Two zinc(II) phthalocyanines (ZnPcs) were conjugated with a monoclonal antibody (MAb) directed against carcinoembryonic antigen (CEA), using an in situ activated carboxylic acid on the ZnPcs. The bioconjugate with the highest ZnPc/MAb ratio of 3 was investigated in vitro for its ability to target and fluorescently label human colorectal HT-29 cells. The ZnPc-CEA MAb 2 was observed to efficiently target HT-29 cells, about 37 times more than unconjugated ZnPc. Furthermore, in the presence of a 4-fold excess of unlabelled anti-CEA antibody, the fluorescence signal of 2 was reduced by ~90% showing that the targeting is CEA-mediated. These studies further confirm the high specificity of Pc-antibody conjugates for antigens over-expressed on tumor cells and warrant further investigations of these immunoconjugates and their derivatives for imaging of colorectal cancer.
phthalocyanine; carcinoembryonic antigen; antibody; colorectal cancer; fluorescence
Various dipyrroles possess important motifs for construction of pyrrole-containing pigments. A series of 1,2-dipyrrolylethynes (4a–d) has been efficiently synthesized using an improved one-pot double Sonagashira coupling from trimethylsilylethyne and various 2-iodopyrroles. The resulting 1,2-dipyrrolylethynes were further transformed into novel indolyl-, ethenyl- and carboranyl-dipyrroles (5–7) using the Larock indole synthesis, stereoselective catalytic hydrogenation, or B10H14. Indolyl-dipyrroles were found to selectively bind fluoride ions using one pyrrolic and the indolyl NHs, whereas the carboranyl- and ethenyl-dipyrroles are potentially valuable precursors for the synthesis of porphyrin isomers and expanded pigments.
carborane; dipyrrole; indole; Larock; Sonagashira
A series of twenty-two BODIPY compounds were synthesized, containing various meso-phenyl and meso-thienyl groups, and their spectroscopic and structural properties were investigated using both experimental and computational methods. Further functionalization of the BODIPY framework via iodination at the 2,6-pyrrolic positions was explored in order to determine the effect of these heavy atoms on the photophysical and cytotoxicity of the meso-aryl-BODIPYs. BODIPYs bearing meso-thienyl substituents showed the largest red-shifted absorptions and emissions and reduced fluorescence quantum yields. The phototoxicity of the BODIPYs in human carcinoma HEp2 cells depends on both the presence of iodines and the nature of the meso-aryl groups. Six of the eleven 2,6-diiodo-BODIPYs investigated showed at least a sevenfold enhancement in phototoxicity (IC50 = 3.5–28 μM at 1.5 J/cm2) compared with the non-iodinated BODIPYs, while the others showed no cytotoxicity, while their singlet oxygen quantum yields ranged from 0.02 to 0.76. Among the series investigated, BODIPYs 2a and 4a bearing electron-donating meso-dimethoxyphenyl substituents showed the highest phototoxicity and dark/phototoxicity ratio, and are therefore the most promising for application in PDT.
BODIPY; PDT; Fluorescence; Phototoxicity; Cellular uptake
Seven polyamine conjugates of a tri(p-carboranylmethylthio)tetrafluorophenylporphyrin were prepared in high yields by sequential substitution of the p-phenyl fluoride of tetrakis(pentafluorophenyl)porphyrin (TPPF), and investigated as boron delivery agents for boron neutron capture therapy (BNCT). The polyamines used were derivatives of the natural-occurring spermine with different lengths of the carbon chains, terminal primary amine groups and, in two of the conjugates, additional aminoethyl moieties. A tri(polyethylene glycol) conjugate was also synthesized for comparison purposes. The polyamine conjugates showed low dark cytotoxicity (IC50 > 400 μM) and low phototoxicity (IC50 > 40 μM at 1.5 J/cm2). All polyamine conjugates, with one exception, showed higher uptake into human glioma T98G cells (up to 12-fold) than the PEG conjugate, and localized preferentially in the cell ER, Golgi and the lysosomes. Our results show that spermine derivatives can serve as effective carriers of boronated porphyrins for the BNCT of tumors.
