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1.
Antioxidants (Basel) ; 12(8)2023 Aug 17.
Artigo em Inglês | MEDLINE | ID: mdl-37627618

RESUMO

Oxidative DNA damage (ODD) by reactive oxygen species (ROS) or reactive nitrogen species (RNS) is an inevitable tradeoff for using oxidation processes by living cells as a source of energy [...].

2.
Free Radic Res ; 54(7): 517-524, 2020 Jul.
Artigo em Inglês | MEDLINE | ID: mdl-32781874

RESUMO

The present study reports radiation-chemical yields of 2.5-diaminoimidazolone (Iz) derivatives in X-irradiated phosphate-buffered solutions of guanosine and double-stranded DNA. Various gassing conditions (air, N20/O2 (4:1), N2O, vacuum) were employed to elucidate the contribution of several alternative pathways leading to Iz in reactions initiated by hydroxyl radical attack on guanine. In all systems, Iz was identified as the second by abundance guanine degradation product after 8-oxoguanine, formed in 1:5 (guanosine) and 1:3.3 (DNA) ratio to the latter in air-saturated solutions. Experimental data strongly suggest that the addition of molecular oxygen to the neutral guanine radical G(-H)• plays a major in Iz production in oxygenated solutions of double-stranded DNA while in other systems it may compete with recombination of G(-H)• with superoxide and/or alkyl peroxyl radicals. The production of Iz through hydroxyl radical attack on 8-oxoguanine was also shown to take place although the chemical yield of Iz (ca 6%) in this process is too low to compete with the other pathways. The linearity of Iz accumulation with dose also indicates a negligible contribution of this channel to its yield in all systems.


Assuntos
Dano ao DNA , DNA/química , Radicais Livres/química , Radical Hidroxila/química , Imidazóis/química , 8-Hidroxi-2'-Desoxiguanosina/química , Animais , DNA/efeitos da radiação , Diaminas/química , Guanosina/química , Masculino , Salmão
3.
Radiat Res ; 192(3): 324-330, 2019 09.
Artigo em Inglês | MEDLINE | ID: mdl-31298612

RESUMO

The production of 2-deoxyribonolactones (C1'-oxidation product), C4'-oxidized abasic sites and C5'-carbonyl terminated strand scission products was investigated in complexes of double-stranded DNA with protamine, poly-L-lysine and spermine exposed to X-ray radiation. The lesions were quantified by high-performance liquid chromatography through the release of the corresponding low-molecular-weight products 5-methylenefuran-2(5H)-one, N-(2'-hydroxy-ethyl)-5-methylene-D3-pyrrolin-2-one and furfural, respectively. All binders were found to increase the relative yield of C1' oxidation up to 40% of the total 2-deoxyribose damage through the indirect effect versus approximately 18% typically found in homogeneous solutions by the same technique. On the contrary, the yield of C5'-oxidation was found to be suppressed almost completely, while in homogeneous solutions it constituted approximately 14% of the total. The observed change in end product distribution is attributed to free valence transfer to and from the complexing agent, although the mechanisms associated with this process remain unclear.


Assuntos
Dano ao DNA/efeitos da radiação , Peptídeos/metabolismo , Poliaminas/metabolismo , Açúcares Ácidos/metabolismo , Oxirredução/efeitos da radiação
4.
Free Radic Res ; 50(7): 756-66, 2016 Jul.
Artigo em Inglês | MEDLINE | ID: mdl-27043476

RESUMO

The products of oxidative damage to double-stranded (ds) DNA initiated by photolytically generated sulfate radical anions SO4(•-) were analyzed using reverse-phase (RP) high-performance liquid chromatography (HPLC). Relative efficiencies of two major pathways were compared: production of 8-oxoguanine (8oxoG) and hydrogen abstraction from the DNA 2-deoxyribose moiety (dR) at C1,' C4,' and C5' positions. The formation of 8oxoG was found to account for 87% of all quantified lesions at low illumination doses. The concentration of 8oxoG quickly reaches a steady state at about one 8oxoG per 100 base pairs due to further oxidation of its products. It was found that another guanine oxidation product identified as 2-amino-5-(2'-alkylamino)-4H-imidazol-4-one (X) was released in significant quantities from its tentative precursor 2-amino-5-[(2'-deoxy-ß-d-erythro-pentofuranosyl)amino]-4H-imidazol-4-one (dIz) upon treatment with primary amines in neutral solutions. The linear dose dependence of X release points to the formation of dIz directly from guanine and not through oxidation of 8oxoG. The damage to dR was found to account for about 13% of the total damage, with majority of lesions (33%) originating from the C4' oxidation. The contribution of C1' oxidation also turned out to be significant (17% of all dR damages) despite of the steric problems associated with the abstraction of the C1'-hydrogen. However, no evidence of base-to-sugar free valence transfer as a possible alternative to direct hydrogen abstraction at C1' was found.


