Dioxadiaza- and trioxadiaza-macrocycles containing one dibenzofuran unit selective for cadmium

The binding properties of dioxadiaza-([17](DBF) N2O2) and trioxadiaza- ([22](DBF)N2O3), macrocyclic ligands containing a rigid dibenzofuran group ( DBF), to metal cations and structural studies of their metal complexes have been carried out. The protonation constants of these two ligands and the stability constants of their complexes with Ca2+, Ba2+, and Mn2+, Co2+, Ni2+, Cu2+, Zn2+ and Cd2+, were determined at 298.2 K in methanol-water ( 1 : 1, v/v), and at ionic strength 0.10 mol dm(-3) in KNO3. The values of the protonation constants of both ligands are similar, indicating that no cavity size effect is observed. Only mononuclear complexes of these ligands with the divalent metal ions studied were found, and their stability constants are lower than expected, especially for the complexes of the macrocycle with smaller cavity size. However, the Cd2+ complex with [ 17]( DBF) N2O2 exhibits the highest value of stability constant for the whole series of metal ions studied, indicating that this ligand reveals a remarkable selectivity for cadmium(II) in the presence of all the metal ions studied, except copper( II), indicating that this ligand reveals a remarkable selectivity for cadmium( II) in the presence of the mentioned metal ions. The crystal structures of H-2[17](DBF)N2O32+ (diprotonated form of the ligand) and of its cadmium complex were determined by X-ray diffraction. The Cd2+ ion fits exactly inside the macrocyclic cavity exhibiting coordination number eight by coordination to all the donor atoms of the ligand, and additionally to two oxygen atoms from one nitrate anion and one oxygen atom from a water molecule. The nickel( II) and copper( II) complexes with the two ligands were further studied by UV-vis-NIR and the copper( II) complexes also by EPR spectroscopic techniques in solution indicating square-pyramidal structures and suggesting that only one nitrogen and oxygen donors of the ligands are bound to the metal. However an additional weak interaction of the second nitrogen cannot be ruled out.

Dihydrogen in cation-substituted zeolites X - an inelastic neutron scattering study

An inelastic neutron scattering (INS) study of the rotational - vibrational spectrum of dihydrogen sorbed by zeolite X having substituted sodium, calcium and zinc cations is reported. The rotational - vibrational spectrum of H-2 was observed at low energy transfer ( below ca. 25 meV, 202 cm(-1)); the vibration was that of the H-2 molecule against the binding site (H-2 - X, not H - H). The vibration frequency was proportional to the polarising power of the cation (Na+ < Ca2+ < Zn2+). Polarisation of the H-2 molecule dominated the interaction of H-2 with this binding site. The total scattering intensity was proportional to the dihydrogen dose. However the vibrational intensities became constant at ca. 0.3 wt% showing that the H-2 binding sites had saturated. Additional dihydrogen appeared as unbound or weakly bound dihydrogen exhibiting recoil.

Conformational and hydration effects of site-selective sodium, calcium and strontium ion binding to the DNA Holliday junction structure d(TCGGTACCGA)(4)

The role of metal ions in determining the solution conformation of the Holliday junction is well established, but to date the picture of metal ion binding from structural studies of the four-way DNA junction is very incomplete. Here we present two refined structures of the Holliday junction formed by the sequence d(TCGGTACCGA) in the presence of Na+ and Ca2+, and separately with Sr2+ to resolutions of 1.85 Angstrom and 1.65 Angstrom, respectively. This sequence includes the ACC core found to promote spontaneous junction formation, but its structure has not previously been reported. Almost complete hydration spheres can be defined for each metal cation. The Na+ sites, the most convincing observation of such sites in junctions to date, are one on either face of the junction crossover region, and stabilise the ordered hydration inside the junction arms. The four Ca2+ sites in the same structure are at the CG/CG steps in the minor groove. The Sr2+ ions occupy the TC/AG, GG/CC, and TA/TA sites in the minor groove, giving ten positions forming two spines of ions, spiralling through the minor grooves within each arm of the stacked-X structure. The two structures were solved in the two different C2 lattices previously observed, with the Sr2+ derivative crystallising in the more highly symmetrical form with two-fold symmetry at its centre. Both structures show an opening of the minor groove face of the junction of 8.4degrees in the Ca2+ and Na+ containing structure, and 13.4degrees in the Sr2+ containing structure. The crossover angles at the junction are 39.3degrees and 43.3degrees, respectively. In addition to this, a relative shift in the base pair stack alignment of the arms of 2.3 Angstrom is observed for the Sr2+ containing structure only. Overall these results provide an insight into the so-far elusive stabilising ion structure for the DNA Holliday junction. (C) 2003 Elsevier Science Ltd. All rights reserved.