BNCT; polyamine; PDT; carborane; porphyrin
Four phthalocyanine (Pc)-peptide conjugates designed to target the epidermal growth factor receptor (EGFR) were synthesized and evaluated in vitro using four cell lines: human carcinoma A431 and HEp2, human colorectal HT-29, and kidney Vero (negative control) cells. Two peptide ligands for EGFR were investigated: EGFR-L1 and -L2, bearing 6 and 13 amino acid residues, respectively. The peptides and Pc-conjugates were shown to bind to EGFR using both theoretical (Autodock) and experimental (SPR) investigations. The Pc-EGFR-L1 conjugates 5a and 5b efficiently targeted EGFR and were internalized, in part due to their cationic charge, whereas the uncharged Pc-EGFR-L2 conjugates 4b and 6a poorly targeted EGFR maybe due to their low aqueous solubility. All conjugates were non-toxic (IC50 > 100 µM) to HT-29 cells, both in the dark and upon light activation (1 J/cm2). Intravenous (iv) administration of conjugate 5b into nude mice bearing A431 and HT-29 human tumor xenografts resulted in a near-IR fluorescence signal at ca. 700 nm, 24 h after administration. Our studies show that Pc-EGFR-L1 conjugates are promising near-IR fluorescent contrast agents for CRC, and potentially other EGFR over-expressing cancers.
The syntheses and spectroscopic properties of a series of pegylated zinc(II)-phthalocyanines (Zn-Pcs) containing one, two or eight tri(ethylene glycol) chains are described. The single molecular structure of a phthalonitrile precursor containing one hydroxyl and one PEG group, and its unique intermolecular hydrogen bonding are presented. The pegylated Pcs are highly soluble in polar organic solvents and have fluorescence quantum yields in the range 0.08–0.28.
PDT; PEG; phthalocyanine; phthalonitrile; fluorescence
A series of amino acid conjugates of chlorin e6, containing lysine or aspartic acid residues in positions 173, 152 or 131 of the macrocycle were synthesized and investigated as photosensitizers for photodynamic therapy of tumors. All three regioisomers were synthesized in good yields and in 5 steps or less from pheophytin a (1). In vitro investigations using human carcinoma HEp2 cells show that the 152-lysyl regioisomers accumulate the most within cells, and the most phototoxic are the 131 regioisomers. The main determinant of biological efficacy appears to be the conjugation site, probably because of molecular conformation. Molecular modeling investigations reveal that the 173-substituted chlorin e6 conjugates are L-shaped, the 152 and 131 regioisomers assume extended conformations, and the 131 derivatives are nearly linear. It is hypothesized that the 131-aspartylchlorin e6 conjugate may be a more efficient photosensitizer for PDT than the commercial currently used 152 derivative.
b-Bilene hydrochlorides are shown to be improved intermediates for the synthesis of metallo-isoporphyrins in enhanced yields (28% vs. 6%). Several new diamagnetic zinc(II) and a novel paramagnetic copper(II) isoporphyrin salts were also obtained using this approach. Metal-free isoporphyrins were also isolated. In vitro studies using human carcinoma HEp2 cells show that all metallo-isoporphyrins accumulate within cells and localize partially in the mitochondria. The zinc-isoporphyrins were found to be moderately phototoxic while the copper complex showed the lowest phototoxicity, maybe as a result of its paramagnetic nature.
intracellular localization; metalloisoporphyrins; porphyrins; synthesis; toxicity
The syntheses, photophysical properties and in vitro biological behavior of a series of nine Zn(II)-phthalocyanines (ZnPcs) bearing one to eight positively-charged trimethylaminophenoxy groups are reported. All ZnPcs are highly soluble in polar organic solvents, and show fluorescence and singlet oxygen quantum yields in the ranges 0.11–0.21 and 0.16–0.47, respectively. The cytotoxicity of the ZnPcs depends on both the number of charges and their site of substitution (α vs. β) on the Pc isoindole units; the most promising for PDT application are the α-substituted di-cationic ZnPcs 6a and 17a.
