Induction of parallel human telomeric G-quadruplex structures by Sr(2+)

Human telomeric DNA forms G-quadruplex secondary structures, which can inhibit telomerase activity and are targets for anti-cancer drugs. Here we show that Sr(2+) can induce human telomeric DNA to form both inter- and intramolecular structures having characteristics consistent with G-quadruplexes. Unlike Na(+) or K(+), Sr(2+) facilitated intermolecular structure formation for oligonucleotides with 2 to 5 5'-d(TTAGGG)-3' repeats. Longer 5'-d(TTAGGG)-3' oligonucleotides formed exclusively intramolecular structures. Altering the 5'-d(TTAGGG)-3' to 5'-d(TTAGAG)-3' in the 1st, 3rd, or 4th repeats of 5'-d(TTAGGG)(4)-3' stabilized the formation of intermolecular structures. However, a more compact, intramolecular structure was still observed when the 2nd repeat was altered. Circular dichroism spectroscopy results suggest that the structures were parallel-stranded, distinguishing them from similar DNA sequences in Na(+) and K(+). This study shows that Sr(2+), promotes parallel-stranded, inter- and intramolecular G-quadruplexes that can serve as models to study DNA substrate recognition by telomerase.     

Structural transition from the random coil to quadruplex of AG(3)(T(2)AG(3))(3) induced by Zn(2+)

Structures of G-quadruplex DNAs can be typically stabilized by monovalent cations such as K(+), Na(+). Some divalent and trivalent cations, such as Sr(2+), Pb(2+), Tb(3+) and Eu(3+), can also induce the formation of G-quadruplex DNA. Here we show that Zn(2+) can induce the human telomeric sequence AG(3)(T(2)AG(3))(3) to fold the G-quadruplex structure by UV absorbance difference spectra and circular dichroism (CD) spectroscopy. At micromolar concentrations, the Zn(2+)-induced changes in the UV absorbance difference spectra and CD spectra are the characteristics of antiparallel G-quadruplexes although the long wavelength CD maximum is around 285 nm rather than the typical value of 295 nm. The binding stoichometry of Zn(2+) per one AG(3)(T(2)AG(3))(3) molecule is four. To our knowledge, the structural transition of human telomeric sequence induced by Zn(2+) was observed for the first time.     

Formation and temperature stability of G-quadruplex structures studied by electronic and vibrational circular dichroism spectroscopy combined with ab initio calculations

Variations in the structure of d(GGGA)(5) oligonucleotide in the presence of Li(+), Na(+), and K(+) ions and its temperature stability were studied using electronic and vibrational circular dichroism, IR absorption, and ab initio calculations with the Becke 3-Lee-Yang-Parr functional at the 6-31G** level. The samples were characterized by nondenaturing gel electrophoresis. Oligonucleotide d(GGGA)(5) in the presence of Li(+) forms a nonplanar single tetramer, with angles of 102 degrees and 171 degrees between neighboring guanine bases. This tetramer changes its geometry at temperatures >50 degrees C, but does not form a quadruplex structure. In the presence of Na(+), the d(GGGA)(5) structure was optimized to almost planar tetramers with an angle of 177 degrees between neighboring guanines. The spectral results suggest that it stacks into a quadruplex helical structure. This quadruplex structure decayed to a single tetramer at temperatures >60 degrees C. The Hartree-Fock energies imply that d(GGGA)(5) prefers to form complexes with Na(+) rather than Li(+). The d(GGGA)(5) structure in the presence of monovalent ions is stabilized against thermal denaturation in the order Li(+) < Na(+) < K(+).     

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 Ca(2+), and separately with Sr(2+) to resolutions of 1.85A and 1.65A, 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 Ca(2+) sites in the same structure are at the CG/CG steps in the minor groove. The Sr(2+) 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 Sr(2+) 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 8.4 degrees in the Ca(2+) and Na(+) containing structure, and 13.4 degrees in the Sr(2+) containing structure. The crossover angles at the junction are 39.3 degrees and 43.3 degrees, respectively. In addition to this, a relative shift in the base pair stack alignment of the arms of 2.3A is observed for the Sr(2+) containing structure only. Overall these results provide an insight into the so-far elusive stabilising ion structure for the DNA Holliday junction.     

