Signal set design for full-diversity low-decoding-complexity differential scaled-unitary STBCs

The problem of designing high rate, full diversity noncoherent space-time block codes (STBCs) with low encoding and decoding complexity is addressed. First, the notion of g-group encodable and g-group decodable linear STBCs is introduced. Then for a known class of rate-1 linear designs, an explicit construction of fully-diverse signal sets that lead to four-group encodable and four-group decodable differential scaled unitary STBCs for any power of two number of antennas is provided. Previous works on differential STBCs either sacrifice decoding complexity for higher rate or sacrifice rate for lower decoding complexity.

Tuning the beta-turn segment in designed peptide beta-hairpins: Construction of a stable type I ' beta-turn nucleus and hairpin-helix transition promoting segments

Designed octapeptides Boc-Leu-Val-Val-Aib-(D)Xxx-Leu- Val-Val-OMe ((D)Xxx = (D)Ala, 3a; (D)Val, 3c and (D)Pro, 5a) and Boc-Leu-Phe-Val-Aib-DAla-Leu-Phe-Val-OMe (3b) have been investigated to construct models of a stable type I' beta-turn nucleated hairpin and to generate systems for investigating helix-hairpin conformational transitions. Peptide 5a, which contains a central Aib-(D)Pro segment, is shown to adopt a stable type I' beta-turn nucleated hairpin structure, stabilized by four cross-strand hydrogen bonds. The stability of the structure in diverse solvents is established by the observation of all diagnostic NOEs expected in a beta-hairpin conformation. Replacement of (D)Pro5 by (D)Ala/(D)Val (3a-c) results in sequences that form beta-hairpins in hydrogen bonding solvents like CD3OH and DMSO-d(6). However, in CDCl3 evidence for population of helical conformations is obtained. Peptide 6b (Boc-Leu-Phe-Val-Aib-Aib-Leu-Phe-Val-OMe), which contains a centrally positioned Aib-Aib segment, provides a clear example of a system, which exhibits a helical conformation in CDCl3 and a significant population of both helices and hairpins in CD3OH and DMSO-d(6). The coexistence of multiple conformations is established by the simultaneous observation of diagnostic NOEs. Control over stereochemistry of the central beta-turn permits generation of models for robust beta-hairpins and also for the construction of systems that may be used to probe helix-hairpin conformational transitions. (c) 2006 Wiley Periodicals, Inc.

Disulfide conformation and design at helix N-termini

To understand structural and thermodynamic features of disulfides within an alpha-helix, a non-redundant dataset comprising of 5025 polypeptide chains containing 2311 disulfides was examined. Thirty-five examples were found of intrahelical disulfides involving a CXXC motif between the N-Cap and third helical positions. GLY and PRO were the most common amino acids at positions 1 and 2, respectively. The N-Cap residue for disulfide bonded CXXC motifs had average values of (-112 +/- 25.2 degrees, 106 +/- 25.4 degrees). To further explore conformational requirements for intrahelical disulfides, CYS pairs were introduced at positions N-Cap-3; 1,4; 7,10 in two helices of an Escherichia coli thioredoxin mutant lacking its active site disulfide (nSS Trx). In both helices, disulfides formed spontaneously during purification only at positions N-Cap-3. Mutant stabilities were characterized by chemical denaturation studies (in both oxidized and reduced states) and differential scanning calorimetry (oxidized state only). All oxidized as well as reduced mutants were destabilized relative to nSS Trx. All mutants were redox active, but showed decreased activity relative to wild-type thioredoxin. Such engineered disulfides can be used to probe helix start sites in proteins of unknown structure and to introduce redox activity into proteins. Conversely, a protein with CYS residues at positions N-Cap and 3 of an alpha-helix is likely to have redox activity.

Stereochemistry of peptides containing 1-aminocycloheptane-1-carboxylic acid (Ac7c)

The crystal structures of four peptides incorporating 1-aminocycloheptane-1-carboxylic acid (Ac7c) are described. Boc-Aib-Ac7c-NHMe and Boc-Pro-Ac7c-Ala-OMe adopt beta-turn conformations stabilized by an intramolecular 4----1 hydrogen bond, the former folding into a type-I/III beta-turn and the latter into a type-II beta-turn. In the dipeptide esters, Boc-Aib-Ac7c-OMe and Boc-Pro-Ac7c-OMe, the Ac7c and Aib residues adopt helical conformations, while the Pro residue remains semi-extended in both the molecules of Boc-Pro-Ac7c-OMe found in the asymmetric unit. The cycloheptane ring of Ac7c residues adopts a twist-chair conformation in all the peptides studied. 1H-NMR studies in CDCl3 and (CD3)2SO and IR studies in CDCl3 suggest that Boc-Aib-Ac7c-NHMe and Boc-Pro-Ac7c-Ala-OMe maintain the beta-turn conformations in solution.

