect of the gramicidin channel on proton conduction. To this end, a detailed analysis of the hop and turn process is presented and compared with the results obtained previously in nonpolar channels.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
CONCLUSIONS AND PERSPECTIVES
REFERENCES
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Molecular model
The molecular model used in the molecular dynamics simulations
described below consists of the head-to-head pentadecapeptide dimer
forming the gA pore, together with water molecules. The system contains
three well-defined sections: the polypeptidic dimer, the single-file
water chain, and two cylindrical caps of water molecules lying outside
the mouths of the channel. The three-dimensional structure of gA has
been determined from solid-state nuclear magnetic resonance
spectroscopy (Arseniev et al., 1985; Ketchem et al., 1997) (Fig. 2).
The starting configuration of the channel was taken from previous
molecular dynamics simulations in which the lipid membrane was modeled
explicitly (Woolf and Roux, 1994). As in previous simulations
(Pomès and Roux, 1996b), harmonic restraining potentials (with a
force constant of 0.1 kcal/mol/Å2) were imposed
on the heavy atoms of the eight Trp indole rings to preserve the
overall fold of the pore without affecting directly the dynamics
fluctuations of backbone atoms lining the pore interior. This
constraint should be viewed as an approximation of the restriction to
indole mobility due to interactions with the lipid membrane, which act
as "anchors" of the indole rings (Woolf and Roux, 1994). In
addition, harmonic constraints with the same force constant were also
imposed on the heavy atoms of the peptide backbone during high-temperature preparation of the unprotonated wire (see below) to
ensure conservation of the secondary structure of the pore.
The CHARMM force field, version 22 (Brooks et al., 1983; MacKerell et
al., 1998), was used to model protein-protein interactions. The 10 water molecules, or proton wire, contained in the gA pore region, were
modeled with the PM6 force field of Stillinger and coworkers
(Stillinger and David, 1978; Stillinger, 1979; Weber and Stillinger,
1982). PM6 is a polarizable and dissociable model of water that
consists of O2
and H+
moieties. It has been used in several previous studies of proton wires
(Pomès and Roux, 1995, 1996a,b, 1998; Drukker et al., 1998; Decornez et al., 1999). This empirical force field reproduces relevant
properties of protonated water chains (Pomès and Roux, 1996a) and
has been shown, in a comparison with results obtained from ab initio
simulations, to capture the essential features of the mechanism of
H+ transport in these systems (Mei et al., 1998).
The parameters used to model PM6-peptide interactions are described
elsewhere (Pomès and Roux, 1996b).
The force fields used for the caps of water molecules lying outside the
pore differed in the protonated and the unprotonated systems. In the
latter case, 14 PM6 water molecules were used in each cap, whereas in
the former case, the TIP3P force field (Jorgensen et al., 1983) was
used to model caps of 36 water molecules each. The parameters governing
PM6-TIP3P interactions are given elsewhere (Pomès and Roux,
1998). Such a hybrid model offers the advantage of low computational
cost compared with an all-PM6 model and allows the inclusion of water
caps sufficiently large to avoid finite-size effects that would
preclude proton diffusion from end to end of the single file
(Pomès and Roux, 1998). Because the TIP3P model is not
dissociable, the hybrid model eliminates the possibility of an escape
of H+ out of the channel during the course of the
simulations. Control simulations of the nonprotonated wire indicated
that the equilibrium conformations of the water chain and the
hydrogen-bonding coordination of interfacial water molecules obtained
with the hybrid model are consistent with those obtained with all-PM6
and all-TIP3P models.
