Synthesis, X-ray structures, and spectroscopic and electrochemical properties of (mu-oxo)bis(mu-carboxylato)diruthenium complexes having six imidazole bases as terminal ligands

Complexes [Ru2O(O2CR)(2)(1-MeIm)(6)](ClO4)(2) (la-c), [Ru2O(O2CR)(2)(ImH)(6)](ClO4)(2) (2a,b), and [Ru2O(O2CR)(2)(4-MeImH)(6)](ClO4)(2) (3a,b) with a (mu-oxo)bis(mu-carboxylato)diruthenium(III) core have been prepared by reacting Ru2Cl(O2CR)(4) with the corresponding imidazole base, viz. 1-methylimidazole (1-MeIm), imidazole (ImH), and 4-methylimidazole (4-MeImH) in methanol, followed by treatment with NaClO4 in water (R: Me, a; C6H4-p-OMe, b; C6H4-p-Me, c). Diruthenium(III,IV) complexes [Ru2O(O2CR)(2)(1-MeIm)(6)](ClO4)(3) (R: Me, 4a; C6H4-p-OMe, 4b; C6H4-p-Me, 4c) have been prepared by one-electron oxidation of 1 in MeCN with K2S2O8 in water. Complexes la, 2a . 3H(2)O, and 4a . 1.5H(2)O have been structurally characterized. Crystal data for the complexes are as follows: la, orthorhombic, P2(1)2(1)2(1), a = 7.659(3) Angstrom, b = 22.366(3) Angstrom, c = 23.688(2) Angstrom, V = 4058(2) Angstrom(3), Z = 4, R = 0.0475, and R-w = 0.0467 for 2669 reflections with F-o > 2 sigma(F-o); 2a . 3H(2)O, triclinic, , a = 13.735(3) Angstrom, b = 14.428(4) Angstrom, c = 20.515(8) Angstrom, alpha = 87.13(3)degrees, beta = 87.61(3)degrees, gamma = 63.92(2)degrees, V = 3646(2) Angstrom(3), Z = 4, R = 0.0485 and R-w = 0.0583 for 10 594 reflections with F-o > 6 sigma(F-o); 4a . 1.5H(2)O triclinic, , a = 11.969(3) Angstrom, b = 12.090(6) Angstrom, c = 17.421(3) Angstrom, alpha = 108.93(2)degrees, beta = 84.42(2)degrees, gamma = 105.97(2)degrees, V = 2292(1) Angstrom(3), Z = 2, R = 0.0567, and R-w = 0.0705 for 6775 reflections with F-o > 6 sigma(F-o). The complexes have a diruthenium unit held by an oxo and two carboxylate ligands, and the imidazole ligands occupy the terminal sites of the core. The Ru-Ru distance and the Ru-O-oxo-Ru angle in la and 2a . 3H(2)O are 3.266(1), 3.272(1) Angstrom and 122.4(4), 120.5(2)degrees, while in 4a . 1.5H(2)O these values are 3.327(1) Angstrom and 133.6(2)degrees. The diruthenium(III) complexes 1-3 are blue in color and they exhibit an intense visible band in the range 560-575 nm. The absorption is charge transfer in nature involving the Ru(III)-d pi and O-oxo-p pi orbitals. The diruthenium(III,IV) complexes are red in color and show an intense band near 500 nm. The diruthenium(III) core readily gets oxidized with K2S2O8 forming quantitatively the diruthenium(III,IV) complex. The visible spectral record of the conversion shows an isosbestic point at 545 nm for 1 and at 535 nm for 2 and 3. Protonation of the oxide bridge by HClO4 in methanol yields the [Ru-2(mu-OH)(mu-O2CR)(2)](3+) core. The hydroxo species shows a visible band al 550 nm. The pK(a) value for la is 2.45. The protonated species are unstable. The 1-MeIm species converts to the diruthenium(III,IV) core, while the imidazole complex converts to [Ru(ImH)(6)](3+) and some uncharacterized products. Complex [Ru(ImH)(6)](ClO4)(3) has been structurally characterized. The diruthenium(III) complexes are essentially diamagnetic and show characteristic H-1 NMR spectra indicating the presence of the dimeric structure in solution. The diruthenium(III,IV) complexes are paramagnetic and display rhombic EPR spectral features. Complexes 1-3 are redox active. Complex 1 shows the one-electron reversible Ru-2(III)/(RuRuIV)-Ru-III, one-electron quasireversible (RuRuIV)-Ru-III/Ru-2(IV), and two-electron quasireversible Ru-2(III)/Ru-2(II) couples near 0.4, 1.5, and -1.0 V vs SCE In MeCN-0.1 M TBAP, respectively, in the cyclic and differential pulse voltammetric studies. Complexes 2 and 3 exhibit only reversible Ru-2(III)/(RuRuIV)-Ru-III and the quasireversible (RuRuIV)-Ru-III/Ru-2(IV) couples near 0.4 and 1.6 V vs SCE, respectively, The observation of a quasireversible one-step two-electron transfer reduction process in 1 is significant considering its relevance to the rapid and reversible Fe-2(III)/Fe-2(II) redox process known for the tribridged diiron core in the oxy and deoxy forms of hemerythrin.

