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Department of Chemical Physics, School of Chemistry, Tel Aviv
University, Ramat Aviv, Tel Aviv 69978, Israel
Contributed by Joshua Jortner, December 22, 2000
The effect of a solvation on the thermodynamics and kinetics
of polyalanine (Ala12) is explored on the basis of its
energy landscapes in vacuum and in an aqueous solution. Both energy
landscapes are characterized by two basins, one associated with
The chemical
environment exerts a fundamental influence on the structure,
thermodynamics, and dynamics of polypeptides. Particularly, the solvent
may affect the dynamics and structure of the polypeptide and
consequently alter its function, as has been demonstrated in a variety
of biologically important phenomena, ranging from the rate of oxygen
uptake in myoglobin to the stabilization of opposite- charged
side-chain pairs at the surface of proteins (1, 2). The variance of the
properties of a polypeptide in different solvents depends on the nature
of the solvent-polypeptide intermolecular interactions, which lead to
a rich repertoire of phenomena. These interactions involve the effect
of organic solvents on the destabilization of the hydrophobic core and
the exposure of side chains, as well as the opposite effects of aqueous
solvents on the protein structures favoring the hydrophilic protein
surface and the hydrophobic core (1, 3). Theoretical and computational evidence (4-6) for medium effects on polypeptide structures has accumulated. Following the Zimm-Bragg theory of the helix-coil equilibrium (7), it has been established that short polypeptides should
not form helices in water. Indeed, numerous studies report that the
relative tendency for helix formation in water is low at physiological
temperatures (6, 8).
The structure of polyalanine peptides is of considerable interest as,
in general, regardless of specific chemical environments, the commonly
reported secondary structure propensity scales for amino acids (9-11)
rank alanine as having the highest The thermodynamics and kinetics of a protein are determined by
its energy landscape (24, 25). The relation between energy landscapes
and kinetics of complex systems, e.g., clusters (26, 27) and proteins
(28), is being explored in terms of a master equation. Previous studies
by Y.L. and O.M.B. showed how structural constraints (29, 30) and
several specific point mutations (31) affect the topography and
topology of the energy landscape of peptides and proteins. Medium
effects on the energy landscape of peptides will elucidate the features
of solvation on the structure, thermodynamics, and dynamics of these
complex systems.
In this paper, we report the observation of dramatically different
energy landscapes of a peptide (dodecaalanine,
Ala12) in vacuum and in water, which reflects the
different environmental chemical properties of its kinetics and
thermodynamic stability in hydrophobic and hydrophilic solvents.
Polyalanine was chosen to explore the effect of solvent on the energy
landscape, because previous experimental (12-14) and computational
(4-6, 15-23) studies demonstrate its structural sensitivity to the
solvent environment. Two energy landscapes of
Ala12 are presented. The first corresponds to the
peptide conformational space in vacuum and represents the peptide
energy landscape in a hydrophobic medium. The second corresponds to the
conformational space in an implicit water solvent and represents the
peptide landscape in aqueous solution. A solvent-induced switchover from the native Reconstruction of an energy landscape relies on collecting a
large sample of conformations, minimizing each of them to the nearest
locally stable minima, and then using these local minima to
characterize the landscape. To obtain an overview of the molecular energy landscape accessible to the polyalanine at physiological temperatures, we sample the conformation space of
Ala12 in each environment by using a
high-temperature molecular dynamics trajectory. To ensure that the
conformational sample will cover the entire conformation space
available to the peptide, we started the high-temperature molecular
dynamics trajectory from two distinct Ala12
conformers: an ideal Technically, in each environment the sampling procedure includes two
1-ns molecular dynamics trajectories [performed with the
CHARMM program (32)], one at 400 K and one at 500 K, for each of the two starting structures. Conformations are sampled every 4 ps along the high-temperature trajectories, resulting in a total of
1,000 conformations of Ala12 in each environment. The protocols of the simulations are similar to those used in previous
work (29, 30). The simulations for Ala12 in water used the EEF1 implicit solvation model to take into account the solvent
effect (33, 34). The EEF1 expresses the solvation free energy as a sum
over group contributions, where the solvation free energy of each group
is corrected for screening by the surrounding groups. In addition to
the sampling simulations, two 350-K trajectories in vacuum, as well as
two 350-K trajectories in water, were performed to study the folding
and unfolding kinetics of the system in these environments. The folding
trajectory started from a The construction of the energy landscapes and the projections of the
folding and unfolding trajectories onto a low-dimensional subspace
(37-39) were obtained by applying the principal component analysis
method (PCA) (38, 39). In this study, we use the root-mean-square
distance of the backbone heavy atoms as the distance measure
between conformations composed of the conformation samples in vacuum
and in solvent. In this case, the principal two-dimensional subspace was found to represent the multidimensional data to an accuracy greater than 50%.
