Characterization of a gamma-aminobutyric acid transport system of rhizobium leguminosarum bv. viciae 3841

Spontaneous mutants of Rhizobium leguminosarum bv. viciae 3841 were isolated that grow faster than the wild type on gamma-aminobutyric acid (GABA) as the sole carbon and nitrogen source. These strains (RU1736 and RU1816) have frameshift mutations (gtsR101 and gtsR102, respectively) in a GntR-type regulator (GtsR) that result in a high rate of constitutive GABA transport. Tn5 mutagenesis and quantitative reverse transcription-PCR showed that GstR regulates expression of a large operon (pRL100242 to pRL100252) on the Sym plasmid that is required for GABA uptake. An ABC transport system, GtsABCD (for GABA transport system) (pRL100248-51), of the spermidine/putrescine family is part of this operon. GtsA is a periplasmic binding protein, GtsB and GtsC are integral membrane proteins, and GtsD is an ATP-binding subunit. Expression of gtsABCD from a lacZ promoter confirmed that it alone is responsible for high rates of GABA transport, enabling rapid growth of strain 3841 on GABA. Gts transports open-chain compounds with four or five carbon atoms with carboxyl and amino groups at, or close to, opposite termini. However, aromatic compounds with similar spacing between carboxyl and amino groups are excellent inhibitors of GABA uptake so they may also be transported. In addition to the ABC transporter, the operon contains two putative mono-oxygenases, a putative hydrolase, a putative aldehyde dehydrogenase, and a succinate semialdehyde dehydrogenase. This suggests the operon may be involved in the transport and breakdown of a more complex precursor to GABA. Gts is not expressed in pea bacteroids, and gtsB mutants are unaltered in their symbiotic phenotype, suggesting that Bra is the only GABA transport system available for amino acid cycling.

EfeUOB (YcdNOB) is a tripartite, acid-induced and CpxAR-regulated, low-pH Fe2+ transporter that is cryptic in Escherichia coli K-12 but functional in E-coli O157 : H7

Escherichia coli possesses iron transporters specific for either Fe2+ or Fe3+. Although Fe2+ is far more soluble than Fe3+, it rapidly oxidizes aerobically at pH >= 7. Thus, FeoAB, the major Fe2+ transporter of E. coli, operates anaerobically. However, Fe2+ remains stable aerobically under acidic conditions, although a low-pH Fe2+ importer has not been previously identified. Here we show that ycdNOB (efeUOB) specifies the first such transporter. efeUOB is repressed at high pH by CpxAR, and is Fe2+-Fur repressed. EfeU is homologous to the high-affinity iron permease, Ftr1p, of Saccharomyces cerevisiae and other fungi. EfeO is periplasmic with a cupredoxin N-terminal domain; EfeB is also periplasmic and is haem peroxidase-like. All three Efe proteins are required for Efe function. The efeU gene of E. coli K-12 is cryptic due to a frameshift mutation - repair of the single-base-pair deletion generates a functional EfeUOB system. In contrast, the efeUOB operon of the enterohaemorrhagic strain, O157:1147, lacks any frameshift and is functional. A 'wild-type' K-12 strain bearing a functional EfeUOB displays a major growth advantage under aerobic, low-pH, low-iron conditions when a competing metal is provided. Fe-55 transport assays confirm the ferrous iron specificity of EfeUOB.

Stabilization of a helical water chain in a metal-organic host of a trinuclear Schiff base complex

Three heterometallic trinuclear Schiff base complexes, [{GuL(1)(H2O)}(2)Ni(CN)(4)]center dot 4H(2)O (1), [{CuL2(H2O)}(2)Ni(CN)(4)] (2), and [{CuL3(H2O)}(2)Ni(CN)(4)] (3) (HL1 = 7-amino-4-methyl-5-azahept-3-en-2-one, HL2 = 7-methylamino-4-methyl-5-azahept-3-en-2-one, and HL3 = 7-dimethylamino-4-methyl-5-azahept-3-en-2-one), were synthesized. All three complexes were characterized by elemental analysis, IR and UV spectroscopies, and thermal analysis. Two of them (1 and 3) were also characterized by single crystal X-ray crystallography. Complex 1 forms a hydrogen-bonded one-dimensional metal-organic framework that stabilizes a helical water chain into its cavity, but when any of the amine hydrogen atoms of the Schiff base are replaced by methyl groups, as in L 2 and L 3, the water chain, vanishes, showing explicitly the importance of the host-guest H-bonding interactions for the stabilization of a water cluster.

