[proteamdavis] Fwd: alpha helix formation via side chain shielding

  • From: Paul Limb <paulimb@xxxxxxxxx>
  • To: proteamdavis@xxxxxxxxxxxxx
  • Date: Sat, 3 Jul 2004 11:25:30 -0700

---------- Forwarded message ----------
From: Paul Limb <paulimb@xxxxxxxxx>
Date: Mon, 28 Jun 2004 17:26:42 -0700
Subject: Re: alpha helix formation via side chain shielding
To: jtmorgan@xxxxxxxxxxx

On Mon, 28 Jun 2004 09:39:30 -0700, Paul Limb <paulimb@xxxxxxxxx> wrote:
> =CE=B1-Helical stabilization by side chain shielding of backbone hydrogen=
> Angel E. Garc=C3=ADa* and Kevin Y. Sanbonmatsu
> Theoretical Division, T10 MS K710, Los Alamos National Laboratory, Los
> Alamos, NM 87545
> Edited by Peter G. Wolynes, University of California, San Diego, La
> Jolla, CA, and approved December 13, 2001, (received for review
> September 20, 2001)
> * To whom reprint requests should be addressed. E-mail: angel@xxxxxxxxxxx=
> This article has been cited by other articles in PMC.
>  Top
>  Abstract
>  Introduction
>  Methods
>  Results and Discussion
>  Conclusion
>  References
>  Abstract
> We study atomic models of the thermodynamics of the structural
> transition of peptides that form =CE=B1-helices. The effect of sequence
> variation on =CE=B1-helix formation for alanine-rich peptides, Ac-Ala21-
> methyl amide (A21) and Ac-A5 (AAARA)3A-methyl amide (Fs peptide), is
> investigated by atomic simulation studies of the thermodynamics of the
> helix-coil transition in explicit water. The simulations show that the
> guanidinium group in the Arg side chains in the Fs peptide interacts
> with the carbonyl group four amino acids upstream in the chain and
> desolvates backbone hydrogen bonds. This desolvation can be directly
> correlated with a higher probability of hydrogen bond formation. We
> find that Fs has higher helical content than A21 at all temperatures.
> A small modification in the AMBER force field reproduces the
> experimental helical content and helix-coil transition temperatures
> for the Fs peptide.
>  Top
>  Abstract
>  Introduction
>  Methods
>  Results and Discussion
>  Conclusion
>  References
>  Introduction
> Detailed all-atom molecular simulation of protein folding has been
> limited by the inadequacy of sampling and possible inaccuracies of the
> semiempirical force fields used in classical simulations. The
> development of techniques for efficient sampling and the refinement of
> semiempirical force fields are crucial for modeling protein folding,
> structure prediction, and complex formation. Small peptides have many
> of the complexities associated with the energy landscape of proteins
> (1) and are ideal systems to understand the role of competing
> interactions in determining protein structures. In this work, we study
> the thermodynamics of the helix-coil transition of short peptides for
> which ample experimental data exist. We use highly parallel algorithms
> that enable the efficient sampling of configurational space. We
> validate our results through comparison with experimental data and
> test the sensitivity of our results to small changes in the
> semiempirical force field.
> The elucidation of =CE=B1-helical formation energetics is relevant for
> understanding protein folding mechanisms. In spite of the large number
> of experimental studies conducted in peptides, there is still much
> debate concerning the propensity of Ala residues to stabilize
> =CE=B1-helices. Ingwall et al. (2) studied runs of Alan, with n =3D 10=E2=
> flanked by Lys runs, and concluded that short (n ~ 10) sequences of
> Ala peptides do not form helices in water (2, 3). Similar conclusions
> were drawn from studies of Ala-rich random sequences. However, short
> (13=E2=80=9321) Ala-rich peptides containing interior charged amino acid =
> chains are found to form helices with 70=E2=80=9390% helical content (4=
> and short runs of Alan (n =3D 13) flanked by two ornithine charged amino
> acid are found to be about 40% helical in water (8, 9). These data
> have been interpreted in terms of a large intrinsic propensity of Ala
> residues to form helices in water. Within the Lifson=E2=80=93Roig (10, 11=
) and
> Zimm=E2=80=93Bragg (12) models for the helix-coil transition, the intrins=
> propensity of an amino acid to form a helix is a measure of the
> interactions of the amino acid with its own and nearest-neighbor amino
> acid backbone (11, 13). Theoretical (14) and experimental studies on
> prenucleated synthetic peptides (15) have suggested that the high
> helical propensity of Ala-containing peptides is a consequence of the
> neighboring side chains and is an effect extrinsic to the Ala side
> chains. Specifically, Vila et al. (14) have argued that the high
> helical propensity of Ala-rich peptides containing large charged side
> chains is stabilized by the effect of the side chains in reducing the
> accessibility of the peptide backbone to water. It has also been
> argued that backbone desolvation by large side chains is responsible
> for helix destabilization (16, 17). Theoretical studies suggest that
> desolvation of the peptide CO and NH groups is energetically
> unfavorable (18). Atomic simulations of the helix-coil transition of
> peptides will help elucidate the role of charged side chains in the
> stabilization of the helical state.
