Conformational flexibility of DNA: polymorphism and handedness

It is shown that left-handed duplexes are possible for A, B, and D forms of DNA. These duplexes are stereochemically satisfactory and are consistent with the observed x-ray intensity data. On scrutiny the refined right-handed models of B and D DNA by Arnott and coworkers are found to be stereochemically unacceptable. It was possible to formulate a stereochemical guideline for molecular model building based on theory and analysis of single-crystal structure data of dinucleoside monophosphate and higher oligomers. This led to both right- and left-handed DNA duplexes. The right-handed B and D DNA duplexes so obtained are stereochemically superior to earlier models and agree well with the observed x-ray intensity data. The observation that DNA can exist in either handedness for all the polymorphous forms of DNA at once explained A in equilibrium B and B in equilibrium D transitions. Hence it is confirmed that polymorphism of DNA is a reflection on the conformational flexibility inherent in DNA, the same cause that ultimately allows DNA in either handedness. The possibility of various types of right- and left-handed duplexes generated by using dinucleoside monophosphate and trinucleoside diphosphate as repeating units resulted in a variety of models, called RL models. All these models have alternating right and left helical segments and inverted stacking at the bend region as suggested by us earlier. It turns out that the B-Z DNA model of Wang et al. is only an example of RL models.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

Proline-containing β-turns in peptides and proteins: Analysis of structural data on globular proteins

Tetrapeptide sequences of the type Z-Pro-Y-X were obtained from the crystal structure data on 34 globular proteins, and used in an analysis of the positional preferences of the individual amino acid residues in the β-turn conformation. The effect of fixing proline as the second position residue in the tetrapeptide sequence was studied by comparing the data obtained on the positional preferences with the corresponding data obtained by Chou and Fasman using the Z-R-Y-X sequence, where no particular residue was fixed in any of the four positions. While, in general, several amino acid residues having relatively very high or very low preferences for specific positions were found to be common to both the Z-Pro-Y-X and Z-R-Y-X sequences, many significant differences were found between the two sets of data, which are to be attributed to specific interactions arising from the presence of the proline residue.

Polymorphism and conformational flexibility of DNA: right and left handed duplexes

Left handed duplexes are shown to be in agreement with the X-ray intensity data of A-, B- and D-forms of DNA. The structures are stereochemically satisfactory because they were obtained following a stereochemical guideline derived from theory and single crystal structure data of nucleic acid components. The same stereochemical guideline also led to right handed duplexes for B- and D-forms of DNA which have stereochemically preferred conformation and hence are superior to those given by Arnott and coworkers.

Sequence-dependent molecular conformation of polynucleotides: right and left-handed helices

Based upon a stereochemical guideline, two topologically distinct types of helicalduplexes have been deduced for a polynucleotide duplex with alternating purine pyrimidine sequence (PAPP): (a) right-handed uniform (RU) helix and (b) left-handed zig-zag (LZ) helix. Both structures have trinucleoside diphosphate as the basic unit wherein the purine pyrimidine fragment has a different conformation from the pyrimidine-purine fragment. Thus, RU and LZ helices represent two different classes of sequence-dependent molecular conformations for PAPP. The conformationalf eatures of an RU helix of PAPP in B-form and three LZ-helices for B-, D- and Z-forms are discussed.

Pi-turns in proteins and peptides: Classification, conformation, occurrence, hydration and sequence.