Methylene spacer-regulated structural variation in cobalt(II/III) complexes with bridging acetate and Salen- or Salpn-type Schiff-base ligands

Two linear, trinuclear mixed-valence complexes, [Co-II{(mu-L-1)(mu-OAc)Co-III (OAc)}(2)] (1) and [Co-II(mu-L-2) (mu-OAc)Co-III(OAc)}(2)] (2) and two mononuclear Con' complexes [Co-III{L-3)(OAc)] (3), and [Co-III {L-4}(OAc)] (4) were prepared and the molecular structures of 1, 2 and 4 elucidated on the basis of X-ray crystallography [OAc = Acetate ion, H2L1 = H(2)Salen 1,6-bis(2-hydroxyphenyl)-2,5-diazahexa-1,5-diene, H2L2 H2Me2-Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene, H2L3 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta1,6-diene, H2L4 = H(2)Me(2)Salpn = 2,8-bis(2-hydroxyphenyl)3,7-diazanona-2,7-dienel. In complexes I and 2, the acetate groups show both monodentate and bridging bidentate coordination modes, whereas chelating bidentate acetate is present in 4. The terminal (CoN2O4)-N-III centres in 1 and 2 exhibit uniform facial arrangements of both non-bridged N2O and bridging O-3 donor sets and the Co-II centre is coordinated to six (four phenoxo and two acetato) oxygen atoms of the bridging ligands. The effective magnetic moment at room temperature corresponds to the presence of high-spin Coll in both 1 and 2. The complexes 1 and 2 are thus Co-III(S = 0)Co-II(S = 3/2)-Co-II(S = 0) trimers. Complexes 3 and 4 are monomeric and diamagnetic containing low-spin Co-III(S = 0) with chelating tetradentate Schiff base and bidentate acetate. Calculations based on DFT rationalise the formation of trinuclear or monomiclear complexes. (C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Facile synthesis of Cu(II) complexes of monocondensed N,N,N donor Schiff base ligands: crystal structure, spectroscopic and magnetic properties

Four new copper(II) complexes, [((CuLN3)-N-1)(2)](ClO4)(2) (1), [(CuL2 N-3)(2)](ClO4)(2) (2), [CuL3(N-3)ClO4)](n) (3) and [CuL4(mu-1,1-N-3)(mu-1,3-N-3)(ClO4)](n) (4) where L-1 = N-1-pyridin-2-yl-methylene-propane-1,3-diamine, L-2 = N-1-(1-pyridin-2-yl-ethylidene)propane-1,3-diamine, L-3 =N-1-(1-pyridin-2-yl-ethylidene)ethane-1,2-diamine and L-4=N-1-(1-pyridin-2-yl-ethylidene)propane-1,2-diamine are four tridentate N,N,N donor Schiff base ligands, have been derived and structurally characterized by X-ray crystallography. Compounds 1 and 2 consist of double basal-apical end-on (EO) azide bridged dinuclear Cu-II complexes with square-pyramidal geometry. In complex 3 the square planar mononuclear [CuL3 (N-3)] units are linked by weakly coordinated perchlorate ions in the axial positions of Cu-II to form a one-dimensional chain. Two such chains are connected by hydrogen bonds involving perchlorate ions and azide groups. Compound 4 consists of 1-D chains in which the Cu-II ions with a square-pyramidal geometry are alternately bridged by single EO and end-to-end (EE) azido ligands, both adopting a basal-apical disposition. Variable temperature (300-2 K) magnetic susceptibility measurements and magnetization measurements at 2 K have been performed. The results reveal that complexes 1 and 2 are antiferromagnetically coupled through azido bridges (J= -12.18 +/- 0.09 and -4.43 +/- 0.1 cm(-1) for 1 and 2, respectively). Complex 3 shows two different magnetic interactions through the two kinds of hydrogen bonds; one is antiferromagnetic (J(1) = - 9.69 +/- 0.03 cm(-1)) and the other is ferromagnetic (J(2) = 1.00 +/- 0.01 cm(-1)). From a magnetic point of view complex 4 is a ferromagnetic dinuclear complex (J= 1.91 +/- 0.01 cm(-1)) coupled through the EO bridge only. The coupling through the EE bridge is practically nil as the N(azido)-Cu-II (axial) distance (2.643 angstrom) is too long. (C) 2006 Elsevier Ltd. All rights reserved.

