Andrei L. Lomize
`Henry I. Mosberg
`College of Pharmacy,
`University of Michigan,
`Ann Arbor, Michigan 48109
`
`Received 5 December 1996;
`accepted 19 February 1997
`
`Thermodynamic Model of
`Secondary Structure for
`a-Helical Peptides
`and Proteins
`
`Abstract: A thermodynamic model describing formation of a-helices by peptides and proteins
`in the absence of specific tertiary interactions has been developed. The model combines free
`energy terms defining a-helix stability in aqueous solution and terms describing immersion of
`every helix or fragment of coil into a micelle or a nonpolar droplet created by the rest of
`protein to calculate averaged or lowest energy partitioning of the peptide chain into helical
`and coil fragments. The a-helix energy in water was calculated with parameters derived from
`peptide substitution and protein engineering data and using estimates of nonpolar contact
`areas between side chains. The energy of nonspecific hydrophobic interactions was estimated
`considering each a-helix or fragment of coil as freely floating in the spherical micelle or
`droplet, and using water/cyclohexane (for micelles) or adjustable (for proteins) side-chain
`transfer energies. The model was verified for 96 and 36 peptides studied by 1H-nmr spectroscopy
`in aqueous solution and in the presence of micelles, respectively ([set 1] and [set 2]) and for
`30 mostly a-helical globular proteins ([set 3]). For peptides, the experimental helix locations
`were identified from the published medium-range nuclear Overhauser effects detected by 1H-
`nmr spectroscopy. For sets 1, 2, and 3, respectively, 93, 100, and 97% of helices were identified
`with average errors in calculation of helix boundaries of 1.3, 2.0, and 4.1 residues per helix
`and an average percentage of correctly calculated helix–coil states of 93, 89, and 81%,
`respectively. Analysis of adjustable parameters of the model (the entropy and enthalpy of the
`helix–coil transition, the transfer energy of the helix backbone, and parameters of the bound
`coil), determined by minimization of the average helix boundary deviation for each set of
`peptides or proteins, demonstrates that, unlike micelles, the interior of the effective protein
`droplet has solubility characteristics different from that for cyclohexane, does not bind frag-
`ments of coil, and lacks interfacial area. q 1997 John Wiley & Sons, Inc. Biopoly 42: 239–
`269, 1997
`
`Keywords: a-helix stability; secondary structure prediction; micelles; protein folding
`
`INTRODUCTION
`
`There are two types of theoretical approaches to
`the protein folding problem. Approaches originating
`from conformational analysis of peptides and poly-
`mer physics consider a protein molecule as a long
`
`polymer chain, the energy of which must be mini-
`mized by searching in the space of torsion angles, 1–3
`or by using simplified lattice models.4 – 6 An alterna-
`tive way of looking at the problem is to represent
`a protein as a system of secondary structure ele-
`ments, 7 – 12 as in every publication describing three-
`
`Correspondence to: Henry I. Mosberg
`Contract grant sponsor: National Institutes of Health
`Contract grant numbers: DA03910 and DA00118
`q 1997 John Wiley & Sons, Inc.
`
`CCC 0006-3525/97/020239-31
`
`239
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`240
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`Lomize and Mosberg
`
`dimensional structures of specific proteins. Only a-
`helices, b-sheets, or short covalently bridged cycles
`(as in conotoxins or in metallothioneins) can be
`stable enough to serve as nucleations initiating pro-
`tein folding, and therefore they are present in 3D
`structures of all known proteins. Cooperative forma-
`tion of backbone hydrogen bonds in a-helices and
`b-sheets provides their high intrinsic stability, and
`simultaneously, burial of the polar main chain,
`which gives an additional energy gain when the
`amphiphilic secondary structure elements aggregate
`with each other, creating the nonpolar protein core.
`A simultaneous or stepwise formation of the sec-
`ondary structure frameworks by the hydropho-
`bically collapsed peptide chain, which is usually
`supplemented by covalent cross-linking in small
`proteins, has been directly demonstrated in experi-
`mental studies of protein folding.13 – 17 In terms of
`secondary structure, the protein folding process can
`be represented as a sequence of the following
`events: (1) formation of a-helices and b-sheets by
`the collapsed peptide chain, (2) assembly of the
`regular secondary structure elements into the protein
`core, and (3) joining of nonregular loops and the
`less stable ‘‘peripheral’’ helices and b-strands to the
`core and the association of independently formed
`domains. A theory of protein self-organization must
`reproduce all these events to calculate the protein
`3D structure.
