The lattice energetics of some polypeptide chains

The interchain energetics of alpha, beta, and PGII conformations of polyglycine, the PPII and left-handed 3.30 fold helical conformations of trans poly-L -proline, and the Yonath and Traub triple helix and left-handed three fold helices of poly(gly-pro-pro) were investigated. Intra- and inter-chain stabilization energies appear to be inversely related, and the interchain stabilization energy can be as large its the intrachain energy. The minimization of the interchain energy can be described by the simultaneous optimization of interchain hydrogen bonding and intermolecular-sidechain digitation. The stability of the poly(gly-pro-pro) triple helix can be readily explained in terms of these two factors. In all cases the experimentally observed lattice packing is predicted, although the calculated lattice constants are slightly larger than those observed. The small differences between observed and predicted lattice constants probably reflect small errors in present conformational potential functions. Homopolymers are probably the best systems to use in the refinement of conformational potential functions because solvent effects arc minimized and the experimentally observed lattice constants provide a check on the configurational calculations.     

Energetics of the structure and chain tilting of antiparallel beta-barrels in proteins

The preferred structural pattern of antiparallel beta-barrels in proteins, described as the right-handed tilting of the peptide strands with respect to the axis of the barrel, is accounted for in terms of intra- and interchain interaction energies. It is related to the preference of beta-sheets for right-handed twisting. Conformational energy computations have been carried out on three eight-stranded antiparallel beta-barrels composed of six-residue strands, in which L-Val and Gly alternate, and having a right-handed, a left-handed, or no tilt. After energy minimization, the relative energies of these structures were 0.0, 8.6, and 46.1 kcal/mol, respectively; i.e., the right-tilted beta-barrel is favored energetically, in agreement with anti-parallel beta-barrels observed in proteins. Tilting of the barrel is favored, relative to the nontilted structure, by both intra- and interstrand interactions, because tilting allows better packing of the bulky side chains. On the other hand, the energy difference between the left- and right-tilted barrels arises essentially from intrachain interactions. This is a consequence of the preference of beta-sheets for a right-handed twist. Space limitations inside the barrel are satisfied if there is an alternation of bulky residues and residues with small or no side chain (preferably Gly) in neighboring positions on adjacent strands. Such a pattern is seen frequently in antiparallel beta-barrels of globular proteins. The computations indicate that a structure with Val...Gly pairs can be accommodated in a beta-barrel with no distortion.     

Packing is a key selection factor in the evolution of protein hydrophobic cores.

The energy derived from optimized van der Waals interactions in closely packed, folded proteins has been proposed to be of similar energetic magnitude to hydrophobicity in stabilizing the native state. If packing is this energetically important, it should influence the evolution of protein core sequences. To test this hypothesis, the occurrence of various amino acid side chains in the major hydrophobic core of staphylococcal nuclease and 42 homologous proteins was determined. Most such positions in this protein family are usually isoleucine, leucine, or valine. Previously we have constructed and measured the stabilities of 12 single, 44 double, 64 triple, and 32 quadruple mutants, representing all possible permutations of these three side chains at two overlapping sets of four positions in the core of staphylococcal nuclease. The stabilities and interaction energies of those mutants with various combinations of the most common, or consensus, sequence were compared to the stabilities of all other mutants. Mutants which had the consensus side-chain combinations were not necessarily the most stable, but usually were found to have the best interaction energies. In other words, these proteins were far more stable than would be predicted from simply summing the observed energetic effects of the component single mutations, apparently reflecting particularly favorable packing interactions that are possible for the most common side chains. An additional 12 mutants which tested possible alternate explanations of the results were constructed. The stabilities and interaction energies of these mutants also support the conclusion that packing is a crucial determinant guiding the sequence evolution of protein cores.     