The cylindrical caps of water molecules were carved from a periodic box
of TIP3P water equilibrated in the bulk, and superimposed onto the
outer turn of the gA monomers. The water molecules overlapping with
heavy atoms of the peptide were deleted, and in all the subsequent simulations, the cap region was subjected to a boundary potential. In
the unprotonated (14-PM6 caps) and protonated (36-TIP3P caps) systems,
radial (cylindrical) restraints acted on the O atoms lying respectively
further than 6.8 and 6.0 Å from the main axis of the channel, and
planar constraints were imposed outside of the ranges 11.0 < z < 15.0 and 11.5 < z < 20 Å from the channel center. These restraining potentials were quadratic
with a force constant of 20 kcal/mol/Å2. The
inner value of the planar constraint was chosen so as to avoid the
artifact of water diffusion in the nonpolar region of the membrane
around the outside of gA. Similarly, planar restraints acting outside
the range 
11 < z < 11 Å (with a force
constant of 20 kcal/mol/Å2) were imposed on the
10 water molecules inside the pore to prevent their diffusion into the
caps. The location of these planar boundaries was chosen so as to
minimize perturbations of the interactions between pore and cap water
molecules, as determined from unbiased simulations. No cutoff was
imposed on nonbonded interactions.
Molecular dynamics simulations
The CHARMM program (Brooks et al., 1983) was used to propagate
the Langevin equation of motion. A friction coefficient of 5 ps1 was applied to all heavy atoms in the
system. After an initial equilibration, the molecular systems were
subjected to successive cycles of umbrella sampling calculations
comprising preparation, equilibration, and production. The preparation
stage was necessary to overcome the relatively long relaxation times
associated with the propagation of bonding defects in the gA channel,
as observed in previous simulations (Pomès and Roux, 1996b).
Uncorrelated configurations of the protonated wire were obtained from
simulations in which the electrostatic interactions between channel and
single-file atoms were turned off. This artificial procedure was seen
to lead to the disappearance of bonding defects and to high mobility of the ionic defect (Pomès and Roux, 1996b). The nonpolar channel resulting from this procedure is similar to the model channels constructed with radial restraints on single-file chains of water molecules, whose properties were characterized in previous studies (Pomès and Roux, 1995, 1996a, 1998). In such systems, complete translocation events from end to end of the single-file region occur in
the order of a few picoseconds so that it is easy to equilibrate ionic
defects by imposing collective reaction coordinate constraints
(Pomès and Roux, 1998) before turning electrostatic interactions
back on for equilibration and data collection (production). Using this
procedure helped to reach statistical convergence in the PMF calculation.
The collective reaction coordinates used to follow the progress of
ionic and bonding defects in the pore are defined as
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(1) |
2e and qH = 1e
and cartesian coordinates zO and
zH. In the case of the unprotonated
wire, µz corresponds to the z
component of the total molecular dipole moment of the 10-pore water
molecules, whereas in the presence of an excess proton
µz/e is the position of the center
of charge along the z axis. These reaction coordinates
reflect the organization of the wire and offer the advantage of a
continuous variable for translocation of both ionic and bonding defects
throughout the length of the pore (Pomès and Roux, 1998). The
detail of the methodology is described below successively for the
unprotonated and protonated systems.
Unprotonated wire
The initial conformation of the (single-file) wire region was obtained by deleting the excess proton from a previously equilibrated protonated gA wire (Pomès and Roux, 1996b). The water molecules were subjected to energy minimization and thermalization (two 10-ps
runs at 150 and 300 K), whereas the peptide was held fixed, and the
procedure was repeated without fixing protein atoms. The subsequent
equilibration consisted of a 60-ps simulation at 300 K, during which
all single-file water-water hydrogen bonds pointed toward the same
mouth of the channel (polarized configuration). The calculation of the
free energy profile, or PMF for the reorientation of the wire (i.e.,
propagation of the bonding defect-see Scheme 1), was obtained from a
series of six molecular dynamics simulations with umbrella sampling,
whereby the reaction coordinate µz was constrained by a harmonic potential
Vi(µz)
= 1/2kµ
(µz µ
-helix). 2) For equilibration, a 5-ps simulation followed, with T = 300 K. 3) For
production, the data were collected from an ensuing 20-ps simulation at
300 K. The preparation stage was required to ensure that several
distinct local minima be sampled that correspond to a given value of
µ
), much longer simulations would be
required to reach statistical convergence at 300 K. The higher
temperature used in the preparation stage enables a larger number of
conformations to be sampled in the relatively short simulation times
amenable to our PMF calculation. For each window in the umbrella
sampling calculation, 32,000 configurations were obtained at 2.5-fs
intervals from a total of 80 ps of simulations. These configurations
were used in the computation of the PMF (see below). The calculations
were repeated with TIP3P single-file water molecules (Jorgensen et al.,
1983) to gauge the influence of the water model in the calculations, as
in similar calculations performed on nonpolar channels (Pomès and
Roux, 1998; Pomès, 1999).
