Solid Phase Synthesis and Circular Dichroism Analysis of (i → i + 4) Cyclic Lactam Analogues of Kisspeptin

The α-helix is one of the most common secondary structure elements adopted by proteins and is commonly stabilized in synthetic peptides via the formation of a covalent side-chain to side-chain lactam bridge. In this study, we explored the application of various side-chain to side-chain lactam bridges to helix stabilization of kisspeptin analogues, an interesting candidate for ligand-based drug discovery with potential as anti-metastatic agents. We successfully synthesised a series of Asp/Lys, Lys/Asp, Glu/Lys and Lys/Glu lactams, finding peptide (1) cyclo(4,8)Tyr-Asn-Trp-Glu-Ala-Phe-Gly-Lys-Arg-Phe-NH₂, to exhibit characteristic α-helical activity in aqueous buffer, in comparison to the linear native peptide, which showed no helical character.     

Conformational studies of a bicyclic,lactam‐constrained parathyroid hormone‐related protein‐derived agonist

The N‐terminal 1–34 segments of both parathyroid hormone (PTH) and parathyroid hormone‐related protein (PTHrP) bind and activate the same membrane receptor in spite of major differences in their amino acid sequence. The hypothesis was made that they share the same bioactive conformation when bound to the receptor. A common structural motif in all bioactive fragments of the hormone in water/trifluoroethanol mixtures or in aqueous solution containing detergent micelles is the presence of two helical segments at the N‐ and C‐termini of the sequence. In order to stabilize the helical structures, we have recently synthesized and studied the PTHrP(1–34) analog [(Lys13–As p¹⁷, Lys26–As p³⁰)]PTHrP(1–34)NH₂, which contains lactam‐constrained Lys‐Asp side chains at positions i, i+4. This very potent agonist exhibits enhanced helix stability with respect to the corresponding linear peptide and also two flexible sites at positions 12 and 19 in 1:1 trifluoroethanol/water. These structural elements have been suggested to play a critical role in bioactivity. In the present work we have extended our conformational studies on the bicyclic lactam‐constrained analog to aqueous solution. By CD, 2D‐NMR and structure calculations we have shown that in water two helical segments are present in the region of the lactam bridges (13–18, and 26–31) with high flexibility around Gly¹² and Arg¹⁹. Thus, the essential structural features observed in the aqueous‐organic medium are maintained in water even if, in this solvent, the overall structure is more flexible. Our findings confirm the stabilizing effect of side‐chain lactam constraints on the α‐helical structure. Copyright © 1999 European Peptide Society and John Wiley & Sons, Ltd.     

Anticooperativity in a Glu-Lys-Glu salt bridge triplet in an isolated alpha-helical peptide

Salt bridges between oppositely charged side chains are well-known to stabilize protein structure, though their contributions vary considerably. Here we study Glu-Lys and Lys-Glu salt bridges, formed when the residues are spaced i, i + 4 surface of an isolated alpha-helix in aqueous solution. Both are stabilizing by -0.60 and -1.02 kcal/mol, respectively, when the interacting residues are fully charged. When the side chains are spaced i, i + 4, i + 8, forming a Glu-Lys-Glu triplet, the second salt bridge provides no additional stabilization to the helix. We attribute this to the inability of the central Lys to form two salt bridges simultaneously. Analysis of these salt bridges in protein structures shows that the Lys-Glu interaction is dominant, with the side chains of the Glu-Lys pair far apart.     

