Conformational transition states of a beta-hairpin peptide between the ordered and disordered conformations in explicit water

The conformational transition states of a beta-hairpin peptide in explicit water were identified from the free energy landscapes obtained from the multicanonical ensemble, using an enhanced conformational sampling calculation. The beta-hairpin conformations were significant at 300 K in the landscape, and the typical nuclear Overhauser effect signals were reproduced, consistent with the previously reported experiment. In contrast, the disordered conformations were predominant at higher temperatures. Among the stable conformations at 300 K, there were several free energy barriers, which were not visible in the landscapes formed with the conventional parameters. We identified the transition states around the saddle points along the putative folding and unfolding paths between the beta-hairpin and the disordered conformations in the landscape. The characteristic features of these transition states are the predominant hydrophobic contacts and the several hydrogen bonds among the side-chains, as well as some of the backbone hydrogen bonds. The unfolding simulations at high temperatures, 400 K and 500 K, and their principal component analyses also provided estimates for the transition state conformations, which agreed well with those at 400 K and 500 K deduced from the current free energy landscapes at 400 K and 500 K, respectively. However, the transition states at high temperatures were much more widely distributed on the landscape than those at 300 K, and their conformations were different.     

Solvent effects on the conformational transition of a model polyalanine peptide

We have investigated the folding of polyalanine by combining discontinuous molecular dynamics simulation with our newly developed off-lattice intermediate-resolution protein model. The thermodynamics of a system containing a single Ac-KA(14)K-NH(2) molecule has been explored by using the replica exchange simulation method to map out the conformational transitions as a function of temperature. We have also explored the influence of solvent type on the folding process by varying the relative strength of the side-chain's hydrophobic interactions and backbone hydrogen bonding interactions. The peptide in our simulations tends to mimic real polyalanine in that it can exist in three distinct structural states: alpha-helix, beta-structures (including beta-hairpin and beta-sheet-like structures), and random coil, depending upon the solvent conditions. At low values of the hydrophobic interaction strength between nonpolar side-chains, the polyalanine peptide undergoes a relatively sharp transition between an alpha-helical conformation at low temperatures and a random-coil conformation at high temperatures. As the hydrophobic interaction strength increases, this transition shifts to higher temperatures. Increasing the hydrophobic interaction strength even further induces a second transition to a beta-hairpin, resulting in an alpha-helical conformation at low temperatures, a beta-hairpin at intermediate temperatures, and a random coil at high temperatures. At very high values of the hydrophobic interaction strength, polyalanines become beta-hairpins and beta-sheet-like structures at low temperatures and random coils at high temperatures. This study of the folding of a single polyalanine-based peptide sets the stage for a study of polyalanine aggregation in a forthcoming paper.     

UV resonance Raman investigation of a 3(10)-helical peptide reveals a rough energy landscape

We used UVRRS at 194 and 204 nm excitation to examine the backbone conformation of a 13-residue polypeptide (gp41(659-671)) that has been shown by NMR to predominantly fold into a 3(10)-helix. Examination of the conformation sensitive AmIII(3) region indicates the peptide has significant populations of beta-turn, PPII, 3(10)-helix, and pi-helix-like conformations but little alpha-helix. We estimate that at 1 degree C on average six of the 12 peptide bonds are in folded conformations (predominantly 3(10)- and pi-helix), while the other six are in unfolded (beta-turn/PPII) conformations. The folded and unfolded populations do not change significantly as the temperature is increased from 1 to 60 degrees C, suggesting a unique energy landscape where the folded and unfolded conformations are essentially degenerate in energy and exhibit identical temperature dependences.     

Molecular dynamics simulations of beta-hairpin folding

Molecular dynamics simulations of beta-hairpin folding have been carried out with a solvent-referenced potential at 274 K. The model peptide V4DPGV4 formed stable beta-hairpin conformations and the beta-hairpin ratio calculated by the DSSP algorithm was about 56% in the 50-ns simulation. Folding into beta-hairpin conformations is independent of the initial conformations. The simulations provided insights into the folding mechanism. The hydrogen bond often formed in a beta-turn first, and then propagated by forming more hydrogen bonds along the strands. Unfolding and refolding occurred repeatedly during the simulations. Both the hydrogen bonding and the hydrophobic interaction played important roles in forming the ordered structure. Without the hydrophobic effect, stable beta-hairpin conformations did not form in the simulations. With the same energy functions, the alanine-based peptide (AAQAA)3Y folded into helical conformations, in agreement with experiments. Folding into an alpha-helix or a beta-hairpin is amino acid sequence-dependent.     