Protonated wire
The starting configuration of the channel with protonated water wire was taken from a previous simulation (Pomès and Roux, 1996b). Two cylindrical caps of 36 water molecules lying outside the
mouths of the channel were added to the system. The energy was
minimized (300 steps of steepest descent) and the caps were briefly
thermalized (5 ps, 300 K) with the rest of the system held fixed. Eight
series of biased simulations or windows were then created, each with a
quadratic restraint
Vi(µz)
differing by their reference µ0.5, 0, 0.5, 1, ... , 2.5, and 3 e·Å. The latter value corresponds to wires in which the excess
proton is located at the interface between bulk and single-file regions
(Pomès and Roux, 1998).
For each of these eight windows, the simulation protocol consisted of
four iterations of the following cycle. 1) For preparation of the
protonated wire, a 300-step SD energy minimization was followed
by 5-ps MD equilibration of the proton in the single-file water
wire at 350 K with wire-channel electrostatic interactions turned off.
2) For equilibration of the channel, a 300-step SD minimization was
followed by 25-ps MD at 300 K with full electrostatic interactions. 3)
Production consisted of 50 ps of data collection at 300 K. This
procedure ensured the generation of four uncorrelated production cycles
to improve configurational averaging. Production times of 200 ps were
generated for each window, for a total of 2560 ps of simulations
including preparation, equilibration, and production.
PMF calculations
The wire configurations produced in the simulations of protonated and unprotonated systems were used to calculate the PMF for ionic and bonding defect translocations, respectively. To this end, the weighted histogram analysis method (Kumar et al., 1992, Roux, 1995) was
used as in similar calculations reported previously (Pomès and
Roux, 1998). Statistical convergence of the PMF was verified by
comparing the profiles obtained from various subsets of configurations.
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RESULTS AND DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
CONCLUSIONS AND PERSPECTIVES
REFERENCES
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Unprotonated wire
Equilibrium structure
The gA channel is a narrow cylindrical pore filled with an array of water molecules arranged as a single file (Arseniev et al., 1985;
Ketchem et al., 1997; Fig. 2). The pore water molecules form a
hydrogen-bonded network comprising both water-water and water-channel
hydrogen bonds (Roux and Karplus, 1994, references therein; Pomès
and Roux, 1996b). A water molecule is considered to belong to the
single file if 1) it makes at most two hydrogen bonds with other water
molecules and 2) at least one of these two coordinating water molecules
is itself a single-file water. Thus defined, the single-file region
contains eight water molecules. In addition, two outlying water
molecules form an interface with water molecules outside the pore. Each
of the eight single-file water molecules is surrounded by two adjacent
water molecules with which it can either donate or accept a hydrogen
and carbonyl O atoms of the channel to which it can donate a hydrogen
atom. The single-file water molecules do not in general accept hydrogen atoms from the channel, because backbone N---H bonds, which are involved in intramolecular hydrogen bonds defining the -helix fold,
do not deviate sufficiently from colinearity with the channel axis to
point toward water O atoms in the lumen.
A representative conformation of the water chain is depicted in Fig.
3. Most water molecules in the wire adopt
the following organization: donation of one H to a channel backbone
carbonyl, donation of the other H to a neighboring water, and
acceptance of one H from the other neighboring water, for a total of
three hydrogen bonds. Such a coordination results in a continuous chain of water-water hydrogen bonds. In the single-file region, water O---H
bonds involved in hydrogen bonding (donation) to the channel are
approximately perpendicular to the channel axis, and most of the
covalent O---H bonds making up the water-water hydrogen-bonded chain
point toward the same entrance of the gA dimer: the hydrogen-bonded chain is preferentially polarized. The projection of the dipole moment
of each of these water molecules along the z axis is
approximately µzi 
±1 e·Å. In addition
to the polarized chain, in general the wire also contains exactly one
water molecule that donates both of its H atoms to the channel. Such
coordination forces the plane of that water molecule to be
approximately perpendicular to the channel axis, with
µzi 0. In general, the two water molecules adjacent to this perpendicular water point one of their O---H bonds toward it. The resulting inversion in the topology of the
hydrogen-bonded network defines what we shall refer to as a bonding
defect.