`Formation of a-helices depends on various fac-
`tors that can be studied separately by considering
`the following, increasingly complicated situations:
`(1) small linear peptides in aqueous solution, where
`stability of each helix depends only on interactions
`between its own residues (Figure 1a); (2) peptide–
`micelle complexes, where each helix is stabilized by
`a combination of the intrahelical and hydrophobic
`interactions with the micelle (Figure 1b); and (3)
`proteins, in which helices are stabilized by specific
`tertiary interactions along with intrahelical and non-
`specific hydrophobic ones (Figure 1c; we denote as
`‘‘specific’’ the interactions between atoms or groups
`that must be described by pairwise potentials, and as
`‘‘nonspecific’’ the interactions of individual groups
`with a medium or averaged surrounding which can
`be described by transfer energies). The helix–coil
`transition is usually treated by Lifson–Roig and
`Zimm–Bragg theories.18 However, even with essen-
`tial modifications, 19 – 22
`these theories and other
`models 23,24 deal only with intrahelical interactions
`(i.e., they describe formation of individual helices
`in water, Figure 1a), or can be modified for the
`specific case of dimeric coiled coils.25 The goal of
`the present work is to develop a thermodynamic
`
`FIGURE 1 Three models of a-helix formation (the
`helices are shown as rectangles, solid circles are hy-
`drophobic side chains): (a) ‘‘peptide in aqueous solu-
`tion’’ (there are only specific interactions between resi-
`dues within each a-helix); (b) ‘‘peptide in complex with
`a micelle’’ (there are specific intrahelical and nonspecific
`hydrophobic interactions of every a-helix with the mi-
`celle) —coil fragments may compete with helices for
`binding with the micelle; (c) ‘‘droplet-like protein’’
`model (each helix and coil fragment floats in the liquid-
`like nonpolar spherical droplet created by the rest of pro-
`tein).
`
`model of a-helix formation that would be applicable
`for micelle-bound peptides and for proteins (Figure
`1b,c). The model, also for the first time, reproduces
`locations of the a-helices identified from medium-
`range NOEs in a representative set of peptides, in-
`stead of using average a-helicities derived from CD
`spectroscopy data, or qualitative comparisons with
`chemical shifts of C aH protons, as in the previous
`theoretical studies of peptides in aqueous solu-
`tion.23,24
`The model can be briefly outlined as follows.
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`a-Helical Peptides and Proteins
`
`241
`
`proach for hydrophobic interactions between side
`chains in helices and a slightly different parametri-
`zation of some other interactions.
`For a peptide in the micelle bound state (Figure
`1b) DGl, the free energy of its bound helix–coil
`partition l relative to a coil in aqueous solution, can
`be given by
`DGl (cid:129) (Eel 0 TDSimm)
`/ (cid:229)
`DG a(ki , mi ) / (cid:229)
`
`DG coil(kj, mj)
`
`(2)
`
`i
`
`j
`
`where Eel is the peptide-micelle electrostatic interac-
`tion energy, DSimm is the immobilization entropy of
`the peptide, 27 and the two sums in this equation are
`free energy changes for bound a-helical and coil
`fragments of m residues starting from residue k.
`Equation (2) can be simplified assuming, first, that
`the equilibrium is strongly shifted toward the bound
`peptide form, so that only bound helix–coil parti-
`tions need be considered, and second, that the total
`energy of electrostatic interactions of charged pep-
`tide groups with the micelle does not depend on the
`secondary structure of the peptide. Then the (Eel
`0 TDSimm) term, which is of crucial importance for
`peptide–micelle binding, can be considered to be
`a constant for all bound helix–coil partitions and
`subtracted in calculations of their relative energies.
`The energies of individual helices are additive
`[as in Eqs. (1) and (2)] when the helices do not
`interact with each other, i.e., for monomeric pep-
`tides lacking tertiary structure (Figure 1a,b), but
`the situation is more complicated in the presence of
`specific tertiary interactions. However, if the tertiary
`interactions are reduced, as in molten globules and
`in the intermediate and transition protein folding
`states, 14,28 – 31 the additivity approximation for helix
`energies can be applied. In a fluctuating compact
`state, each a-helix can be considered as floating
`in a dynamically averaged interior of a nonpolar
`spherical droplet created by the rest of the protein
`(Figure 1c) and stabilized independently of other
`helices by intrahelical and nonspecific hydrophobic
`interactions, similar to the micelle-bound peptides.