Effect of minerals on casein micelle stability of cows' milk

The effects of minerals on casein micelle stability of individual cows' milk, throughout a complete lactation, were investigated. Calcium and calcium ions, magnesium, phosphorus, sodium, potassium and citrate contents were analysed, together with the following physical properties of milk; pH, ethanol stability, rennet clotting time and coagulum firmness. There was an inverse non-linear relationship between free calcium ion concentration and ethanol stability (ES; r=0.84). Rennet coagulation time showed a weaker relationship with free calcium ion concentration (r=0.44) but a stronger relationship with pH (r=0.66). In addition, samples containing higher amounts of free calcium ions produced a firmer gel. Citrate in natural samples acts as a stabilizing factor, as it slightly improves milk stability. Potassium, on the other hand, exhibited a negative correlation, but only with rennet clotting time (r=-0.52). Throughout lactation the average values were; free Ca 21 concentration 1.88 mm,, pH 6.63, ES 83.2% and clotting time 13.6 min. The equilibrium relationship between pH and free Ca2+ concentration was investigated by adjusting milk pH from 5.9 to 7.1, using acid and alkali. There was a good inverse linear relationship between pH and log (free Ca 21) for individual milk samples, with a gradient of -0.62 and a standard deviation of 0.042.

Changes in physical properties of bovine milk from the colostrum period to early lactation

The aim of this study was to analyze individual cows' samples from the colostrum, postcolostrum, and early lactation periods to investigate how milk composition, physical properties, stability, and suitability for processing change throughout this period. Attention was paid to the first week postpartum in which the composition of bovine mammary secretion can change markedly. Properties including pH, titratable acidity, ethanol stability (ES), rennet clotting time, and casein micelle size were analyzed, together with some compositional factors such as fat, total protein, lactose, total and ionic calcium, magnesium, citrate, phosphorus, sodium, and potassium. Total Ca (36.2 mM) and free ionic Ca (2.58 mM), Mg (5.9 mM), P (32.2 mM), and Na (24.1 mM) appeared to be high on d 5 postpartum, having decreased substantially over the first 5 d; they gradually decreased thereafter. The average pH on d 5 was only 6.49, compared with 6.64 at 1 mo postpartum. Stability measurements showed that the average ES on d 5 was 70% and the rennet clotting time was 12.2 min, which were significantly lower than values at later stages. A number of milk properties including ES, pH, protein content, and Ca2+ concentration could be useful for identifying the point of transition from colostrum to the early lactation period. Knowing the composition and physical properties of colostrum and postcolostrum secretions will help establish when such milk is suitable for processing and determine the best use for that milk.

The interactions of flavonoids within neuronal signalling pathways

Emerging evidence suggests that dietary phytochemicals, in particular flavonoids, may exert beneficial effects in the central nervous system by protecting neurons against stress-induced injury, by suppressing neuroinflammation and by promoting neurocognitive performance, through changes in synaptic plasticity. It is likely that flavonoids exert such effects in neurons, through selective actions on different components within a number of protein kinase and lipid kinase signalling cascades, such as phosphatidylinositol-3 kinase (PI3K)/Akt, protein kinase C and mitogen-activated protein kinase. This review details the potential inhibitory or stimulatory actions of flavonoids within these pathways, and describes how such interactions are likely to affect cellular function through changes in the activation state of target molecules and/or by modulating gene expression. Although, precise sites of action are presently unknown, their abilities to: (1) bind to ATP binding sites on enzymes and receptors; (2) modulate the activity of kinases directly; (3) affect the function of important phosphatases; (4) preserve neuronal Ca2+ homeostasis; and (5) modulate signalling cascades lying downstream of kinases, are explored. Future research directions are outlined in relation to their precise site(s) of action within the signalling pathways and the sequence of events that allow them to regulate neuronal function in the central nervous system.