Stabilization of two smallest possible diastereomeric beta-hairpins in a water soluble tetrapeptide containing non-coded alpha-amino isobutyric acid (Aib) and m-amino benzoic acid

Single crystal X-ray diffraction study reveals that the water soluble tetrapeptide H2N-Ile-Aib-Leu-m-ABA-CO2H, containing non-coded Aib (alpha-amino isobutyric acid) and m-ABA (meta-amino benzoic acid), crystallizes with two smallest possible diastereomeric beta-hairpin molecules in the asymmetric unit. Although in both of the molecules the chiralities at Ile(1) and Leu(3) are S, a conformational reversal in the back bone chain is observed to produce the beta-hairpins with beta-turn conformations of type II and II'. Interestingly Aib which is known to adopt helical conformation, adopts unusual semi-extended conformation with phi: -49.5(5)degrees, psi: 135.2(5)degrees in type II and phi: 50.6(6)degrees. psi: -137.0(4)degrees in type II' for occupying the i + 1 position of the beta-turns. The two hairpin molecules are further interlocked through intermolecular hydrogen bonds and electrostatic interactions between CO2- and -+NH3 groups to form dimeric supramolecular beta-hairpin aggregate in the crystal state. The CD measurement and 2D NMR study of the peptide in aqueous medium support the existence of beta-hairpin structure in water. (C) 2009 Elsevier B.V. All rights reserved.

Bis- and tris-(methylphosphonic) acid derivatives of a 14-membered tetraazamacrocycle containing pyridine: synthesis, protonation and complexation studies

Two N-methylphosphonic acid derivatives of a 14-membered tetraazamacrocycle containing pyridine have been synthesized, H4L1 and H6L2. The protonation constants of these compounds and the stability constants of complexes of both ligands with Ni2+, Cu2+ and Zn2+ were determined by potentiometric methods at 298 K and ionic strength 0.10 mol dm(-3) in NMe4NO3. The high overall basicity of both compounds is ascribed to the presence of the phosphonate arms. H-1 and P-31 NMR spectroscopic titrations were performed to elucidate the sequence of protonation, which were complemented by conformational analysis studies. The complexes of these ligands have stability constants of the order of or higher than those formed with ligands having the same macrocyclic backbone but acetate arms. At pH = 7 the highest pM values were found for solutions containing the compound with three acetate groups, followed immediately by those of H6L2, however, as expected, the increasing pH favours the complexes of ligands containing phosphonate groups. The single-crystal structure of Na-2[Cu(HL1)]NO3.8H(2)O has shown that the coordination geometry around the copper atom is a distorted square pyramid. Three nitrogen atoms of the macrocyclic backbone and one oxygen atom from one methylphosphonate arm define the basal plane, and the apical coordination is accomplished via the nitrogen atom trans to the pyridine ring of the macrocycle. To achieve this geometric arrangement, the macrocycle adopts a folded conformation. This structure seems consistent with Uv-vis-NIR spectroscopy for the Ni2+ and the Cu2+ complexes and with the EPR for the latter.