`Then, the energies of individual helices and coil
`fragments in a protein can also be simply summed:
`DGl (cid:129) (cid:229)
`
`i
`
`DG a(ki , mi )
`/ (cid:229)
`DG coil(kj, mj) / DG *
`
`(3)
`
`j
`
`where the energies of the bound helices and coil
`
`FIGURE 2 Helix–coil partitions as conformational
`states of the peptide chain. The coil in aqueous solution
`serves as a reference state with zero energy. The helices
`A, B, and C, shown as rectangles, with DG (cid:155) 0, are
`more stable than the coil. The helices compete with each
`other, and partition 1 consisting of two (A / B) helices
`can be of lower energy than partition 2 containing only
`helix C overlapped with A and B, even if helix C has
`lower energy than either of the individual A and B helices.
`Helix D (DG (cid:156) 0) is less stable than coil but may be
`detected spectroscopically. Partitions 1–4 are in equilib-
`rium with each other and all may contribute to observed
`parameters of nmr and CD spectra.
`
`Each partition of a peptide into helix and coil frag-
`ments (Figure 2) can be considered as a molecular
`conformational state defined by the variables N, k1,
`m1, . . . , ki , mi , . . . , kN, and mN, where N is the
`number of helices in the molecule, and where ki
`and mi (i (cid:129) 1, 2, . . . , N) represent the number of
`the first residue and the length, respectively, for
`each helix. Like coil or folded protein states, each
`helix–coil partition is an ensemble of conformers
`defined by torsion angles w, c, x, and, judging from
`molecular dynamics simulations, 26 interconversions
`of the partitions, i.e., lengthening, shortening, or
`breaking of helices, are slower than rotations of side
`chains and coil fluctuations.
`For a peptide in aqueous solution (Figure 1a),
`the unfolding free energy, DGl, of helix-coil parti-
`tion l can be written as the sum of the helix–coil
`free energy differences, DG a(ki , mi ), for all indi-
`vidual a-helices from the partition:
`
`Nl
`
`DGl (cid:129) (cid:229)
`i(cid:129)1
`
`DG a(ki , mi )
`
`(1)
`
`where Nl is the number of helices in partition l. The
`energies of individual helices in water, DG a(ki ,
`mi ), were calculated here with parameters derived
`from peptide substitution and protein engineering
`data, similar to that in the work of Munoz and Ser-
`rano, 23,24 but using a more physically justified ap-
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`
`Free Energy of a-Helix
`in Aqueous Solution
`
`The helix–coil free energy difference, DG a(k, m), for
`a fragment of peptide chain of m residues, starting from
`residue k, can be divided into the contribution of main-
`chain interactions ( DG mch), which is the free energy
`difference for the ‘‘host’’ polyAla peptide, the interac-
`tions of side chains with the helix backbone ( DG sch
`int )
`that describes free energy changes associated with re-
`placement of the host Ala C bH3 group by other side
`chains, 34,35 the hydrogen-bonding and electrostatic inter-
`36 –38
`actions between polar side chains in water, DG sch
`hb
`and the hydrophobic interactions of side-chains DG sch
`pho
`(Refs. 39 and 40):
`
`
`
`pho (4)hb / DG schDG a(ki , mi ) (cid:129) DG mch / DG schint / DG sch
`
`
`
`
`
`242
`
`Lomize and Mosberg
`
`segments can be calculated similar to that for mi-
`celle-bound peptides, and the DG * term arises from
`loss of entropy by aggregating helices and is as-
`sumed to be a constant, independent of the helix–
`coil partition. Then, the relative energies of the he-
`lix–coil partitions can be approximated by the first
`two sums from this equation, which differ from un-
`folding free energies by the term DG *.