> We present all-atom simulations of the thermodynamics of the
> helix-coil transition with explicit aqueous solvent. Molecular
> dynamics (MD) simulations have been applied to describe the unfolding
> of =CE=B1-helices (19, 20) and helix formation kinetics on short peptides
> (21=E2=80=9327). Hummer et al. (26, 27) provided a detailed analysis of t=
> helix formation kinetics of pentapeptides of A5, AAGAA, and G5, over a
> broad range of temperatures. The nucleation mechanism was found to be
> diffusive for helix formation, whereas it showed an Ahrenius behavior
> for helix breaking. Helix formation (and nucleation) for this
> pentapeptide showed no temperature dependence, in agreement with the
> interpretation of nucleation originally described by Zimm and Bragg
> (12). Recently, Daura et al. (28, 29) published an exhaustive analysis
> of the helix-coil transition of =CE=B2 peptides by MD simulations. These
> simulations constitute the most detailed kinetics and stability
> analysis of the helix-coil transition from MD simulations to date.
> We apply the replica exchange MD (REMD) method to the equilibrium
> folding/unfolding thermodynamics of a 21-aa peptide with a large
> propensity of forming =CE=B1-helical structures in water at room
> temperature. We simulated a 21-residue peptide containing Arg, Ac-A5
> (AAARA)3A-methyl amide (NMe) (Fs peptide, where Fs stands for folded
> short), which has been widely described in the experimental literature
> (30=E2=80=9334). To establish the role of sequence variation in the forma=
> of =CE=B1-helices, we also simulated a peptide containing only Ala
> residues, Ac-A21-Nme (A21). The folding of these peptides is
> completely modeled by the force field, and the results are shown to be
> independent of initial configurations of the systems. A21 is not
> easily accessible to experimentation due to its limited solubility.
> However, sequences containing long runs of Ala flanked by charged
> amino acids have been widely studied (2, 8, 9).
> The explicit treatment of the aqueous solvent with the TIP3P model
> (35) provides molecular evidence for the stabilization of =CE=B1-helices =
> large side chains. Extensive REMD simulations (36, 37) exceeding 1.5
> =CE=BCs of sampling over a broad temperature range (275=E2=80=93550 K) sh=
ow that
> peptides containing Arg are significantly more stable than peptides
> containing only Ala.
> The enhanced stability of shielded hydrogen bonds can be explained in
> terms of the competition for backbone hydrogen bonds between water
> molecules and backbone donors and acceptors. Thermal fluctuations can
> cause local opening and closing of backbone CO=C2=B7=C2=B7=C2=B7NH hydrog=
en bonds.
> When the local environment is shielded from access to water, the
> hydrogen bond-breaking event is energetically unfavorable, because the
> availability of water molecules to participate in favorable H-bonding
> interactions near unshielded carbonyls can stabilize local opening of
> the hydrogen bond, as has been observed in crystal structures (38).
> The destabilization of the water-bridged opened CO=C2=B7=C2=B7=C2=B7NH hy=
drogen bonds
> by side chain shielding results in the stabilization of the shielded
> hydrogen bond conformation, which contributes to the overall stability
> of helical conformations. The Arg side chain partially shields the
> carbonyl oxygen of the fourth amino acid upstream from the Arg. The
> favorable positively charged guanidinium ion interaction with the
> carbonyl oxygen atom also stabilizes the shielded conformation.
> Given the large amount of data on the thermodynamics of the Fs
> peptide, we validate the adequacy and sensitivity of the force field
> in describing the helix-coil transition. We find that by applying a
> small modification of the Cornell et al. (39) force field, we can
> reasonably reproduce the melting temperature (T) of the Fs peptide.