Solvent Effect on the Flexibility of Ala12.
The flexibility of polypeptides in different solvents is expected
to differ because of the different type of intermolecular interactions
between the solvent and peptide molecules. For example, whereas the
Chemistry
Solvent effects on the energy landscapes and folding kinetics of
polyalanine
Abstract
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Abstract
Introduction
Methods
Conclusion
References
-helical structures and the other with coil and 
-structures of
the peptide. In both environments, the basin that corresponds to the
-helical structure is considerably narrower than the basin
corresponding to the -state, reflecting their different
contributions to the entropy of the peptide. In vacuum, the -helical
state of Ala12 constitutes the native state, in agreement
with common helical propensity scales, whereas in the aqueous medium,
the -helical state is destabilized, and the -state becomes the
native state. Thus solvation has a dramatic effect on the energy
landscape of this peptide, resulting in an inverted stability of the
two states. Different folding and unfolding time scales for
Ala12 in hydrophilic and hydrophobic chemical environments
are caused by the higher entropy of the native state in water relative
to vacuum. The concept of a helical propensity has to be extended to
incorporate environmental solvent effects.
Introduction
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Abstract
Introduction
Methods
Conclusion
References
-helical propensity. However,
experimental (12-14) and computational (4-6, 15-23) studies showed
that polyalanines tend to adopt random-coil conformations in aqueous
solution. The ambiguity of the helical propensities, even for alanine,
which is known as an excellent helix former, may indicate that these
helical propensity scales do not reflect the intrinsic properties of
individual residues irrespective of the environment, and that solvent
effects have to be taken into account.
-helical state in vacuum to the native -state in
aqueous solution is manifested, whereas the implications of the
environmentally inverted stability for the thermodynamics and dynamics
of this peptide are explored.
Methods
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Abstract
Introduction
Methods
Conclusion
References
-helix and a -hairpin.
-hairpin conformation (0% -helical and
83% -sheet), and the unfolding trajectory started from an
-helical conformation (100% -helical and 0% -sheet). The
transition time of the folding reaction, 
, was defined as the
first passage time (
) from the -hairpin to an -helical
structure with 100% -helical content. Similarly, the transition
time of the unfolding reaction, , was defined as the time
required to unwind the helix and to obtain a structure with 0%
-helical content and 83% -sheet. The -helical and -sheet contents of any conformation of the conformation samples and of the
folding/unfolding trajectories were calculated by using the DSSP program (35). In addition, to estimate the effect of
solvation on the stability of the two states of
Ala12 in vacuum, we collected 200 -helical
conformations and 200 -hairpin conformations of Ala12, each sampled along 0.4-ns trajectories at
300 K by using vacuum, the EEF1 implicit solvation model, and the TIP3P
explicit water models (36).
-helical state of polyalanine is stable in organic media (4, 19,
23), its stability decreases in aqueous solutions, because water
molecules interact with the peptide polar groups, which form the
CO(i)NH(i + 4) hydrogen bonds. Inevitably, the destabilization of the -helix hydrogen bonds may result in
destabilization and even unwinding of the entire polyalanine -helix.
Accordingly, the helical conformation of polyalanine may be more
dominant in an organic medium than in water, whereas the coil
structures, in which the polar groups are exposed to the solvent, are
likely to be more accessible in water than in organic medium. The
larger the number of conformations that a peptide can adopt, the larger are its entropy and flexibility.
-helical and
-sheet conformations. This sampling procedure was selected to
overcome energetic and entropic barriers. The sampled conformations
were annealed back to 300 K to ensure that the resulting conformations
are accessible at physiological temperatures. The multidimensional
conformation spaces of Ala12 in vacuum and in
aqueous solvent were jointly projected onto the same three-dimensional subspace as shown in Fig. 1a.
A comparison between the relative volume of each conformation sample
and their overlap clearly outlines the effect of solvent on the
flexibility of the peptide. For Ala12, a larger
volume of conformation space is accessible in the aqueous solvent than
in vacuum, indicating that in water the peptide can adopt conformations
that are unlikely in vacuum. Fig.