Structural diversity and extreme stability of unimolecular Oxytricha nova telomeric G-quadruplex

Oxytricha nova telomeric DNA contains guanine-rich short-tandem repeat sequences (GGGGTTTT) n and terminates as a single strand at the 3'-end. This single-stranded overhang forms a novel DNA structure, namely, G-quadruplex, comprising four quartets. In this study, we investigated the structures and dynamics of unimolecular Oxytricha nova ( O. nova) telomeric G-quadruplexes by performing single molecule fluorescence resonance energy transfer (FRET) spectroscopy and bulk circular dichroism (CD) measurements. We observed that unimolecular O. nova G-quadruplexes exhibit structural polymorphism according to monovalent cations. In the presence of Na (+), only antiparallel conformation is detected, which was demonstrated in previous studies; however, in the presence of K (+), they fold into two different conformations, a parallel conformation and an antiparallel one different from that induced by Na (+). Furthermore, these G-quadruplexes show extremely high stability in their dynamics when compared with human G-quadruplexes. While human telomeric G-quadruplexes that possess three quartets display fast dynamic behavior (<100 s) at low K (+) concentrations or high temperatures, O. nova G-quadruplexes maintain their conformational state for a long time (>1000 s), even at the lowest K (+) concentration and the highest temperature investigated. This high stability is primarily due to an extra quartet that results in additional cation coordination. In addition to cation coordination, we propose that other factors such as base stacking and the size of the thymine loop may contribute to the stability of O. nova G-quadruplexes; this is based on the fact that the O. nova G-quadruplexes were observed to be more stable than the human ones in the presence of Li (+), which is known to greatly destabilize G-quadruplexes because of imprecise coordination. This extreme stability of four-quartet G-quadruplexes enables telomere protection even in the absence of protective proteins or in the case of abrupt environmental changes, although only a single G-quadruplex structure can be derived from the short single-stranded overhang.     

K+ and Na+-induced self-assembly of telomeric oligonucleotide d(TTAGGG)n

The telomeric DNA oligomers, d(TTAGGG)(n), where n=1, 2, 4, could self-associate into the multi-stranded structures in appropriate condition, exhibited different CD spectra. The presense of Na(+) was more advantage to facilitate the formation of anti-parallel conformation, but the presense of K(+) enhanced their thermal stability. Spectroscopic analysis of 3, 3'-diethyloxadicarbocyanine (DODC) showed the formation of hairpin quadruplex structures for d(TTAGGG)(2) and d(TTAGGG)(4), but d(TTAGGG) could not. The four-stranded tetraplexes and branched nanowire formed in the presense of K(+) or Na(+) alone were observed by atomic force microscopy (AFM). The ability of d(TTAGGG)(n) to self-assemble into four-stranded tetraplexes and nanowires depends strongly on the number of repeating units and ionic environment. A model to explain how these structures formed is proposed.     

Streptomyces lividans potassium channel contains poly-(R)-3-hydroxybutyrate and inorganic polyphosphate

The Streptomyces lividans KcsA potassium channel, a homotetramer of 17.6 kDa subunits, was found to contain two nonproteinaceous polymers, namely, poly-(R)-3-hydroxybutyrate (PHB) and inorganic polyphosphate (polyP). PHB and polyP are ubiquitous cellular constituents with a demonstrated capacity for cation selection and transport. PHB was detected in both tetramer and monomer species of KcsA by reaction to anti-PHB IgG on Western blots, and estimated as 28 monomer units of PHB per KcsA tetramer by a chemical assay in which PHB is converted to its unique degradation product, crotonic acid. PolyP was detected in KcsA tetramers, but not in monomers, by metachromatic reaction to o-toluidine blue stain on SDS-PAGE gels. A band of free polyP was also visible, suggesting that polyP is released when tetramers dissociate. The exopolyphosphatase of Saccharomyces cerevisiae degraded the free polyP, but tetramer-associated polyP was not affected, indicating it was inaccessible to the enzyme. PolyP in KcsA was estimated as 15 monomer units per tetramer by an enzymatic assay in which polyphosphate kinase is used to transfer phosphates from polyP to [(14)C]ADP, yielding [(14)C]ATP. The experimentally determined isoelectric point of KcsA tetramer was 6.5-7.5, substantially more acidic than the theoretical pI of 10.3, and consistent with the inclusion of a polyanion. The results suggest that PHB is covalently bound to KcsA subunits while polyP is held within tetramers by ionic forces. It is posited that KcsA protein creates an environment in which PHB/polyP is selective for K(+). The basic amino acids attenuate the negative charge density of polyP, thereby transforming the cation binding preference from multivalent to monovalent, and discrimination between K(+) and Na(+) is accomplished by adjusting the ligand geometry in cation binding cavities formed by PHB and polyP.     