> This force field also gives values for the helix propagation and
> nucleation parameters for Ala measured by Yang et al. (9) but in
> disagreement with other experimental measurements (2, 3). Our
> calculations show that the Arg side chain significantly stabilizes the
> helix state of the Fs peptide, in agreement with Williams et al. (15)
> and Vila et al. (14). However, we also find that A21 is 34% helical at
> 275 K, consistent with Spek et al. (8) and in disagreement with an
> estimate of 1% helical content calculated from the helix nucleation
> and propagation parameters extracted from measurements by Ingwall et
> al. and Platzer et al. (2, 3).
>  Top
>  Abstract
>  Introduction
>  Methods
>  Results and Discussion
>  Conclusion
>  References
>  Methods
> The Ac-A21-Nme peptide is contained in a cubic box containing 2,640
> TIP3P water molecules (35). The initial configurations for the
> replicas are generated by a 1.0-ns simulation of the extended peptide,
> in vacuo, at 1,000 K. Configurations sampled during the last 0.9 ns
> are clustered on the basis of their pairwise rms distance (rmsd). We
> select 32 structures from different clusters. Each of the structures
> is at least 2.5 =C3=85 in rmsd from any structure belonging to other
> clusters. No biases are imposed regarding secondary structure or
> energy. The selected configurations are solvated and randomly assigned
> as initial configurations for the 32 replicas. The dimensions of the
> solvated system cubic box are each 43.5 =C3=85, which is 1.5 times the
> linear dimension of the folded =CE=B1-helix. To test the reliability of t=
> equilibrium sampling, we performed two studies of the A21 peptide,
> starting from different configurations: random configurations and
> =CE=B1-helical configurations.
> The Fs peptide [Ac-A5(AAARA)3A-Nme] is contained in a cubic box with a
> side of 43.7 =C3=85 containing 2,660 TIP3P water molecules. The Arg
> residues are modeled in their charged state. The initial
> configurations are selected from a 1-ns simulation at 700 K of 42
> identical solvated systems, starting from an =CE=B1-helical configuration
> and random velocities. The helical content of the starting
> configurations ranges from 15 to 73%. The Fs peptide is simulated in
> the T range of 275=E2=80=93551 K.
> The solvated systems are subjected to 500 steps of steepest-descent
> energy minimization and a 100-ps MD simulation at constant pressure
> and temperature, with P =3D 1 atm (1 atm =3D 101.3 kPa) and T =3D 300 K. =
> use the force field of Cornell et al. (39) and the suite of programs
> in AMBER 4.1 (40), modified to include the generalized reaction field
> treatment of electrostatic interactions (41, 42) (with a cutoff of 8.0
> =C3=85) and the REMD algorithm. Nonbonded pair lists were updated every 1=
> integration steps. The integration step in all simulations is 0.002
> ps. The system is coupled to an external heat bath with relaxation
> time of 0.1 ps (43). All bonds involving hydrogen atoms are
> constrained by using SHAKE with a tolerance of 0.0005 =C3=85 (40). We stu=
> the full thermodynamic stability of the Fs and A21 peptides by the
> REMD algorithm described by Sugita and Okamoto (36, 37). The
> temperatures of the replicas are chosen to maintain an exchange rate
> among replicas of 8=E2=80=9320%. Exchanges are attempted every 125 integr=
> steps (0.25 ps).
> For A21 with random initial configurations, we simulate 32 replicas
> with T =3D 275=E2=80=93456 K, spanning a range of T in which the peptide =
> folded and unfolded states. We also simulate 48 replicas with T =3D
> 275=E2=80=93501 K for A21 with annealed =CE=B1-helical configurations. Fo=
r the Fs
> peptide, we simulate 42 replicas with T =3D 275=E2=80=93550 K. We also pe=
> simulations of the A21 (42 replicas with annealed =CE=B1-helical initial
> configurations) and Fs peptides (46 replicas with annealed =CE=B1-helical
> configurations) by using a modified force field described below. All
> systems are simulated for 8 ns/replica. The total simulation time for
> the A21 and Fs peptides is 976 and 704 ns, respectively.
> We analyze the configurations generated by the REMD simulations in
> terms of the backbone (, y) dihedral angles, helical content, and the
> coordination number of water molecules to the carbonyl oxygen atoms.