Energy landscape and dynamics of the beta-hairpin G peptide and its isomers: Topology and sequences

We have investigated free energy landscape [MM/PBSA + normal modes entropy] of permutations in the G peptide (41-56) from the protein G B1 domain by studying six isomers corresponding to moving the hydrophobic cluster along the beta-strands (toward the turn: T1, AGEWTYDDKTFTVTET; T2, GEDTWDYATFTVTKTE; T3, GEDDWTYATFTVTKTE; toward the end: E1, WTYDDAGETKTFTVT; E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV). The free energy terms include molecular mechanics energy, Poisson-Boltzmann electrostatic solvation energy, surface area solvation energy, and conformational entropy estimated by using normal mode analysis. From the wild type to T1, then T3, and finally T2, we see a progressively changing energy landscape, toward a less stable beta-hairpin structure. Moving the hydrophobic cluster outside toward the end region causes a greater change in the energy landscape. alpha-Helical instead of a beta-hairpin structure was the most stable form for the E2 isomer. However, no matter how much the sequence changes, for all variants studied, ideal "native" beta-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. In general, we find that the energy landscape is dependent on the hydrophobic cluster topology and on the sequence. Our present study indicates that the key is the relative conformational energies of the different conformations. Changes in the sequence strongly modulate the relative stabilities of topologically similar regions in the energy landscape, rather than redefine the topology space. This finding is consistent with a population redistribution in the process of protein folding. The limited variation of topological space, compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance.     

Conformational interconversion in compstatin probed with molecular dynamics simulations

Compstatin is a 13-residue cyclic peptide that has the potential to become a therapeutic agent against unregulated complement activation. In our effort to understand the structural and dynamic characteristics of compstatin that form the basis for rational and combinatorial optimization of structure and activity, we performed 1-ns molecular dynamics (MD) simulations. We used as input in the MD simulations the ensemble of 21 lowest energy NMR structures, the average minimized structure, and a global optimization structure. At the end of the MD simulations we identified five conformations, with populations ranging between 9% and 44%. These conformations are as follows: 1) coil with alphaR-alphaR beta-turn, as was the conformation of the initial ensemble of NMR structures; 2) beta-hairpin with epsilon-alphaR beta-turn; 3) beta-hairpin with alphaR-alphaR beta-turn; 4) beta-hairpin with alphaR-beta beta-turn; and 5) alpha-helical. Conformational switch was possible with small amplitude backbone motions of the order of 0.1-0.4 A and free energy barrier crossing of 2-11 kcal/mol. All of the 21 MD structures corresponding to the NMR ensemble possessed a beta-turn, with 14 structures retaining the alphaR-alphaR beta-turn type, but the average minimized structure and the global optimization structures were converted to alpha-helical conformations. Overall, the MD simulations have aided to gain insight into the conformational space sampled by compstatin and have provided a measure of conformational interconversion. The calculated conformers will be useful as structural and possibly dynamic templates for optimization in the design of compstatin using structure-activity relations (SAR) or dynamics-activity relations (DAR).     

Folding landscapes of the Alzheimer amyloid-beta(12-28) peptide

The energy landscape for folding of the 12-28 fragment of the Alzheimer amyloid beta (Abeta) peptide is characterized using replica-exchange molecular dynamics simulations with an all-atom peptide model and explicit solvent. At physiological temperatures, the peptide exists mostly as a collapsed random coil, populating a small fraction (less than 10%) of hairpins with a beta-turn at position V18F19, with another 10% of hairpin-like conformations possessing a bend rather than a turn in the central VFFA positions. A small fraction of the populated states, approximately 14%, adopt polyproline II (PPII) conformations. Folding of the structured hairpin states proceeds through the assembly of two locally stable segments, VFFAE and EDVGS. The interactions stabilizing these locally folded structural motifs are in conflict with those stabilizing the global fold of A12-28, a signature of underlying residual frustration in this peptide. At increased temperature, the population of both beta-strand and PPII conformations diminishes in favor of beta-turn and random-coil states. On the basis of the conformational preferences of Abeta 12-28 monomers, two models for the molecular structure of amyloid fibrils formed by this peptide are proposed.     