`All possible helix–coil partitions are in equilib-
`rium with each other (Figure 2), including single
`helices, which are less stable than coil, but still
`detectable spectroscopically. This situation can be
`treated using Boltzmann averaging of the parti-
`tions 32 to calculate local a-helicities that can be
`compared with spectroscopically observed parame-
`ters. The number of the possible partitions grows
`rapidly with the chain length, which makes such
`calculations impossible for proteins. However, we
`show here that even the single lowest energy helix–
`coil partition (Figure 2) can satisfactorily reproduce
`experimentally observed locations of the helices,
`which are additionally stabilized by hydrophobic
`interactions with the micelles or with the rest of the
`protein. If the helix energies are additive, the search
`for the lowest free energy helix–coil partition (i.e.,
`the global energy minimization with respect to the
`N, k1, m1, k2, m2, . . . , kN, mN variables) can be
`easily performed using the dynamic programming
`algorithm.33
`
`METHODS
`
`The computational procedure implemented here in the
`program FRAMEWORK consists of the following steps:
`(1) Calculation of a-helix and bound coil energies for
`each fragment of the molecule, depending on the chosen
`model [‘‘peptide in aqueous solution,’’ ‘‘peptide in mi-
`celle,’’ or ‘‘droplet-like protein’’; Eqs. (1) – (20)]. (2)
`Boltzmann averaging of helix–coil partitions to calculate
`the local a-helicities of every tripeptide fragment of the
`molecule [Eqs. (21) and (22)] or search for the lowest
`energy helix–coil partition [Eqs. (23) and (24). (3)
`Minimization of the average deviation of calculated and
`experimental boundaries of a-helices [Eq. (25)] with
`respect to several adjustable parameters of the model.
`The average helix boundary deviation [Eq. (25)] was
`implemented, since the widely used percentage of cor-
`rectly calculated secondary structure states ( a, b, or non-
`regular) does not properly reflect success or failure of a
`prediction algorithm: a wrong prediction that sperm
`whale myoglobin, for example, is a single long helix
`would have a ‘‘success’’ rate as high as 89%, while the
`correct identification of all myoglobin helices with a
`small ((cid:130) 10%) error in the ends of each helix would
`produce the same success rate.
`
`Main-Chain Interactions. The helix–coil free energy
`difference for the host polyAla peptide is given by
`
`DG mch(ki , mi ) (cid:129) (mi 0 2)DH 0 miTDS
`
`(5)
`
`where DH is the enthalpy of the hydrogen-bonding inter-
`action between two peptide groups in the a-helix, and
`DS is the conformational entropy change per residue dur-
`ing the helix–coil transition.34 The DH and DS contribu-
`tions measured by Hermans 41 and Scholtz et al.42 are
`considered here as adjustable parameters of the model
`and must be determined independently by fit of calculated
`and experimentally identified positions of a-helices in
`peptides.
`
`Side-Chain–Main-Chain Interactions. The energy
`of interaction between side-chains and the a-helix back-
`bone DG sch
`int was calculated as the sum of corresponding
`published free energy differences DDG sch
`, measured by
`i
`replacing the host Ala residue in model peptides and
`proteins:
`
`int (cid:129) (cid:229)k/m01
`
`DG sch
`
`i(cid:129)k01
`
`DDG sch
`i
`
`(6)
`
`where the replacement energies DDG sch
`depend on the
`i
`type of side chain i and its position within the a-helix or
`nearby: the energies can be different in the middle of the
`a-helix and near its termini, in positions denoted as N *-
`Ncap-N1-N2-N3-rrr-C3-C2-C1-Ccap-C *. The corre-
`sponding a-helix propensities (DDG sch) measured for
`different peptides and proteins are not perfectly mutually
`consistent, and some of them reproduce the nmr-detected
`peptide helices more satisfactorily than others. Attempts
`to reproduce the peptide helices led to the parametrization
`and interpretation of the published a-helix propensity
`data described below.
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`
`Middle Helix, C-Turn, C-Cap, and N-Turn Posi-
`tions. Because of the two-state behavior of proteins, the
`corresponding protein engineering scales were derived
`directly from thermodynamic measurements, while the
`corresponding energies for peptides have been obtained
`by using theories of the helix–coil transition. Remark-
`ably, the averaging of two protein engineering scales
`measured in the middle helix positions (for a-helical di-
`mers 43 and 44 site of T4 lysozyme 44) gives a set of
`DDG sch values that is nearly identical (the correlation
`coefficient is 0.98) to the scale independently developed
`for 10 residues by Lyu et al.45 using the model ‘‘EXK’’
`peptide. The ‘‘EXK’’ peptide, which is stabilized by nu-
`merous ionic pairs and by the N-capping motif, also has
`a protein-like two state behavior, as can be seen from the
`similar DDG sch energies calculated using two-state and
`multistate models from CD data.45 Thus, all these three
`middle-helix scales are consistent and can simply be aver-
`aged to reduce the experimental errors. The correspond-
`ing average DDG sch values used here (Table I) are close
`to the AGADIR scale 23,24 for all but Pro and Gly residues,
`and to the scale of Chakrabatty et al.53 for all residues,
`except Val, Phe, Trp, Pro, and Gly.