Di-cationic Zn(II)-phthalocyanines (ZnPcs) are promising photosensitizers for the photodynamic therapy (PDT) of cancers and for photoinactivation of viruses and bacteria. Pegylation of photosensitizers in general enhances their water-solubility and tumor cell accumulation. A series of pegylated di-cationic ZnPcs were synthesized from conjugation of a low molecular weight PEG group to a pre-formed Pc macrocycle, or by mixed condensation involving a pegylated phthalonitrile. All pegylated ZnPcs were highly soluble in polar organic solvents but were insoluble in water; they have intense Q absorptions centered at 680 nm and fluorescence quantum yields of ca. 0.2 in DMF. The non-pegylated di-cationic ZnPc 6a formed large aggregates, which were visualized by atomic force microscopy. The cytotoxicity, cellular uptake and subcellular distribution of all cationic ZnPcs were investigated in human carcinoma HEp2 cells. The most phototoxic compounds were found to be the α-substituted Pcs. Among these, Pcs 4a and 16a were the most effective (IC50 ca. 10 μM at 1.5 J/cm2), in part due to the presence of a PEG group and the two positive charges in close proximity (separated by an ethylene group) in these macrocycles. The β-substituted ZcPcs 6b and 4b accumulated the most within HEp2 cells but had low photocytoxicity (IC50 > 100 μM at 1.5 J/cm2), possibly as a result of their lower electron density of the ring and more extended conformations compared with the α-substituted Pcs. The results show that the charge distribution about the Pc macrocycle and the intracellular localization of the cationic ZnPcs mainly determine their photodynamic activity.
phthalocyanine; PDT; pegylation; cationic photosensitizer
Background and Objective
Boronated porphyrins have emerged as promising dual sensitizers for use in both photo-dynamic therapy (PDT) and boron neutron capture therapy (BNCT), by virtue of their known tumor affinity, low cytotoxicity in dark conditions, and easy synthesis with high boron content. Octa-anionic 5,10,15,20-tetra[3,5-(nido-carboranylmethyl)phenyl] porphyrin (H2OCP) is a boronated porphyrin having eight boron clusters linked to the porphyrin ring. To evaluate H2OCP’s applicability to both PDT and BNCT, we performed an in vitro and ex vivo study using F98 rat glioma cells.
Materials and Methods
We examined the time-dependent cellular uptake of H2OCP by measuring the boron concentration over time, and compared the cellular uptake/clearance of boron after exposure to H2OCP in conjunction with boronophenylalanine (BPA) and sodium borocaptate (BSH), both of which are currently used in clinical BNCT studies. We evaluated the cytotoxicity of H2OCP-mediated PDT using a colony-forming assay and assessed the tumor-igenicity of the implantation of pre-treated cells using Kaplan–Meier survival curves. Fluorescence microscopy was also performed to evaluate the cellular uptake of H2OCP.
H2OCP accumulated within cells to a greater extent than BPA/BSH, and H2OCP was retained inside the cells to approximately the same extent as BSH. The cell-surviving fraction following laser irradiation (8 J/cm2, 18 hours after exposure to 10 μg B/ml H2OCP) was <0.05. The median survival times of the pre-treated cell-implanted rats were longer than those of the untreated group (P < 0.05). The fluorescence of H2OCP was clearly demonstrated within the tumor cells by fluorescence microscopy.
H2OCP has been proven to be a promising photosensitizer for PDT. H2OCP has also been proposed as a potentially effective replacement of BPA or BSH, or as a replacement of both BPA/BSH. Our study provides more evidence that H2OCP could be an effective novel dual sensitizing agent for use in both PDT and BNCT.
boron neutron capture therapy; boronated porphyrin; F98 rat glioma cells; H2OCP; photodynamic diagnosis; photodynamic therapy
N-Substituted porphyrins are well known for the distortion they exhibit of the porphyrin plane through the sp3 hybridization of one of the pyrrolenic units. They have served as model compounds in investigations of many biochemical processes. In this paper, we developed an efficient route to N-substituted porphyrins, and report the synthesis of a series of new N-substituted cobaltacarborane-porphyrins containing one or two cobaltabisdicarbollide anions linked by (CH2CH2O)2 chains to either the core porphyrin nitrogens or to a meso-aminophenyl group. These conjugates show different degrees of distortion of the porphyrin macrocycle, which affect their spectroscopic and electrochemical properties. In particular, the core N-substituted conjugates show significant fluorescence quenching in comparison with the non-core substituted macrocycles. The X-ray structures of two targeted core N-cobaltacarborane porphyrin conjugates are presented. The electrochemical and spectroelectrochemical properties of these porphyrin conjugates were investigated; while the peripheral N-substituted cobaltacarboranylporphyrins undergo three reversible reductions and three reversible oxidations (two attributed to the porphyrin and one to the CoIII cluster), the core N-substituted porphyrins exhibit complicated electrochemical behavior with coupled chemical reactions.