Assuntos
Ânions/química , Dano ao DNA , Guanina/química , Imidazóis/química , Sulfatos/química , Hidrogênio/química , Oxirredução
5.
Radiat Res ; 181(2): 131-7, 2014 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-24410455

RESUMO

A novel analytical high-performance liquid chromatography (HPLC)-based method of quantification of the yields of C4'-oxidized abasic sites, 1, in oxidatively damaged DNA has been elaborated. This new approach is based on efficient conversion of 1 into N-substituted 5-methylene-Δ(3)-pyrrolin-2-ones, 2, upon treatment of damaged DNA with primary amines in neutral or slightly acidic solutions with subsequent quantification of 2 by HPLC. The absolute and relative radiation-chemical yields of 1 in irradiated DNA solutions were re-evaluated using this method. The yields were compared with those of other 2-deoxyribose degradation products including 5-methylene-2(5H)-furanone, malondialdehyde, and furfural resulting from the C1', C4' and C5'-oxidations, respectively. The yield of free base release (FBR) determined in the same systems was employed as an internal measure of the total oxidative damage to the 2-deoxyribose moiety. Application of this technique identifies 1 as the most abundant sugar lesion in double-stranded (ds) DNA irradiated under air in solution (36% FBR). In single-stranded (ss) DNA this product is second by abundance (33% FBR) after 2-deoxyribonolactones (C1'-oxidation; 43% FBR). The production of nucleoside-5'-aldehydes (C5'-oxidation; 14% and 5% FBR in dsDNA and ssDNA, respectively) is in the third place. Taken together with the parallel reaction channel that converts C4'-radicals into malondialdehyde and 3'-phosphoglycolates, our results identify the C4'-oxidation as a prevalent pathway of oxidative damage to the sugar-phosphate backbone (50% or more of all 2-deoxyribose damages) in indirectly damaged DNA.


Assuntos
Cromatografia Líquida de Alta Pressão/métodos , Dano ao DNA , DNA/química , DNA/genética , Desoxirribose/metabolismo , Raios gama/efeitos adversos , DNA/metabolismo , Oxirredução/efeitos da radiação
6.
Nucleic Acids Res ; 38(2): 428-40, 2010 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-19892827

RESUMO

The 5R thymine glycol (5R-Tg) DNA lesion exists as a mixture of cis-(5R,6S) and trans-(5R,6R) epimers; these modulate base excision repair. We examine the 7:3 cis-(5R,6S):trans-(5R,6R) mixture of epimers paired opposite adenine in the 5'-GTgG-3' sequence with regard to nucleotide excision repair. Human XPA recognizes the lesion comparably to the C8-dG acetylaminoflourene (AAF) adduct, whereas XPC/HR23B recognition of Tg is superior. 5R-Tg is processed by the Escherichia coli UvrA and UvrABC proteins less efficiently than the C8-dG AAF adduct. For the cis-(5R, 6S) epimer Tg and A are inserted into the helix, remaining in the Watson-Crick alignment. The Tg N3H imine and A N(6) amine protons undergo increased solvent exchange. Stacking between Tg and the 3'-neighbor G*C base pair is disrupted. The solvent accessible surface and T(2) relaxation of Tg increases. Molecular dynamics calculations predict that the axial conformation of the Tg CH(3) group is favored; propeller twisting of the Tg*A pair and hydrogen bonding between Tg OH6 and the N7 atom of the 3'-neighbor guanine alleviate steric clash with the 5'-neighbor base pair. Tg also destabilizes the 5'-neighbor G*C base pair. This may facilitate flipping both base pairs from the helix, enabling XPC/HR23B recognition prior to recruitment of XPA.