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i) indicates that statistical
convergence is not achieved within 20 ns. Nevertheless, this analysis
underlines important features in the organization of the
hydrogen-bonded network. The preferred arrangement of the wire is
reflected in the dominance of a hydrogen-bonding coordination of three
for the single-file water molecules (indices 2-9). The seemingly high
occurrence of null H bond coordination between water and channel (12%)
reflects the fact that a multiple choice of carbonyl O atoms often
results in bifurcated H bonds, which are not counted. The bonding
defect, characterized by donation of 2 H to the channel, is
preferentially at water 2, 3, 8, or 9, near the end of the single file.
This bonding defect is not necessarily a hydrogen-bonding defect:
although water molecules 2, 3, 8, and 9 are more likely than the other
single-file water molecules to be engaged in only one water-water bond,
they are also more likely to form a total of four H bonds. However,
even if the hydrogen-bonded chain is continuous, the local inversion of
its polarity precludes passage of protons in the sense of a Grotthuss
mechanism (see Fig. 1). Finally, interfacial water molecules (indices 1 and 10) often make two hydrogen bonds with outlying water molecules,
preferably as acceptors. This preferred orientation reflects the
presence of an intervening bonding defect.
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-helical secondary structure and its assembly as a head-to-head homodimer, possesses no net dipole moment. Rather, the polarization is
an intrinsic property of the single-file water chain, which was
attributed to the maximization of favorable water dipole-dipole interactions in nonpolar channels (Pomès and Roux, 1998;
Pomès, 1999). The presence of a bonding defect in the preferred
conformations of the unprotonated water wire in gA contrasts with the
fully polarized chains obtained in hydrophobic channel models. Full polarization is driven by the optimization of dipole-dipole
interactions between the single-file water molecules. The preferred
location of the bonding defect, near the end of the single file,
maximizes the length of the polarized segment in gA.
Dynamic fluctuations
Pore water molecules can adopt three distinct polarization states corresponding respectively to µzi +1, 1
(polarized), and 0 e·Å (bonding defect). The reorientation of
water molecules gives rise to unitary transitions between these three
states, which results in the displacement of the bonding defect. This process, which occurs spontaneously in the simulations, is depicted schematically in Fig. 4. The
conformations of the wire include metastable states in which one water
molecule is a bonding defect, as well as transient conformations in
which two adjacent water molecules are perpendicular to the channel
axis. The unitary translocation of a bonding defect arises from the
succession of two elementary reorientation steps. First, a water
molecule adjacent to the bonding defect (µzi±1 = 0) reorients from a polarized state (µzi = ±1) to perpendicular (µzi = 0). This process
replaces one water-to-water H bond by a water-to-channel H bond, which
creates a hydrogen-bonding defect, in a configuration which is
sometimes referred to as negative Bjerrum defect, whereby two adjacent
water O atoms are without an intervening H atom. Inversely, in the
second step water i ± 1 reorients from
µzi±1 = 0 to 
1, which eliminates the hydrogen-bonding defect in the wire and completes the unitary progression of the bonding defect. Thus, the hydrogen-bonding coordination provided by gA determines at once the nature of the bonding defect and the detailed mechanism for its migration
(Pomès, 1999). It is the alternation of the two types of bonding
defects that mediates the unitary migration of a bonding defect in the gA channel.
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i µzi, is depicted at
the bottom of Fig. 5. The total dipole moment of the chain is highly
sensitive to transitions in the orientation of individual water
molecules and reflects the position of the bonding defect. The
cooperativity of water reorientation was noted in earlier simulations
(Chiu et al., 1989), and it was shown that the process is influenced by
fluctuations in the conformation of the channel (Chiu et al., 1991).