Anion-directed template synthesis and hydrolysis of mono-condensed Schiff base of 1,3-pentanediamine and o-hydroxyacetophenone in Ni-II and Cu-II complexes

Bis(o-hydroxyacetophenone)nickel(II) dihydrate, on reaction with 1,3-pentanediamine, yields a bis-chelate complex [NiL2]center dot 2H(2)O (1) of mono-condensed tridentate Schiff base ligand HL {2-[1-(3-aminopentylimino)ethyl]phenol}. The Schiff base has been freed from the complex by precipitating the Nil, as a dimethylglyoximato complex. HL reacts smoothly with Ni(SCN)(2)center dot 4H(2)O furnishing the complex [NiL(NCS)] (2) and with CuCl2 center dot 2H(2)O in the presence of NaN3 or NH4SCN producing [CuL(N-3)](2) (3) or [CuL(NCS)] (4). On the other hand, upon reaction with Cu(ClO4)(2)center dot 6H(2)O and Cu(NO3)(2)center dot 3H(2)O, the Schiff base undergoes hydrolysis to yield ternary complexes [Cu(hap)(pn)(H2O)]ClO4 (5) and [Cu(hap)(pn)(H2O)]NO3 (6), respectively (Hhap = o-hydroxyacetophenone and pn = 1,3-pentanediamine). The ligand HL undergoes hydrolysis also on reaction with Ni(ClO4)(2)center dot 6H(2)O or Ni(NO3)(2)center dot 6H(2)O to yield [Ni(hap)(2)] (7). The structures of the complexes 2, 3, 5, 6, and 7 have been confirmed by single-crystal X-ray analysis. In complex 2, Ni-II possesses square-planar geometry, being coordinated by the tridentate mono-negative Schiff base, L and the isothiocyanate group. The coordination environment around Cu-II in complex 3 is very similar to that in complex 2 but here two units are joined together by end-on, axial-equatorial azide bridges to result in a dimer in which the geometry around Cu-II is square pyramidal. In both 5 and 6, the Cu-II atoms display the square-pyramidal environment; the equatorial sites being coordinated by the two amine groups of 1,3-pentanediamine and two oxygen atoms of o-hydroxyacetophenone. The axial site is coordinated by a water molecule. Complex 7 is a square-planar complex with the Ni atom bonded to four oxygen atoms from two hap moieties. The mononuclear units of 2 and dinuclear units of 3 are linked by strong hydrogen bonds to form a one-dimensional network. The mononuclear units of 5 and 6 are joined together to form a dimer by very strong hydrogen bonds through the coordinated water molecule. These dimers are further involved in hydrogen bonding with the respective counteranions to form 2-D net-like open frameworks. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Solvent-Assisted Formation of Vesicles by a Self-Assembling Ni-3-Schiff Base Complex

A linear trinuclear Ni-Schiff base complex [Ni-3(salpen)(2)(PhCH2COO)(2)(EtOH)] has been synthesized by combining Ni(ClO4)(2)center dot 6H(2)O, phenyl acetic acid (C6H5CH2COOH), and the Schiff base ligand, N,N'-bis(salicylidene)-1,3-pentanediamine (H(2)salpen). This complex is self-assembled through hydrogen bonding and C-H-g interaction in the solid state to generate a sheet-like architecture, while in organic solvent (CH2Cl2), it forms vesicles with a mean diameter of 290 nm and fused vesicles, depending upon the concentration of the solution. These vesicles act as an excellent carrier of dye molecules in CH2Cl2. The morphology of the complex has been determined by scanning electron microscopy and transmission electron microscopy experiments, and the encapsulation of dye has been examined by confocal microscopic image and electronic absorption spectra.

Supramolecular beta-sheet and nanofibril formation by self-assembling tripeptides containing an N-terminally located gamma-aminobutyric acid residue