> Equilibrium quantities, based on ensemble averages at each
> temperature, are evaluated over the last 4 ns/replica of each
> simulation. Hydration properties are calculated over the last 1 ns of
> the trajectories. Block averages over 0.25 ns are performed to
> estimate errors in the ensemble averages. Unless otherwise specified,
> we are reporting the results for the 32-replica system for A21 that
> started from random configurations. We show below that the helical
> contents as a function of T for both systems are within one standard
> deviation. Sampled configurations are labeled by a sequence of 21 h or
> cs, depending on the  and y angles of each amino acid. We labeled (,
> y) pairs as hs if the  =3D =E2=88=9260 =C2=B1 30 and y =3D =E2=88=9247 =
=C2=B1 30 degrees, and as cs,
> otherwise. Calculations of the helical content follow the Lifson=E2=80=93=
> model, where n (n =E2=89=A5 3) consecutive hs make a helical segment of l=
> n =E2=88=92 2. Acetylated and amidated peptides with 21-aa sequence can h=
ave a
> maximum helical length of 19. We expect calculations of the helical
> content based on local variations in the structure (i.e., from
> dihedral angles) to be similar to IR and Raman measurements but larger
> than CD measurements (30).
>  Top
>  Abstract
>  Introduction
>  Methods
>  Results and Discussion
>  Conclusion
>  References
>  Results and Discussion
> First, we verify that the REMD method gives reliable thermodynamics by
> showing the independence of the results obtained in different
> calculations. Fig. 1 shows the average helical content as a function
> of temperature for A21, for two different simulations, one for the
> 32-replica system (with random starting configurations) and the other
> for the 48-replica system (with all =CE=B1-helical starting
> configurations). The helical content profile describes a moderately
> cooperative helix-coil transition, with T1/2 =3D 357 K, where T1/2 is
> the temperature at which the helical content is 0.5. The helical
> content at 275 K is 90% and below 10% at 450 K. The two curves are
> within one standard deviation, with the exception of very high
> temperatures, where the 32-replica system shows slightly lower helical
> content, a result of the larger number of replicas and the higher
> temperature range of the 42-replica system. The T1/2 for both systems
> is the same (357 K). The bottom curves in Fig. 1 show the average
> number of helical segments as a function of temperature. The largest
> average number of helical segments occurs near T1/2. The similarity of
> the two melting curves is an indication that the REMD simulations are
> equilibrated within the 8.0 ns simulated here.
> The simulations of the helix-coil transition of Fs are similar to
> those of A21; however, an important distinction is the enhanced
> thermostability of Fs, T1/2 =E2=89=88 400 K. The transition T measured by=
> spectroscopy is 334 K (30), which is higher than the estimated value
> by CD (31=E2=80=9333). The helical content at 275 K is 90%. Thompson et a=
> estimate this value to be 80% for a fluorescent labeled peptide,
> whereas Agadir predicts 85% for the acetylated peptide (33, 44). The
> helix-coil transition temperatures (taken as T1/2) are higher than
> those experimentally observed for the Fs peptide. The T1/2 for A21 is
> not known but is clearly overestimated in our calculations. The
> Lifson=E2=80=93Roig helix propagation and nucleation parameters for A21 w=
> the Cornell et al. (39) force field are found to be w0 =3D 2.58 and v0 =
> 0.755 at 273 K, which correspond to s0 =3D 1.47 and =CF=820 =3D 0.06 (11)=
. The
> calculated values for =CF=82 are in disagreement with reported values of
> 0.0008 (2, 3, 13) and 0.004 (9).
> We use our equilibrated thermodynamics calculations on the Fs and A21
> peptides to test the reliability and sensitivity of the force field.
> The force fields used in classical modeling are semiempirical in
> nature and rely on their validation by comparison with experimental
> data. It has been argued that the Cornell et al. force field (39)
> overestimates the helical propensities of peptides (45). Kollman et
> al. have developed the parameter set termed PARM96, which consisted
> only of the modification of the torsion potential for  and y angles
> (46, 47). Using the PARM96 force field, we performed REMD calculations
> and found that PARM96 gives negligible helical content for the Fs
> peptide and gives large populations of =CE=B2 hairpins (unpublished
> results). The changes made in PARM96 motivated us to modify the
> Cornell et al. (PARM94) force field, by setting the torsion potential
> for  and y to zero and by using this modified force field as a bare
> force field that can be further modified by perturbations.