Assuntos
Dano ao DNA , Enzimas Reparadoras do DNA/metabolismo , Proteínas de Ligação a DNA/metabolismo , Timina/análogos & derivados , Proteína de Xeroderma Pigmentoso Grupo A/metabolismo , Pareamento de Bases , Sequência de Bases , Sítios de Ligação , DNA/química , Endodesoxirribonucleases/metabolismo , Proteínas de Escherichia coli/metabolismo , Humanos , Modelos Moleculares , Ressonância Magnética Nuclear Biomolecular , Prótons , Estereoisomerismo , Timina/química , Timina/metabolismo
7.
Cardiovasc Res ; 86(1): 20-8, 2010 Apr 01.
Artigo em Inglês | MEDLINE | ID: mdl-20015977

RESUMO

AIMS: Beta-adrenergic receptor (beta-AR) stimulation induces apoptosis in adult rat ventricular myocytes (ARVMs) via the activation of glycogen synthase kinase-3beta (GSK-3beta) and mitochondrial pathways. However, beta-AR stimulation induces apoptosis only in a fraction ( approximately 15-20%) of ARVMs. We hypothesized that ARVMs may secrete/release a survival factor(s) which protects 80-85% of cells from apoptosis. METHODS AND RESULTS: Using two-dimensional gel electrophoresis followed by MALDI TOF and MS/MS, we identified ubiquitin (Ub) in the conditioned media of ARVMs treated with beta-AR agonist (isoproterenol). Western blot analysis confirmed increased Ub levels in the conditioned media 3 and 6 h after beta-AR stimulation. Inhibition of beta1-AR and beta2-AR subtypes inhibited beta-AR-stimulated increases in extracellular levels of Ub, whereas activation of adenylyl cyclase using forskolin mimicked the effects of beta-AR stimulation. Incubation of cells with exogenous biotinylated Ub followed by western blot analysis of the cell lysates showed uptake of extracellular Ub into cells, which was found to be higher after beta-AR stimulation (1.9 +/- 0.4-fold; P < 0.05 vs. control, n = 6). Pre-treatment with Ub inhibited beta-AR-stimulated increases in apoptosis. Inhibition of phosphoinositide 3-kinase using wortmannin and LY-294002 prevented anti-apoptotic effects of extracellular Ub. Ub pre-treatment inhibited beta-AR-stimulated activation of GSK-3beta and c-Jun N-terminal kinase (JNK) and increases in the levels of cytosolic cytochrome c. The use of methylated Ub suggested that the anti-apoptotic effects of extracellular Ub are mediated via monoubiquitination. CONCLUSION: beta-AR stimulation increases levels of Ub in the conditioned media. Extracellular Ub plays a protective role in beta-AR-stimulated apoptosis, possibly via the inactivation of GSK-3beta/JNK and mitochondrial pathways.


Assuntos
Quinase 3 da Glicogênio Sintase/metabolismo , Miócitos Cardíacos/citologia , Miócitos Cardíacos/metabolismo , Receptores Adrenérgicos beta/metabolismo , Ubiquitina/metabolismo , Adenilil Ciclases/metabolismo , Agonistas Adrenérgicos beta/farmacologia , Animais , Apoptose/fisiologia , Sobrevivência Celular/fisiologia , Células Cultivadas , Meios de Cultivo Condicionados/farmacologia , Citocromos c/metabolismo , Espaço Extracelular/metabolismo , Quinase 3 da Glicogênio Sintase/genética , Glicogênio Sintase Quinase 3 beta , Proteínas de Fluorescência Verde/genética , Isoproterenol/farmacologia , Proteínas Quinases JNK Ativadas por Mitógeno/metabolismo , Masculino , Mitocôndrias/metabolismo , Miócitos Cardíacos/efeitos dos fármacos , Ratos , Ratos Sprague-Dawley , Espectrometria de Massas por Ionização e Dessorção a Laser Assistida por Matriz , Ubiquitinação/fisiologia
8.
Radiat Res ; 171(3): 342-8, 2009 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-19267561

RESUMO

2-Deoxyribonolactone lesions were identified as major products of radiation damage to DNA mediated by o,o'-diphenyleneiodonium cations in a hydroxyl radical-scavenging environment. The highest selectivity toward deoxyribonolactone formation (up to 86% of all sugar-phosphate damages) and the overall reaction efficiency (up to 40% of all radiation-generated intermediates converted into products) was displayed by derivatives with positively charged (2-aminoethylthio)acetylamino and (2-aminoethylamino)acetylamino side chains. The reaction can be useful for random single-step incorporation of deoxyribonolactone lesions into single- and double-stranded oligonucleotides and highly polymerized DNA directly in commonly used buffers (PBS, phosphate, Tris-HCl, etc.) at room temperature. In combination with HPLC separation, this technique can serve as a source of short (<6 mer) sequences containing deoxyribonolactone lesions at known positions.