2a shows three of the
conformations sampled in an aqueous environment selected from the
region that does not overlap with the conformation space of
Ala12 in vacuum. These structures illustrate that
the larger flexibility of Ala12 in aqueous
solution is mainly because of unwinding of the helix and a solvation of
all backbone polar groups that were involved in the stabilization of
the -helix. In water, random-coil structures are reasonable because
the loss of intramolecular interaction is compensated by intermolecular
interactions with water molecules.
View larger version (52K):
[in a new window]
Fig. 1.
A joint two-dimensional projection of the conformation space of
Ala12. (a) Conformations sampled in vacuum
(full circles) and with implicit water molecules (empty triangles).
(b) Conformations in both samples with -helical
content larger than 50%. (c) Conformations in both
samples with -sheet content larger than 50%. Ellipses are drawn to
emphasize the Ala12 conformations in vacuum (solid line)
and in solvent (dashed line). Conformations 1-9 are shown in Fig. 2.
View larger version (29K):
[in a new window]
Fig. 2.
Conformations of Ala12. (a)
Conformations selected from the region in the conformation space, which
is accessible only in an aqueous solvent (Fig. 1a).
(b) Conformations selected from the region of
-helical conformations (Fig. 1b). (c)
Conformations selected from the region of -sheet conformations (Fig.
1c).
-helical content larger than 50%
is shown in Fig. 1b. A partial projection of conformations (in both conformation samples) that are characterized by a -sheet content larger than 50% is shown in Fig. 1c. The relatively
smaller region of the helical conformations in both conformation spaces (Fig. 1b) in comparison to the region of -sheet
conformations (Fig. 1c) indicates that helical structures
are much more rigid than -hairpin structures. Moreover, whereas the
regions corresponding to -helical conformations sampled in vacuum
and in aqueous solvent significantly overlap, as expected, less overlap
is observed between the regions corresponding to -sheet structures.
Three -helical conformations of Ala12 placed
in the -helical region (Fig. 1b) are shown in Fig.
2b. Similarly, Fig. 2c shows three -structures selected from the corresponding region in conformation spaces (Fig.
1c). These structures illustrate the larger flexibility of
the -sheet in comparison with the -helical structures.
The accessibility and equilibrium population of the -helical
and the -sheet structures of both conformational samples, in vacuum
and in aqueous solution, is expected to be different because their
relative stability and the barrier heights that separate them are
affected by the environment. Only the energy landscape can explain the
relative stability of the conformations of the sampled conformation
space and the dynamics between them. For Ala12 in
vacuum as well as in water, the energy landscape can be constructed,
being based on the conformational samples, by plotting the energy of
each conformation versus the geometrical axes obtained by applying the
PCA procedure (38).
Energy Landscape of Ala12 in Vacuum.
The energy landscape of Ala12 in vacuum (Fig.
3a) is composed of two main
basins. One basin is shallow and broad, and the other is narrow and
deep. In fact, these two basins, which are different in energy,
correspond to conformations with different secondary structures. The
broad and shallow basin mainly corresponds to coil and -structures,
whereas the narrow and deep basin corresponds to -helical
conformations (Fig. 3b). A comparison between the sizes of
the two basins reflects the relative flexibility of the two
corresponding structures. The broad basin of the coil and the
-structures, in comparison to the narrow basin of the -helical structures, illustrates that the coil and -structures are much more
flexible and occupy most of the peptide conformation space. Namely, the
basin of the -structures includes various structures such as
-hairpin, -strand, and random coil, whereas the basin corresponding to the -helical structures includes structures with
different -helical content (examples for -helical and
-structures are shown in Fig. 2 b and c,
respectively).
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-helical
and a -state (which includes coil and -structures). The
-helical conformation in vacuum is more stable by 11.6 kcal/mol
than the -hairpin conformation (Table
1). The greater stability of the
-helical state in vacuum is in accord with common helical propensity
scales, which rank alanine as the residue with the highest helical
propensity. However, whereas Ala12 adopts an
-helix at physiological temperatures, the energy landscape suggests
that the energetic barrier crossing is possible at higher temperatures,
and a transition from the -helical to the -basin can occur. In
the () processes in vacuum, we expect that
E > 0 (<0) and S > 0 (<0).
When a barrier crossing is possible, the reaction 
is in
favor of the -state because of its large configurational entropy
that decreases the free energy change of the reaction as the
temperature increases.