The new models of the human telomere d[AGGG(TTAGGG)3] in K+ solution

The human telomeric sequence d[AGGG(TTAGGG)(3)] has been found to form different types of G-quadruplex structures. NMR revealed that in Na(+) solution this 22 nucleotide (nt) sequence exhibits an antiparallel structure, whereas crystallographic studies in the presence of K(+) showed a dramatically different parallel structure. The structure of this 22 nt sequence in the presence of K(+) has drawn intense interest as the intracellular K(+) concentration is greater than that of Na(+). However, the question of the type of structure for the 22 nt telomeric sequence in K(+) solution remains open. In this study, we substituted the Gs in the sequence with 8-bromoguanine and examined the resultant structures and thermal stabilities by circular dichroism (CD) spectroscopy. The results suggest that the 22 nt in K(+) solution exists as a mixture of mixed-parallel/antiparallel and chair-type G-quadruplex. To date, the exact structure of human telomeric G-quadruplex in K(+) solution is extremely controversial. The present study provides valuable information for understanding the discrepancies between the crystal and solution studies. We discuss the possible implications of the structure in understanding higher-order telomeric DNA structure and T-loop formation.     

Binding of Dissolved Strontium by Micrococcus luteus

Resting cells of Micrococcus luteus have been shown to remove strontium (Sr) from dilute aqueous solutions of SrCl₂ at pH 7. Loadings of 25 mg of Sr per g of cell dry weight were achieved by cells exposed to a solution containing 50 ppm (mg/liter) of Sr. Sr binding occurred in the absence of nutrients and did not require metabolic activity. Initial binding was quite rapid (<0.5 h), although a slow, spontaneous release of Sr was observed over time. Sr binding was inhibited in the presence of polyvalent cations but not monovalent cations. Ca and Sr were bound preferentially over all other cations tested. Sr-binding activity was localized on the cell envelope and was sensitive to various chemical and physical pretreatments. Bound Sr was displaced by divalent ions or by H⁺. Other monovalent ions were less effective. Bound Sr was also removed by various chelating agents. It was concluded that Sr binding by M. luteus is a reversible equilibrium process. Both ion exchange mediated by acidic cell surface components and intracellular uptake may be involved in this activity.     

Locating monovalent cations in the grooves of B-DNA

Here we demonstrate that monovalent cations can localize around B-DNA in geometrically regular, sequence-specific sites in oligonucleotide crystals. Positions of monovalent ions were determined from high-resolution X-ray diffraction of DNA crystals grown in the presence of thallium(I) cations (Tl(+)). Tl(+) has previously been shown to be a useful K(+) mimic. Tl(+) positions determined by refinement of model to data are consistent with positions determined using isomorphous F(Tl) - F(K) difference Fouriers and anomalous difference Fouriers. None of the observed Tl(+) sites surrounding CGCGAATTCGCG are fully occupied by Tl(+) ions. The most highly occupied sites, located within the G-tract major groove, have estimated occupancies ranging from 20% to 35%. The occupancies of the minor groove sites are estimated to be around 10%. The Tl(+) positions in general are not in direct proximity to phosphate groups. The A-tract major groove appears devoid of localized cations. The majority of the observed Tl(+) ions interact with a single duplex and so are not engaged in lattice interactions or crystal packing. The locations of the cation sites are dictated by coordination geometry, electronegative potential, avoidance of electropositive amino groups, and cation-pi interactions. It appears that partially dehydrated monovalent cations, hydrated divalent cations, and polyamines compete for a common binding region on the floor of the G-tract major groove.     