Photoinduced DNA and Protein Cleavage Activity of Ferrocene-Appended L-Methionine Reduced Schiff Base Copper(II) Complexes of Phenanthroline Bases

Ferrocene-appended ternary copper(H) complexes of phenanthroline bases having CuN3OS coordination with an axial Cu-S bond derived from L-methionine reduced Schiff base shows red light induced oxidative DNA cleavage activity following a hydroxyl radical pathway. The dipyridophenazine complex, in addition, displays photoinduced oxidative cleavage of bovine serum albumin protein in UV-A light.

Singlet emission studies on porphyrins appended with heterocyclic bases

Porphyrins appended in the meso positions with 1,2-diazole, indole and quinoline are shown to exhibit enhanced fluorescence quantum yields relative to meso tetraphenyl porphyrin. The singlet emission yields decrease with the number of appended heterocyclic bases. An intramolecular charge transfer resonance mechanism has been advanced to interpret these results.

Photocytotoxic Lanthanum(III) and Gadolinium(III) Complexes of Phenanthroline Bases Showing Light-Induced DNA Cleavage Activity

Lanthanide complexes of formulation [La(B)(2)(NO3)(3)] (1-3) and [Gd(B)(2)(NO3)(3)] (4-6), where B is a N,N-donor phenanthroline base, namely, 1,10-phenanthroline (phen in 1, 4),dipyrido[3,2-d2',3'-f]quinoxaline (dpq in 2,5) and dipyrido[3,2-a2',3'-c]phenazine (dppz in 3, 6), have been prepared, characterized from physicochemical data, and their photoinduced DNA and protein cleavage activity studied The photocytotoxicity of the dppz complexes 3 and 6 has been studied using HeLa cancer cells. The complexes exhibitligand centered bands in the UV region The dppz complexes show thelowest energy band at 380 nm in N,N-dimethylformamide (DMF) The La(III)complexes are diamagnetic. The Gd(III) complexes (4-6) have magneticmoments that correspond to seven unpaired electrons The complexes are1(.)1 electrolytic in aqueous DMF The dpq and dppz complexes in DMFshow ligand-based reductions. The complexes display moderate binding propensity to calf thymus DNA giving binding constant values in the range of 5.7 x 10(4)-5.8 x 10(5) M-1 with a relative order. 3, 6 (dppz)> 2, 5 (dpq) > 1, 4 (phen) The binding data suggest DNA surface and/or groove binding nature of the complexes. The complexes do not show any hydrolytic cleavage of plasmid supercoiled pUC19 DNA. The dpq and dppz complexes efficiently cleave SC DNA to its nicked circular form onexposure to UV-A light of 365 nm at nanomolar complex concentration. Mechanistic studies reveal the involvement of singlet oxygen (O-1(2)) and hydroxyl radical (HO center dot) as the cleavage active species.The complexes show binding propensity to bovine serum albumin (BSA)protein giving K-BSA values of similar to 10(5) M-1. The dppz complexes 3 and 6 show BSA protein cleavage activity in UV-A light of 365 nm The dppz complexes 3 and 6 exhibit significant photocytotoxicity in HeLa cells giving respective IC50 values of 341 nM and 573 nM in UV-A light of 365 nm for an exposure time of 15 min (IC50 > 100 mu M in dark for both the complexes) Control experiments show significant dark and phototoxicity of the dppz base alone (IC50 = 413 nM in light with 4 h incubation in dark and 116 mu M in dark with 24 h incubation). A significant decrease in the dark toxicity of the dppz base is observedon binding to the lanthanide ions while retaining similar phototoxicity.