A priori crystal structure prediction of native celluloses

The packing of beta-1,4-glucopyranose chains has been modeled to further elaborate the molecular structures of native cellulose microfibrils. A chain pairing procedure was implemented that evaluates the optimal interchain distance and energy for all possible settings of the two chains. Starting with a rigid model of an isolated chain, its interaction with a second chain was studied at various helix-axis translations and mutual rotational orientations while keeping the chains at van der Waals separation. For each setting, the sum of the van der Waals and hydrogen-bonding energy was calculated. No energy minimization was performed during the initial screening, but the energy and interchain distances were mapped to a three-dimensional grid, with evaluation of parallel settings of the cellulose chains. The emergence of several energy minima suggests that parallel chains of cellulose can be paired in a variety of stable orientations. A further analysis considered all possible parallel arrangements occurring between a cellulose chain pair and a further cellulose chain. Among all the low-energy three-chain models, only a few of them yield closely packed three-dimensional arrangements. From these, unit-cell dimensions as well as lattice symmetry were derived; interestingly two of them correspond closely to the observed allomorphs of crystalline native cellulose. The most favorable structural models were then optimized using a minicrystal procedure in conjunction with the MM3 force field. The two best crystal lattice predictions were for a triclinic (P(1)) and a monoclinic (P2(1)) arrangement with unit cell dimensions a = 0.63, b = 0.69, c = 1.036 nm, alpha = 113.0, beta = 121.1, gamma = 76.0 degrees, and a = 0.87, b = 0.75, c = 1.036 nm, gamma = 94.1 degrees, respectively. They correspond closely to the respective lattice symmetry and unit-cell dimensions that have been reported for cellulose Ialpha and cellulose Ibeta allomorphs. The suitability of the modeling protocol is endorsed by the agreement between the predicted and experimental unit-cell dimensions. The results provide pertinent information toward the construction of macromolecular models of microfibrils.     

Excitation energy transfer in chlorosomes of green bacteria: theoretical and experimental studies.

A theory of excitation energy transfer within the chlorosomal antennae of green bacteria has been developed for an exciton model of aggregation of bacteriochlorophyll (BChl) c (d or e). This model of six exciton-coupled BChl chains with low packing density, approximating that in vivo, and interchain distances of approximately 2 nm was generated to yield the key spectral features found in natural antennae, i.e., the exciton level structure revealed by spectral hole burning experiments and polarization of all the levels parallel to the long axis of the chlorosome. With picosecond fluorescence spectroscopy it was demonstrated that the theory explains the antenna-size-dependent kinetics of fluorescence decay in chlorosomal antenna, measured for intact cells of different cultures of the green bacterium C. aurantiacus, with different chlorosomal antenna size determined by electron microscopic examination of the ultrathin sections of the cells. The data suggest a possible mechanism of excitation energy transfer within the chlorosome that implies the formation of a cylindrical exciton, delocalized over a tubular aggregate of BChl c chains, and Forster-type transfer of such a cylindrical exciton between the nearest tubular BChl c aggregates as well as to BChl a of the baseplate.     

Ribosomal subunit orientations determined in the monomeric ribosome by single and by double-labeling immune electron microscopy

The energies of two and three-chain antiparallel and parallel β-sheets have been minimized. The chains were considered to be equivalent. In each case, chains consisting of four and of eight l-alanine residues, respectively, with CH₃CO- and -NHCH₃ end groups were examined. Computations were carried out both for chains constrained to have a regular structure (i.e. the same φ and ψ dihedral angles for each residue) and for chains in which the regularity constraint was relaxed. All computed minimum-energy β-sheets were found to have a right-handed twist, as observed in proteins. As in the case of right-handed α-helices, it is the intrastrand non-bonded interaction energy that plays the key role in forcing β-sheets of l-amino acid residues to adopt a right-handed twist. The non-bonded energy contribution favoring the right-handed twist is the result of many small pairwise interatomic interactions involving the C^βH₃ groups. Polyglycine β-sheets, lacking the C^βH₃ side-chains, are not twisted. The twist of the poly-l-alanine sheet diminishes as the number of residues per chain increases, in agreement with observations. The twist of the four-residue chain increases somewhat (because of interstrand non-bonded interactions, also involving the C^βH₃ groups) in going from a single chain to a two-chain antiparallel structure, but then decreases slightly in going from a two-chain to a three-chain structure. β-Sheets in observed protein structures sometimes have a larger twist than those in the structures computed here. This may be due to irregularities in amino acid sequence and in hydrogenbonding patterns in the observed sheets, or to long-range interactions in proteins. The minimized energies of parallel β-sheets are considerably higher than those of the corresponding antiparallel β-sheets, indicating that parallel β-sheets are intrinsically less stable. This finding about the two kinds of β-sheets agrees with suggestions based on analyses of β-sheets observed in proteins. The energy difference between antiparallel and parallel β-sheets is due to closer packing of the chains and a more favorable alignment of the peptide dipoles in the antiparallel structures. The hydrogen-bond geometry in the computed antiparallel structures is very close to that proposed by Arnott et al. (1967) for the β-form of poly-l-alanine.     