`In the helix C-turn (C2 position), 46 the experimental
`DDG sch energies are different: they are larger than in the
`middle of the a-helix by 0.3–0.5 kcal/mol for aromatic
`Trp, Phe, and Tyr residues and Cys, by (cid:130) 0.4 kcal/mol
`for b-branched Ile and Val side chains, by 0.1–0.2 kcal/
`mol for linear side chains containing a C gH2 group (Leu,
`Met, Glu, Gln), and are unchanged for Gly and the short
`polar Ser and Asn side chains (Table I). These energeti-
`cally unfavorable effects probably arise from shielding
`of unpaired carbonyls at the C-terminus of the a-helix
`by the g substituents of the side chains and the larger
`accessibility of the nonpolar g substituents themselves in
`the C-turn, compared to that in the middle of the a-helix.
`If the C2 side chain has a trans orientation (x 1 (cid:130) 1807),
`its g-methyl group or aromatic ring (of Phe, for example)
`reduces accessibility of the closest (C2) free C|O main
`chain oxygen by 26 or 36%, respectively, while the acces-
`sibilities of the nonpolar g-methyl or aromatic ring them-
`selves are increased by (cid:130) 11 A˚ 2 (the equivalent transfer
`energy is (cid:130) /0.2 kcal/mol) compared to that in the
`middle of a-helix. At the same time, the accessibilities
`of the C|O groups and side chains are not affected in
`the C-turn if the side chains have gauche orientations
`(x 1 (cid:130) 0607). As discussed below, this solvation effect
`changes preferred conformations of side chains in the C-
`turn from trans to gauche.
`The destabilization in C-turn positions is less for Lys
`and Arg compared with other residues with linear chains,
`and for His compared to other aromatic residues (Table
`I), probably because of small ((cid:130) 00.2 kcal/mol) electro-
`static attractions between the positively charged side
`chains and the helix dipole (as a result, the DDG sch ener-
`gies of Lys and Arg in the middle of the helix and C-
`turn are identical, Table I). Repulsions of the Asp side
`chain with the helix dipole increases its DDG sch energy
`
`a-Helical Peptides and Proteins
`
`243
`
`by (cid:130) /0.2 kcal/mol in C-turn positions compared to
`middle helix positions (Table I). The influence of electro-
`static interactions is smaller for the Glu residue ((cid:130) /0.1
`kcal/mol), because its longer, flexible side chain can
`move away from the helix reducing the electrostatic re-
`pulsion. The electrostatic interactions of side chains at
`the C-terminus of the helix are weaker than at the N-
`terminus (00.6 to 00.9 kcal/mol 54) because the interac-
`tions depend on the spatial position of the charged groups
`relative to the helix dipole. The C a-C b bonds of side
`chains are tilted relative to the helix axis and directed
`toward the helix N-terminus. As a result, in the N-turn,
`the COO0 groups of Asp and Glu side chains are situated
`close to the helix dipole axis, near unsatisfied local di-
`poles of backbone NH groups, and may even form hydro-
`gen bonds with them, while the positively charged side
`chains in the C-turn are far from the helix dipole axis.
`However, when His, Lys, or Arg residues occupy the C-
`cap position and their w and c angles are in the left-
`handed helix area of the Ramachandran map (the struc-
`tural motif of His 18 in barnase), the positively charged
`side chains are brought into the same position relative to
`the helix dipole as the negatively charged side chains in
`the N-turn: they are situated near the helix axis and can
`form hydrogen bonds with the main chain C|O groups,
`thus producing stronger electrostatic interactions: (cid:130) 00.6
`kcal/mol.55 Stabilization of a-helices by positively
`charged side chains, observed for model peptides, 56 may
`arise chiefly from this C-capping interaction. No special
`contributions for electrostatic interactions in the C-turn
`were used since they are already included in the C-turn
`DDG sch energies, and an average energy of electrostatic
`interactions for His, Lys, and Arg residues in the C-
`cap position was considered as an adjustable parameter,
`whose optimum value was found to be 00.4 kcal/mol. No
`other contributions were used for C-cap residues because
`experimental data here are contradictory: some studies 57
`clearly demonstrate the significance of the C-capping in-
`teractions, especially for Asn residues, while others 48
`show that these interactions are negligible.