Ferrocene-Conjugated L-Tryptophan Copper(II) Complexes of Phenanthroline Bases Showing DNA Photocleavage Activity and Cytotoxicity

Ferrocene-conjugated L-tryptophan (L-Trp) reduced Schiff base (Fc-TrpH) copper(II) complexes [Cu(Fc-Trp)(L)](ClO(4)) of phenanthroline bases (L), viz. 2,2'-bipyridine (bpy in 1), 1,10-phenanthroline (phen in 2), dipyrido[3,2-d:2',3'-f]quinoxaline (dpq in 3), and dipyrido[3,2-a:2',3'-c]phenazine (dppz in 4), were prepared and characterized and their photocytotoxicity studied. Cationic reduced Schiff base (Ph-TrpH) complexes [Cu(Ph-Trp)(L)(H(2)O)] (ClO(4)) (L = phen in 5; dppz in 6) having the ferrocenyl moiety replaced by a phenyl group and the Zn(II) analogue (7) of complex 4 were prepared and used as control species. The crystal structures of 1 and 5 with respective square-planar CuN(3)O and square-pyramidal CuN(3)O(2) coordination geometry show significantly different core structures. Complexes 1-4 exhibit a Cu(II)-Cu(I) redox couple near -0.1 V and the Fc(+)-Fc couple at similar to 0.5 V vs SCE in DMF-0.1 M [Bu(4)(n)N] (ClO(4)) (Fc = ferrocenyl moiety). The complexes display a copper(II)-based d-d band near 600 nm and a Fc-centered band at similar to 450 nm in DMF-Tris-HCl buffer. The complexes are efficient binders to calf thymus DNA. They are synthetic chemical nucleases in the presence of thiol or H(2)O(2), forming hydroxyl radicals. The photoactive complexes are cleavers of pUC19 DNA in visible light, forming hydroxyl radicals. Complexes 2-6 show photocytotoxicity in HeLa cancer cells, giving IC(50) values of 4.7, 10.2, 1.3, 4.8, and 4.3 mu M, respectively, in visible light with the appearance of apoptotic bodies. The complexes also show photocytotoxicity in MCF-7 cancer cells. Nuclear chromatin cleavage has been observed with acridine orange/ethidium bromide (AO/EB) dual staining with complex 4 in visible light. The complexes induce caspase-independent apoptosis in the HeLa cells.

Ferrocene-Conjugated Copper(II) Complexes of L-Methionine and Phenanthroline Bases: Synthesis, Structure, and Photocytotoxic Activity