Three terminally protected tripeptides Boc-gamma-Abu-Val-Leu-OMe 1, Boc-gamma-Abu-Leu-Phe-OMe 2 and Boc-gamma-Abu-Val-Tyr-OMe 3 (gamma-Abu = gamma-aminobutyric acid) each containing an N-terminally positioned gamma-aminobutyric acid residue have been synthesized, purified and studied. FT-IR studies of all these peptides revealed that these peptides form intermolecularly hydrogen bonded supramolecular beta-sheet structures. Peptides 1, 2 and 3 adopt extended backbone beta-strand molecular structures in crystals. Crystal packing of all these peptides demonstrates that these beta-strand structures self-assemble to form intermolecularly H-bonded parallel beta-sheet structures. Peptide 3 uses a side chain tyrosyl -OH group as an additional hydrogen bonding functionality in addition to the backbone CONH groups to pack in crystals. Transmission electron microscopic studies of all peptides indicate that they self-assemble to form nanofibrillar structures of an average diameter of 65 nm. These peptide fibrils exhibit amyloid-like behavior as they bind to a physiological dye Congo red and show a characteristic green-gold birefringence under polarizing microscope.

One-pot synthesis and characterization of soluble poly(aryl ether-ketone)s having pendant carboxyl groups

Aromatic poly(ether-ketone)s having pendant carboxyl groups have been obtained by direct, one-pot, Friedel-Crafts copolycondensation of 4,4'-diphenoxybenzophenone with a mixture of terephthaloyl chloride (TC) and trimellitic anhydride acid chloride (TAAC), over a wide range of TAAC/TC molar ratios, in the presence of anhydrous aluminum chloride. The syntheses were performed as precipitation-polycondensations, and the polymers were obtained in particulate form. Besides globular particles of polymer, small quantities of elongated, needlelike particles were observed when the mole ratio TAAC/TC was less than 1. Use of X-ray microdiffraction with synchrotron radiation has revealed that the needlelike material consists of a cyclic compound containing 10 phenylene units, i.e., the crystals are of a [2 + 2] macrocyclic dimer. The polymers obtained are soluble in strong acids and in mixtures of methanesulfonic acid or trifluoroacetic acid with chlorinated hydrocarbons. The molecular structures of the polymers were confirmed by H-1 and C-13 NMR spectroscopy. Reaction of TAAC with 4,4'-diphenoxybenzophenone produced mainly meta-orientation of the resulting ketone linkages. The size of the polymer particles, their molecular weights, and the melting behavior of the products obtained depend on the TAAC/TC ratio used. Ortho-keto acid residues, formed during reaction of anhydride groups of TAAC with 4,4'-diphenoxybenzophenone, exhibit ring-chain tautomerism. A carboxyl-containing aromatic polyketone derived from p-terphenyl, and thus having with no ether linkages in the main chain, was prepared by analogous chemistry, and functional derivatives of carboxy-substituted polyketones were also obtained and characterized.

Long-term monounsaturated fatty acid diets reduce platelet aggregation in healthy young subjects

The aim of the present study was to compare the response of a range of atherogenic and thrombogenic risk markers to two dietary levels of saturated fatty acid (SFA) substitution with monounsaturated fatty acids (MUFA) in students living in a university hall of residence. Although the benefits of such diets have been reported for plasma lipoproteins in high-risk groups, more needs to be known about effects of more modest SFA-MUFA substitutions over the long term and in young healthy adults. In a parallel design over 16 weeks, fifty-one healthy young subjects were randomised to one of two diets: (1) a moderate-MUFA diet in which 16 g dietary SFA/100 g total fatty acids were substituted with MUFA (n 25); (2) a high-MUFA diet in which 33 g dietary SFA/100 g total fatty acids were substituted with MUFA (n 26). All subjects followed an 8-week run-in diet (reference diet), with a fatty acid composition close to the UK average values. There were no differences in plasma lipid responses between the two diets over 16 weeks of the study with similar reductions in total cholesterol (P<0.001) and LDL-cholesterol (P<0.01) in both groups; a small but significant reduction in HDL-cholesterol was also observed in both groups (P<0.01). Platelet responses to ADP (P<0.01) and arachidonic acid (P<0.05) differed with time on the two diets; at 16 weeks, platelet aggregatory response to ADP was significantly lower on the high-MUFA than the moderate-MUFA (P<0.01) diet; ADP responses were also significantly lower within this group at 8 (P< 0.05) and 16 (P< 0.01) weeks compared with baseline. There were no differences in fasting factor VII activity (factors VIII and VIIag), fibrinogen concentration or tissue-type plasminogen activator activity between the diets. There were no differences in postprandial factor VIII responses to a standard meal (area under the curve) between the diets after 16 weeks, but postprandial factor VIII response was lower than on the high-MUFA diet compared with baseline (P<0.01). In conclusion, a high-MUFA diet sustains potentially beneficial effects on platelet aggregation and postprandial activation of factor VII. Moderate or high substitution of MUFA for SFA achieves similar reductions in fasting blood lipids in young healthy subjects.