porphyrin; cobaltacarborane; reduction; oxidation
Several 2-iodopyrroles are used in Pd(0) catalyzed homocoupling reactions at room temperature in the presence of water to efficiently synthesize 2,2′-bipyrroles. These 2,2′-bipyrroles are strongly luminous materials and have high fluorescence quantum yields.
bipyrrole; homocoupling; iodopyrrole; palladium
Boron neutron capture therapy (BNCT) is based on the nuclear capture and fission reactions that occur when non-radioactive 10B is irradiated with low energy thermal neutrons to produce α-particles (10B[n,α]7Li). Carboranylporphyrins are a class of substituted porphyrins containing multiple carborane clusters. Three of these have been evaluated in the present study: 5,10,15,20-tetra-(4-nido-carboranyphenyl)tetrabenzoporphyrin (H2TBP), 5,10,15,20-tetra-(4-nido-carboranylphenyl)porphyrin (H2TCP) and 5,15-di-[3,5-(nido-carboranylmethyl)phenyl]-porphyrin (H2DCP). The goals of this study were two-fold. First, to determine the biodistribution of H2TBP, H2TCP and H2DCP following intracerebral (i.c.) administration by means of short term (30 min) convection enhanced delivery (CED) or sustained delivery over 24 h by osmotic pumps to F98 glioma bearing rats. Second, to determine the efficacy of H2TCP and H2TBP as boron delivery agents for BNCT in F98 glioma bearing rats. Tumor boron concentrations immediately after i.c. osmotic pump delivery were high (36–88 µg/g) and they remained so at 24 h (62–103 µg/g) The corresponding normal brain concentrations were low (0.8–5.2 µg/g) and the blood and liver concentrations were all undetectable. Based on these data, therapy studies were initiated at the Massachusetts Institute of Technology (MIT) Research Reactor (MITRR) with H2TCP and H2TBP 24 h after CED or osmotic pump delivery. Mean survival times (MST) of untreated and irradiated control rats were 23±3 and 27±3 d, respectively, while animals that received H2TCP or H2TBP, followed by BNCT, had a MST of 35±4 d and 44±10 d, respectively, which were better than those obtained following i.v. administration of boronophenylalanine (37±3 d). However, since the tumor boron concentrations of the carboranylporphyrins were 3–5X > i.v. BPA (~25 µg/g), we had expected that the MSTs would have been greater. Histopathologic examination of brains of BNCT treated rats revealed that there were large numbers of porphyrin-laden macrophages, as well as extracellular accumulations of porphyrins indicating that the seemingly high tumor boron concentrations did not represent the true tumor cellular uptake. Our data are the first to show that carboranyl porphyrins are effective delivery agents for BNCT of an experimental brain tumor. Based on these results, we now are in the process of evaluating carboranylporphyrins that could have enhanced cellular uptake following administration and improved therapeutic efficacy.
convection enhanced delivery; carboranylporphyrins; boron neutron capture therapy; F98 rat glioma
Carborane-functionalized conducting polymer films have been
electrogenerated in dichloromethane from the anodic oxidation of
ortho- (1), meta-
(3) and para-carborane (4)
isomers linked to two 2-thienyl units. The corresponding electrochemical
response was characterized by a broad reversible redox system corresponding to
the p-doping/undoping of the polythiophene backbone, the formal potential of
which increased in the order poly(1) < poly(3) <
poly(4), from ca. 0.50 to 1.15 V vs Ag/Ag+
10−2 M. From further UV–visible spectroscopy
analysis, the optical band gap was estimated at 1.8, 2.0 and 2.2 eV for
poly(1), poly(3) and poly(4),
respectively. The more conjugated and electroconductive character of
poly(1) is ascribed to a more planar conformation of the
conjugated backbone resulting from an intramolecular
β–β′ cyclization reaction
in the monomer, consequently yielding a fused conjugated polymer. Molecular
modeling calculations using the DFT method support this hypothesis. The surface
topography and maps of the conductive domains of the electropolymerized films
were evaluated by conducting probe AFM. The three polymers exhibit fairly
similar morphological characteristics and a surface roughness of ~2 nm.