Ferrocene-conjugated reduced Schiff base (Fc-metH) copper(II) complexes of L-methionine and phenanthroline bases, namely, Cu(Fc-met)(B)](NO3), where B is 1,10-phenanthroline (phen in 1), dipyrido3,2-d:2',3'-f]quinoxaline (dpq in 2), dipyrido3,2-a:2',3'-c]phenazine (dppz in 3), and 2-(naphthalen-1-yl)-1H-imidazo4,5-f]1,10]phenanthroline (nip in 4), were prepared and characterized and their photocytotoxicity studied (Fc = ferrocenyl moiety). Complexes Cu(Ph-met)(B)](NO3) of the reduced Schiff base from benzaldehyde and L-methionine (Ph-metH) and B (phen in 5, dppz in 6) were prepared and used as control species. Complexes 1 and 5 were structurally characterized by X-ray crystallography. Complex 1 as a discrete monomer has a CuN3OS core with the thiomethyl group as the axial ligand. Complex 5 has a polymeric structure with a CuN3O2 core in the solid state. Complexes 5 and 6 are formulated as Cu(Ph-met)(B)(H2O)] (NO3) in an aqueous phase based on the mass spectral data. Complexes 1-4 showed the Cu(II)-Cu(I) and Fc(+)-Fc redox couples at similar to 0.0 and similar to 0.5 V vs SCE, respectively, in DMF-0.1 M (Bu4N)-N-n](ClO4). A Cu(II)-based weak d-d band near 600 nm and a relatively strong ferrocenyl band at similar to 450 nm were observed in DMF-Tris-HCl buffer (1:4 v/v). The complexes bind to calf thymus DNA, exhibit moderate chemical nuclease activity forming (OH)-O-center dot radical species, and are efficient photocleavers of pUC19 DNA in visible light of 454, 568, and 647 rim, forming (OH)-O-center dot radical as the reactive oxygen species. They are cytotoxic in HeLa (human cervical cancer) and MCF-7 (human breast cancer) cells, showing an enhancement of cytotoxicity upon visible light irradiation. Significant change in the nuclear morphology of the HeLa cells was observed with 3 in visible light compared to the nonirradiated sample. Confocal imaging using 4 showed its nuclear localization within the HeLa cells.

Variable-Temperature EPR and Transport Studies on Poly(4,4'-methylenedianiline): Evidence for Bipolarons

The correlation between magnetic and transport properties is examined by studying poly(4,4'-methylenedianiline)(PMDA) salts and their bases using EPR and conductivity measurements. Five different PMDA salts (doped polymers)were prepared by chemical polymerization of 4,4'-methylenedianiline using different protonic acids. The PMDA bases were obtained by dedoping the salts using ammonium hydroxide. Ambient temperature electrical conductivity measurements show evidence for the doped PMDA system to be highly disordered. The EPR spectra of the samples were recorded in the range 20-200 "C, and the results were analyzed on the basis of the polaron-bipolaron model, which is typical of nondegenerate systems. Both PMDA salts and their bases consist of self-trapped, highly mobile polarons or radical cations. EPR studies on PMDA salts show evidence for the presence of thermally activated and temperature independent (or Pauli type) paramagnetism while the bases show thermally activated, Pauli and Curie-Weiss types of paramagnetism. The paramagnetism arises due to polarons.It is proposed that charge transport takes place through both polarons and bipolarons.

Synthesis, crystal structures, DNA binding and cleavage activity of L-glutamine copper(II) complexes of heterocyclic bases

Ternary L-glutamine (L-gln) copper(II) complexes [Cu(L-gln)(B)(H2O)](X) (B = 2,2'-bipyridine (bpy), X = 0.5SO(4)(2-), 1; B = 1,10-phenanthroline (phen), X = ClO4-, 2) and [Cu(L-gln)(dpq)(ClO4)] (3) (dpq, dipyridoquinoxaline) are prepared and characterized by physicochemical methods. The DNA binding and cleavage activity of the complexes have been studied. Complexes 1-3 are structurally characterized by X-ray crystallography. The complexes show distorted square pyramidal (4+1) CuN3O2 coordination geometry in which the N,O-donor amino acid and the N, N-donor heterocyclic base bind at the basal plane with a H2O or perchlorate as the axial ligand. The crystal structures of the complexes exhibit chemically significant hydrogen bonding interactions besides showing coordination polymer formation. The complexes display a d-d electronic band in the range of 610-630 nm in aqueous-dimethylformamide (DMF) solution (9:1 v/v). The quasireversible cyclic voltammetric response observed near -0.1 V versus SCE in DMF-TBAP is assignable to the Cu(II)/Cu(I) couple. The binding affinity of the complexes to calf thymus (CT) DNA follows the order: 3 (dpq) > 2 (phen) >> 1 (bpy). Complexes 2 and 3 show DNA cleavage activity in dark in the presence of 3-mercaptopropionic acid (MPA) as a reducing agent via a mechanistic pathway forming hydroxyl radical as the reactive species. The dpq complex 3 shows efficient photoinduced DNA cleavage activity on irradiation with a monochromatic UV light of 365 nm in absence of any external reagent. The cleavage efficiency of the DNA minor groove binding complexes follows the order:3 > 2 >> 1. The dpq complex exhibits photocleavage of DNA on irradiation with visible light of 647.1 nm. Mechanistic data on the photo-induced DNA cleavage reactions reveal the involvement of singlet oxygen (O-1(2)) as the reactive species in a type-II pathway. (C) 2008 Elsevier B.V. All rights reserved.