Although thermal fluctuations of the chain take the bonding defect (and the polarization of the chain) back and forth from end to end of the
single file, this process is infrequent (it occurs only 12 times in the
20-ns simulation). This, together with cooperativity, suggests an
energy-activated process.
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PMF for the propagation of a bonding defect
The free energy profile for the translocation of a bonding defect, as calculated with umbrella sampling, is shown in Fig. 6. The results obtained for the two water models used, TIP3P and PM6, are qualitatively similar to each other. The preferred location of the bonding defect at water molecules 2 and 9 is reflected in the presence of a free energy well at µz = ±6.5 e·Å, which corresponds to mostly-polarized conformations in which eight of the ten pore water molecules form an oriented hydrogen-bonded chain. The interconversion between these two polarized conformations involves an activation energy barrier centered at µz = 0, which corresponds to a hydrogen-bonding defect located between water molecules 5 and 6 (µz5 = µz6 = 0). The barrier height is 3.8 kcal/mol with the polarizable water model PM6 and 2.2 kcal/mol with the TIP3P model. The PMF profile obtained from earlier simulations of a nonpolar channel of nine PM6 water molecules (Pomès and Roux, 1998), also shown in Fig. 6, is qualitatively similar but involves a
much larger free energy barrier. At 7.6 kcal/mol, this barrier is about
twice as large as that obtained for PM6 in the gA channel. Thus, the
primary effect of the channel appears to be to catalyze the propagation
of a bonding defect throughout the single file.
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Protonated wire
Structure
A representative structure of the protonated water chain is shown in Fig. 7. The presence of the excess proton modifies the strength and the topology of water-water hydrogen bonds. As discussed in detail elsewhere (Pomès and Roux, 1995,
1996a,b), in a single-file environment the hydrated proton can
generally be described either as a hydronium, OH
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). When the proton is near the middle of
the wire (as in Fig. 7), these defects are located preferentially at
either end of the single-file region, whereas when the excess proton is
closer to one of the mouths, the defect is located near the other mouth.
Dynamic fluctuations
The rapid exchange of H+ in the chain of water molecules in gA occurs spontaneously with thermal fluctuations at 300 K (Pomès and Roux, 1996b). As depicted schematically in Fig.
8, this exchange involves transitions
between successive hydronium-like and Zundel-cation-like arrangements
of the water molecules. Accordingly, the dynamic relay of
H+ in the proton wire may be easily followed
either by monitoring at every snapshot of the simulation, which O atom
is closest to three H nuclei (hydronium-like water molecule), or
alternatively, by monitoring the position of the shortest OO separation
(proton-sharing water dimer). These two reaction coordinates are
complementary ways to view the translocation process (Pomès and
Roux, 1996b). However, neither of these representations describes the
translocation process fully, because they implicitly assume that
hopping of the excess proton is entirely determined by the local
arrangement of the one or two water molecule(s) closest to it. Rapid
cascades in the movement of the hydrated proton over as many as six or seven water molecules were observed occasionally, suggesting that collective fluctuations are important to long-range transport (Pomès and Roux, 1996b).
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).
Conversely, it might be expected that the entry of
H+ at one end of an unprotonated single file
would hasten the translocation of the bonding defect via stabilization
of one polarized conformation of the wire relative to the other. The
polarization of water molecules induced by the presence of
Na+ at the entrance of the channel was noted in
an earlier computational study of gA (Jordan, 1990).
The displacement of ionic and bonding defects occurs on different time
scales. The migration of bonding defects is governed by water
reorientation events that were observed to occur infrequently in the
range of 100 ps or longer. This is significantly slower than the
movement of H+, which takes place in the
picosecond or subpicosecond time range (Pomès and Roux, 1996b).