`In N-turn (N1-N3) positions, a small (00.2 kcal/mol)
`correction of the middle helix scale was applied for the
`short polar Ser, Thr, and Asn residues and for Gly based
`on results of Serrano et al.58 The DDG sch of Pro in N2 and
`N3 positions was reduced to 1 kcal/mol, 59,60 since the Pro
`side chain in the N turn of the a-helix causes steric hin-
`drances with the preceding residue but does not produce an
`energetically unfavorable kink in the a-helix (this correlates
`with the much higher statistical occurrence of Pro in N-turn
`compared to middle helix positions).61
`The pH dependence of all electrostatic contributions
`and pKs for charged side chains were taken into account
`as in the work of Munoz and Serrano.24 Energies of elec-
`trostatic interactions of completely ionized side chains in
`N-turn positions with the helix dipole were considered
`as adjustable parameters, and their optimum values were
`00.9 kcal/mol for Asp and Glu in the N1 and N2 posi-
`tions (the ‘‘capping box’’ N3 residues were treated sepa-
`
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`244
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`Lomize and Mosberg
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`Table I a-Helix ‘‘Propensities’’ (DDGsch) and Transfer Energies (DG sch
`tr ) of Side Chains
`
`DDG sch (kcal/mol)
`
`DG sch
`tr
`
`(kcal/mol)
`
`Residue
`
`Middle
`Helixa
`
`C-turn
`Positionsb
`
`Leu
`Ile
`Val
`Phe
`Trp
`Met
`Pro
`Ala
`Cys
`Tyr
`Gly
`Thr
`Ser
`His
`Lys
`Gln
`Glu
`Asn
`Asp
`Arg
`
`0.14
`0.35
`0.46
`0.37
`0.35
`0.20
`3.40
`0.0
`0.49
`0.42
`0.86
`0.54
`0.43
`0.55
`0.17
`0.30
`0.46
`0.63
`0.53
`0.14
`
`0.35
`0.81
`0.88
`0.69
`0.84
`0.31
`3.40
`0.0
`0.82
`0.82
`0.91
`0.79
`0.41
`0.78
`0.19
`0.48
`0.55
`0.66
`0.71
`0.14
`
`N-Cap
`Positionsc
`00.17
`00.10
`0.01
`00.17
`00.41
`00.06
`00.06
`0.0
`00.08
`00.25
`00.34
`00.19
`00.34
`00.17
`0.06
`0.22
`00.17
`00.52
`00.51
`0.0
`
`Cyclohexane
`Coild
`03.91
`03.76
`02.89
`02.00
`01.63
`01.79
`02.23
`00.94
`00.89
`0.86
`00.29
`3.32
`3.99
`5.29
`6.38
`6.37
`7.53
`7.23
`9.39
`15.75
`
`Cyclohexane
`a-Helixd
`03.01
`02.63
`01.97
`01.99
`01.58
`01.36
`01.00
`00.63
`00.57
`0.85
`00.25
`2.38
`3.06
`5.82
`7.25
`7.03
`8.23
`7.71
`9.81
`16.49
`
`Protein
`a-Helixe
`02.10
`01.89
`01.40
`02.03
`01.68
`01.47
`00.49
`00.21
`01.68
`00.63
`00.14
`0.00
`2.10
`5.8
`7.2
`7.0
`8.2
`7.7
`9.8
`16.5
`
`a Average parameters for the host a-helix dimers,43 EXK model peptide,45 and T4 lysozyme44 (the data for the 44 and 131 sites
`were averaged).
`b Data of Horovitz et al.46
`c Calculated using two-state helix–coil approximation from data of Chakrabatty et al.47 and Doig and Baldwin48 (peptide of 17
`residues with uncharged N-terminus); pH dependencies of the energies were not taken into account: the data are for charged Glu and
`Asp and uncharged His and Cys residues (pH (cid:129) 7). The N-capping energies for Asn, Ser, Thr, and Gly residues in the ‘‘capping box’’
`combination (when Glu residue occupies N3 position in helix) for peptides were 00.58, 00.74, 00.59, and 00.25 kcal/mol, respectively,
`and the optimized N-capping energies for proteins for the Asp, Asn, Ser, and Thr residues were 00.8, 00.7, 00.5, and 00.4 kcal/mol,
`respectively, with any residue occupying the N3 position.