Assuntos
Dano ao DNA , DNA/genética , DNA/metabolismo , Oniocompostos/química , Oniocompostos/farmacologia , Efeitos da Radiação , Açúcares Ácidos/metabolismo , Animais , Sequência de Bases , Soluções Tampão , Bovinos , Cromatografia Líquida de Alta Pressão , Relação Dose-Resposta à Radiação , Oligodesoxirribonucleotídeos/genética , Oligodesoxirribonucleotídeos/metabolismo , Oniocompostos/metabolismo , Oxirredução , Especificidade por Substrato
9.
Rapid Commun Mass Spectrom ; 21(16): 2743-9, 2007.
Artigo em Inglês | MEDLINE | ID: mdl-17659658

RESUMO

Human replication protein A (RPA) is a single-stranded DNA (ssDNA)-binding protein with three subunits. The largest subunit, p70, contains a conserved (cysteine)(4)-type zinc-finger motif that has been implicated in the regulation of DNA replication and repair. Previous studies indicated that the ssDNA-binding activity of RPA could be redox-regulated via reversible oxidation of cysteines in the zinc-finger motif. We exposed recombinant human RPA to hydrogen peroxide and characterized the oxidized protein by liquid chromatography/tandem mass spectrometric (LC/MS/MS) analyses. Our results demonstrated that, upon H(2)O(2) treatment, four cysteines, which reside at the zinc-finger motif of the p70 subunit, could result in the formation of two pairs of intramolecular disulfides, Cys481-Cys486 and Cys500-Cys503; no cysteine sulfinic acid or cysteine sulfonic acid could be found. Moreover, the other 11 cysteines in this protein remained intact. The results demonstrated that the formation of disulfide bonds at the zinc-finger site was responsible for the redox regulation of the DNA-binding activity of RPA.


Assuntos
DNA/química , Dissulfetos/química , Proteína de Replicação A/química , Espectrometria de Massas por Ionização por Electrospray/métodos , Sítios de Ligação , Cromatografia Líquida de Alta Pressão/métodos , Humanos , Ligação Proteica , Reprodutibilidade dos Testes , Sensibilidade e Especificidade
10.
Biochemistry ; 46(28): 8226-33, 2007 Jul 17.
Artigo em Inglês | MEDLINE | ID: mdl-17583916

RESUMO

Human replication protein A (RPA), a heterotrimer composed of RPA70, RPA32, and RPA14 subunits, contains four single-stranded DNA (ssDNA) binding domains (DBD): DBD-A, DBD-B, and DBD-C in RPA70 and DBD-D in RPA32. Although crystallographic or NMR structures of these DBDs and a trimerization core have been determined, the structure of the full length of RPA or the RPA-ssDNA complex remains unknown. In this article, we have examined the structural features of RPA interaction with ssDNA by fluorescence spectroscopy. Using a set of oligonucleotides (dT) with varying lengths as a molecular ruler and also as the substrate, we have determined at single-nucleotide resolution the relative positions of the ssDNA with interacting intrinsic tryptophans of RPA. Our results revealed that Trp528 in DBD-C and Trp107 in DBD-D contact ssDNA at the 16th and 24th nucleotides (nt) from the 5'-end of the substrate, respectively. Evaluation of the relative spatial arrangement of RPA domains in the RPA-ssDNA complex suggested that DBD-B and DBD-C are spaced by about 4 nt ( approximately 19 A) apart, whereas DBD-C and DBD-D are spaced by about 7 nt ( approximately 34 A). On the basis of these geometric constraints, a global structure model for the binding of the major RPA DBDs to ssDNA was proposed.