> Fig. 2 shows a comparison of the helix content profiles as a function
> of T for the Fs and A21 peptides with the PARM94 and modified force
> fields. From the helical percentages at various T, we estimate that
> the force field variation results in 3.7 kJ/mol and 0.8 kJ/mol free
> energy differences for A21 and Fs, respectively, at 300 K. The
> difference in free energy between A21 and Fs, with the modified force
> field, at 350 K, is 5.8 kJ/mol. This difference in stability results
> from the Arg side chain. The modified force field gives T1/2 of 345 K
> and 90% helical content at 275 K for the Fs peptide. The results
> obtained with the modified force field are in much better agreement
> with experimental data for Fs (30=E2=80=9333). For A21, we obtained a 34%
> helical content at 275 K. Spek et al.'s data suggest the helical
> content of A13 flanked by charged amino acid side chains is near 40%
> at 273 K in 1 M NaCl solution (8). Ingwall et al.'s (2) measurements
> would suggest a 1% helical content for A21. The Lifson=E2=80=93Roig helix
> propagation and nucleation parameters for A21 with the modified force
> field are found to be w0 =3D 1.37 and v0 =3D 0.076 at 273 K, which
> correspond to s0 =3D 1.3 and =CF=820 =3D 0.004 (11). Our values for =CF=
=82 are in
> agreement with Yang et al. (9) (=CF=820 =3D 0.004 =C2=B1 0.002 for assume=
d values
> of s0 =3D 1.4 =E2=88=92 1.7) and in disagreement with those of Scheraga (=
13) (s0
> =3D 1.08 and =CF=820 =3D 0.0008, at 273 K). Our calculations are consiste=
> with intrinsic helix formation by Ala.
> We fit the Zimm=E2=80=93Bragg helix propagation parameter to a thermodyna=
> model to extract the enthalpy (=CE=94H) and entropy (=CE=94S) changes ass=
> with helix propagation. Assuming a linear T dependence on the specific
> heat, and taking the unfolded state as reference, we get =CE=94H(273 K) =
> =E2=88=924.6 kJ/mol, =CE=94S(273 K) =3D =E2=88=9215 J/K-mol, and =CE=94Cp=
(273 K) =3D =E2=88=9260 J/mol=C2=B7=C2=B7=C2=B7K,
> and =CE=94Cp(383 K) =3D 0. A similar fitting of the nucleation parameter
> gives =CE=94H=CF=82(273) =3D 8.1 kJ/mol, and =CE=94S=CF=82(273) =3D =E2=
=88=9215 J/K-mol.
> Simulations using the modified and original force fields describe
> higher stability of the Fs peptide over A21. To test the hypothesis
> that chain desolvation might be responsible for this stabilization
> (14) and to provide a molecular description of the shielding, we study
> the coordination of water to the peptide backbone over the last 2
> ns/replica of the simulations. Fig. 3 shows the water coordination
> number for the peptide backbone carbonyl oxygen. Carbonyl oxygen atoms
> involved in backbone hydrogen bonding, on average, have one
> coordinated water molecule. End carbonyl oxygen atoms not
> participating in hydrogen bonds have two coordinated water molecules.
> Shielded carbonyl oxygen atoms have zero coordinated water molecules.
> At low T, the peptide is in the =CE=B1-helical conformation and has a
> coordination number of one. At high T, the peptide is in the coil
> conformation and shows a coordination number between 1.0 and 2.0,
> which is the case for the Ala21 peptide. The low coordination number
> of carbonyl oxygens at high T (for example, at position 6 of A21 at
> 456 K, shown in Fig. 3) is a consequence of multiple intramolecular
> hydrogen bonds that are not necessarily consistent with an =CE=B1-helical
> conformation.
> For the Fs peptide, we observe that at low T, the coordination number
> adopts a number of 0.5 at three positions along the sequence. The
> atoms with low coordination correspond to carbonyl oxygens four
> residues before Arg side chains, which are shielded from water by the
> Arg side chain. There are two configurations, shown in Fig. 4, which
> yield coordination numbers of 1 and zero. On average, they are equally
> populated, yielding a coordination number of 0.5. The coordination
> number patterns did not change with the force field at the lowest
> temperatures.