For this reason, the average position of H+ may
remain in the vicinity of its starting point over simulations of a few
hundred picoseconds. In the present work, successive simulations for
which the excess proton was equilibrated at various positions were used
to overcome the separation of time scales between ionic and bonding
defect translocation. The collective reaction coordinate,
µz, used in the present study reflects the polarization of the wire by taking into account not only the position of the excess proton but also the relative distribution of O and H
nuclei along the channel axis z (Pomès and Roux,
1998). Thus, this reaction coordinate incorporates the presence of
bonding defects in gA.
PMF for the propagation of an ionic defect
Because bonding defects move on a time scale comparable with that of the simulations, it is important that the ensemble of conformations used for the calculation of the PMF cover not only the displacement of H+ but also of the bonding defect. This proved essential to the proper convergence of the PMF for the migration of an excess proton from end to end of the single-file region, which is shown in Fig. 9. This profile represents the reversible thermodynamic work for the complete translocation of the protonic defect. At µz = 0, the center of charge is located on average near the center of the channel, whereas numerical values of µz ±3 e·Å
correspond to configurations in which H+ is
located at the extremity of the polarized water chain with the ionic
defect near z = ±10 Å and the total dipole moment of the wire pointing away at 7 Å. The largely activation-less PMF profile suggests a diffusive mechanism for proton hopping. The shallow
well centered at the origin indicates that the excess proton is
somewhat better "solvated" near the dimer junction with a moderate
preference over outlying single-file locations reflected by a
1-kcal/mol drop in free energy. This could be due in part to the
propensity of extremal water molecules to form bonding defects. A
corollary to the polarization of water around the excess proton is that
H+ is always hosted by polarized water molecules,
never by a bonding defect. In addition, finite-size effects could lead
to an artificial bias in proton location. In studies of nonpolar
channels without water caps, the excess proton remained localized near
the center of the wire, whereas in the presence of droplets of 25 water
molecules, H+ was evenly distributed (Pomès
and Roux, 1998). A similar effect was also observed in another study
(Mei et al., 1998). In the present study, increasing the size of the
caps from 36 to 64 water molecules each (results not shown) did not
affect significantly the equilibrium distribution of
H+ in the single file. This indicates that the
water caps used in the present study are adequately large and do not
underlie the bias in proton location.
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) is also depicted in Fig. 9. This profile, which was
obtained in a very similar water system consisting of a single file of
nine water molecule between spherical droplets of 25 water molecules
each ("dumbbell" model), is a broad single well in the region
2.0 < µz < 2.0 e·Å. This
result indicates that in the absence of hydrogen-bonding partners to
water molecules in the pore, no work is required to relay an excess
proton from one end of the single file water chain to the other. This
result is largely reproduced in gA, which suggests that the local
environment provided by the channel is well suited for proton mobility.
Thus, based on the present results it appears that the periodicity of
groups presented by gramicidin provides no binding site or "trap"
of protons in the single-file region.
Gramicidin as a proton duct
Our choice of molecular system reflects the focus of this work on
the specific contributions made by the peptide on proton conduction
through a comparison of the molecular mechanisms obtained in nonpolar
channels and in gA. This incremental, comparative approach presents the
advantage of mitigating the effect of systematic errors inherent to
empirical energy functions. Clearly, this approach also limits the
scope of our conclusions. The absence of the lipid membrane precludes a
realistic treatment of long-range electrostatic interactions, which
play a role in the translocation of ions. Based on studies of proton
permeation in which Trp residues were fluorinated and replaced by Phe
residues, it has been proposed that dipole-dipole interactions between
water molecules and indole rings could play a role in the preferred
arrangement of water molecules in the channel, particularly near the
mouths of the pore (Phillips et al., 1999). Our simplified
representation of the bulk-water/channel interface makes the model
inadequate to the treatment of such effects, as well as of the entrance
and exit of protons and of water molecules.
The present results highlight the effect of water-water and
water-channel hydrogen-bonding interactions at play in gA (Pomès and Roux, 1996b). The fine balance between these forces modulates the
structure and dynamic fluctuations of the hydrogen-bonded network,
which in turn govern the mechanisms of translocation of bonding and
ionic defects in the single-file region of the channel. For a valid
description of the mechanism it is therefore essential that the
relative strengths of water-water and water-channel interactions be
adequately modeled. Quantitative discrepancies in the activation energy
for the reorientation of the water wire in gA (Fig. 6) obtained with
PM6 and TIP3P reflect the different nature of these two water models.