Cyclam derivatives containing three acetate pendant arms: synthesis, acid-base, metal complexation and structural studies

The ligands 1,4,8,11-tetraazacyclotetradecane-1,4,8-triacetic-11-methylphosphonic acid (H(5)te3a1p) and 1,4,8,11-tetraazacyclotetradecane-1,4,8-triacetic acid (H(3)te3a) were synthesized, the former one for the first time. The syntheses of these ligands were achieved from reactions on 1,4,8,11-tetraazacyclotetradecane-1,4,8-tris( carbamoylmethyl) hydroiodide (te3am center dot HI), and compounds (Hte3am)(+), 1, and (H(7)te3a1p)(2+), 4, were characterized by X-ray diffraction. Structures of two other compounds resulting from side-reactions, (H(2)te2lac)(2+), 2, and (H(4)te2a2p(OEt2))(2+), 3, were also determined by X-ray diffraction. Potentiometric titrations of H(5)te3a1p and H(3)te3a were performed at 298.2 K and ionic strength 0.10 mol dm(-3) in NMe4NO3 to determine their protonation constants. H-1 and P-31 NMR titrations of H(5)te3a1p were carried out in order to determine the very high first protonation constant of this ligand and to elucidate the sequence of protonation. Potentiometric studies of the two ligands with Ca2+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Pb2+ metal ions performed in the same experimental conditions showed that the complexes of H5te3a1p present very high thermodynamic stability while complexes of H(3)te3a, particularly Co2+ and Zn2+, are even more stable. P-31 NMR spectra of the cadmium(II) complex of H(5)te3a1p showed that the phosphonate moiety was coordinated to the metal ion. The UV-vis-NIR spectroscopic data and magnetic moment values of Co2+ and Ni2+ complexes of H(5)te3a1p and H(3)te3a together with the EPR of the corresponding Cu2+ complexes indicated that all these complexes adopt distorted octahedral coordination geometries in solution. This was confirmed by the single crystal structure of [Cu-2(Hte3a)(H2O)(3)Cl]Cl-0.5(ClO4)(0.5) center dot 2H(2)O that showed two distorted octahedral copper centres bridged by a N-acetate pendant arm with a Cu center dot center dot center dot Cu distance of 4.890(1) angstrom. The first one is encapsulated into the macrocyclic cavity surrounded by four nitrogen and two oxygen donors from the macrocycle, whereas the second one is on the periphery of the macrocycle and is coordinated to two oxygen atoms of one acetate pendant arm in chelating fashion, one chloride and three water molecules.

The production, purification and characterisation of two novel alpha-D-mannosidases from Aspergillus phoenicis

1,6-alpha-D-Mannosidase from Aspergillits phoenicis was purified by anion-exchange chromatography, chromatofocussing and size-exclusion chromatography. The apparent molecular weight was 74 kDa by SDS-PAGE and 81 kDa by native-PAGE. The isoelectric point was 4.6. 1,6-alpha-D-Mannosidase had a temperature optimum of 60 degrees C, a pH optimum of 4.0-4.5. a K-m of 14 mM with alpha-D-Manp-(1 -> 6)-D-Manp as substrate. It was strongly inhibited by Mn2+ and did not need Ca2+ or any other metal cofactor of those tested. The enzyme cleaves specifically (1 -> 6)-linked mannobiose and has no activity towards any other linkages, p-nitrophenyl-alpha-D-mannopyranoside or baker's yeast mannan. 1,3(1,6)-alpha-D-Mannosidase from A. phoenicis was purified by anion-exchange chromatography, chromatofocus sing and size-exclusion chromatography. The apparent molecular weight was 97 kDa by SDS-PAGE and 110 kDa by native-PAGE. The 1,3(1,6)-alpha-D-mannosidase enzyme existed as two charge isomers or isoforms. The isoelectric points of these were 4.3 and 4.8 by isoelectric focussing. It cleaves alpha-D-Manp-(1 -> 3)-D-Manp 10 times faster than alpha-D-Manp-(1 -> 6)-D-Manp, has very low activity towards p-nitrophenyl-alpha-D-mannopyranoside and baker's yeast mannan, and no activity towards alpha-D-Manp-(1 -> 2)-D-Manp. The activity towards (1 -> 3)-linked mannobiose is strongly activated by 1 mM Ca2+ and inhibited by 10 mM EDTA, while (1 -> 6)-activity is unaffected, indicating that the two activities may be associated with different polypeptides. It is also possible that one polypeptide may have two active sites catalysing distinct activities. (c) 2005 Elsevier Ltd. All rights reserved.