> The shielding of the backbone carbonyl atoms by the Arg side chains
> can be directly correlated to hydrogen bond formation probabilities
> along the peptide chain. Fig. 5 shows the amino acid probability of
> participation in an =CE=B1-helical conformation as a function of
> temperature, for T =3D 275, 300, 325, 350, and 400 K. Although the
> amount of =CE=B1-helical formation changes with the modification of the
> force field, the patterns of relative helical content along the
> sequence, at each T, are similar: the end amino acids have a lower
> probability of sampling the helical region of the =E2=80=93y map. The
> probability increases toward the center of the chain and decreases
> toward the C terminus. This pattern is maintained at all temperatures,
> but with a lower overall probability at higher temperatures. For the
> Fs peptide below 350 K, we observe high helical propensity, relative
> to neighboring amino acids, for amino acids 7, 12, and 17. The Arg
> residues are at positions 9, 14, and 19, and the low-coordination
> number carbonyl oxygens are at positions 5, 10, and 15. The amino
> acids with larger relative helical propensities correspond to the
> central amino acid, i, between the shielded carbonyl oxygen, i =E2=88=92 =
> and the Arg, i + 2. The shielded hydrogen bond is between the carbonyl
> oxygen at i =E2=88=92 2 and the amino group at i + 2.
>  Top
>  Abstract
>  Introduction
>  Methods
>  Results and Discussion
>  Conclusion
>  References
>  Conclusion
> We have used the REMD algorithm to study the effect of sequence
> variation on =CE=B1-helix formation for Fs peptide and A21. This is, to o=
> knowledge, the first all-atom calculation of the helix-coil transition
> thermodynamics of peptides in explicit solvent over a wide temperature
> range. The helix-coil transitions are moderately cooperative over a
> broad temperature range, in agreement with experimental data (30=E2=80=93=
> and with the Lifson=E2=80=93Roig nearest-neighbor model for short peptide=
> (11).
> Analysis of the coordination number of water molecules to the backbone
> carbonyl oxygens along the sequence and over a broad T range indicates
> that the additional stabilization observed for the Fs peptide relative
> to the A21 peptide is produced by the partial shielding of the
> backbone hydrogen bonds from water. This shielding is provided by the
> Arg side chains. Vila et al. (14) proposed that =CE=B1-helical
> stabilization is induced by bulky side chains (both polar and
> nonpolar), which sequester water away from backbone atoms. They
> modeled this effect in Monte Carlo simulations with an implicit
> treatment of hydration effects. Our simulations verify this and
> provide a microscopic description of the side chain-shielding effect
> in terms of the desolvation of the backbone hydrogen bonds using an
> explicit treatment of the solvent. Details of the shielding not
> described by Vila et al. (14) are the shielding by Arg at site i of
> the carbonyl oxygen at i =E2=88=92 4 and the energetically favorable
> interaction of the charged side chain with the carbonyl oxygen.
> Simulations of sequences containing Lys and Glu side chains show that
> the Lys side chain has an interaction with the backbone similar to Arg
> in the Fs peptide (T. Ghosh, S. Garde, & A.E.G., unpublished results).
> The stabilizing effect of the charged side chain interaction with the
> carbonyl oxygen may explain why Ala-to-Leu substitutions destabilize
> helix formation (17).
> We use our equilibrated thermodynamics calculations to validate the
> force field used and to test the sensitivity of the results to details
> in the force field. We find that a slight modification of the force
> field (39) gives a transition temperature for the Fs peptide that is
> in good agreement with the experimentally determined T. The modified
> force field estimates the helical content of A21 to be 34% at 275 K,
> and the T1/2 is estimated to be near 240=E2=80=93270 K, based on extrapol=
> of the calculated helical content profile. The helical propagation and
> nucleation parameters obtained for A21 at 273 K (s0 =3D 1.3 and =CF=820 =
> 0.004) are consistent with intrinsic helix formation by Ala. Periodic
> Ala-to-Arg substitutions, as in Fs, increase the helical propensity.
> The exhaustive sampling and validation of simulations results with
> experimental data done in our studies provide a reliable method for
> further refining semiempirical force fields.
>   Acknowledgments
> We thank H. A. Scheraga, J. A. Schellman, and N. R. Kallenbach, S.
> Garde, and T. Ghosh for insightful comments. This work was funded by
> the U.S. Department of Energy under contract W-740-ENG-36 and the
> Laboratory Directed Research and Development Program at Los Alamos
> National Laboratory. Computer access to the Los Alamos National
> Laboratory Nirvana supercomputer is gratefully acknowledged.
>   Abbreviations
> MD, molecular dynamics; REMD, replica exchange MD; NMe, methyl amide.

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