Effect of altered dietary n-3 fatty acid intake upon plasma lipid fatty acid composition, conversion of [C-13]alpha-linolenic acid to longer-chain fatty acids and partitioning towards beta-oxidation in older men

The effect of increased dietary intakes of alpha-linolenic acid (ALNA) or eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) for 2 months upon plasma lipid composition and capacity for conversion of ALNA to longer-chain metabolites was investigated in healthy men (52 (SD 12) years). After a 4-week baseline period when the subjects substituted a control spread, a test meal containing [U-C-13]ALNA (700 mg) was consumed to measure conversion to EPA, docosapentaenoic acid (DPA) and DHA over 48 h. Subjects were then randomised to one of three groups for 8 weeks before repeating the tracer study: (1) continued on same intake (control, n 5); (2) increased ALNA intake (10 g/d, n 4); (3) increased EPA+DHA intake (1.5 g/d, n 5). At baseline, apparent fractional conversion of labelled ALNA was: EPA 2.80, DPA 1.20 and DRA 0.04%. After 8 weeks on the control diet, plasma lipid composition and [C-13]ALNA conversion remained unchanged compared with baseline. The high-ALNA diet resulted in raised plasma triacylglycerol-EPA and -DPA concentrations and phosphatidylcholine-EPA concentration, whilst [C-13]ALNA conversion was similar to baseline. The high-(EPA+DHA) diet raised plasma phosphatidylcholine-EPA and -DHA concentrations, decreased [C-13]ALNA conversion to EPA (2-fold) and DPA (4-fold), whilst [C-13]ALNA conversion to DHA was unchanged. The dietary interventions did not alter partitioning of ALNA towards beta-oxidation. The present results indicate ALNA conversion was down-regulated by increased product (EPA+DHA) availability, but was not up-regulated by increased substrate (ALNA) consumption. This suggests regulation of ALNA conversion may limit the influence of variations in dietary n-3 fatty acid intake on plasma lipid compositions.

Circulating triacylglycerol and apoE levels in response to EPA and docosahexaenoic acid supplementation in adult human subjects

High doses of n-3 PUFA found in fish oils can reduce the circulating concentration of triacylglycerol (TG), which may contribute to the positive impact of these fatty acids on the risk of CVD. The present study aimed to establish the differential impact of EPA and docosahexaenoic (DHA) on plasma lipids and apo in adults. Forty-two normolipidaemic adult subjects completed a double-blind placebo controlled parallel study, receiving an EPA-rich oil (4.8 g EPA/d), DHA-rich oil (4.9 g DHA/d) or olive oil as control, for a period of 4 weeks. No effects of treatment on total cholesterol, LDL-cholesterol or HDL-cholesterol were evident. There was a significant 22% reduction in TG level relative to the control value following the DHA treatment (P=0.032), with the 15% decrease in the EPA group failing to reach significance (P=0-258). There were no significant inter-group differences in response to treatment for plasma apoA1, -C3 or -E levels, although a significant 15% within-group increase in apoE was evident in the EPA (P=0.006) and DHA (P=0.003) groups. In addition, a within-group decrease in the apoAI:HDL-cholesterol ratio was observed in the DHA group, suggesting a positive impact of DHA on HDL particle size. The DHA intervention resulted in a significant increase in the proportion of EPA P=0.000 and DHA P=0.000 in plasma phospholipids, whilst significant increases in EPA P=0.000 and docosapentacnoic acid P=0.002, but not DHA P=0.193, were evident following EPA supplementation (P<0.05). Our present results indicate that DHA may be more efficacious than EPA in improving the plasma lipid profile.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.