Understanding the structural characteristics of compstatin by conformational space annealing

The structural characteristics of the 13-residue compstatin molecule are investigated using the conformational space annealing (CSA) method with CHARMM force field and the GBSA continuum solvent model. In order to sample conformations in the energy range of the minimized NMR structures, we have used the stopping criterion to the CSA search when a conformation whose energy is less than -490 kcal/mol is found. With this stopping criterion, a great variety of conformations are generated around experimentally known structures. Twenty independent CSA runs starting from random states find 1000 representative conformations in the energy landscape of the compstatin, which are classified into thirty-one structural families. The majority of the conformations (94.4%) are in the coil state. Other conformers containing a 3(10)-helix, a pi-helix, a beta-hairpin, and an alpha-helix are also found.     

Sequence swapping does not result in conformation swapping for the beta4/beta5 and beta8/beta9 beta-hairpin turns in human acidic fibroblast growth factor

The beta-turn is the most common type of nonrepetitive structure in globular proteins, comprising ~25% of all residues; however, a detailed understanding of effects of specific residues upon beta-turn stability and conformation is lacking. Human acidic fibroblast growth factor (FGF-1) is a member of the beta-trefoil superfold and contains a total of five beta-hairpin structures (antiparallel beta-sheets connected by a reverse turn). beta-Turns related by the characteristic threefold structural symmetry of this superfold exhibit different primary structures, and in some cases, different secondary structures. As such, they represent a useful system with which to study the role that turn sequences play in determining structure, stability, and folding of the protein. Two turns related by the threefold structural symmetry, the beta4/beta5 and beta8/beta9 turns, were subjected to both sequence-swapping and poly-glycine substitution mutations, and the effects upon stability, folding, and structure were investigated. In the wild-type protein these turns are of identical length, but exhibit different conformations. These conformations were observed to be retained during sequence-swapping and glycine substitution mutagenesis. The results indicate that the beta-turn structure at these positions is not determined by the turn sequence. Structural analysis suggests that residues flanking the turn are a primary structural determinant of the conformation within the turn.     

The roles of turn formation and cross-strand interactions in fibrillization of peptides derived from the OspA single-layer beta-sheet

We previously demonstrated that a beta-hairpin peptide, termed BH(9-10), derived from a single-layer beta-sheet of Borrelia OspA protein, formed a native-like beta-turn in trifluoroethanol (TFE) solution, and it assembled into amyloid-like fibrils at higher TFE concentrations. This peptide is highly charged, and fibrillization of such a hydrophilic peptide is quite unusual. In this study, we designed a circularly permutated peptide of BH(9-10), termed BH(10-9). When folded into their respective beta-hairpin structures found in OspA, these peptides would have identical cross-strand interactions but different turns connecting the strands. NMR study revealed that BH(10-9) had little propensity to form a turn structure both in aqueous and TFE solutions. At higher TFE concentration, BH(10-9) precipitated with a concomitant alpha-to-beta conformational conversion, in a similar manner to the BH(9-10) fibrillization. However, the BH(10-9) precipitates were nonfibrillar aggregation. The precipitation kinetics of BH(10-9) was exponential, consistent with a first-order molecular assembly reaction, while the fibrillization of BH(9-10) showed sigmoidal kinetics, indicative of a two-step reaction consisting of nucleation and molecular assembly. The correlation between native-like turn formation and fibrillization of our peptide system strongly suggests that BH(9-10) adopts a native-like beta-hairpin conformation in the fibrils. Remarkably, seeding with the preformed BH(10-9) precipitates changed the two-step BH(9-10) fibrillization to a one-step molecular assembly reaction, and disrupted the BH(9-10) fibril structure, indicating interactions between the BH(10-9) aggregates and the BH(9-10) peptide. Our results suggest that, in these peptides, cross-strand interactions are the driving force for molecular assembly, and turn formation limits modes of peptide assembly.     