Assuntos
DNA de Cadeia Simples/metabolismo , Proteína de Replicação A/química , Sítios de Ligação , DNA de Cadeia Simples/química , Humanos , Modelos Moleculares , Mutação , Ligação Proteica , Estrutura Terciária de Proteína , Proteína de Replicação A/genética , Proteína de Replicação A/metabolismo , Espectrometria de Fluorescência
11.
Biochemistry ; 45(51): 15921-30, 2006 Dec 26.
Artigo em Inglês | MEDLINE | ID: mdl-17176115

RESUMO

Human XPA is an important DNA damage recognition protein in nucleotide excision repair (NER). We previously observed that XPA binds to the DNA lesion as a homodimer [Liu, Y., Liu, Y., Yang, Z., Utzat, C., Wang, G., Basu, A. K., and Zou, Y. (2005) Biochemistry 44, 7361-7368]. Herein we report that XPA recognized undamaged DNA double-strand/single-strand (ds-ssDNA) junctions containing ssDNA branches with binding affinity (Kd = 49.1 +/- 5.1 nM) much higher than its ability to bind to DNA damage. The recognized DNA junction structures include the Y-shape junction (with both 3'- and 5'-ssDNA branches), 3'-overhang junction (with a 3'-ssDNA branch), and 5'-overhang junction (with a 5'-ssDNA branch). Using gel filtration chromatography and gel mobility shift assays, we showed that the highly efficient binding appeared to be carried out by the XPA monomer and that the binding was largely independent of RPA. Furthermore, XPA efficiently bound to six-nucleotide mismatched DNA bubble substrates with or without DNA adducts including C8 guanine adducts of AF, AAF, and AP and the T[6,4]T photoproducts. Using a set of defined DNA substrates with varying degrees of DNA bending, we also found that the XPC-HR23B complex recognized DNA bending, whereas neither XPA nor the XPA-RPA complex could bind to bent DNA. We propose that, besides DNA damage recognition, XPA may also play a novel role in stabilizing, via its high affinity to ds-ssDNA junctions, the DNA strand opening surrounding the lesion for stable formation of preincision NER intermediates. Our results provide a plausible mechanistic interpretation for the indispensable requirement of XPA for both global genome and transcription-coupled repairs. Since ds-ssDNA junctions are common intermediates in many DNA metabolic pathways, the additional potential role of XPA in cellular processes is discussed.


Assuntos
DNA de Cadeia Simples/metabolismo , Proteínas de Ligação a DNA/metabolismo , Conformação de Ácido Nucleico , Proteína de Xeroderma Pigmentoso Grupo A/metabolismo , Animais , Baculoviridae/genética , Sequência de Bases , Linhagem Celular , Adutos de DNA/química , Adutos de DNA/metabolismo , Dano ao DNA , Reparo do DNA , DNA de Cadeia Simples/química , Proteínas de Ligação a DNA/química , Proteínas de Ligação a DNA/genética , Humanos , Dados de Sequência Molecular , Ligação Proteica/genética , Spodoptera/genética , Proteína de Xeroderma Pigmentoso Grupo A/genética
12.
Radiat Res ; 166(1 Pt 1): 9-18, 2006 Jul.
Artigo em Inglês | MEDLINE | ID: mdl-16808625

RESUMO

Radioprotection of DNA from direct-type radiation damage by histones has been studied in model systems using complexes of positively charged polypeptides (PCPs) with DNA. PCPs bind to DNA via ionic interactions mimicking the mode of DNA-histone binding. Direct radiation damage to DNA in films of DNA-PCP complexes was quantified as unaltered base release, which correlates closely with DNA strand breaks. All types of PCPs tested protected DNA from radiation, with the maximum radioprotection being approximately 2.5-fold compared with non-complexed DNA. Conformational changes of the DNA induced by PCPs or repair of free radical damage on the DNA sugar moiety by PCPs are considered the most feasible mechanisms of radioprotection of DNA. The degree of radioprotection of DNA by polylysine (PL) increased dramatically on going from pure DNA to a molar ratio of PL monomer:DNA nucleotide approximately 1:2, while a further increase in the PL:DNA ratio did not offer more radioprotection. This concentration dependence is in agreement with the model of PCP binding to DNA that assumes preferential binding of positively charged side groups to DNA phosphates in the minor groove, so that the maximum occupancy of all minor-groove PCP binding sites is at a molar ratio of PCP:DNA = 1:2.