A rate-one full-diversity low-complexity space-time-frequency block code (STFBC) for 4-Tx MIMO-OFDM

It is known that by employing space-time-frequency codes (STFCs) to frequency selective MIMO-OFDM systems, all the three diversity viz spatial, temporal and multipath can be exploited. There exists space-time-frequency block codes (STFBCs) designed using orthogonal designs with constellation precoder to get full diversity (Z.Liu, Y.Xin and G.Giannakis IEEE Trans. Signal Processing, Oct. 2002). Since orthogonal designs of rate one exists only for two transmit antennas, for more than two transmit antennas STFBCs of rate-one and full-diversity cannot be constructed using orthogonal designs. This paper presents a STFBC scheme of rate one for four transmit antennas designed using quasi-orthogonal designs along with co-ordinate interleaved orthogonal designs (Zafar Ali Khan and B. Sundar Rajan Proc: ISIT 2002). Conditions on the signal sets that give full-diversity are identified. Simulation results are presented to show the superiority of our codes over the existing ones.

A systematic design of high-rate full-diversity space-frequency codes for MIMO-OFDM systems

This paper presents a systematic construction of high-rate and full-diversity space-frequency block codes for MIMO-OFDM systems. While all prior constructions offer only a maximum rate of one complex symbol per channel use, our construction yields rate equal to the number of transmit antennas and simultaneously achieves full-diversity. The proposed construction works for arbitrary number of transmit antennas and arbitrary channel power delay profile. A key step in this construction is the generalization of the stacked matrix code design criteria given by Bolcskei et.al., (IEEE WCNC 2000). Explicit equivalence of our generalized code design criteria with the Hadamard-product based criteria of W. Su et.al., (lEEE Trans. Sig. Proc. Nov 2003) is established and new high-rate codes are constructed using our criteria.

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n(t) denote the number of transmit antennas and T the block interval. For any n(t) <= T, a unified construction of (n(t) x T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2(K)-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the S-ary case corresponding to constellations of size S-K. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

BER analysis of space-time block codes from generalized complex orthogonal designs for M-PSK

In this paper, we present an analysis for the bit error rate (BER) performance of space-time block codes (STBC) from generalized complex orthogonal designs for M-PSK modulation. In STBCs from complex orthogonal designs (COD), the norms of the column vectors are the same (e.g., Alamouti code). However, in generalized COD (GCOD), the norms of the column vectors may not necessarily be the same (e.g., the rate-3/5 and rate-7/11 codes by Su and Xia in [1]). STBCs from GCOD are of interest because of the high rates that they can achieve (in [2], it has been shown that the maximum achievable rate for STBCs from GCOD is bounded by 4/5). While the BER performance of STBCs: from COD (e.g., Alamouti code) can be simply obtained from existing analytical expressions for receive diversity with the same diversity order by appropriately scaling the SNR, this can not be done for STBCs from GCOD (because of the unequal norms of the column vectors). Our contribution in this paper is that we derive analytical expressions for the BER performance of any STBC from GCOD. Our BER analysis for the GCOD captures the performance of STBCs from COD as special cases. We validate our results with two STBCs from GCOD reported by Su and Xia in [1], for 5 and 6 transmit antennas (G(5) and G(6) in [1]) with rates 7/11 and 3/5, respectively.