`d Mole fraction based water–cyclohexane transfer energies49 corrected for burial of side-chain analogues in a-helix and coil (as
`described below); for Ser and Thr forming hydrogen bonds with backbone of their own a-helix,50 the transfer energies were corrected
`by 01.5 kcal/mol, the energy of a buried hydrogen bond in proteins.51,52
`e Parameters obtained by minimization of helix boundary deviation with respect to side-chain transfer energies for a set of 30
`proteins. For hydrophilic side chains (His and subsequent residues in the table), the energies could not be defined by this adjustment
`and correspond to the cyclohexane scale.
`
`rately), and /0.5 kcal/mol for His, Lys, and Arg in the
`N1, N2, and N3 positions, close to the 0.6–0.9 kcal/mol
`estimated by mutagenesis.54 DDG sch of Glu, Asp, and
`Gln residues in the capping box 62 N3 position (00.40,
`00.11, and 00.09 kcal/mol, respectively) were calcu-
`lated using as the first approximation the all-or-none two-
`state model from CD data.63
`
`N-Cap and N * and C * Positions. In contrast to the
`middle helix positions, the N-capping energies identified
`by protein engineering are highly variable: 02.2 to 00.4
`kcal/mol for Asn, 02.1 to 00.9 kcal/mol for Ser, and
`00.6 to 0.1 for Gly in the capping box motif.58,64–66 This
`can be explained by ‘‘context-dependent factors’’: unlike
`residues in the a-helix, the replaced N-cap residues have
`
`different main chain w and c angles, 64 and form extra
`hydrogen bonds with sequentially distant residues of the
`protein and with bound water molecules, as observed, for
`example, in substitution sites Thr 59-Glu 62 of T4 lyso-
`zyme 64 and Ser 31-Glu 34 of chymotrypsin inhibitor II.66
`The DDG sch energies for the N-cap position applied here
`(Table I) were calculated using the two-state model from
`CD data of Chakrabatty et al.47 and Doig and Baldwin, 48
`and for the special case of the capping box (Glu residue
`occupies N3 position), from data of Zhou et al.63 for Gly,
`Asn, and Ser residues. These two-state peptide energies
`(00.58, 00.74, and 00.25 kcal/mol, for Asn, Ser, and
`Gly, respectively, with the capping box motif, for exam-
`ple) are close to the lower limits estimated by protein
`engineering.
`
`/ 8K26$$5476
`
`06-17-97 09:16:43
`
`bpa
`
`W: Biopolymers
`
`5476
`
`6
`
`

`
`a-Helical Peptides and Proteins
`
`245
`
`Table II The Replacement Energies (DDGsch, kcal/mol) of Nonpolar Side Chains in the N* Positiona
`
`N* Position Residue
`
`Val
`Ile
`Leu
`Met
`Phed
`
`Intrinsic Contributionb
`00.2
`00.3
`00.4
`00.6
`0.0
`
`Energy of Interaction with
`Leu in N4 Positionc
`00.4
`00.4
`00.6
`00.5
`00.3
`
`Energy of Interaction with
`Leu in N7 Positionc
`
`0.0
`00.1
`00.2
`0.0
`0.0
`
`a The energies, relative to the reference Ala-containing peptide, were calculated using the all-or-none two state model (as described
`below) from u222 ellipticities for a series of model peptides published by Munoz and Serrano.72
`b The intrinsic helix-stabilizing contribution of bulky N* aliphatic residues (Ile, Leu, Val, or Met) was observed even when the N4
`residue is Ala, probably because of hydrophobic interactions between the N* side chain and CbH2(3) groups of N3 and N4 residues,72
`similar to helix-stabilizing interactions of nonpolar N-cap residues.48
`c The same energies were applied when Ile or Met occupied the N4 and N7 positions.
`d The same energies were used for Tyr and Trp residues.