Current–voltage (I–V) characteristics of
conducting AFM tip-carborane polymer–ITO junctions showed that
poly(1) had the highest conductivity.
The structure of the ring-opened product from direct oxidation of meso-tetraarylporphyrins has been controversial for three decades. Herein we show that bilitrienones 2 are obtained from oxidation of metal-free dodecasubstituted porphyrins 1 in the presence of sodium nitrite, trifluoroacetic acid and air oxygen. The presence of the para-nonyl groups in 1b stabilized the corresponding bilitrienone 2b, which was characterized by X-ray crystallography. In the absence of the para-nonyl groups bilitrienone 2a undergoes a rapid hydration reaction, giving biladienone 3a as the major isolated product. The molecular structures of 2b and 3a, and. the photochemical isomerization of 3a are discussed.
This study was designed to provide more detailed information on the subcellular sites of binding of the porphycene, termed 9-capronyloxytetrakis (methoxyethyl) porphycene (CPO), with a fluorescence resonance energy transfer (FRET) technique. The proximity of CPO to two fluorescent probes was determined: nonyl acridine orange (NAO), a dye with specific affinity for the mitochondrial lipid cardiolipin, and dihexaoxacarbocyanine iodide (DiOC6), an agent that labels the endoplasmic reticulum (ER). FRET spectra indicated energy transfer between DiOC6 and CPO but no significant transfer between NAO and CPO. These results confirm data obtained by fluorescence microscopy, suggesting a similar pattern of subcellular localization by CPO and DiOC6 but not by CPO and NAO. However, when cells containing CPO were irradiated and then loaded with NAO, FRET between the two fluorophores was observed. Hence, a relocalization of CPO can occur during irradiation. These data provide an explanation for recent studies on CPO-catalyzed photodamage to both ER and mitochondrial Bcl-2.
Syntheses of two new cobaltacarborane–phthalocyanine conjugates, one anionic (Pc 6) and one zwitterionic (Pc 7), were accomplished via cyclotetramerization of the corresponding cobaltacarborane-substituted phthalonitriles (4 or 5) with excess phthalonitrile in quinoline. X-ray structures of two phthalonitrile precursors (2 and 3) were obtained and are discussed, and the absorption and emission properties of the two cobaltacarborane–phthalocyanine conjugates in several solvents were investigated. The anionic conjugate 6 exists mainly as a monomer in polar organic solvents and has fluorescence quantum yields in the region 0.2–0.3. The zwitterionic conjugate 7 aggregates in solution and displays lower quantum yields ~0.1 in organic solvents.
Cobaltacarborane; Phthalocyanine; BNCT; PDT
New cobalt(III) bis(dicarbollide) complexes covalently linked to two 2-oligothienyl units have been synthesized and electropolymerized in acetonitrile electrolyte in order to produce the corresponding polythiophene films containing in-chain metallic centers. The polymer films electrogenerated from the bithienyl (4b) and terthienyl (4c) derivatives display redox processes attributed to the Co(III)/Co(II) couple at ca. −1.1 V vs SCE and to the p-doping/undoping of the expected quaterthienyl and sexithienyl segments at ca. 0.8 V vs SCE. In contrast, the anodic oxidation of the thienyl (4a) derivative leads to passivation of the electrode surface. As the length of the oligothiophene substituents increases, the metallic and dicarbollide cage carbon atoms contributions in the HOMO decrease dramatically so that the highest occupied frontier orbitals of 4b and 4c can be considered as almost purely oligothiophene-based. From further UV–vis spectroscopy analysis, it is demonstrated that the polymer incorporating the sexithienyl segments is more conjugated than that with the quaterthienyl segments as the absorption maximum for the interband π–π* transition was observed at 410 and 448 nm for poly(4b) and poly(4c) respectively. Furthermore, these polymers display a more extended degree of conjugation than the parent oligothiophenes. Such features indicate a significant electronic delocalization through the cobaltabisdicarbollide moiety. Their conducting probe atomic force microscopy characterization indicates that poly(4b) and poly(4c) behave like heavily doped semiconductors rather than pure semiconductors. Mean conductivity values extracted from the current–voltage profiles are 1.4 ×10−4 and 7.5 ×10−4 S cm−1 for poly(4b) and poly(4c), respectively. Such materials are found to be efficient for the electrocatalytic reduction of protons to dihydrogen, as exemplified for poly(4b). The overpotential for hydrogen evolution is significantly decreased by ca. 230 mV with respect to that obtained with the bare electrode (measured for a current density of 1.4 mA cm−2 in the presence of 20 mM HBF4).