Role of interchain interactions in the stabilization of the right-handed twist of beta-sheets

Conformational energy computations have been carried out for parallel and antiparallel beta-sheets composed of poly-L-Val and poly-L-Ile peptide chains, each consisting of four and of six residues, respectively, with CH3CO- and-NHCH3 end groups. The beta-sheets considered contained three and five equivalent chains, respectively. All computed minimum-energy beta-sheets were found to have a large right-handed twist of a magnitude that corresponds to the mean twist of beta-sheets observed in globular proteins. The twist has the same sign but is much larger than in beta-sheets of poly-L-Ala, because of intra- and interchain interactions between the bulky beta-branched side-chains. While the right-handed twist is a result of intrachain interactions between side-chains in the case of poly-L-Val, these interactions would favor a left-handed twist in poly-L-Ile, and the right-handed twist in the latter is a result of interchain interactions. Parallel beta-sheets are more stable than antiparallel sheets for both poly-L-Val and poly-L-Ile, in contrast to poly-L-Ala. This result agrees with observations on the preferred orientation of the chains in oligopeptides that form beta-structures. It also explains the observed high relative frequencies of occurrence of Val and Ile residues in parallel beta-sheets, as compared with antiparallel sheets, in globular proteins.     

Packing interactions of aib-containing helices: Molecular modeling of parallel dimers of simple hydrophobic helices and of alamethicin

α-Aminoisobutyric acid (Aib) is a helicogenic α,α-dimethyl amino acid found in channel-forming peptaibols such as alamethicin. Possible effects of Aib on helix–helix packing are analyzed. Simulated annealing via restrained molecular dynamics is used to generate ensembles of approximately parallel helix dimers. Analysis of variations in geometrical and energetic parameters within ensembles defines how tightly a pair of helices interact. Simple hydrophobic helix dimers are compared: Ala₂₀, Leu₂₀, Aib₂₀, and P20, the latter a simple channel-forming peptide [G. Menestrina, K. P. Voges, G, Jung, and G. Boheim (1986) Journal of Membrane Biology, Vol. 93, pp. 111–132]. Ala₂₀ and Leu₂₀ dimers exhibit well-defined ridges-in-grooves packing with helix crossing angles (Ω) of the order of +20°. Aib₂₀ α-helix dimers are much more loosely packed, as evidenced by a wide range of Ω values and small helix-helix interaction energies. However, when in a 3₁₀ conformation Aib₂₀ helices pack in three well-defined parallel modes, with Ω ca. ?15°, +5°, and 10°. Comparison of helix–helix interaction energies suggests that dimerization may favor the 3₁₀ conformation. P20, with 8 Aib residues, also shows looser packing of α-helices. The results of these studies of hydrophobic helix dimers are analyzed in the context of the ridges-in-grooves packing model. Simulations are extended to dimers of alamethicin, and of an alamethicin derivative in which all Aib residues are replaced by Leu. This substitution has little effect on helix–helix packing. Rather, such interactions appear to be sensitive to interactions between polar side chains. Overall, the results suggest that Aib may modulate the packing of simple hydrophobic helices, in favor of looser interactions. For more complex amphipathic helices, interactions between polar side chains may be more critical. © 1995 John Wiley & Sons, Inc.     