Elucidating the role of Trp105 in the KPC-2 ��-lactamase

The molecular basis of resistance to β‐lactams and β‐lactam‐β‐lactamase inhibitor combinations in the KPC family of class A enzymes is of extreme importance to the future design of effective β‐lactam therapy. Recent crystal structures of KPC‐2 and other class A β‐lactamases suggest that Ambler position Trp105 may be of importance in binding β‐lactam compounds. Based on this notion, we explored the role of residue Trp105 in KPC‐2 by conducting site‐saturation mutagenesis at this position. Escherichia coli DH10B cells expressing the Trp105Phe, ‐Tyr, ‐Asn, and ‐His KPC‐2 variants possessed minimal inhibitory concentrations (MICs) similar to E. coli cells expressing wild type (WT) KPC‐2. Interestingly, most of the variants showed increased MICs to ampicillin‐clavulanic acid but not to ampicillin‐sulbactam or piperacillin‐tazobactam. To explain the biochemical basis of this behavior, four variants (Trp105Phe, ‐Asn, ‐Leu, and ‐Val) were studied in detail. Consistent with the MIC data, the Trp105Phe β‐lactamase displayed improved catalytic efficiencies, k_cat/K_m, toward piperacillin, cephalothin, and nitrocefin, but slightly decreased k_cat/K_m toward cefotaxime and imipenem when compared to WT β‐lactamase. The Trp105Asn variant exhibited increased K_ms for all substrates. In contrast, the Trp105Leu and ‐Val substituted enzymes demonstrated notably decreased catalytic efficiencies (k_cat/K_m) for all substrates. With respect to clavulanic acid, the K_is and partition ratios were increased for the Trp105Phe, ‐Asn, and ‐Val variants. We conclude that interactions between Trp105 of KPC‐2 and the β‐lactam are essential for hydrolysis of substrates. Taken together, kinetic and molecular modeling studies define the role of Trp105 in β‐lactam and β‐lactamase inhibitor discrimination.     

Studying the Structural and Folding Features of Long‐Sequence Trichobrachin Peptides

In this theoretical study, the folding processes of long‐sequence trichobrachin peptides (i.e., TB IIb peptides) were investigated by molecular dynamics methods. The formation of various helical structures (i.e., 3₁₀‐, α‐, and left‐handed α‐helices) was studied with regard to the entire sequence of peptides, as well as to each amino acid. The results pointed out that TB IIb molecules showed a propensity to form helical conformations, and they could be characterized by 3₁₀‐helical structure rather than by α‐helical structure. The formation of local (i.e., i←i+3 and i←i+4) as well as of non‐local (i.e., i←i+n, where n>4; and all i→i+n) H‐bonds was also examined. The results revealed that the occurrence of local, helix‐stabilizing H‐bonds was in agreement with the appearance of helical conformations, and the non‐local H‐bonds did not produce relevant effects on the evolution of helical structures. Based on the data obtained by our structural investigation, differences were observed between the TB IIb peptides, according to the type of amino acid located in the 17th position of their sequences. In summary, the folding processes were explored for TB IIb molecules, and our theoretical study led to the conclusion that these long‐sequence peptaibols showed characteristic structural and folding features.     

A CD and an nmr study of multiple bradykinin conformations in aqueous trifluoroethanol solutions

CD and nmr studies have been carried out on aqueous trifluoroethanol (TFE) solutions of bradykinin (BK) and a bradykinin antagonist. The CD results exhibit a striking effect of TFE on the spectra of BK, with sequence Arg-Pro-Pro-Gly-Phe-Ser-Pro-Phe-Arg, and the BK antagonist, with sequence D -Arg-Arg-Pro-Hyp-Gly-Thi-D -Ser-D -Cpg-Cpg-Arg [where Hyp is 4-hydroxy-L -proline; Thi refers to β-(2-thienyl)-L -alanine and Cpg refers to α-cyclopentylglycine]. The effect of increasing concentration of TFE in water on the difference ellipticity at 222 nm was examined and showed that BK may be a mixture of at least two different conformers, one of which largely forms when the TFE concentration is increased beyond 80%. The linear extrapolation of 100% of the difference ellipticity of BK at low TFE concentrations yields a value in agreement with that shown by the BK antagonist, indicating that the conformation of BK at the lower TFE concentrations is similar to that of the BK antagonist. The conformational analysis was carried out using both one-dimensional and two-dimensional ¹H-nmr techniques. The total correlation spectroscopy (TOCSY) spectrum of BK in a 60/40% (v/v) TFE/H₂O solution at 10°C and a nuclear Overhauser effect spectroscopy (NOESY) spectrum that shows only sequential H_α(i) – NH(i + 1) or the H_α(i) – H_δδ′(i + 1) NOEs indicate that the majority of the molecules adopt an all-trans extended conformation. The TOCSY for BK in the 95/5% (v/v) TFE/H₂O solution shows that there are two major conformations in the solution with about equal population. The NOESY experiment shows two new important cross peaks for one conformation, namely Pro²(α)-Pro³ (α) and the Pro²(α)-Gly⁴(NH), indicating a cis Pro²-Pro³ bond and a type VI β-turn between residues Arg¹ and Gly⁴ involving cis proline at position 3, respectively. The low temperature coefficient of Gly⁴ for this conformation suggests the presence of an intramolecular hydrogen bond, therefore a type VIa β-turn is present. The other conformation is all trans and extended. The BK antafonist shows difference CD spectra in TFE solutions referred to H₂O that are superficially indicative of a β-bend. However, nmr speaks against this possibility, as only one set of peaks were observed in the TOCSY and NOESY experiments, indicating an all-trans extended confirmation over the range of TFE concentrations. The BK-antagonist CD data suggest that solvent perturbation of the CD of an extended confirmation perturbation of the optical activity of the thienyl moiety of the peptide since the CD spectrum of N-acetyl-β-thienyl-L -alanine N-methylamide is strongly perturbed by TFE. The present results again demonstrate the complementary relationship between CD and nmr. © 1994 John Wiley & Sons, Inc.     