G protein ss gamma subunits mediate presynaptic inhibition of transmitter release from rat superior cervical ganglion neurones in culture

The activation of presynaptic G protein-coupled receptors (GPCRs) is widely reported to inhibit transmitter release; however, the lack of accessibility of many presynaptic terminals has limited direct analysis of signalling mediators. We studied GPCR-mediated inhibition of fast cholinergic transmission between superior cervical ganglion neurones (SCGNs) in culture. The adrenoceptor agonist noradrenaline (NA) caused a dose-related reduction in evoked excitatory postsynaptic potentials (EPSPs). NA-induced EPSP decrease was accompanied by effects on the presynaptic action potential (AP), reducing AP duration and amplitude of the after-hyperpolarization (AHP), without affecting the pre- and postsynaptic membrane potential. All effects of NA were blocked by yohimbine and synaptic transmission was reduced by clonidine, consistent with an action at presynaptic alpha 2-adrenoceptors. NA-induced inhibition of transmission was sensitive to pre-incubation of SCGNs with pertussis toxin (PTX), implicating the involvement of G alpha(i)/(o)beta y subunits. Expression of G alpha transducin, an agent which sequesters G protein beta gamma (G beta y) subunits, in the presynaptic neurone caused a time-dependent attenuation of NA-induced inhibition. Injection of purified G beta gamma subunits into the presynaptic neurone inhibited transmission, and also reduced the AHP amplitude. Furthermore, NA-induced inhibition was occluded by pre-injection of G beta gamma subunits. The Ca2+ channel blocker Cd2+ mimicked NA effects on transmitter release. Cd2+, NA and G beta gamma subunits also inhibited somatic Ca2+ current. In contrast to effects on AP-evoked transmitter release, NA had no clear action on AP-independent EPSPs induced by hypertonic solutions. These results demonstrate that G beta gamma subunits functionally mediate inhibition of transmitter release by alpha 2-adrenoceptors and represent important regulators of synaptic transmission at mammalian presynaptic terminals.

Analysis of second messenger pathways stimulated by different chemokines acting at the chemokine receptor

The chemokine receptor, CCR5, responds to several chemokines leading to changes in activity in several signalling pathways. Here, we investigated the ability of different chemokines to provide differential activation of pathways. The effects of five CC chemokines acting at CCR5 were investigated for their ability to inhibit forskolin- stimulated 3'-5'-cyclic adenosine monophosphate (cAMP) accumulation and to stimulate Ca2+ mobilisation. in Chinese hamster ovary (CHO) cells expressing CCR5. Macrophage inflammatory protein 1 alpha (D26A) (MIP-1 alpha (D26A), CCL3 (D26A)), regulated on activation, normal T-cell expressed and secreted (RANTES, CCLS), MIP-1 beta (CCL4) and monocyte chemoattractant protein 2 (MCP-2, CCL8) were able to inhibit forskolin -stimulated CAMP accumulation, whilst MCP-4 (CCL13) could not elicit a response. CCL3 (D26A), CCL4, CCLS, CCL8 and CCL13 were able to stimulate Ca2+ mobilisation. through CCRS, although CCL3 (D26A) and CCL5 exhibited biphasic concentration-response curves. The Ca2+ responses induced by CCL4, CCL5, CCL8 and CCL13 were abolished by pertussis toxin, whereas the response to CCL3 (D26A) was only partially inhibited by pertussis toxin, indicating G(i/o)-independent signalling induced by this chemokine. Although the rank order of potency of chemokines was similar between the two assays, certain chemokines displayed different pharmacological profiles in cAMP inhibition and Ca2+ mobilisation assays. For instance, whilst CCL13 could not inhibit forskolin-stimulated cAMP accumulation, this chemokine was able to induce Ca2+ mobilisation via CCR5. It is concluded that different chemokines acting at CCR5 can induce different pharmacological responses, which may account for the broad spectrum of chemokines that can act at CCRS. (C) 2007 Elsevier Inc. All rights reserved.