Lecithin bilayers. Density measurement and molecular interactions.

Density measurement are reported for bilayer dispersions of a series of saturated lecithins. For chain lengths with, respectively, 14, 15, 16, 17, and 18 carbons per chain, the values for the volume changes at the main transition are 0.027, 0.031, 0.037, 0.040 and 0.045 ml/g. The main transition temperature extrapolates with increasing chain length to the melting temperature of polyethylene. Volume changes at the lower transition are an order of magnitude smaller than the main transition. Single phase thermal expansion coefficients are also reported. The combination of X-ray data and density data indicated that the volume changes are predominantly due to the hydrocarbon chains, thus enabling the volume vCH2 of the methylene groups to be computed as a function of temperature. From this and knowledge of intermolecular interactions in hydrocarbon chains, the change in the interchain van der Waals energy, delta UvdW, at the main transition is computed for the lecithins and also for the alkanes and polyethylene at the melting transition. Using the experimental enthalpies of transition and delta UvdW, the energy equation is consistently balanced for all three systems. This yields estimates of the change in the number of gauche rotamers in the lecithins at the main transition. The consistency of these calculations supports the conclusion that the most important molecular energies for the main transition in lecithin bilayers are the hydrocarbon chain interactions and the rotational isomeric energies, and the conclusion that the main phase transition is analogous to the melting transition in the alkanes from the hexagonal phase to the liquid phase, but with some modifications.     

Energetics of multihelix interactions in protein folding: application to myoglobin

Conformational-energy calculations have been carried out in order to determine favorable packing arrangements within a group of α-helices. The influence of side chains and of the number of interacting α-helices on the mode of packing was analyzed. In this work, our earlier methods for computing the packing energy of a pair of α-helices [Chou, K.-C., Némethy, G. & Scheraga, H. A. (1984) J. Am. Chem. Soc. 106 , 3161–3170] have been extended to treat the interactions among several helices. Also, new algorithms allow the matching of standard peptide geometry to x-ray coordinates of helical complexes and the analysis of interrelations between several helices. As a specific test case, the packing of three neighboring α-helices, viz., the A, G, and H helices of sperm whale myoglobin, was considered. Minimum-energy arrangements were computed for the separate A-H and the G-H α-helix pairs as well as for the A-G-H three-helix complex. For the packing of the nearly antiparallel G and H α-helices, the same optimal structure was obtained in two- and three-helix complexes, indicating that a single packing arrangement is specifically favored by interhelix interactions. For the pair of nearly perpendicular A and H α-helices, interactions are less specific, so that there is no unique optimal structure in the two-helix complex; in the three-helix complex, however, a specific mode of packing is favored even for the A-H pair. This result indicates that the presence of other nearby α-helices can influence the packing of a given α-helix pair. The computed arrangement of the A-G-H complex is very close to that of the crystallographically determined structure. These results can be used to make deductions about the likely sequence of events in protein folding, where, in this particular case, it appears that the G-H helix pair may form first and then induce proper orientation of the A helix.     

Membrane transport through α-heltical bundles. IV. Preliminary model building investigation of helix-helix interactions