Acyl acceptor recognition by Enterococcus faecium l,d‐transpeptidase Ldtfm

In Mycobacterium tuberculosis and ampicillin‐resistant mutants of Enterococcus faecium, the classical target of β‐lactam antibiotics is bypassed by l ,d ‐transpeptidases that form unusual 3 → 3 peptidoglycan cross‐links. β‐lactams of the carbapenem class, such as ertapenem, are mimics of the acyl donor substrate and inactivate l ,d ‐transpeptidases by acylation of their catalytic cysteine. We have blocked the acyl donor site of E. faecium l ,d ‐transpeptidase Ldt_fm by ertapenem and identified the acyl acceptor site based on analyses of chemical shift perturbations induced by binding of peptidoglycan fragments to the resulting acylenzyme. An nuclear magnetic resonance (NMR)‐driven docking structure of the complex revealed key hydrogen interactions between the acyl acceptor and Ldt_fm that were evaluated by site‐directed mutagenesis and development of a cross‐linking assay. Three residues are reported as critical for stabilisation of the acceptor in the Ldt_fm active site and proper orientation of the nucleophilic nitrogen for the attack of the acylenzyme carbonyl. Identification of the catalytic pocket dedicated to the acceptor substrate opens new perspectives for the design of inhibitors with an original mode of action that could act alone or in synergy with β‐lactams.     

Analysis of protein crystallographic structural data: analysis of the orientation of peptide planes

A new dihedral angle parameter θ′, defined by C_i?1|N_i…C_i|N_i+1, involving pairs of backbone atoms in two adjacent peptide planes is used in this paper to analyse the relative orientation of the peptide planes in a protein chain. The equiangle contours for this parameter on the ?+ψ in an approximately linear way. Thus, θ′ serves as a good single parameter representation for chainfolding characterization by bringing out the relative orientation of successive peptide planes. Unlike the earlier proposed θ which gives the gross folding features, θ′ can be applied for nonregular helical features. Its utility in the detection of bend regions in protein chains is compared with that of θ through theoretically calculated tables as well as examples from actual proteins.     

The effect of the cosolvent trifluoroethanol on a tryptophan side chain orientation in the hydrophobic core of troponin C

The unique biophysical properties of tryptophan residues have been exploited for decades to monitor protein structure and dynamics using a variety of spectroscopic techniques, such as fluorescence and nuclear magnetic resonance (NMR). We recently designed a tryptophan mutant in the regulatory N‐domain of cardiac troponin C (F77W‐cNTnC) to study the domain orientation of troponin C in muscle fibers using solid‐state NMR. In our previous study, we determined the NMR structure of calcium‐saturated mutant F77W‐V82A‐cNTnC in the presence of 19% 2,2,2‐trifluoroethanol (TFE). TFE is a widely used cosolvent in the biophysical characterization of the solution structures of peptides and proteins. It is generally assumed that the structures are unchanged in the presence of cosolvents at relatively low concentrations, and this has been verified for TFE at the level of the overall secondary and tertiary structure for several calcium regulatory proteins. Here, we present the NMR solution structure of the calcium saturated F77W‐cNTnC in presence of its biological binding partner troponin I peptide (cTnI_144–163) and in the absence of TFE. We have also characterized a panel of six F77W‐cNTnC structures in the presence and absence TFE, cTnI_144–163, and the extra mutation V82A, and used ¹⁹F NMR to characterize the effect of TFE on the F77(5fW) analog. Our results show that although TFE did not perturb the overall protein structure, TFE did induce a change in the orientation of the indole ring of the buried tryptophan side chain from the anticipated position based upon homology with other proteins, highlighting the potential dangers of the use of cosolvents.     