`
`A further helix-stabilizing contribution arises from hy-
`drophobic interactions of flanking N * and C * residues
`with the a-helix.67 The hydrophobic contact between side
`chains in the N * and N4 positions, the ‘‘hydrophobic-
`staple’’ motif, 68 can be detected by nuclear Overhauser
`effects (NOEs) between the side chains in peptide a-
`helices.63,69–71 The corresponding contributions to helix
`energy (Table II) were estimated using the two-state
`model from u 222 ellipticities published by Munoz and
`Serrano 72 for a series of model peptides, and it was as-
`sumed that the ‘‘hydrophobic staple’’ motif can exist only
`in combination with characteristic N-capping residues
`(Ser, Thr, Asn, Asp, or Gly). These energies are smaller
`by 0.1–0.4 kcal/mol than was estimated using the AGA-
`DIR program.72
`A similar hydrophobic interaction at the C-terminus
`of the a-helix between the bulky C * and C4 or C1 side
`chain when the C-cap residue is Gly, 73 the ‘‘Schellman
`motif,’’ is very common for proteins, 61,74 and has also
`been found in crystal structures of a-helical peptides 75
`and detected by nmr spectroscopy for peptides in the
`presence of SDS micelles 76–79 or trifluoroethanol.71,80 The
`Schellman motif is only marginally stable in water: no
`NOEs between the C * and C1 or C4 side chains were
`observed in a model peptide, though analysis of CD spec-
`tra indicated that the interaction does contribute a little
`to a-helix stability.80 The optimum adjustable energy for
`the Schellman motif (considered as a single parameter
`for all combinations of bulky Val, Phe, Tyr, Lys, Arg,
`Leu, Ile, Met, or Trp residues, but excluding contacts of
`two positively charged side chains) was identified as
`00.3 kcal/mol.
`
`Interactions Between Side Chains in the a-He-
`lix. H-Bonding and Electrostatic Interactions of Side
`Chains. The helix-stabilizing interactions of polar side
`chains in water, arising from their hydrogen bonding and
`electrostatic attraction, have been investigated using sev-
`eral model peptides 36–38,81,82 and range up to 00.5 kcal/
`
`mol. Based on the published data, the following estima-
`tions of the interaction energies with completely ionized
`side chains were used in the present work: Glu i–Lys,
`Arg i{4: 00.5 kcal/mol; Asp i–Lys, Arg i{3, Asp i–Arg i/4,
`Gln i–Asn, Asp, Glu i/4; and Glu i–Asn i/4, and Lys i–
`Asp i/4: 00.4 kcal/mol; Asp i–Arg, Lys i/3: 00.3 kcal/
`mol. All these pairs are present in a-helical proteins. Two
`more hydrogen bonding side-chain pairs were taken into
`account with a tentative assigned energy of 00.5 kcal/
`mol: the Glu, Asp i–Trp i/4 pair present as Glu 136-Trp 140
`in colicin (1col, the four-letter codes indicate names of
`Protein Data Bank files 83), and Asp 87–Trp 91 in interleu-
`kin 4 (1rcb; the Trp residue is in the last turn of each of
`the helices and has x 1 (cid:130) 0607), and the Ser i–Gln i/1
`pair that can be present only at the C-terminus of the a-
`helix (as Ser 245–Glu 246 of thermolysin, 2tmn), or imme-
`diately preceding a Pro-induced helix kink (as Ser 215–
`Gln 216 in glucoamylase, 3gly, and Ser 21–Gln 22 in cyto-
`chrome c *, 2ccy).
`The total contribution of the interactions between the
`polar side chains was calculated assuming additivity of
`their pairwise DDG sch
`ij energies:
`
`hb (cid:129) (cid:229)k/m04
`
`DG sch
`
`i(cid:129)k
`
`DDG sch
`ij,hb
`
`(7)
`
`j(cid:129)i/3,4
`
`This additivity approximation means that each side
`chain i interacts simultaneously with all surrounding side
`chains (in i 0 4 and i / 4 positions, for example) rather
`than adopting any fixed orientation in solution. This situa-
`tion can be expected for long flexible Lys, Arg, Glu, and
`Gln side chains, but not for aromatic side chains since
`they have preferred x 1 orientations in the a-helix, as
`discussed below, and therefore do not interact simultane-
`ously and equally well with other side chains in opposite
`i / 4 and i 0 4 directions.
`Hydrophobic Interactions Between ‘‘Rotationally
`Frozen’’ Side Chains. The energies of hydrophobic
`intera