Parthenogenetic activation of mouse oocytes by strontium chloride: a search for the best conditions

Strontium has been successfully used to induce activation of mouse oocytes in nuclear transfer and other experiments, but the optimum treatment conditions have not been studied systematically. When cumulus-free oocytes were treated with 10mM SrCl(2) for 0.5-5h, activation rates (88.4+/-4.1 to 91.2+/-2.7%) did not differ (mean+/-S.E.; P>0.2), but rate of blastulation (57.3+/-3.5%) and cell number per blastocyst (45.0+/-2.4) were the highest after treatment for 2.5h. When treated with 1-20mM SrCl(2) for 2.5h, the activation rate and cell number per blastocyst were higher (P<0.02) after 10mM SrCl(2) treatment than other treatments. The best activation and development were obtained with Ca(2+)-free Sr(2+) medium, but the activation rate was low (37.7+/-1.6%) in Ca(2+)-containing medium. Activation rates were the same, regardless of the presence or absence of cytochalasin B (CB) in the activating medium, but the blastulation rate was higher (P<0.001) in the presence of CB. Only 70% of the cumulus-enclosed oocytes were activated and 10% blastulated after a 10 min exposure to 1.6mM SrCl(2), and many lysed, with increased intensity of Sr(2+) treatment. The presence of CB in SrCl(2) medium markedly reduced lysis of cumulus-enclosed oocytes. Media M16 and CZB did not differ when used as activating media. Only 10.5% of the oocytes collected 13 h post hCG were activated by Sr(2+) treatment alone, with 34% blastulating, but rates of activation and blastulation increased (P<0.001) to 94 and 60%, respectively, when they were further treated with 6-dimethylaminopurine (6-DMAP). The total and ICM cell numbers were less (P<0.001) in parthenotes than in the in vivo fertilized embryos. In conclusion, the concentration and duration of SrCl(2) treatment and the presence or absence of CB in activating medium and cumulus cells had marked effects on mouse oocyte activation and development. To obtain the best activation and development, cumulus-free oocytes collected 18 h post hCG should be treated for 2.5h with 10mM SrCl(2) in Ca(2+)-free medium supplemented with 5 microg/mL of CB.     

BRACO19 analog dimers with improved inhibition of telomerase and hPot 1

Human chromosomes terminate with telomeres, which contain double-stranded G-rich, repetitive DNA followed by a single-stranded overhang of the G-rich sequence. Single-stranded oligonucleotides containing G-rich telomeric repeats have been observed in vitro to fold into a variety of G-quadruplex topologies depending on the solution conditions. G-quadruplex structures are notable in part because G-quadruplex ligands inhibit both the enzyme telomerase and other telomere-binding proteins. Because telomerase is required for growth by the majority of cancers, G-quadruplex-stabilizing ligands have become an attractive platform for anticancer drug discovery. Here, we present the preparation and biochemical activities of a novel series of 3,6-disubstituted acridine dimers modeled after the known G-quadruplex ligand BRACO19. These BRACO19 Analog Dimer (BAD) ligands were shown to bind to human telomeric DNA and promote the formation of intramolecular G-quadruplexes in the absence of monovalent cations. As expected, the BAD ligands bound to telomeric DNA with a 1:1 stoichiometry, whereas the parent compound BRACO19, a monomer, bound with a 2:1 stoichiometry. The BAD ligands exhibited potent inhibition of human telomerase with IC₅₀ values similar to or lower than those of BRACO19. Furthermore, the BAD ligands displayed greater potency in the inhibition of hPot1 and increased selectivity for G-quadruplex DNA when compared to BRACO19. Collectively, these experiments support the hypothesis that there is an increased potency and selectivity to be gained in the design of G-quadruplex-stabilizing agents that incorporate multiple interactions.     