Assuntos
Dano ao DNA , DNA/química , DNA/efeitos da radiação , Modelos Químicos , Peptídeos/química , Peptídeos/efeitos da radiação , Protetores contra Radiação/química , Simulação por Computador , Relação Dose-Resposta à Radiação , Ligação Proteica/efeitos da radiação , Doses de Radiação , Eletricidade Estática
14.
Radiat Res ; 163(1): 85-9, 2005 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-15606311

RESUMO

Release of 5-methylene-2-furanone (5-MF), a characteristic marker of DNA deoxyribose oxidative damage at the C1' position, was observed in significant quantities from X-irradiated DNA. This observation, which held for DNA irradiated either in aqueous solution or as a film, requires postirradiation treatment at 90 degrees C in the presence of polyamines and divalent metal cations at biological pH. The 5-MF product was quantified by using reverse-phase HPLC. The radiation chemical yield of 5-MF comprised more than 30% of the yield of total unaltered base release. Polylysine, spermine and Be(II) showed the strongest catalytic effect on 5-MF release, while Zn(II), Cu(II), Ni(II), putrescine and Mg(II) were substantially less efficient. We have hypothesized that the 5-MF release from irradiated DNA occurs through catalytic decomposition of the 2'-deoxyribonolactone (dL) precursor through two consecutive beta- and delta-phosphate elimination reactions. A stepwise character of the process was indicated by the S-shaped time course of 5-MF accumulation. If dL proves to be the precursor to 5-MF formation, it would then follow that dL is a very important lesion generated in DNA by ionizing radiation.


Assuntos
Dano ao DNA/efeitos da radiação , DNA/química , DNA/efeitos da radiação , Furanos/síntese química , Metais/química , Poliaminas/química , Catálise , Cátions Bivalentes/química , Cátions Bivalentes/efeitos da radiação , Relação Dose-Resposta à Radiação , Metais/efeitos da radiação , Poliaminas/efeitos da radiação , Polieletrólitos , Doses de Radiação , Soluções , Temperatura , Água/química , Raios X
15.
J Phys Chem B ; 108(7): 2432-7, 2004 Feb 19.
Artigo em Inglês | MEDLINE | ID: mdl-17375182

RESUMO

In this study we report analytical solutions for both time-dependent and steady-state problems of unbiased charge transfer through a regular DNA sequence via a hopping mechanism. The phenomenon is treated as a diffusion of charge in a one-dimensional array of equally spaced and energetically equivalent temporary trapping sites. The solutions take into account the rates of charge hopping (k), side reactions (k(r)), and charge transfer to a terminal charge acceptor (k(t)). A detailed analysis of the time-dependent problem is performed for the diffusion-controlled regime, i.e., under the assumption that k(t) >> k, which is also equivalent to the fast relaxation limit of charge trapping. The analysis shows that the kinetics of charge hopping through DNA is always multiexponential, but under certain circumstances it can be asymptotically approximated by a single-exponential term. In that case, the efficiency of charge transfer can be characterized by a single rate constant k(CT) = 1.23kN(-2) + k(r), where N is the DNA length expressed in terms of the number of equidistant trapping sites and k(r) is the rate of competing chemical processes. The absolute yield of charge transfer under steady-state conditions in general is obtained as Y(infinity) = omega [alpha sinh(alphaN) + omega cosh(alphaN)](-1), where alpha = (2k(r)/k)(1/2) and omega = 2k(t)/k. For the diffusion-controlled regime and small N, in particular, it turns into the known "algebraic" dependence Y(infinity) = [1 + (k(r)/k)N(2)](-1). At large N the solution is asymptotically exponential with the parameter alpha mimicking the tunneling parameter beta in agreement with earlier predictions. Similar equations and distance dependencies have also been obtained for the damage ratios at the intermediate and terminal trapping sites in DNA. The nonlinear least-squares fit of one of these equations to experimental yields of guanine oxidation available from the literature returns kinetic parameters that are in reasonable agreement with those obtained by Bixon et al. [Proc. Natl. Acad. Sci. U.S.A.1999, 96, 11713-11716] by numerical simulations, suggesting that these two approaches are physically equivalent.

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