conducting polymers; metallopolymers; polythiophenes; carboranes; electropolymerization
This study was designed to examine modes of cell death after photodynamic therapy (PDT). Murine leukemia L1210 cells and human prostate Bax-deficient DU-145 cells were examined after PDT-induced photodamage to the endoplasmic reticulum (ER). Previous studies indicated that this treatment resulted in a substantial loss of Bcl-2 function. Both apoptosis and autophagy occurred in L1210 cells after ER photodamage with the latter predominating after 24 hr. These processes were characterized by altered cellular morphology, chromatin condensation, loss of mitochondrial membrane potential and formation of vacuoles containing cytosolic components. Western blots demonstrated processing of LC3-I to LC3-II, a marker for autophagy. In DU145 cells, PDT initiated only autophagy. Phosphatidylinositol (PI) 3-kinase inhibitors suppressed autophagy in both cell lines as indicated by inhibition of vacuolization and LC3 processing. Inhibitors of apoptosis and/or autophagy were then used to delineate the contributions of the two pathways to the effects of PDT. Given the ability of autophagy to upregulate MHC-11 peptide presentation, autophagy may play a role in the ability of photodynamic therapy to stimulate immunologic recognition of target cells.
apoptosis; autophagy; photodynamic therapy
A series of carboranylporphyrins containing either amine or phosphonic acid functionalities and two to six closo-carborane clusters have been synthesized via a [2+2] condensation of a dimethylamino- or diethylphosphonate-substituted dipyrromethane with a dicarboranylmethyl-benzaldehyde. The X-ray structures of four key reaction intermediates (1, 2, 3 and 4a) and of two target porphyrins, the diphosphonate ester- and the diamino-tetracarboranylporphyrins 5b and 6a are presented and discussed. In vitro studies using human carcinoma HEp2 and human glioblastoma T98G cells show that these porphyrins are non-toxic in the dark up to 100 μM concentrations, and that a tetracarboranylporphyrin bearing two quaternary ammonium groups is the most efficiently taken up by cells at short times (up to 8 h), followed by a dicarboranylporphyrin bearing three phosphonic acid substituents. All carboranylporphyrins delivered therapeutic amounts of boron to T98G cells and localized mainly within the cell lysosomes.
BNCT; carborane; porphyrin; cytotoxicity; cellular uptake
In the title molecule, C15H18O2S, the dimethylcyclohexadiene unit is slightly non-planar, having a folded conformation with the two double-bond planes forming a dihedral angle of 3.9 (6)°. Methyl groups of the dimethylcyclohexadiene ring tilt away from each other, forming internal C—C—C(Me) angles approximately 11° greater than the exterior angles.
The title molecule, C19H21N3, an important precursor in the synthesis of porphyrin–fentanyl conjugates, has its piperidine ring in the chair conformation, with endocyclic torsion-angle magnitudes in the range 53.26 (8)–60.63 (9)°. The C N group is axial, while the CH2Ph and NHPh groups are equatorial. The NH group does not engage in strong hydrogen bonding, but forms an intermolecular N—H⋯N interaction.
The title molecule, C30H28N2O4, has crystallographic twofold rotation symmetry, with the pyrrole planes forming a dihedral angle of 40.49 (4)°. The pyrrole N—H donor and adjacent ester carbonyl acceptor form R
2(10) hydrogen-bonded rings about inversion centers, leading to chains of hydrogen-bonded molecules along .
The title molecule, C24H20N2O4S2, has crystallographic inversion symmetry with a triple-bond distance of 1.206 (2) Å. The alkyne is not quite linear, with a C—C C angle of 175.78 (16)°. The planar pyrrole rings are parallel but offset from coplanarity by 0.318 (1) Å. The conformation of the sulfonyl group with respect to the pyrrole ring is such that an O atom is nearly eclipsed with this ring, having an O—S—N—C torsion angle of 3.48 (11)°. C—H⋯O interactions [C⋯O 3.278 (2) Å, 136° about H] between pyrrole H and sulfonyl O atoms lead to the formation of ladder-like chains.