The i + 5-->i hydrogen bonded turn conformation (pi-turn) with the fifth residue adopting alpha L conformation is frequently found at the C-terminus of helices in proteins and hence is speculated to be a "helix termination signal." An analysis of the occurrence of i + 5-->i hydrogen bonded turn conformation at any general position in proteins (not specifically at the helix C-terminus), using coordinates of 228 protein crystal structures determined by X-ray crystallography to better than 2.5 A resolution is reported in this paper. Of 486 detected pi-turn conformations, 367 have the (i + 4)th residue in alpha L conformation, generally occurring at the C-terminus of alpha-helices, consistent with previous observations. However, a significant number (111) of pi-turn conformations occur with (i + 4)th residue in alpha R conformation also, generally occurring in alpha-helices as distortions either at the terminii or at the middle, a novel finding. These two sets of pi-turn conformations are referred to by the names pi alpha L and pi alpha R-turns, respectively, depending upon whether the (i + 4)th residue adopts alpha L or alpha R conformations. Four pi-turns, named pi alpha L'-turns, were noticed to be mirror images of pi alpha L-turns, and four more pi-turns, which have the (i + 4)th residue in beta conformation and denoted as pi beta-turns, occur as a part of hairpin bend connecting twisted beta-strands. Consecutive pi-turns occur, but only with pi alpha R-turns. The preference for amino acid residues is different in pi alpha L and pi alpha R-turns. However, both show a preference for Pro after the C-termini. Hydrophilic residues are preferred at positions i + 1, i + 2, and i + 3 of pi alpha L-turns, whereas positions i and i + 5 prefer hydrophobic residues. Residue i + 4 in pi alpha L-turns is mainly Gly and less often Asn. Although pi alpha R-turns generally occur as distortions in helices, their amino acid preference is different from that of helices. Poor helix formers, such as His, Tyr, and Asn, also were found to be preferred for pi alpha R-turns, whereas good helix former Ala is not preferred. pi-Turns in peptides provide a picture of the pi-turn at atomic resolution. Only nine peptide-based pi-turns are reported so far, and all of them belong to pi alpha L-turn type with an achiral residue in position i + 4. The results are of importance for structure prediction, modeling, and de novo design of proteins.

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

Expanding the Peptide beta-Turn in alpha gamma Hybrid Sequences: 12 Atom Hydrogen Bonded Helical and Hairpin Turns

Hybrid peptide segments containing contiguous alpha and gamma amino acid residues can form C-12 hydrogen bonded turns which may be considered as backbone expanded analogues of C-10 beta-turns) found in alpha alpha segments. Exploration of the regular hydrogen bonded conformations accessible for hybrid alpha gamma sequences is facilitated by the use of a stereochemically constrained gamma amino acid residue gabapentin (1-aminomethylcyclohexaneacetic acid, Gpn), in which the two torsion angles about C-gamma-C-beta (theta(1)) and C-beta-C-alpha (theta(2)) are predominantly restricted to gauche conformations. The crystal structures of the octapeptides Boc-Gpn-Aib-Gpn-Aib-Gpn-Aib-Gpn-Aib-OMe (1) and Boc-Leu-Phe-Val-Aib-Gpn-Leu-Phe-Val-OMe (2) reveal two distinct conformations for the Aib-Gpn segment. Peptide 1 forms a continuous helix over the Aib(2)-Aib(6) segment, while the peptide 2 forms beta-hairpin structure stabilized by four cross-strand hydrogen bonds with the Aib-Gpn segment forming a nonhelical C-12 turn. The robustness of the helix in peptide 1 in solution is demonstrated by NMR methods. Peptide 2 is conformationally fragile in solution with evidence of beta-hairpin conformations being obtained in methanol. Theoretical calculations permit delineation of the various C-12 hydrogen bonded structures which are energetically feasible in alpha gamma and gamma alpha sequences.

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.

A one point shock capturing kinetic scheme for hyperbolic conservation laws

We have presented a new low dissipative kinetic scheme based on a modified Courant Splitting of the molecular velocity through a parameter φ. Conditions for the split fluxes derived based on equilibrium determine φ for a one point shock. It turns out that φ is a function of the Left and Right states to the shock and that these states should satisfy the Rankine-Hugoniot Jump condition. Hence φ is utilized in regions where the gradients are sufficiently high, and is switched to unity in smooth regions. Numerical results confirm a discrete shock structure with a single interior point when the shock is aligned with the grid.

A hitchhiker's guide to a crowded syconium: how do fig nematodes find the right ride?