Monoclinic polymorph of Boc-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe(anhydrous). Parallel packing of 3(10)-/alpha-helices and a transition of helix type

The structures of two crystal forms of Boc-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe have been determined. The triclinic form (P1, Z = 1) from DMSO/H2O crystallizes as a dihydrate (Karle, Sukumar & Balaram (1986) Proc, Natl, Acad. Sci. USA 83, 9284-9288). The monoclinic form (P2(1), Z = 2) crystallized from dioxane is anhydrous. The conformation of the peptide is essentially the same in both crystal system, but small changes in conformational angles are associated with a shift of the helix from a predominantly alpha-type to a predominantly 3(10)-type. The r.m.s. deviation of 33 atoms in the backbone and C beta positions of residues 2-8 is only 0.29 A between molecules in the two polymorphs. In both space groups, the helical molecules pack in a parallel fashion, rather than antiparallel. The only intermolecular hydrogen bonding is head-to-tail between helices. There are no lateral hydrogen bonds. In the P2(1) cell, a = 9.422(2) A, b = 36.392(11) A, c = 10.548(2) A, beta = 111.31(2) degrees and V = 3369.3 A for 2 molecules of C60H97N11O13 per cell.

Parallel and antiparallel aggregation of alpha-helices. Crystal structures of two apolar decapeptides X-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe (X = Boc, Ac)

An apolar helical decapeptide with different end groups, Boc- or Ac-, crystallizes in a completely parallel fashion for the Boc-analog and in an antiparallel fashion for the Ac-analog. In both crystals, the packing motif consists of rows of parallel molecules. In the Boc-crystals, adjacent rows assemble with the helix axes pointed in the same direction. In the Ac-crystals, adjacent rows assemble with the helix axes pointed in opposite directions. The conformations of the molecules in both crystals are quite similar, predominantly alpha-helical, except for the tryptophanyl side chain where chi 1 congruent to 60 degrees in the Boc- analog and congruent to 180 degrees in the Ac-analog. As a result, there is one lateral hydrogen bond between helices, N(1 epsilon)...O(7), in the Ac-analog. The structures do not provide a ready rationalization of packing preference in terms of side-chain interactions and do not support a major role for helix dipole interactions in determining helix orientation in crystals. The crystal parameters are as follow. Boc-analog: C60H97N11O13.C3H7OH, space group Pl with a = 10.250(3) A, b = 12.451(4) A, c = 15.077(6) A, alpha = 96.55(3) degrees, beta = 92.31(3) degrees, gamma = 106.37(3) degrees, Z = 1, R = 5.5% for 5581 data ([F] greater than 3.0 sigma(F)), resolution 0.89 A. Ac-analog: C57H91N11O12, space group P2(1) with a = 9.965(1) A, b = 19.707(3) A, c = 16.648(3) A, beta = 94.08(1), Z = 2, R = 7.2% for 2530 data ([F] greater than 3.0 sigma(F)), resolution 1.00 A.

Stereochemistry of peptides containing 1-aminocycloheptane-1-carboxylic acid (Ac-c)

The crystal structures of four peptides incorporating 1-aminocycloheptane-1-carboxylic acid (Ac7c) are described. Boc-Aib-Ac7c-NHMe and Boc-Pro-Ac7c-Ala-OMe adopt beta-turn conformations stabilized by an intramolecular 4----1 hydrogen bond, the former folding into a type-I/III beta-turn and the latter into a type-II beta-turn. In the dipeptide esters, Boc-Aib-Ac7c-OMe and Boc-Pro-Ac7c-OMe, the Ac7c and Aib residues adopt helical conformations, while the Pro residue remains semi-extended in both the molecules of Boc-Pro-Ac7c-OMe found in the asymmetric unit. The cycloheptane ring of Ac7c residues adopts a twist-chair conformation in all the peptides studied. 1H-NMR studies in CDCl3 and (CD3)2SO and IR studies in CDCl3 suggest that Boc-Aib-Ac7c-NHMe and Boc-Pro-Ac7c-Ala-OMe maintain the beta-turn conformations in solution.

Zervamicins, a structurally characterised peptide model for membrane ion channels

Voltage dependent membrane channels are formed by the zervamicins, a group of α-aminoisobutyric acid containing peptides. The role of polar residues like Thr, Gln and Hyp in promoting helical bundle formation is established by dramatically reduced channel lifetimes for a synthetic apolar analog. Crystal structures of Leu1-zervamicin reveal association of bent helices. Polar contacts between convex faces result in an ‘hour glass’ like arrangement of an aqueous channel with a central constriction. The structure suggests that gating mechanisms may involve movement of the Gln11 carboxamide group. Gln3 may play a role in modulating the size of the channel mouth.

Ion channel formation by zervamicin-IIB. A molecular modelling study.