Rigid ferrocenophane and its metal complexes with transition and alkaline-earth metal ions

The rigid [6]ferrocenophane, L-1, was synthesised by condensation of 1,1'-ferrocene dicarbaldehyde with trans-1,2-diaminocyclohexane in high dilution at r.t. followed by reduction. When other experimental conditions were employed, the [6,6,6]ferrocenephane (L-2) was also obtained. Both compounds were characterised by single crystal X-ray crystallography. The protonation of L-1 and its metal complexation were evaluated by the effect on the electron-transfer process of the ferrocene (fc) unit of L-1 using cyclic voltammetry (CV) and square wave voltammetry (SWV) in anhydrous CH3CN solution and in 0.1 M (Bu4NPF6)-Bu-n as the supporting electrolyte. The electrochemical process of L-1 between 300 and 900 mV is complicated by amine oxidation. On the other hand, an anodic shift from the fc/fc(+) wave of L-1 of 249, 225, 81 and 61 mV was observed by formation of Zn2+, Ni2+, Pd2+ and Cu2+ complexes, respectively. Whereas Mg2+ and Ca2+ only have with L-1 weak interactions and they promote the acid-base equilibrium of L-1. This reveals that L-1 is an interesting molecular redox sensor for detection of Zn2+ and Ni2+, although the kinetics of the Zn2+ complex formation is much faster than that of the Ni2+ one. The X-ray crystal structure of [(PdLCl2)-Cl-1] was determined and showed a square-planar environment with Pd(II) and Fe(II) centres separated by 3.781(1) angstrom. The experimental anodic shifts were elucidated by DFT calculations on the [(MLCl2)-Cl-1] series and they are related to the nature of the HOMO of these complexes and a four-electron, two-orbital interaction.

Calpain-10 interacts with plasma saturated fatty acid concentrations to influence insulin resistance in individuals with the metabolic syndrome

Background: Calpain-10 protein (intracellular Ca2+-dependent cysteine protease) may play a role in glucose metabolism, pancreatic β cell function, and regulation of thermogenesis. Several CAPN10 polymorphic sites have been studied for their potential use as risk markers for type 2 diabetes and the metabolic syndrome (MetS). Fatty acids are key metabolic regulators that may interact with genetic factors and influence glucose metabolism. Objective: The objective was to examine whether the genetic variability at the CAPN10 gene locus is associated with the degree of insulin resistance and plasma fatty acid concentrations in subjects with MetS. Design: The insulin sensitivity index, glucose effectiveness, insulin resistance [homeostasis model assessment of insulin resistance (HOMA-IR)], insulin secretion (disposition index, acute insulin response, and HOMA of β cell function), plasma fatty acid composition, and 5 CAPN10 single nucleotide polymorphisms (SNPs) were determined in a cross-sectional analysis of 452 subjects with MetS participating in the LIPGENE dietary intervention cohort. Results: The rs2953171 SNP interacted with plasma total saturated fatty acid (SFA) concentrations, which were significantly associated with insulin sensitivity (P < 0.031 for fasting insulin, P < 0.028 for HOMA-IR, and P < 0.012 for glucose effectiveness). The G/G genotype was associated with lower fasting insulin concentrations, lower HOMA-IR, and higher glucose effectiveness in subjects with low SFA concentrations (below the median) than in subjects with the minor A allele (G/A and A/A). In contrast, subjects with the G/G allele with the highest SFA concentrations (above the median) had higher fasting insulin and HOMA-IR values and lower glucose effectiveness than did subjects with the A allele. Conclusion: The rs2953171 polymorphism at the CAPN10 gene locus may influence insulin sensitivity by interacting with the plasma fatty acid composition in subjects with MetS. This trial was registered at clinicaltrials.gov as NCT00429195.