Despite this difference, the qualitative agreement obtained for the
mechanism of translocation of a bonding defect indicates that both
models, which exhibit identical mechanisms of reorientation in nonpolar
channels (Pomès, 1999), also respond consistently to gA. In
particular, the two models are in agreement regarding the coordination
of water molecules, the nature of the bonding defect, and its preferred
distribution in the unprotonated wire.
The relationship between water coordination and hop versus turn
mobility in proton wires has been discussed elsewhere in a comparison
of the Grotthuss mechanism in liquid water, in nonpolar channels, and
in gA (Pomès, 1999). Implications of the molecular mechanism for
the permeation of H+ in nonpolar channels were
proposed in terms of proton leakage via transient hydrogen-bonded
chains (Pomès and Roux, 1998). In the absence of water-channel
hydrogen-bonding interactions, each water molecule in the wire is
tightly coordinated to both of its neighbors. As a result, there are no
bonding defects in the chain and water molecules move in concert (i.e.,
cooperative motions of the O atoms are enhanced). Both of these effects
conspire to the high mobility of H+ in
single-file arrays of water molecules embedded in nonpolar channels
(Pomès and Roux, 1996b). However, the large activation energy
calculated for the reorientation of water molecules (Pomès and Roux, 1998; Pomès, 1999) suggests that the turn step of the Grotthuss mechanism would be prohibitively long compared with the
lifetime of single-file hydrogen-bonded arrays of water in a nonpolar
cavity. Thus, transient water chains, which have been proposed to
mediate the leakage of protons through pure lipid membranes (Nagle,
1987; Marrink et al., 1996; Paula et al., 1997) and to play a role in
the uptake of H+ in proton pumps (Wikström,
1998), would be suited at best to the passage of only one proton before
breaking apart. In such a mechanism, the rate-limiting step for proton
transport would be the nucleation of the wire.
By contrast to leakage, efficient proton-relaying channels such as gA
provide a different mechanism for the rapid succession of proton
conduction cycles. The analysis of this and previous simulation studies
(Pomès and Roux, 1996b; Pomès, 1999) offers clues as to why
gA constitutes a more effective proton duct than hypothetical
hydrophobic counterparts. This is achieved by assisting the
proton-relay chain in tackling the dual and seemingly contradictory requirement of a proton wire: to enable strong (water-water) hydrogen bonds between relaying groups for the rapid transfer and relay of
H+ and to help weaken (and break) these hydrogen
bonds so as to facilitate the reorientation of proton-relaying groups.
Locally, ideal solvation of protons in aqueous systems is achieved by a
coordination of three hydrogen-bond acceptors, because that is the
coordination of protonated water molecules in OH). In the single-file region of gA, carbonyl O atoms of the peptide provide the
extra hydrogen-bond acceptor that is missing in nonpolar channels (Fig.
8). Thus, the effect of gA on proton solvation (i.e., on the
stabilization of an ionic defect) is similar to that observed above
regarding the two forms of bonding defects (Fig. 4): the hydrogen-bond
structure stabilizes both forms of the ionic defect (and by the same
token, of larger protonated clusters of the form OnH
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CONCLUSIONS AND PERSPECTIVES |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
CONCLUSIONS AND PERSPECTIVES
REFERENCES
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We studied the complete translocations of a protonic defect and of
a bonding defect by water molecules in the single-file region of the gA
channel. We found that the mobility of an excess proton in gA is
essentially determined by the fine structure and the dynamic
fluctuations of the hydrogen-bonded network. The translocation of
H+ is mediated by spontaneous (thermal)
fluctuations in the relative positions of oxygen atoms in the wire. In
this diffusive mechanism, a shallow free-energy well slightly favors
the presence of the excess proton near the middle of the channel. The
unprotonated water chain adopts either one of two polarized
conformations corresponding to oriented donor-acceptor hydrogen-bond
pattern along the channel axis. Interconversion between these two
conformations is an activated process that occurs via the sequential
reorientation of water molecules of the wire. The effect of hydrogen
bonding between channel and water on proton conduction was analyzed by
comparison to the results obtained previously in a study of model
nonpolar channels, in which such interactions were missing (Pomès
and Roux, 1998). This analysis revealed that hydrogen-bond donation from water to the backbone carbonyl oxygen atoms lining the pore interior not only offers a compromise for the solvation and the mobility of an excess proton, it also enables the emergence of a
bonding defect and facilitates its transport.