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-hairpin conformation to an -helical
conformation, projected on the two-state vacuum energy landscape of
Ala12. The projection of the trajectory onto the
energy landscape demonstrates the two competing factors of a
protein-folding process: energy versus entropy. In the case of
Ala12, the peptide spends 10.7 ns in the highly
entropic -basin (nonnative state) before it undergoes a transition
to the energetically favorable -helical state (native state) and
adopts an ideal -helix conformation after 11.2 ns (Table 1). In the
opposite case of the 350-K unfolding simulation shown in Fig.
4b, starting with the ideal -helix of
Ala12, it took 8.8 ns to escape from the -helix basin into the nonnative -basin adopting a -hairpin structure after 9.2 ns. The heavy lines in the projected
folding/unfolding trajectories of Fig. 4 a and
b emphasize the successive structures before
entering/escaping the -helical basin. These two trajectories show
that there are several, perhaps many, pathways for these reactions, and
that this system has a transition region with more than one transition
state, rather than a single transition state, as classical chemical
kinetics would suggest (35, 40). The two trajectories are presented
here as an indication of the effect of entropy on the folding and
unfolding processes. However, to infer from the transition times of the
two processes, more trajectories should be collected, starting with
different initial conditions.
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Energy Landscape of Ala12 in an Aqueous Solvent.
The gross features of the energy landscape of
Ala12 in aqueous solution (Fig.
5a) are qualitatively similar
to the corresponding energy landscape in vacuum, which is composed of
two basins. One basin is associated with -helical structures, and
the other corresponds to coil and -structures. However, the
quantitative features of the two basins are drastically different in
aqueous solution and in vacuum. Although in vacuum the -helical
state constitutes the stable state (Fig. 3a), this state
becomes destabilized in an aqueous environment, and the stable state is
the one related to the -structure. Fig. 5a depicts the
two-state energy landscape of Ala12 in implicit
water projected onto a two-dimensional subspace. The secondary
structure characteristic of the two basins is shown in Fig.
5b. In this case, unlike in vacuum, the two first principal coordinates obtained by the PCA procedure are not sufficient to distinguish between the two states, and additional coordinates are
required to better characterize the energy landscape. To overcome this
difficulty, we have separately plotted (Fig. 5a) the
landscape for all structures with an -helical content of 50% or
more (the higher and narrower surface) and the landscape corresponding
to all other conformations of this polypeptide. The lesser success of
the PCA method in capturing the topography of the energy landscape in
water originates from the fact that in water,
Ala12 is more flexible than in vacuum and can
populate a broader range of conformations with the root-mean-square
distance being comparable to that between -helical and -sheet
conformations.
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-helical state in an aqueous
medium is less stable by 9.4 kcal/mol relative to the -hairpin
conformation, which is the global minimum of
Ala12 in water (Table 1). For the
() reaction in solution, we have E > 0 (<0) and expect S < 0 (>0), because of the large
configurational entropy of the -structures. The lower stability of
the helical state of the peptide in water is because of solvation of
the polar group, which otherwise participates in the
CO(i)NH(i + 4) hydrogen-bond network that
defines the -helix structure. The energy gap between the -hairpin
and the other -structures is about 4 kcal/mol. In water there is
only a relatively small thermodynamic preference for the -hairpin
structure in comparison to the higher preference of the -helix in
vacuum. This hints to the fact that in aqueous solution, polyalanine
may adopt a variety of open structures. The high flexibility of
Ala12 in water is reflected by the broadness of
the native basin that corresponds to the coil and -structures. To
estimate the effect of solvation on the stability of the two states of
Ala12 in vacuum, we calculate the average
energies of Ala12's -helical and -hairpin
conformations collected from 0.4-ns trajectories at 300 K by using
vacuum, implicit solvent, and explicit solvent models (see Table
2). The results of both implicit and explicit solvent calculations indicate that solvation destabilizes the
helical structure of Ala12 and that in a
hydrophilic environment, the -hairpin structure is the more stable
state of Ala12. However, whereas the energy gap
between the two states is about 10 kcal/mol in vacuum, the gap in
aqueous solvent is only 4-5 kcal/mol.