Helix formation in model peptides based on nucleolin TPAKK motifs

The structures formed by peptide models of the N-terminal domain of the nucleolar protein nucleolin were studied by CD and nmr. The sequences of the peptides are based on the putative nucleic acid binding sequence motif TPAKK: The peptides TP1 and TP2 have the sequence acetyl-G(ATPAKKAA)_nG-amide, with n = 1 and 2, respectively. CD measurements indicate structural changes in both peptides when the lysine side chains are uncharged by increasing the pH or acetylation of the side-chain amines. When trifluoroethanol (TFE) is added, more extensive structural changes are observed, resembling helical structure based on nmr nuclear Overhauser effect (NOE) and C^α proton chemical shift changes, and CD spectra. The structure formed in 0.5M NaClO₄ as observed by nmr is similar to that when the lysine side chains are acetylated, due presumably to interactions of perchlorate ion with side-chain charges on lysines. The helical structure observed in TPAKK motifs may be stabilized via N-capping interactions involving threonine. The structures observed in TFE suggest that the Thr-Pro sequence initiates short helical segments in TPAKK motifs, and these helical structures might interact with nucleic acids, presumably via interactions between lysines and threonines of nucleolin. © 1995 John Wiley & Sons, Inc.     

Transformation of the ϕ-ψ plot for proteins to a new representation with local helicity and peptide torsional angles as variables

A new representation of protein structure is obtained by the angular coordinate transformations η_i = (?_i+1?ψ_i)/2 and ξ_i = ?_i+1+ψ_i with careful mathematical attention to the cyclical boundary conditions of all of the variables involved. From published ?-ψ data it is possible to obtain a new η-ξ plot. As the angle ξ_i is varied from – 180° through 0° to + 180° in this plot, the local helicity of the polypeptide chain changes continuously and contiguously without sudden reversals in handedness. The variable, η_i, gives the torsional position of the ith peptide group. Some peptide groups in proteins, such as the second peptide residue in a type II β-turn, are nonhydrogen-bonded and can undergo considerable torsional oscillation. In such cases the η angle should be represented by a line whose length reflects the allowed dynamical variations in the peptide torsional position. Certain peptide residues in proteins may be able to undergo a complete torsional rotation of 360°. Such residues would be represented on the η-ξ plot as a straight line across the plot parallel to the abscissa. Other examples of the possible usefulness of this plot are also given.     

On 3LEZ,a Deep‐Sea Halophilic Protein with in vitro Class‐A β‐Lactamase Activity: Molecular‐Dynamics,Docking, and Reactivity Simulations

This work shows that a deep‐sea protein, 3LEZ, with known in vitro β‐lactamase activity, proved stable, substantially in the conformation detected by X‐ray diffraction of the crystal, when subjected to molecular‐dynamics (MD) simulations under conditions compatible with shallow seas. Docking simulations showed that the β‐lactamase active site S85 of 3LEZ (S70 in Ambler numbering) is the preferential binding pocket for not only β‐lactam antibiotics and inhibitors, but, surprisingly, also for a wide variety of other biologically active compounds in various chemical classes, including marine metabolites. In line with the in vitro β‐lactamase activity, a) affinities on docking β‐lactam antibiotics and inhibitors onto 3LEZ were found to roughly parallel published K_m and K_i values, obtained from Michaelis? Menten kinetics under room conditions, and b) DFT calculations agreed with experiments that the irreversible reaction of the β‐lactamase inhibitor clavulanic acid with the whole S85 catalytic center of 3LEZ is spontaneous. These observations must be viewed in the light that a) the compounds in other chemical classes showed comparable affinities, and, in some cases, even higher than β‐lactams, for the S85 active site, b) K_m and K_i data are not available at the high hydrostatic pressure of the deep sea, where 3LEZ is believed to have evolved, c) an inverse order of affinities for the β‐lactams, with respect to both experimentation and simulations at room conditions, was observed from comparative docking simulations with 3LEZ derived from MD under high hydrostatic pressure. Although MD requires a general assessment for high hydrostatic pressure before c) above is given the same weight as all other observations, this work questions the conclusion that the in vitro determined β‐lactamase activity represents the ecological role of 3LEZ.     