Among the challenges facing the study of biological ion transport
mechanisms, particularly in the case of proton movement, are the
difficulty to detect ion movement experimentally and to relate
structure and function. The present study has opened the way to a
better understanding of ion channel structure-function relationships by
allowing the first confrontation of a molecular-level proton
translocation mechanism with experimental measurements. Based on the
results presented here, a framework model was developed for
single-proton transport flux through gramicidin (Schumaker et al.,
2000, 2001). That model describes the transport of
H+ (ionic defect) and of a bonding defect by
potential of mean-force profiles (Figs. 6 and 9) and diffusion
coefficients obtained from molecular dynamics simulations. Proton
entrance and exit in and out of the single-file region, which were not
studied by molecular dynamics in the present model, are represented
parametrically. A reasonable choice of these parameters yields a good
fit to experimental proton conductance data (Eisenman et al., 1980).
Theoretical approaches have begun to provide unprecedented and meaningful insight on the transient events governing proton relay mechanisms. Whereas the detailed studies performed to date on biological systems have been limited to the water chain embedded in the gramicidin channel, the results of these studies provide both a framework for understanding the basic physical principles at play in water wires and an impetus for the study of relay mechanisms in more complex proton wires. What is emerging from this and preceding studies of water wires is that the control of proton movement in biomolecular systems may be achieved with subtle local structural fluctuations of hydrogen bonded networks of low dimensionality, which are themselves determined by the fine hydrogen-bonding coordination, arrangement, and topology of proton-relay groups. The low dimensionality of a biological proton wire offers the possibility of a tight control of the geometry and the topology of hydrogen-bond interactions. The low-amplitude fluctuations of a flexible array (the proton wire) are thus mastered by a comparatively rigid environment presenting a few "judiciously disposed" hydrogen-bond partners.
Efficient proton conduction requires a wire that can alternatively form strong hydrogen bonds and break them relatively easily with thermal fluctuations. Water molecules are well suited for that, because water is ubiquitous in biological systems and forms highly modulable hydrogen-bonded networks. gA has harnessed those properties to assist both hop and turn steps of the Grotthuss mechanism. By the same token, it may be expected that somewhat similar features in the coordination of hydrogen-bond networks will be observed in other biomolecules that provide efficient ducts for the passive long-range relay of H+. In particular, based on the present study the detailed characterization of the structure of hydrogen-bonded arrays of water molecules embedded in channels and enzyme cavities might offer a clue as to their ability to mediate rapid proton transport. Inversely, it is likely that other proteic matrices make use of the coordination properties (both static and dynamic) of water molecules and of other titratable groups to control the long-range transport of protons in other ways: for the selectivity, delay, gating, pumping, and blockage of protons.
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ACKNOWLEDGMENTS |
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Stimulating discussions with Samuel Cukierman, Mark Schumaker, and Ching-Hsing Yu are gratefully acknowledged. We also thank C.-H. Yu for his help in the preparation of Table 1. This work was supported by a grant from the Canadian Institutes of Health Research. R.P. is a CRCP Chairholder.
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FOOTNOTES |
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.
Address reprint requests to Dr. Régis Pomès, Structural Biology & Biochemistry, Hospital for Sick Children, 555 University Avenue, Toronto, Ontario M5G 1X8, Canada. Tel.: 416-813-5686; Fax: 416-813-5022; E-mail: pomes{at}sickkids.ca.
Submitted August 14, 2001, and accepted for publication January 22, 2002.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
CONCLUSIONS AND PERSPECTIVES
REFERENCES
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