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coil transition in implicit water
projected onto the energy landscape of the solvated
Ala12. The time required for the helix to unwind
is 3.9 ns, being faster by more than a factor of two than for the same
process in vacuum. In explicit water at 300 K,
Ala12 unfolds after 1 ns, indicating that
although the unfolding process in implicit solvent is faster than in
vacuum, it does not entirely represent the solvent effect on the
folding/unfolding reactions. Recall that in vacuum, the helix-to-coil
process is driven only by increasing entropy, whereas in an aqueous
medium, the process is also driven by decreasing energy, which,
together with the increase in entropy, makes the helixcoil
transition much faster. On the other hand, the reverse process,
coilhelix, is predicted to be much slower in an aqueous environment
relative to its rate in vacuum. Although in vacuum this process
proceeds because of decreasing energy, in solvent the process is
characterized by positive free energy change because of an increase in
energy and a decrease in entropy (see Table 1). Fig. 6b
shows a projection of a 100-ns 350-K trajectory on the energy landscape
of Ala12 in aqueous solution. Because during these 100 ns a transition to the nonnative state, which corresponds to
the -helical structures, was not observed, the unfolding trajectory is presented only with respect to the native basin. The coilhelix transition time in aqueous solution is longer than 100 ns, being slower
by more than an order of magnitude than the corresponding transition
time in vacuum (
11 ns, according to Fig. 4a). The different kinetics behavior can be traced to the environmental effect
on the energy landscapes (Figs. 3a and 5a) that
makes the free energy change of the coilhelix transition positive
over the entire temperature range.
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Conclusion |
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Abstract
Introduction
Methods
Conclusion
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Our study demonstrates that the environment has a
significant effect on the energy landscape of
Ala12 polypeptide. Although the energy landscapes
of Ala12 in hydrophilic and hydrophobic media are
both composed of two basins, one associated with -helical and the
other with coil and -structures, their relative properties are
markedly affected by the environment. In both media, the large flexibility of the -structures implies that most of the peptide configurational entropy originates from this state, whereas the contribution of the -helical state to the total entropy is smaller. The main effect of the environment is exerted on the relative stability
of the two states that make up the energy landscape. Although the
-helical state is the stable state in a hydrophobic environment, it
is destabilized under hydrophilic conditions, and then the -state
becomes the more stable one. The inversion of the stability of the two
states because of polar solvation results in a native state in aqueous
solution that is characterized by larger entropy and, consequently, by
a very efficient folding process.
Accordingly, polyalanine is expected to adopt an -helical
conformation in a nonpolar organic solvent and -structures with coil
conformations in a polar aqueous solution. Solid-state (i.e., hydrophobic environment) (42-45) and aqueous solution (12-14)
measurements of polyalanine support its conformational dependence on
the chemical environments with the ubiquity of the -helix and
-structures prevailing in hydrophobic and in polar environments,
respectively. The dependence of the conformation of alanine on the
solvent characteristics (i.e., the polarity and dielectric constant of
the solvent) is supported by experimental evidence that the helical
propensity of alanine in water shows a dramatic increase on addition of
certain alcohols (e.g., trifluoroethanol) (46, 47). Recently, it was proposed that alcohol may act on the exposed CO and NH groups by
diminishing their exposure to the solvent, i.e., shifting the conformational equilibrium toward more compact structures, such as
-helical conformation (23). An alternative proposal for shifting the
helix-coil equilibrium of polyalanine toward an -helical conformation is to introduce charged residues into the sequence (48,
49); however, in this case, the tendency to form the -helix should
not be associated with the -helical propensity of alanine discussed herein.
Additional information emerges concerning temperature-dependent
conformations. The energy landscape of Ala12 in a
nonpolar medium implies that the reaction is
thermodynamically characterized by E > 0 and
S > 0, whereon G for this reaction
will decrease with increasing temperature. Consequently, the
equilibrium of the reaction in a hydrophobic environment is
predicted to shift toward the -state with increasing temperature.
Thus, the significant preference of the -helical conformation of
polyalanine in a hydrophobic environment at 300 K can be reduced at
higher temperatures. Experimentally, solid-state measurements of
polyalanine indicate that the conformation of
Ala200 is shifted from -helix at lower
temperatures to -sheet at higher temperatures (44). The energy
landscape of Ala12 in an aqueous
solvent suggests that because the reaction is
characterized by E > 0 and S < 0 (i.e., G > 0 for all of the temperature
range), the temperature does not affect the ratio of the - and
-conformations of polyalanine in water, and thus
Ala12 adopts -structures in aqueous solutions.
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Acknowledgements |
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We are grateful to Professor R. S. Berry for stimulating comments.
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Abbreviation |
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PCA, principal component analysis method.
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Footnotes |
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* To whom reprint requests should be addressed. E-mail: jortner{at}chemsg1.tau.ac.il.
Present address: Bio Information Technologies
(Bio-I.T.) Ltd., 1 Betzalel St., Ramat Gan 52521, Israel.
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References |
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Abstract
Introduction
Methods
Conclusion
References
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