Thermodynamic and kinetic characterization of a beta-hairpin peptide in solution: an extended phase space sampling by molecular dynamics simulations in explicit water

The folding of the amyloidogenic H1 peptide MKHMAGAAAAGAVV taken from the syrian hamster prion protein is explored in explicit aqueous solution at 300 K using long time scale all-atom molecular dynamics simulations for a total simulation time of 1.1 mus. The system, initially modeled as an alpha-helix, preferentially adopts a beta-hairpin structure and several unfolding/refolding events are observed, yielding a very short average beta-hairpin folding time of approximately 200 ns. The long time scale accessed by our simulations and the reversibility of the folding allow to properly explore the configurational space of the peptide in solution. The free energy profile, as a function of the principal components (essential eigenvectors) of motion, describing the main conformational transitions, shows the characteristic features of a funneled landscape, with a downhill surface toward the beta-hairpin folded basin. However, the analysis of the peptide thermodynamic stability, reveals that the beta-hairpin in solution is rather unstable. These results are in good agreement with several experimental evidences, according to which the isolated H1 peptide adopts very rapidly in water beta-sheet structure, leading to amyloid fibril precipitates [Nguyen et al., Biochemistry 1995;34:4186-4192; Inouye et al., J Struct Biol 1998;122:247-255]. Moreover, in this article we also characterize the diffusion behavior in conformational space, investigating its relations with folding/unfolding conditions.     

Solution structure of a K+-channel blocker from the scorpion Tityus cambridgei

A new K(+)-channel blocking peptide identified from the scorpion venom of Tityus cambridgei (Tc1) is composed of 23 amino acid residues linked with three disulfide bridges. Tc1 is the shortest known toxin from scorpion venom that recognizes the Shaker B K(+) channels and the voltage-dependent K(+) channels in the brain. Synthetic Tc1 was produced using solid-phase synthesis, and its activity was found to be the same as that of native Tc1. The pairings of three disulfide bridges in the synthetic Tc1 were identified by NMR experiments. The NMR solution structures of Tc1 were determined by simulated annealing and energy-minimization calculations using the X-PLOR program. The results showed that Tc1 contains an alpha-helix and a 3(10)-helix at N-terminal Gly(4)-Lys(10) and a double-stranded beta-sheet at Gly(13)-Ile(16) and Arg(19)-Tyr(23), with a type I' beta-turn at Asn(17)-Gly(18). Superposition of each structure with the best structure yielded an average root mean square deviation of 0.26 +/- 0.05 A for the backbone atoms and of 1.40 +/- 0.23 A for heavy atoms in residues 2 to 23. The three-dimensional structure of Tc1 was compared with two structurally and functionally related scorpion toxins, charybdotoxin (ChTx) and noxiustoxin (NTx). We concluded that the C-terminal structure is the most important region for the blocking activity of voltage-gated (Kv-type) channels for scorpion K(+)-channel blockers. We also found that some of the residues in the larger scorpion K(+)-channel blockers (31 to 40 amino acids) are not involved in K(+)-channel blocking activity.     

A molecular dynamics study of the 41-56 beta-hairpin from B1 domain of protein G.

The structural and dynamical behavior of the 41-56 beta-hairpin from the protein G B1 domain (GB1) has been studied at different temperatures using molecular dynamics (MD) simulations in an aqueous environment. The purpose of these simulations is to establish the stability of this hairpin in view of its possible role as a nucleation site for protein folding. The conformation of the peptide in the crystallographic structure of the protein GB1 (native conformation) was lost in all simulations. The new equilibrium conformations are stable for several nanoseconds at 300K (>10 ns), 350 K (>6.5 ns), and even at 450 K (up to 2.5 ns). The new structures have very similar hairpin-like conformations with properties in agreement with available experimental nuclear Overhauser effect (NOE) data. The stability of the structure in the hydrophobic core region during the simulations is consistent with the experimental data and provides further evidence for the role played by hydrophobic interactions in hairpin structures. Essential dynamics analysis shows that the dynamics of the peptide at different temperatures spans basically the same essential subspace. The main equilibrium motions in this subspace involve large fluctuations of the residues in the turn and ends regions. Of the six interchain hydrogen bonds, the inner four remain stable during the simulations. The space spanned by the first two eigenvectors, as sampled at 450 K, includes almost all of the 47 different hairpin structures found in the database. Finally, analysis of the hydration of the 300 K average conformations shows that the hydration sites observed in the native conformation are still well hydrated in the equilibrium MD ensemble.     