Conformational Analysis of the β-amyloid Peptide Fragment, β(12–28)

Abstract

NMR and CD spectroscopy have been used to examine the conformation of the peptide, β(12–28), (VHHQKLVFFAEDVGSNK) in aqueous and 60% TFE/40% H₂0 solution at pH 2.4. In 60% TFE solution, the peptide is helical as confirmed by the CD spectrum and by the pattern of the NOE cross peaks detected in the NOESY spectrum of the peptide. In aqueous solution, the peptide adopts a more extended and flexible conformation. Broadening of resonances at low temperature, temperature-dependent changes in the chemical shifts of several of the CH_α resonances and the observation of a number of NOE contacts between the hydrophobic side-chain protons of the peptide are indicative of aggregation in aqueous solution. The behavior of β(12–28) in 60% TFE and in aqueous solution are consistent with the overall conformation and aggregation behavior reported for the larger peptide fragment, β(1–28) and the parent β-amyloid peptide.     

Main-chain Dynamics of a Partially Folded Protein:15N NMR Relaxation Measurements of Hen Egg White Lysozyme Denatured in Trifluoroethanol

¹⁵N NMR relaxation measurements have been used to study the dynamic behaviour of the main-chain of hen lysozyme in a partially folded state, formed in a 70% (v/v) trifluoroethanol (TFE)/30% water mixture at 37°C and pH 2. This state is characterised by helical secondary structure in the absence of extensive tertiary interactions. The NMR relaxation data were interpreted by mapping of spectral density functions and by derivation of segmental as well as global order parameters. The results imply that the dynamics of lysozyme in TFE can, at least for the great majority of residues, be adequately described by internal motions which are superimposed on an overall isotropic tumbling of the molecule. Although the dynamic behaviour shows substantial variations along the polypeptide chain, it correlates well with the conformational preferences identified in the TFE state by other NMR parameters. Segments of the polypeptide chain which are part of persistent helical structures are highly restricted in their motion (S²> 0.8, with effective internal correlation times τ_e< 200 ps) but are also found to experience conformational exchange on a millisecond timescale. Regions which are stabilised in less persistent helical structure possess greater flexibility (0.6 <S²< 0.8, 200 ps < τ_e< 1 ns) and those which lack defined conformational preferences are highly flexible (S²< 0.6, τ_e∼1 ns). The dynamic behaviour of the main-chain was found to be correlated with other local features of the polypeptide chain, including hydrophobicity and the position of the disulphide bridges. Despite the absence of extensive tertiary interactions, preferential stabilisation of native-like secondary structure by TFE results in a pattern of main-chain dynamics which is similar to that of the native state.     

β-Alanine containing cyclic peptides with turned structure: The “pseudo type II β-turn.” VI

In the present paper we describe the synthesis, purification, single crystal x-ray analysis, and nmr solution characterization, combined with restrained molecular dynamic simulations, of the cyclic hexapeptide cyclo-(L -Pro-L -Phe-β-Ala)₂. The peptide was synthesized by classical solution methods and the cyclization of the free hexapeptide was accomplished in good yields in diluted methylene chloride solution using N,N-dicyclohexyl-carbodiimide. The compound crystallizes in the monoclinic space group P2₁ from methanol-dichloro-methane solution. The two identical halves of the molecule adopt in the solid state two different conformations. One β-Ala-L -Pro peptide bond is trans, while the second is cis. The molecule is present in dimethylsulfoxide d₆ solutions as a mixture of conformational families. One of these corresponds to a C₂ symmetrical molecule with both β-Ala-Pro cis peptide bonds, while the second major conformation is very similar to that observed in the solid state. All Pro-Phe segments, both in the solid state and the symmetrical and unsym-metrical solution conformations, display ?,ψ angles close to that of position i + 1 and i + 2 of type II β-turns. In addition, the segments preceeded by a trans β-Ala-Pro peptide bond are characterized by a typical i ← i + 3 hydrogen bond, which is absent in the conformer containing a cis β-Ala-Pro peptide bond. The latter conformation corresponds to a new structural domain we define as the “pseudo type II β-turn.” © 1994 John Wiley & Sons, Inc.     