P>1Organisms with low mobility, living within ephemeral environments,need to find vehicles that can disperse them reliably to new environments. The requirement for specificity in this passenger-vehicle relationship is enhanced within a tritrophic interaction when the environment of passenger and vehicle is provided by a third organism. Such relationships pose many interesting questions about specificity within a tritrophic framework. 2. Central to understanding how these tritrophic systems have evolved, is knowing how they function now. Determining the proximal cues and sensory modalities used by passengers to find vehicles and to discriminate between reliable and non-reliable vehicles is, therefore, essential to this investigation. 3. The ancient, co-evolved and highly species-specific nursery pollination mutualism between figs and fig wasps is host to species-specific plant-parasitic nematodes which use fig wasps to travel between figs. Since individual globular fig inflorescences, i.e. syconia, serve as incubators for hundreds of developing pollinating and parasitic wasps, a dispersal-stage nematode within such a chemically,complex and physically crowded environment is faced with the dilemma of choosing the right vehicle for dispersal into a new fig. Such a system therefore affords excellent opportunities to investigate mechanisms that contribute to the evolution of specificity between the passenger and the vehicle. 4. In this study of fig-wasp-nematode tritrophic interactions in Ficus racemosa within which seven wasp species can breed, we demonstrate using two-choice as well as cafeteria assays that plant-parasitic nematodes (Schistonchus racemosa) do not hitch rides randomly on available eclosing wasps within the fig syconium, but are specifically attracted, at close range, i.e. 3 mm distance, to only that vehicle which can quickly, within a few hours, reliably transfer it to another fig. This vehicle is the female pollinating wasp. Male wasps and female parasitic wasps are inappropriate vehicles since the former are wingless and die within the fig, while the latter never enter another fig. Nematodes distinguished between female pollinating wasps and other female parasitic wasps using volatiles and cuticular hydrocarbons. Nematodes could not distinguish between cuticular hydrocarbons of male and female pollinators but used other cues, such as volatiles, at close range, to find female pollinating wasps with which they have probably had a long history of chemical adaptation. 5. This study opens up new questions and hypotheses about the evolution and maintenance of specificity in fig-wasp-nematode tritrophic interactions.

Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.

Beta-turns in nascent procollagen are sites of posttranslational enzymatic hydroxylation of proline

The selective hydroxylation of proline residues in nascent procollagen chains by prolyl hydroxylase (EC 1.14.11.2) can be understood in terms of the conformational feature of the -Pro-Gly-segments in linear peptides and globular proteins. The folded beta-turn conformation in such segments appears to be the conformational requirement for proline hydroxylation. The available data on the hydroxylation of native and synthetic substrates of prolyl hydroxylase are explained on the basis of the extent of beta-turn formation in them. Taken in conjunction with the conformational features of the hydroxyproline residue, our results bring out the conformational reason for the posttranslational proline hydroxylation which, it is proposed, leads to the "straightening" of the beta-turn segments into the linear triple-helical conformation.

Conformational analysis of the right-hand twisted antiparallel β-Structure

The conformational analysis of a pair of two-linked peptide units in the anti-parallel arrangement is reported here with a view to study the effect of association of one chain with the other. The pair of two-linked peptide units were fixed in space through the hydrogen bonds between them, in accordance with certain hydrogen bond criteria. Model building was undertaken to ascertain whether the proximity of the side-chains could be used to eliminate any one of the right-hand twisted, left-hand twisted or regular β-structures. Stereochemically, it was found possible with all of them. The preference for a right-hand twisted β-structure, however, was indicated by the classical energy calculations. The relevance of the results thus obtained is discussed in the context of the preferential right-hand twist of the β-pleated sheets present in globular proteins. The agreement between the minimum energy conformations obtained for the pair of two-linked peptide units and the globular protein data is also indicated.

Peptide models for b-turns.A circular dichroism study

The circular dichroism spectra of four 0-turn model peptides, Z-Aib-Pro-Aib-Pro- OMe (l), Piv-Pro-Aib-NHMe (2), Piv-Pro-D-Ala-NHMe (3) and Piv-Pro-Val-NHMe (4) have been examined under a wide range of solvent conditions, using methanol, hexafluoroisopropanol and cyclohexane. Type I and Type I1 0-turns have been observed for peptides 1 and 2 respectively, in the solid state, while the Pro-D-Ala sequence adopts a Type I1 Sturn in a related peptide crystal structure. A class C spectrum is observed for 1 in various solvents, suggesting a variant of a Type I(II1) structure. The Type I1 f3-turn is characterized by a CD spectrum having two positive CD bands at - 230 nm and - 202 nm, a feature observed in Piv-Pro- D-Ala-NHMe in cyclohexane and methanol and for Piv-Pro-Aib-NHMe in methanol. Peptide 2 exhibits solvent dependent CD spectra, which may be rationalized by considering Type 11, I11 and V reverse turn structures. Piv-Pro- Val-NHMe adopts nonaturn structures in polar solvents, but exhibits a class B spectrum in cyclohexane suggesting a population of Type I &turns.