Previously we made order of magnitude estimates that suggested the possibility of forming proton wires between facing α-helices joined by knobs-into-holes packing (Dunker, Marvin, Zaleske & Jones, 1976; Dunker & Marvin, 1978). Such structures may be a feature of membrane proteins. Since our original work, another type of packing, called ridges-into-grooves, has been identified as a way of meshing adjoining α-helices. Using precision (CPK) molecular models, we have investigated the possibility of forming proton wires: (1) in order to improve on our previous order of magnitude estimates, and (2) in order to evaluate the different kinds of packing interfaces for their ability to support stereochemically feasible proton wires.We found knobs-into-holes and ridges-into=grooves packing to support exactly the same proton wires. The positions of the side chains are determined more by the geometry of the hydrogen-bonding network rather than by the type of packing originally used to locate the appropriate residues. Thus, we suggest that a new name is needed for such packing, which we propose to call “H-bond packing”.In our earlier investigations we arbitrarily restricted our attention to proton wires parallel to the packing interface. By lifting this restriction, we found it possible to construct many additional types of wires. The model building exercises suggested that both parallel-to-the-interface and non-parallel-to-the-interface wires are feasible, except that the non-parallel wires are restricted in length depending on the angle with the interface, whereas the parallel wires apparently can be continued indefinitely. The various types of wires share local hydrogen bonding patterns and so could easily connect together.In our model building of several representative wires, we investigated the limitations with regard to type of and combinations of side chains. We also determined possible variations in the origins of such side chains on the helical backbones.These preliminary model building studies provide the basis for determining possible hydrogen bonding between the helical segments of membrane proteins. From these data we are formulating preliminary proposals for the helix-helix interactions of the bacteriorhodopsin molecule, which are to be presented in future paper.     

Design, synthesis and structural characterization of model heterodimeric coiled-coil proteins.

We report the design and synthesis of model heterodimeric coiled-coil proteins and the packing contribution of interchain hetero-hydrophobic side-chains to coiled-coil stability. The heterodimeric coiled-coils are obtained by oxidizing two 35-residue polypeptide chains, each containing a cysteine residue at position 2 and differing in amino acid sequences in the hydrophobic positions ("a" and "d") responsible for the formation and stabilization of the coiled-coil. In each peptide, a single Ala residue was substituted for Leu at position "a" or "d". The formation and stability of heterodimeric coiled-coils were investigated by circular dichroism studies in the presence and absence of guanidine hydrochloride and compared to the corresponding homodimeric coiled-coils. The coiled-coil proteins with an Ala substitution at position "a" were less stable than those with an Ala substitution at position "d" in both the homodimeric (Ala-Ala interchain interactions) and heterodimeric (Leu-Ala interchain interactions ) coiled-coils. The 70-residue disulfide bridged peptides (homo- and heterodimeric coiled-coils) can be readily separated by reversed-phase chromatography (RPC) even though they have identical amino acid compositions as well as in the hydrophobic "a" and "d" positions. The elution of the 70-residue peptides prior to their corresponding 35-residue monomers suggests that these proteins are retaining a large portion of their coiled-coil structure during RPC at pH2 and their retention behavior correlates with protein stability.     

Configurational statistics of single chains of α-linked glucans

Unperturbed chain conformations are evaluated assuming separable chain configuration energies. Spatial chain propagations are constructed assuming an equiprobable occurrence of conformational states within topographically selected portions of the allowed energy space. Random coil dimensions, along with spatial representations of some single chains of α-linked glucans, such as amylose, pseudo-nigerose, nigeran and linear dextran are reported. Significant architectural differences are observed for these different α-linked glucan chains, since disordered random-coil as well as persistent pseudo-helical character, either cyclic or linear, are found, depending on the type of glycosidic linkage.     

Reorientational and Conformational Ordering Processes at Elevated Pressures in 1,2-Dioleoyl Phosphatidylcholine: A Raman and Infrared Spectroscopic Study

Raman and infrared spectra of fully hydrated bilayers of 1,2-dioleoyl phosphatidylcholine (DOPC) were measured at increasing hydrostatic pressures up to -37 kbar. Under ambient conditions aqueous dispersions of DOPC are in the liquid crystalline state. The application of an external hydrostatic pressure induces conformational and dynamic ordering processes in DOPC, which trigger a first-order structural phase transition at 5 kbar from a disordered liquid crystalline state to a highly ordered gel state. In the gel phase the methylene chains of each molecule are fully extended and the two all-trans chain segments on both sides of the rigid cis double bond form a bent structure. The bent oleoyl chains in each molecule, as well as in neighboring molecules are packed parallel to each other. To achieve this parallel interchain packing, the double bonds of the sn-1 and sn-2 chains of each molecule must be aligned at the same position with respect to the bilayer interface which is achieved by a rotation of the C—C bonds in the glycerol moiety in the head group. The extremely strong interchain interactions in the gel phase of DOPC are unique for this lipid with cis dimono-unsaturated acyl chains. Our experimental results suggest that in the pressure-induced gel phase of DOPC the olefinic CH bonds are rotated out of the phase of the bent oleoyl chains and that the oleoyl chains of opposing bilayers bend towards opposite directions.     