Tetrahelical forms of the fragile X syndrome expanded sequence d(CGG)(n) are destabilized by two heterogeneous nuclear ribonucleoprotein-related telomeric DNA-binding proteins

Formations of hairpin and tetrahelical structures by the trinucleotide repeat sequence d(CGG)(n) might contribute to its expansion in fragile X syndrome. Here we show that tetraplex structures of d(CGG)(n) are destabilized by two mammalian heterogeneous nuclear ribonucleoprotein-related tetraplex telomeric DNA-binding and -stabilizing proteins, quadruplex telomeric DNA-binding protein 42 (qTBP42) (Sarig, G., Weisman-Shomer, P., Erlitzki, R., and Fry, M. (1997) J. Biol. Chem. 272, 4474-4482) and unimolecular quadruplex telomeric DNA-binding protein 25 (uqTBP25) (Erlitzki, R., and Fry, M. (1997) J. Biol. Chem. 272, 15881-15890). Blunt-ended and 3'-tailed or 3'- and 5'-tailed bimolecular tetraplex structures of d(CGG)(n) and guanine-sparse 20-/46-mer partial DNA duplex were progressively destabilized by increasing amounts of qTBP42 or uqTBP25 in time-dependent and ATP- or Mg(2+)-independent reactions. By contrast, tetraplex structures of telomeric and IgG sequences or guanine-rich double-stranded DNA resisted destabilization by qTBP42 or uqTBP25. Increased stability of tetraplex d(CGG)(n) in the presence of K(+) or Na(+) ions or at lowered reaction temperature diminished the destabilizing activity of uqTBP25. The contrasting stabilization of tetraplex telomeric DNA and destabilization of tetraplex d(CGG)(n) by qTBP42 and uqTBP25 suggested that sequence or structural differences between these tetraplexes might serve as cues for the differential stabilizing/destabilizing activities.     

Crystal structures and spectroscopic characterization of galactitol complexes of trivalent lanthanide and divalent alkaline earth chlorides

Crystal structures and FT-IR spectra of metal ion-galactitol (C6H14O6, the ligand here abbreviated as L) complexes: 2LaCl3*C6H14O6*10H2O and SrCl2*C6H14O6 complexes are reported. Crystal data of lanthanide chlorides (La3+, Nd3+, Sm3+, Eu3+, Tb3+)-galactitol complexes and alkaline earth chlorides (Ca2+, Sr2+)-galactitol complexes published earlier are summarized. Unlike other lanthanide ion-galactitol complexes (2MCl3*C6H14O6*14H2O), lanthanum ions give rise to two different structures: LaCl3*C6H14O6*6H2O (LaL1) and 2LaCl3*C6H14O6*10H2O (LaL2). Sr2+-galactitol complexes also crystallized with two structures: SrCl2*C6H14O6*4H2O (SrL1) and SrCl2*C6H14O6 (SrL2). These metal ions thus give different coordination structures with galactitol. The crystal structures and FT-IR spectra of lanthanide ion and alkaline earth ion-galactitol complexes were integrated to interpret the coordination modes of different metal ions. Similar IR spectra demonstrate the same coordination modes of the complexes.     

Structure of the human telomere in Na+ solution: an antiparallel (2+2) G-quadruplex scaffold reveals additional diversity

Single-stranded DNA overhangs at the ends of human telomeric repeats are capable of adopting four-stranded G-quadruplex structures, which could serve as potential anticancer targets. Out of the five reported intramolecular human telomeric G-quadruplex structures, four were formed in the presence of K⁺ ions and only one in the presence of Na⁺ ions, leading often to a perception that this structural polymorphism occurs exclusively in the presence of K⁺ but not Na⁺. Here we present the structure of a new antiparallel (2+2) G-quadruplex formed by a derivative of a 27-nt human telomeric sequence in Na⁺ solution, which comprises a novel core arrangement distinct from the known topologies. This structure complements the previously elucidated basket-type human telomeric G-quadruplex to serve as reference structures in Na⁺-containing environment. These structures, together with the coexistence of other conformations in Na⁺ solution as observed by nuclear magnetic resonance spectroscopy, establish the polymorphic nature of human telomeric repeats beyond the influence of K⁺ ions.     