Computational and experimental determination of the alpha-helix unfolding reaction coordinate

We demonstrate a calculated alpha-helix peptide folding energy landscape which accurately simulates the first experimentally measured alpha-helix melting energy landscape. We examine a 21-amino acid, mainly polyalanine peptide and calculate the free energy along the Psi Ramachandran angle secondary folding coordinate. The experimental free energy landscape was determined using UV resonance Raman spectroscopy. The relative free energy values are very close as are the equilibrium peptide conformations. We find 2.3 kcal/mol activation barriers between the alpha-helix-like and PPII-like basins. We also find that the alpha-helix-like conformations are quite defective and the alpha-helix-like structure dynamically samples 310-helix and pi-bulges.     

Free energy landscapes of peptides by enhanced conformational sampling

The free energy landscapes of peptide conformations in water have been observed by the enhanced conformational sampling method, applying the selectively enhanced multicanonical molecular dynamics simulations. The conformations of the peptide dimers, -Gly-Gly-, -Gly-Ala-, -Gly-Ser-, -Ala-Gly-, -Asn-Gly-, -Pro-Gly-, -Pro-Ala-, and -Ala-Ala-, which were all blocked with N-terminal acetyl and C-terminal N-methyl groups, were individually sampled with the explicit TIP3P water molecules. From each simulation trajectory, we obtained the canonical ensemble at 300 K, from which the individual three-dimensional landscape was drawn by the potential of mean force using the three reaction coordinates: the backbone dihedral angle, psi, of the first amino acid, the backbone dihedral angle, phi, of the second amino acid, and the distance between the carbonyl oxygen of the N-terminal acetyl group and the C-terminal amide proton. The most stable state and several meta-stable states correspond to extended conformations and typical beta-turn conformations, and their free energy values were accounted for from the potentials of mean force at the states. In addition, the contributions from the intra-molecular energies of peptides and those from the hydration effects were analyzed. Consequently, the stable beta-turn conformations in the free energy landscape were consistent with the empirically preferred beta-turn types for each amino acid sequence. The thermodynamic values for the hydration effect were decomposed and they correlated well with the empirical values estimated from the solvent accessible surface area of each molecular conformation during the trajectories. The origin of the architecture of protein local fragments was analyzed from the viewpoint of the free energy and its decomposed factors.     

Effects of solvent on the structure of the Alzheimer amyloid-beta(25-35) peptide

The free energy landscape for folding of the Alzheimer's amyloid-beta(25-35) peptide is explored using replica exchange molecular dynamics in both pure water and in HFIP/water cosolvent. This amphiphilic peptide is a natural by-product of the Alzheimer's amyloid-beta(1-40) peptide and retains the toxicity of its full-length counterpart as well as the ability to aggregate into beta-sheet-rich fibrils. Our simulations reveal that the peptide preferentially populates a helical structure in apolar organic solvent, while in pure water, the peptide adopts collapsed coil conformations and to a lesser extent beta-hairpin conformations. The beta-hairpin is characterized by a type II' beta-turn involving residues G29 and A30 and two short beta-strands involving residues N27, K28, I31, and I32. The hairpin is stabilized by backbone hydrogen-bonding interactions between residues K28 and I31; S26 and G33; and by side-chain-to-side-chain interactions between N27 and I32. Implications regarding the mechanism of aggregation of this peptide into fibrils and the role of the environment in modulating secondary structure are discussed.     

The folding landscape of an alpha-lytic protease variant reveals the role of a conserved beta-hairpin in the development of kinetic stability