Theoretical conformational analysis of phospholipids: Influence of the parallelism of the β and γ alkyl chains on the glycerol moiety conformations. Anchoring of the aliphatic chains at the hydrophobic-hydrophilic interface

Conformational analysis by empirical energy calculation of glyceryldibutanoate phosphatidylethanolamine, taking into account constraints occuring in bilayers of phospholipids, was carried out by means of energy maps and energy minimization. Variation of the interchain distance and imposed parallelism of the alkyl chains in the vicinity of the carboxyl groups induce conformational changes in the glycerol moiety. It is possible to increase the interchain distance during melting without notably increasing the conformational energy of the glycerol moiety (less than 1 kcal/mol when the distance varies from 0.48–0.60 nm). However the number of stable conformations decreases as the distance increases and eventually, the glycerol moiety becomes rigid.     

Protein destabilization by electrostatic repulsions in the two-stranded alpha-helical coiled-coil/leucine zipper.

The destabilizing effect of electrostatic repulsions on protein stability has been studied by using synthetic two-stranded alpha-helical coiled-coils as a model system. The native coiled-coil consists of two identical 35-residue polypeptide chains with a heptad repeat QgVaGbAcLdQeKf and a Cys residue at position 2 to allow formation of an interchain disulfide bridge. This peptide, designed to contain no intrahelical or interhelical electrostatic interactions, forms a stable coiled-coil structure at 20 degrees C in benign medium (50 mM KCl, 25 mM PO4, pH 7) with a [urea]1/2 value of 6.1 M. Four mutant coiled-coils were designed to contain one or two Glu substitutions for Gln per polypeptide chain. The resulting coiled-coils contained potential i to i' + 5 Glu-Glu interchain repulsions (denoted as peptide E2(15,20)), i to i' + 2 Glu-Glu interchain repulsions (denoted E2(20,22)), or no interchain ionic interactions (denoted E2(13,22) and E1(20)). The stabilities of the coiled-coils were determined by measuring the ellipticities at 222 nm as a function of urea or guanidine hydrochloride concentration at 20 degrees C in the presence and absence of an interchain disulfide bridge. At pH 7, in the presence of urea, the stabilities of E2(13,22) and E2(20,22) were identical suggesting that the potential i to i' + 2 interchain Glu-Glu repulsion in the E2(20,22) coiled-coil does not occur. In contrast, the mutant E2(15,20) is substantially less stable than E2(13,22) or E2(15,20) by 0.9 kcal/mol due to the presence of two i to i' + 5 interchain Glu-Glu repulsions, which destabilize the coiled-coil by 0.45 kcal/mol each. At pH 3 the coiled-coils were found to increase in stability as the number of Glu substitutions were increased. This, combined with reversed-phase HPLC results at pH 7 and pH 2, supports the conclusion that the protonated Glu side chains present at low pH are significantly more hydrophobic than Gln side chains which are in turn more hydrophobic than the ionized Glu side chains present at neutral pH. The protonated Glu residues increase the hydrophobicity of the coiled-coil interface leading to higher coiled-coil stability. The guanidine hydrochloride results at pH 7 show similar stabilities between the native and mutant coiled-coils indicating that guanidine hydrochloride masks electrostatic repulsions due to its ionic nature and that Glu and Gln in the e and g positions of the heptad repeat have very similar effects on coiled-coil stability in the presence of GdnHCl.     