Zervamicin-IIB (Zrv-IIB) is a 16 residue peptaibol which forms voltage-activated, multiple conductance level channels in planar lipid bilayers. A molecular model of Zrv-IIB channels is presented. The structure of monomeric Zrv-IIB is based upon the crystal structure of Zervamicin-Leu. The helical backbone is kinked by a hydroxyproline residue at position 10. Zrv-IIB channels are modelled as helix bundles of from 4 to 8 parallel helices surrounding a central pore. The monomers are packed with their C-terminal helical segments in close contact, and the bundles are stabilized by hydrogen bonds between glutamine 11 and hydroxyproline 10 of adjacent helices. Interaction energy profiles for movement of three different probes species (K+, Cl- and water) through the central pore are analyzed. The conformations of: (a) the sidechain of glutamine 3; (b) the hydroxyl group of hydroxyproline 10; and (c) the C-terminal hydroxyl group are "optimized" in order to maximize favourable interactions between the channel and the probes, resulting in favourable interaction energy profiles for all three. This suggests that conformational flexibility of polar sidechains enables the channel lining to mimic an aqueous environment.

Peptide mimics for structural features in proteins. Crystal structures of three heptapeptide helices with a C-terminal 6-->1 hydrogen bond.

The crystal structure determination of three heptapeptides containing alpha-aminoisobutyryl (Aib) residues as a means of helix stabilization provides a high-resolution characterization of 6-->1 hydrogen-bonded conformations, reminiscent of helix-terminating structural features in proteins. The crystal parameters for the three peptides, Boc-Val-Aib-X-Aib-Ala-Aib-Y-OMe, where X and Y are Phe, Leu (I), Leu, Phe (II) and Leu, Leu (III) are: (I) space group P1, Z = 1, a = 9.903 A, b = 10.709 A, c = 11.969 A, alpha = 102.94 degrees, beta = 103.41 degrees, gamma = 92.72 degrees, R = 4.55%; (II) space group P21, Z = 2, a = 10.052 A, b = 17.653 A, c = 13.510 A, beta = 108.45 degrees, R = 4.49%; (III) space group P1, Z = 2 (two independent molecules IIIa and IIIb in the asymmetric unit), a = 10.833 A, b = 13.850 A, c = 16.928 A, alpha = 99.77 degrees, beta = 105.90 degrees, gamma = 90.64 degrees, R = 8.54%. In all cases the helices form 3(10)/alpha-helical (or 3(10)helical) structures, with helical columns formed by head-to-tail hydrogen bonding. The helices assemble in an all-parallel motif in crystals I and III and in an antiparallel motif in II. In the four crystallographically characterized molecules, I, II, IIIa and IIIb, Aib(6) adopts a left-handed helical (hL) conformation with positive phi, psi values, resulting in 6-->1 hydrogen-bond formation between Aib(2) CO and Leu(7)/Phe(7) NH groups. In addition a 4-->1 hydrogen bond is seen between Aib(3) CO and Aib(6) NH groups. This pattern of hydrogen bonding is often observed at the C-terminus of helices proteins, with the terminal pi-type turn being formed by four residues adopting the hRhRhRhL conformation.

Conformational characteristics of asparaginyl residues in proteins

Backbone conformations at 1064 asparaginyl residues in 123 non-homologous, high-resolution X-ray structures of proteins were analysed. Asn adopts conformations in left-handed x-helical region and other partially allowed regions in the Ramachandran map more readily than any other non-glycyl residue. Asn conformational clusters in the (phi,psi) regions of left-handed alpha-helix, right-handed alpha-helix and extended (beta) strands were investigated in detail for their occurrence in various secondary structures, especially in beta-turn regions. Preferences were observed for Asn conformations in different positions in various beta-turn types, including the first and fourth positions of the turn. Asparaginyl residues with extended conformations are found to occur frequently in irregular regions, although they are expected to occur predominantly in extended strands or in the third position of type II beta-turns. Asn conformations at the N-cap positions of helices strongly prefer extended conformation than alpha(L), which seems to be characteristic of non-glycyl residues at that position. In the linkers connecting two extended strands and those connecting an alpha-helix and an extended strand, Asn with alpha(L) or alpha(R) conformation is more favoured than Asn with the beta-conformation. Analysis of Asn-Asn doublets and Asn-X-Asn triplets permitted identification of conformational families in such sequences. Results of this investigation provide useful hints in modelling Asn-rich regions in proteins such as malaria parasite coat protein. (C) Munksgaard 1994.