α,β-Dehydro-amino acid residues in the design of peptide structures: Synthesis,crystal structure,and molecular conformation of two homologous peptides—N-Ac-Dehydro-Phe-L-Leu-OCH3 and N-Ac-Dehydro-Phe-NorVal-OCH3

The dehydro-residue containing peptides N-Ac-dehydro-Phe-L -Leu-OCH₃ ( I ) and N-Ac-dehydro-Phe-NorVal-OCH₃ ( II ) were synthesized by the usual workup procedures. The peptides crystallize from their solutions in methanol in space group P6₅: ( I ) a = b = 12.528(2) Å, c = 21.653(5) Å; ( II ) a = b = 12.532(2) Å, c = 21.695(4) Å. The structures were determined by direct methods. Both peptides adopt similar conformations with ?,ψ of dehydro-Phe as follows: ( I ) ?57.0(5)° and ?37.0(5)°; ( II ) ?56.0(5),° and ?37.5(5)°. The observed data on dehydro-Phe when placed at the (i + 1) position show that the ?,ψ values of dehydro-Phe are either ?60°, 140° or ?60°, ?30°. The conformation of ?60°, 140° can be accommodated only with a flexible residue at the (i + 2) position while the ?,ψ values of ?60°, ?30° are obtained with a bulky residue at the (i + 2) position as in the present structures. The molecules are packed in a helical way along the c axis. These are held by two strong intermolecular hydrogen bonds involving both NH as donors and acetyl group and dehydro-Phe oxygen atoms as acceptors. © 1994 John Wiley & Sons, Inc.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

Design of Peptides Using α,β-Dehydro-residues: Synthesis,Crystal Structure and Molecular Conformation of N-Boc-L-Val-ΔPhe–ΔPhe-L-Ala-OCH3

To obtain general rules of peptide design using α,β-dehydro-residues, a sequence with two consecutive ΔPhe-residues, Boc-L -Val-ΔPhe–ΔPhe- L -Ala-OCH₃, was synthesized by azlactone method in solution phase. The peptide was crystallized from its solution in an acetone/water mixture (70:30) in space group P6₁ with a=b=14.912(3) Å, c= 25.548(5) Å, V=4912.0(6) ų. The structure was determined by direct methods and refined by a full matrix least-squares procedure to an R value of 0.079 for 2891 observed [I?3σ(I)] reflections. The backbone torsion angles ?₁=?54(1)°, ψ₁= 129(1)°, ω₁=?177(1)°, ?₂ =57(1)°, ψ₂=15(1)°, ω₂ =?170(1)°, ?₃=80(1)°, ψ₃ =7(2)°, ω₃=?177(1)°, ?₄ =?108(1)° and ψ^T₄=?34 (1)° suggest that the peptide adopts a folded conformation with two overlapping β-turns of types II and III′. These turns are stabilized by two intramolecular hydrogen bonds between the CO of the Boc group and the NH of ΔPhe³ and the CO of Val¹ and the NH of Ala⁴. The torsion angles of ΔPhe² and ΔPhe³ side chains are similar and indicate that the two ΔPhe residues are essentially planar. The folded molecules form head-to- tail intermolecular hydrogen bonds giving rise to continuous helical columns which run parallel to the c-axis. This structure established the formation of two β-turns of types II and III′ respectively for sequences containing two consecutive ΔPhe residues at (i+2) and (i+3) positions with a branched β-carbon residue at one end of the tetrapeptide.     

A method for determining the crystal orientation for any tilt position when using a transmission electron microscope double-tilt specimen holder

A method is described in this short communiction which provides a rapid and precise determination of the crystal specimen orientation in any tilt position when using a doule-tilt holder in the transmission electron microscope (TEM). It is necessary to establish three pairs of tilt angles (α_i, β_i) (i = 1, 2, 3) where three recognized directions of the crystal specimen are aligned to the electron beam direction respectively, in order to determine the crystal specimen orientation for any tilt position in a double-tilt specimen holder. In addition, the tilt position (α, β), where any orientation [ u v w] is aligned to the beam direction, can be determined with the aid of this method.A software system for computer applications of the above method has beed developed.