Conformational and geometrical properties of β-sheets in proteins: II. Antiparallel and mixed β-sheets

The present work treats the conformational and geometrical properties of antiparallel and mixed β-sheets, following the approach described in the first paper of this series (Salemme & Weatherford, 1981). As shown, antiparallel structures possess conformational degrees of freedom that allow them to assume a greater diversity of spatial configurations than occur in parallel sheets. This configurational flexibility principally owes its origin to the potential variability of the interchain hydrogen bond geometry in antiparallel structures. As a consequence of this inherent elasticity of antiparallel β-sheets, their extended spatial configurations strongly reflect effects arising from local or extended side-chain packing interactions. Although the continuously deformable characteristics of antiparallel sheets frequently result in the attainment of spatial configurations that cannot be quantitatively modeled as hydrogen-bonded arrays of conformationally identical polypeptide chains, several observed sheets are nevertheless shown to be accurately approximated as conformationally regular arrays that typically yield model versus observed fits of less than 1 Å for corresponding α-carbon atoms.     

Thermodynamics of protein-peptide interactions in the ribonuclease-S system studied by molecular dynamics and free energy calculations.

Hydrophobic interactions between the S-peptide and S-protein in the ribonuclease-S complex are probed using molecular dynamics simulations and free energy calculations. Three successive mutations at the buried position Met13 are simulated: Met----Leu, Leu----Ile, and Ile----Val, for which X-ray structures and experimental thermodynamic data are available. The calculations give theoretical estimates of the changes in binding free energies associated with these mutations. The calculated free energy differences are small (0-1.6 kcal/mol), in agreement with experiment. However the simulated structures deviate significantly from the experimental ones (mean deviation approximately 1.5-2 A), and a large uncertainty in the calculated free energies (1-2 kcal/mol) arises from the multiple minimum problem. Indeed, multiple conformations are available to the side chains around the mutation site, and the sampling of dihedral rotamer transitions is limited, despite long simulations. Fluctuations within each local minimum give rise to a small statistical error. However the uncertainty due to multiple conformations is much greater than the uncertainty due to random statistical errors. In our work, an artificial cancellation of errors arose because we studied conformations of the RNase complex and of the S-peptide that were very similar. In general, the criterion for a precise simulation is not merely to reduce the random statistical error, as has been suggested, but rather to sample all the important local minima along the mutation pathway, and to reduce the statistical error for each one. Our calculations suggest that the packing changes associated with the mutations are energetically small and localized, and largely cancel when the complex and the S-peptide are compared. Solvation of the methionine side chain partial charges in the S-peptide and the complex appear to be energetically equivalent, so that removing them (as in Met13----Leu, Ile, Val) does not affect binding. Enthalpy and entropy changes could not be estimated reliably.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Structural hierarchy controls deformation behavior of collagen

The structure of collagen, the most abundant protein in mammals, consists of a triple helix composed of three helical polypeptide chains. The deformation behavior of collagen is governed by molecular mechanisms that involve the interaction between different helical hierarchies found in collagen. Here, we report results of Steered Molecular Dynamics study of the full-length collagen molecule (～290 nm). The collagen molecule is extended at various pulling rates ranging from 0.00003/ps to 0.012/ps. These simulations reveal a new level of hierarchy exhibited by collagen: helicity of the triple chain. This level of hierarchy is apparent at the 290 nm length and cannot be observed in the 7-9 nm models often described to evaluate collagen mechanics. The deformation mechanisms in collagen are governed by all three levels of hierarchy, helicity of single chain (level-1), helical triple helix (level-2), and hereby described helicity of the triple chain (level-3). The mechanics resulting from the three levels is described by an interlocking gear analogy. In addition, remarkably, the full-length collagen does not show much unwinding of triple helix unlike that exhibited by short collagen models. Further, the full-length collagen does not show significant unwinding of the triple helix, unlike that exhibited by short collagen. Also reported is that the interchain hydrogen bond energy in the full-length collagen is significantly smaller than the overall interchain nonbonded interaction energies, suggesting that the nonbonded interactions have far more important role than hydrogen bonds in the mechanics of collagen. However, hydrogen bonding is essential for the triple helical conformation of the collagen. Hence, although mechanics of collagen is controlled by nonbonded interchain interaction energies, the confirmation of collagen is attributed to the interchain hydrogen bonding.