Novel Functionalised Troger's Bases: Synthesis of a New Class of Troger's Base Analogues Containing Dicarboxyl Functionality

The synthesis of three new Troger's base analogues, each functionalized with two carboxyl groups, is described. Copyright.

Photo-induced double-strand DNA and site-specific protein cleavage activity of L-histidine (mu-oxo)diiron(III) complexes of heterocyclic bases

Three oxo-bridged diiron(III) complexes of L-histidine and heterocyclic bases [Fe-2(mu-O)(L-his)(2)(B)(2)](ClO4)(2) (1-3), where B is 2,2'-bipyridine (bpy),1,10-phenanthroline (phen), dipyrido[3,2-d:2',3'-f]quinoxaline (dpq), were prepared and characterized. The bpy complex 1 was structurally characterized by X-ray crystallography. The molecular structure showed a {Fe-2(mu-O)} core in which iron(III) in a FeN4O2 coordination is bound to tridentate monoanionic L-histidine and bidentate bpy ligands. The Fe center dot center dot center dot Fe distance is similar to 3.5 angstrom. The Fe-O-Fe unit is essentially linear, giving a bond angle of similar to 172 degrees. The complexes showed irreversible cyclic voltammetric cathodic response near -0.1 V vs. SCE in H2O-0.1 M KCl. The binuclear units displayed antiferromagnetic interaction between two high-spin (S = 5/2) iron(III) centers giving a -J value of -110 cm(-1). The complexes showed good DNA binding propensity giving a binding constant value of similar to 10(5) M-1. Isothermal titration calorimetric data indicated single binding mode to the DNA. The binding was found to be driven by negative free energy change and enthalpy. The dpq complex 3 showed oxidative double-strand DNA cleavage on exposure to UV-A and visible light. The phen complex 2 displayed single-strand photocleavage of DNA. The DNA double-strand breaks were rationalized from theoretical molecular docking calculations. Mechanistic investigations showed formation of hydroxyl radicals as the reactive species through photodecarboxylation of the L-histidine ligand. The complexes exhibited good binding propensity to bovine serum albumin (BSA) protein in Tris-HCl/NaCl buffer medium. The dpq complex 3 showed UV-A light-induced site-specific oxidative BSA cleavage forming fragments of similar to 45 kDa and similar to 20 kDa molecular weights via SOH pathway.

Interaction of rat testis protein, TP, with nucleic acids in vitro. Fluorescence quenching, UV absorption, and thermal denaturation studies

The nucleic acid binding properties of the testis protein, TP, were studied with the help of physical techniques, namely, fluorescence quenching, UV difference absorption spectroscopy, and thermal melting. Results of quenching of tyrosine fluorescence of TP upon its binding to double-stranded and denatured rat liver nucleosome core DNA and poly(rA) suggest that the tyrosine residues of TP interact/intercalate with the bases of these nucleic acids. From the fluorescence quenching data, obtained at 50 mM NaCl concentration, the apparent association constants for binding of TP to native and denatured DNA and poly(rA) were calculated to be 4.4 X 10(3) M-1, 2.86 X 10(4) M-1, and 8.5 X 10(4) M-1, respectively. UV difference absorption spectra upon TP binding to poly(rA) and rat liver core DNA showed a TP-induced hyperchromicity at 260 nm which is suggestive of local melting of poly(rA) and DNA. The results from thermal melting studies of binding of TP to calf thymus DNA at 1 mM NaCl as well as 50 mM NaCl showed that although at 1 mM NaCl TP brings about a slight stabilization of the DNA against thermal melting, a destabilization of the DNA was observed at 50 mM NaCl. From these results it is concluded that TP, having a higher affinity for single-stranded nucleic acids, destabilizes double- stranded DNA, thus behaving like a DNA-melting protein.