Tetraplex structure formation in the thrombin-binding DNA aptamer by metal cations measured by vibrational spectroscopy

Formation of intramolecular tetraplex structures by the thrombin-binding DNA aptamer (TBA) in the presence of K(+), Pb(2+), Ba(2+), Sr(2+) and Mn(2+) has been studied by vibrational spectroscopy. All tetraplex structures contain G-G Hoogsteen type base pairing, both C2'endo/anti and C2'endo/syn deoxyguanosine glycosidic conformations and local B like form DNA phosphate geometries. Addition of Pb(2+) ions modifies the structure by interacting at the level of the guanine carbonyl groups. The very important downshift of the guanine C6=O6 carbonyl vibration mode in the TBA spectrum induced by the addition of one Pb(2+) ion per TBA molecule is in agreement with a localization of the metal ion between both guanine quartets. FTIR melting experiments show an important stabilization of the tetraplex structure upon addition of Pb(2+) ions (DeltaT = 15 degrees C). This strong interaction of lead cations may be correlated with a change in the geometry of the cage formed by the two guanine quartets. A similar but weaker effect is observed for barium and strontium cations.     

Molecular dynamics simulation of a palmitoyl-oleoyl phosphatidylserine bilayer with Na+ counterions and NaCl

Two 40 ns molecular dynamics simulations of a palmitoyl-oleoyl phosphatidylserine (POPS) lipid bilayer in the liquid crystalline phase with Na(+) counterions and NaCl were carried out to investigate the structure of the negatively charged lipid bilayer and the effect of salt (NaCl) on the lipid bilayer structure. Na(+) ions were found to penetrate deep into the ester region of the water/lipid interface of the bilayer. Interaction of the Na(+) ions with the lipid bilayer is accompanied by a loss of water molecules around the ion and a simultaneous increase in the number of ester carbonyl oxygen atoms binding the ion, which define an octahedral and square pyramidal geometry. The amine group of the lipid molecule is involved in the formation of inter- and intramolecular hydrogen bonds with the carboxylate and the phosphodiester groups of the lipid molecule. The area per lipid of the POPS bilayer is unaffected by the presence of 0.15M NaCl. There is a small increase in the order parameter of carbon atoms in the beginning of the alkyl chain in the presence of NaCl. This is due to a greater number of Na(+) ions being coordinated by the ester carbonyl oxygen atoms in the water/lipid interface region of the POPS bilayer.     

Raman microspectroscopic study of effects of Na(I) and Mg(II) ions on low pH induced DNA structural changes

In this work a confocal Raman microspectrometer is used to investigate the influence of Na(+) and Mg(2+) ions on the DNA structural changes induced by low pH. Measurements are carried out on calf thymus DNA at neutral pH (7) and pH 3 in the presence of low and high concentrations of Na(+) and Mg(2+) ions, respectively. It is found that low concentrations of Na(+) ions do not protect DNA against binding of H(+). High concentrations of monovalent ions can prevent protonation of the DNA double helix. Our Raman spectra show that low concentrations of Mg(2+) ions partly protect DNA against protonation of cytosine (line at 1262 cm(-1)) but do not protect adenine and guanine N(7) against binding of H(+) (characteristic lines at 1304 and 1488 cm(-1), respectively). High concentrations of Mg(2+) can prevent protonation of cytosine and protonation of adenine (disruption of AT pairs). By analyzing the line at 1488 cm(-1), which obtains most of its intensity from a guanine vibration, high magnesium salt protect the N(7) of guanine against protonation. A high salt concentration can prevent protonation of guanine, cytosine, and adenine in DNA. Higher salt concentrations cause less DNA protonation than lower salt concentrations. Magnesium ions are found to be more effective in protecting DNA against binding of H(+) as compared with calcium ions presented in a previous study. Divalent metal cations (Mg(2+), Ca(2+)) are more effective in protecting DNA against protonation than monovalent ions (Na(+)).     

Onset of DNA aggregation in presence of monovalent and multivalent counterions

We address theoretically aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration c(DNA) is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on c(DNA), having the form alphac(DNA) + beta. The coefficients alpha and beta are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: 1), the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; 2), the Poisson-Boltzmann theory overestimates the number of condensed multivalent ions at high monovalent salt concentrations; and 3), our analysis of the data indicates that the DNA charge is not overcompensated by spermine at the onset of aggregation.