Most secreted bacterial proteases, including alpha-lytic protease (alphaLP), are synthesized with covalently attached pro regions necessary for their folding. The alphaLP folding landscape revealed that its pro region, a potent folding catalyst, is required to circumvent an extremely large folding free energy of activation that appears to be a consequence of its unique unfolding transition. Remarkably, the alphaLP native state is thermodynamically unstable; a large unfolding free energy barrier is solely responsible for the persistence of its native state. Although alphaLP folding is well characterized, the structural origins of its remarkable folding mechanism remain unclear. A conserved beta-hairpin in the C-terminal domain was identified as a structural element whose formation and positioning may contribute to the large folding free energy barrier. In this article, we characterize the folding of an alphaLP variant with a more favorable beta-hairpin turn conformation (alphaLP(beta-turn)). Indeed, alphaLP(beta-turn) pro region-catalyzed folding is faster than that for alphaLP. However, instead of accelerating spontaneous folding, alphaLP(beta-turn) actually unfolds more slowly than alphaLP. Our data support a model where the beta-hairpin is formed early, but its packing with a loop in the N-terminal domain happens late in the folding reaction. This tight packing at the domain interface enhances the kinetic stability of alphaLP(beta-turn), to nearly the same degree as the change between alphaLP and a faster folding homolog. However, alphaLP(beta-turn) has impaired proteolytic activity that negates the beneficial folding properties of this variant. This study demonstrates the evolutionary limitations imposed by the simultaneous optimization of folding and functional properties.     

Effects of turn residues on beta-hairpin folding--a molecular dynamics study.

Folding of beta-hairpin structures of synthetic peptides has been simulated using the molecular dynamics method with a solvent-referenced potential. Two similar sequences, Ac-MQIFVKS(D)PGKTITLKV-NH(2) and Ac-MQIFVKS(L)PGKTITLKV-NH(2), derived from the N-terminal beta-hairpin of ubiquitin, were used to study the effects of turn residues in beta-hairpin folding. The simulations were carried out for 80 ns at 297 K. With extended initial conformation, the (D)P-containing peptide folded into a stable 2:2 beta-hairpin conformation with a type II' beta-turn at (D)PG. The overall beta-hairpin ratio, calculated by the DSSP algorithm, was 32.6%. With randomly generated initial conformations, the peptide also formed the stable 2:2 beta-hairpin conformation. The interactions among the side chains in the 2:2 beta-hairpin were almost identical to those in the native protein. These interactions reduced the solvation energy upon folding and stabilized the beta-hairpin conformation. Without the solvent effect, the peptide did not fold into stable beta-hairpin structures. The solvent effect is crucial for the formation of the beta-hairpin conformation. The effect of the temperature has also been studied. The (L)P-containing peptide did not fold into a stable beta-hairpin conformation and had a much lower beta-hairpin ratio (16.6%). The( L)P-containing peptide has similar favorable side-chain interactions, but the turn formed by (L)PG does not connect well with the right-handed twist of the beta-strands. For comparison, the isolated N-terminal peptide of ubiquitin, Ac-MQIFVKTLTGKTITLEV-NH(2), was also simulated and its beta-hairpin ratio was low, indicating that the beta-hairpin in the native structure is stabilized by the interaction with the protein environment. These simulation results agreed qualitatively with the available experimental findings.     

Alternative type I and I' turn conformations in the beta8/beta9 beta-hairpin of human acidic fibroblast growth factor

Human acidic fibroblast growth factor (FGF-1) has a beta-trefoil structure, one of the fundamental protein superfolds. The X-ray crystal structures of wild-type and various mutant forms of FGF-1 have been solved in five different space groups: C2, C222(1), P2(1) (four molecules/asu), P2(1) (three molecules/asu), and P2(1)2(1)2(1). These structures reveal two characteristically different conformations for the beta8/beta9 beta-hairpin comprising residue positions 90-94. This region in the wild-type FGF-1 structure (P2(1), four molecules/asu), a his-tagged His93-->Gly mutant (P2(1), three molecules/asu) and a his-tagged Asn106-->Gly mutant (P2(1)2(1)2(1)) adopts a 3:5 beta-hairpin known as a type I (1-4) G1 beta-bulge (containing a type I turn). However, a his-tagged form of wild-type FGF-1 (C222(1)) and a his-tagged Leu44-->Phe mutant (C2) adopt a 3:3 beta-hairpin (containing a type I' turn) for this same region. A feature that distinguishes these two types of beta-hairpin structures is the number and location of side chain positions with eclipsed C(beta) and main-chain carbonyl oxygen groups (Psi is equivalent to +60 degrees). The effects of glycine mutations upon stability, at positions within the hairpin, have been used to identify the most likely structure in solution. Type I' turns in the structural data bank are quite rare, and a survey of these turns reveals that a large percentage exhibit crystal contacts within 3.0 A. This suggests that many of the type I' turns in X-ray structures may be adopted due to crystal packing effects.