X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

New ternary copper(II) complexes of L-alanine and heterocyclic bases: DNA binding and oxidative DNA cleavage activity

Four new ternary copper(II) complexes of alpha-amino acid having polypyridyl bases of general formulation [Cu(L-ala)(B)(H2O)](X)(1-4), where L-ala is L-alanine, B is an N,N-donor heterocyclic base, viz. 2,2'-bipyridine (bpy, 1), 1,10-phenanthroline (phen, 2) and 5,6-phenanthroline dione (dione, 3), dipyrido[3,2:2',3'-f] quinoxaline (dpq, 4), and X = ClO4-/NO3- are synthesized, characterized by various spectroscopic and X-ray crystallographic methods. The complexes show a distorted square-pyramidal (4 + 1) CuN3O2 coordination geometry. The one-electron paramagnetic complexes (1-4) display a low energy d-d band near 600 nm in aqueous medium and show a quasi-reversible cyclic voltammetric response due to one-electron Cu(II)/Cu(I) reduction near - 100 mV (versus SCE) in DMF-0.1 M TBAP. Binding interactions of the complexes with calf thymus DNA (CT-DNA) were investigated by UV-Vis absorption titration, ethidium bromide displacement assay, viscometric titration experiment and DNA melting studies. All the complexes barring the complexes 1 and 3 are avid binder to the CT-DNA in the DNA minor groove giving an order: 4 > 2 >>>1, 3. The complexes 2 and 4 show appreciable chemical nuclease activity in the presence of 3-mercaptopropionic acid (MPA) as a reducing agent. Hydroxyl radical was investigated to be the DNA cleavage active species. Control experiments in the presence of distamycin-A show primarily minor groove-binding propensity for the complexes 2 and 4 to the DNA.

Theoretical calculations of base-base interactions in nucleic acids: I Stacking interactions in free bases

Stacking interactions in free bases were computed on the basis of molecular association. The results of the calculations were compared with the stacking patterns observed in a few single crystals of nucleic acid components as examples. The following are the conclusions: (i) there can be two types of stacking pattern classified as normal and inverted types for any two interacting bases and both can be energetically favourable (ii) in both the types the stacking interaction is a combined effect of the overlap of the interacting bases and relative positions and orientations of the atomic centres of the two bases (iii) crystal symmetry and H-bonding interaction may influence stacking patterns.

Anomalous reaction-diffusion as a model of nonexponential DNA escape kinetics

We show that data from recent experiments carried out on the kinetics of DNA escape from alpha-hemolysin nanopores [M. Wiggin, C. Tropini, C. T. Cossa, N. N. Jetha, and A. Marziali, Biophys. J. 95, 5317 (2008)] may be rationalized by a model of chain dynamics based on the anomalous diffusion of a particle moving in a harmonic well in the presence of a delta function sink. The experiments of Wiggin found, among other things, that the occasional occurrence of unusually long escape times in the distribution of chain trapping events led to nonexponential decays in the survival probability, S(t), of the DNA molecules within the nanopore. Wiggin ascribed this nonexponentiality to the existence of a distribution of trapping potentials, which they suggested was theresult of stochastic interactions between the bases of the DNA and the amino acids located on the surface of the nanopore. Based on this idea, they showed that the experimentally determined S(t) could be well fit in both the short and long time regimes by a function of the form (1+t/tau)(-alpha) (the so called Becquerel function). In our model, S(t) is found to be given by a Mittag-Leffler function at short times and by a generalized Mittag-Leffler function at long times. By suitable choice of certain parameter values, these functions are found to fit the experimental S(t) even better than the Becquerel function. Anomalous diffusion of DNA within the trap prior to escape over a barrier of fixed height may therefore provide a second, plausible explanation of the data, and may offer fresh perspectives on similar trapping and escape problems.