Feasibility of using dialysis for determining calcium ion concentration and pH in calcium-fortified soymilk at high temperature

Dialysis was performed to examine some of the properties of the soluble phase of calcium (Ca) fortified soymilk at high temperatures. Dialysates were obtained while heating soymilk at temperatures of 80 and 100 °C for 1 h and 121 °C for 15 min. It was found that the pH, total Ca, and ionic Ca of dialysates obtained at high temperature were all lower than in their corresponding nonheated Ca-fortified soymilk. Increasing temperature from 80 to 100 °C hardly affected Ca ion concentration ([Ca2+]) of dialysate obtained from Ca chloride-fortified soymilk, but it increased [Ca2+] in dialysates of Ca gluconate-fortified soymilk and Ca lactate-fortified soymilk fortified with 5 to 6 mM Ca. Dialysates obtained at 100 °C had lower pH than dialysate prepared at 80 °C. Higher Ca additions to soymilk caused a significant (P≤ 0.05) reduction in pH and an increase in [Ca2+] of these dialysates. When soymilk was dialyzed at 121 °C, pH, total Ca, and ionic Ca were further reduced. Freezing point depression (FPD) of dialysates increased as temperature increased but were lower than corresponding soymilk samples. This approach provides a means of estimating pH and ionic Ca in soymilks at high temperatures, in order to better understand their combined role on soymilk coagulation.

Mineral partitioning in milk and milk permeates at high temperature

The soluble phase of milk was separated at 20 and 80°C using ultrafiltration. The resulting permeates were then subjected to further ultrafiltration and dialysis at close to these two temperatures. It was found that pH, Ca2+ and soluble Ca decreased as the separation temperature increased both in original UF permeates and in dialysates obtained from these permeates, but P decreased only slightly. The major reason for these changes was due to the precipitation of calcium phosphate/citrate complexes onto the casein micelle with concomitant release of H+. The pH of both permeates and dialysates from milk at 20°C were slightly higher than for milk. When UF permeates collected at 20 and 80°C, were each dialysed at both these temperatures, the dialysate collected at 80°C showed much less temperature dependence for pH and ionic calcium compared with that collected at 20°C. This is in contrast to milk, which shows considerable temperature dependence for pH and ionic calcium. Further experiments revealed that the pH and Ca2+ concentration of permeates showed high temperature dependence above the temperature at which they were separated, but a much lower temperature dependence below that temperature. These findings suggest that dialysis and UF of milk at high temperature provide the best means yet for estimating the pH and ionic calcium of milk at that temperature.

Modulation of endothelial cell KCa3.1 Channels during endothelium-derived hyperpolarizing factor signaling in mesenteric resistance arteries

Arterial hyperpolarization to acetylcholine (ACh) reflects coactivation of KCa3.1 (IKCa) channels and KCa2.3 (SKCa) channels in the endothelium that transfers through myoendothelial gap junctions and diffusible factor(s) to affect smooth muscle relaxation (endothelium-derived hyperpolarizing factor [EDHF] response). However, ACh can differentially activate KCa3.1 and KCa2.3 channels, and we investigated the mechanisms responsible in rat mesenteric arteries. KCa3.1 channel input to EDHF hyperpolarization was enhanced by reducing external [Ca2+]o but blocked either with forskolin to activate protein kinase A or by limiting smooth muscle [Ca2+]i increases stimulated by phenylephrine depolarization. Imaging [Ca2+]i within the endothelial cell projections forming myoendothelial gap junctions revealed increases in cytoplasmic [Ca2+]i during endothelial stimulation with ACh that were unaffected by simultaneous increases in muscle [Ca2+]i evoked by phenylephrine. If gap junctions were uncoupled, KCa3.1 channels became the predominant input to EDHF hyperpolarization, and relaxation was inhibited with ouabain, implicating a crucial link through Na+/K+-ATPase. There was no evidence for an equivalent link through KCa2.3 channels nor between these channels and the putative EDHF pathway involving natriuretic peptide receptor-C. Reconstruction of confocal z-stack images from pressurized arteries revealed KCa2.3 immunostain at endothelial cell borders, including endothelial cell projections, whereas KCa3.1 channels and Na+/K+-ATPase {alpha}2/{alpha}3 subunits were highly concentrated in endothelial cell projections and adjacent to myoendothelial gap junctions. Thus, extracellular [Ca2+]o appears to modify KCa3.1 channel activity through a protein kinase A-dependent mechanism independent of changes in endothelial [Ca2+]i. The resulting hyperpolarization links to arterial relaxation largely through Na+/K+-ATPase, possibly reflecting K+ acting as an EDHF. In contrast, KCa2.3 hyperpolarization appears mainly to affect relaxation through myoendothelial gap junctions. Overall, these data suggest that K+ and myoendothelial coupling evoke EDHF-mediated relaxation through distinct, definable pathways.